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Design of a realtime high speed recognizer for unconstrained handprinted alphanumeric characters Wong, Ing Hoo 1985

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DESIGN OF A REALTIME HIGH SPEED RECOGNIZER FOR UNCONSTRAINED HANDPRINTED ALPHANUMERIC CHARACTERS By ING HOO WONG B.E . E l e c . (Hons.), U n i v e r s i t y of Melbourne A u s t r a l i a , 1980 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE ^ i n THE FACULTY OF GRADUATE STUDIES Department of E l e c t r i c a l E n g i n e e r i n g We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA Fe b r u a r y 1985 © Ing Hoo Wong In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the r e q u i r e m e n t s f o r an advanced degree a t the The U n i v e r s i t y of B r i t i s h C o l u m b i a , I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head of my Department or by h i s or her r e p r e s e n t a t i v e s . I t i s unde r s t o o d t h a t c o p y i n g or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n permi s s i o n . ELECTRICAL ENGINEERING The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date: F e b r u a r y 1985 i i A b s t r a c t . T h i s t h e s i s p r e s e n t s the d e s i g n of a r e c o g n i z e r f o r u n c o n s t r a i n e d h a n d p r i n t e d a l p h a n u m e r i c c h a r a c t e r s . The d e s i g n i s based on a t h i n n i n g p r o c e s s t h a t i s c a p a b l e of p r o d u c i n g t h i n n e d images w i t h w e l l d e f i n e d f e a t u r e s t h a t a r e c o n s i d e r e d e s s e n t i a l f o r c h a r a c t e r image d e s c r i p t i o n and r e c o g n i t i o n . By c h o o s i n g the t o p o l o g i c a l p o i n t s of the t h i n n e d ( ' l i n e ' ) c h a r a c t e r image as these d e s i r e d f e a t u r e s , the t h i n n i n g p r o c e s s a c h i e v e s not o n l y a h i g h degree of d a t a r e d u c t i o n but a l s o t r a n s f o r m s a b i n a r y image i n t o a d i s c r e t e form of l i n e d r awing t h a t can be r e p r e s e n t e d by g raphs. As a r e s u l t p o w e r f u l g r a p h i c a l a n a l y s i s t e c h n i q u e s can be a p p l i e d t o a n a l y z e and c l a s s i f y the image. The image c l a s s i f i c a t i o n i s performed i n two s t a g e s . F i r s t l y , a t e c h n i q u e f o r i d e n t i f y i n g the t o p o l o g i c a l p o i n t s i n the t h i n n e d image i s d e v e l o p e d . These t o p o l o g i c a l p o i n t s r e p r e s e n t the g l o b a l f e a t u r e s of t h e image and because of t h e i r i n v a r i a n c e t o e l a s t i c d e f o r m a t i o n s , they a r e used f o r image p r e c l a s s i f i c a t i o n . P r e c l a s s i f i c a t i o n r e s u l t s i n a s u b s t a n t i a l r e d u c t i o n i n the e n t r o p y of the i n p u t image. The subsequent p r o c e s s can c o n c e n t r a t e o n l y on the d i f f e r e n t i a t i o n of images t h a t a r e t o p o l o g i c a l l y e q u i v a l e n t . I n the p r e c l a s s i f i e r s i m p l e l o g i c o p e r a t i o n s l o c a l i z e d t o the immediate neighbourhood of each p i x e l a r e used. These o p e r a t i o n s a r e a l s o h i g h l y independent and easy t o implement u s i n g V L S I . A g r a p h i c a l t e c h n i q u e f o r image e x t r a c t i o n and r e p r e s e n t a t i o n c a l l e d the c h a i n coded d i g r a p h r e p r e s e n t a t i o n i s i n t r o d u c e d . The t e c h n i q u e uses g l o b a l f e a t u r e s such as nodes and the Freeman's c h a i n codes f o r d i g i t a l c u r v e s as branches. The c h a i n coded d i g r a p h c o n t a i n s a l l the i n f o r m a t i o n t h a t i s p r e s e n t i n the t h i n n e d image. T h i s a v o i d s u s i n g the image f e a t u r e e x t r a c t i o n approach f o r image d e s c r i p t i o n and da t a r e d u c t i o n (a d i f f i c u l t p r o c e s s t o o p t i m i z e ) w i t h o u t s a c r i f y i n g speed or c o m p l e x i t y . A f t e r p r e c l a s s i f i c a t i o n , a second stage of the r e c o g n i t i o n p r o c e s s a n a l y s e s t h e c h a i n coded d i g r a p h u s i n g the concept of a t t r i b u t e d r e l a t i o n a l graph (ARG). ARG r e p r e s e n t a t i o n of the image can be o b t a i n e d r e a d i l y t h r o u g h s i m p l e t r a n s f o r m a t i o n s or r e w r i t i n g r u l e s from the c h a i n coded d i g r a p h . The ARG r e p r e s e n t a t i o n of an image d e s c r i b e s the shape p r i m i t i v e s i n the image and t h e i r r e l a t i o n s h i p s . F i n a l c l a s s i f i c a t i o n of the i n p u t image can be made by comparing i t s ARG w i t h the ARGs of known c h a r a c t e r s . The f i n a l c l a s s i f i c a t i o n i n v o l v e s o n l y the comparison of ARGs of a p r e d e t e r m i n e d t o p o l o g y . T h i s i n f o r m a t i o n i s c r u c i a l t o the d e s i g n of a matching a l g o r i t h m c a l l e d the r e f e r e n c e g u i d e d i n e x a c t matching p r o c e d u r e , d e s i g n e d f o r h i g h speed matching of c h a r a c t e r image ARGs. T h i s graph matching p r o c e d u r e i s shown t o be much f a s t e r than o t h e r c o n v e n t i o n a l graph matching p r o c e d u r e s . The d e s i g n e d r e c o g n i z e r i s implemented i n P a s c a l on the PDP11/23 and VAX 11/750 computer. Test u s i n g Munson's da t a shows a h i g h r e c o g n i t i o n r a t e of 91.46%. However, the r e c o g n i z e r i s d e s i g n e d w i t h the aim of an e v e n t u a l i m p l e m e n t a t i o n u s i n g VLSI and a l s o as a b a s i c r e c o g n i z e r f o r f u r t h e r r e s e a r c h i n r e a d i n g machines. T h e r e f o r e i t s f u l l p o t e n t i a l i s y e t t o be r e a l i z e d . N e v e r t h e l e s s , the e x p e r i m e n t s w i t h Munson's d a t a i l l u s t r a t e s the e f f e c t i v e n e s s of the d e s i g n approach and the advantages i t o f f e r s as a b a s i c system f o r f u t u r e r e s e a r c h . T a b l e of c o n t e n t s . Page A b s t r a c t . . i i T a ble of c o n t e n t s v L i s t of f i g u r e s v i i L i s t of t a b l e s i x Acknowledgements x I. INTRODUCTION 1 1. B a s i c c h a r a c t e r r e c o g n i t i o n p r o c e s s 3 2. Problem d e f i n i t i o n - A statement of o b j e c t i v e s . ..7 3. Data base 10 I I . FINAL PREPROCESSING AND DATA REDUCTION 11 1 . I n t r o d u c t i o n 11 2. B a s i c d i s c r e t e geometry and d e f i n i t i o n s 13 2.1 B a s i c d e f i n i t i o n s 13 2.2 S p e c i f i c a t i o n s f o r t h i n n e d images 14 3. Design r u l e s f o r the m o d i f i e d t h i n n i n g a l g o r i t h m 16 3.1 D e f i n i t i o n s f o r the t h i n n i n g a l g o r i t h m 16 3.2 Implementation of t h i n n i n g a l g o r i t h m and t e s t r e s u l t s 24 4. D i s c u s s i o n 27 I I I . IMAGE EXTRACTION, REPRESENTATION AND PRECLASSIF I CATION 32 1. I n t r o d u c t i o n 32 2. Image d e f i n i t i o n 35 2.1 B a s i c c o n c e p t s - d i s c r e t e c u r v e geometry and graph 35 2.2 G l o b a l f e a t u r e d e t e c t i o n and e x t r a c t i o n 39 3. Image e x t r a c t i o n 46 3.1 Data s t r u c t u r e . 46 3.2 Image e x t r a c t i o n and s p u r i o u s branch p r u n i n g p rocedure 47 v i page 4. Image p r e c l a s s i f i c a t i o n 51 4.1 Input e n t r o p y r e d u c t i o n due t o p r e c l a s s i f i c a t i o n 52 5. D i s c u s s i o n 54 IV. FINAL IMAGE CLASSIFICATION 61 1 . I n t r o d u c t i o n 61 2. A t t r i b u t e d r e l a t i o n a l graphs - An i n t r o d u c t i o n . ..63 2.1 B a s i c d e f i n i t i o n and t e r m i n o l o g y 63 2.2 ARG d e f o r m a t i o n models 66 2.3 D e f o r m a t i o n d i s t a n c e measures f o r ARG 68 '3. T r a n s f o r m a t i o n of c h a i n coded d i g r a p h t o ARG 71 3.1 R e w r i t i n g of node p r i m i t i v e s 72 3.2 R e w r i t i n g of branch p r i m i t i v e s 73 3.2.1 Length a t t r i b u t e d e f i n i t i o n and e x t r a c t i o n 75 3.2.2 C u r v a t u r e a t t r i b u t e d e f i n i t i o n and e x t r a c t i o n 76 3.3.3 D e f i n i t i o n and e x t r a c t i o n of 0 1 and 82. . . 7 9 4. ARG matching 86 4.1 Concept of r e f e r e n c e guided matching 86 4.2 D i s t a n c e m a t r i x and r e f e r e n c e g u i d e d i n e x a c t matching p r o c e d u r e 89 4.2.1 C o m p u t a t i o n a l c o m p l e x i t y 93 5. F i n a l r e c o g n i z e r i m p l e m e n t a t i o n and performance. .95 5.1 F i n a l r e c o g n i z e r i m p l e m e n t a t i o n 95 5.2 Performance w i t h Munson's data 98 V . CONCLUSION AND FUTURE DEVELOPMENTS 105 R e f e r e n c e s . 109 v i i L i s t of f i g u r e s . F i g u r e page 1.1 B l o c k diagram of a t y p i c a l o p t i c a l r e c o g n i t i o n p r o c e s s 3 1.2 B l o c k diagram of f i n a l r e c o g n i z e r 9 2.1 P i x e l s P1 - P8 are l o c a l n e i g h b o u r s of a p i x e l P 13 2.2 L o c a l neighbourhood of a m u l t i p l e p i x e l P 17 2.3 L o c a l neighbourhood of a t e n t a t i v e l y m u l t i p l e p i x e l P 17 2.4 L o c a l neighbourhood of t e n t a t i v e l y m u l t i p l e p i x e l s t h a t a r e removable 18 2.5 Test image 19 2.6a Test image t h i n n i n g w i t h o r i g i n a l P a v l i d i s a l g o r i t h m 20 2.6b Test image t h i n n i n g w i t h m o d i f i e d a l g o r i t h m 21 2.7 Sample b i n a r y c h a r a c t e r s from Munson's d a t a 29 2.8a Sample b i n a r y c h a r a c t e r s t h i n n e d w i t h o r i g i n a l P a v l i d i s a l g o r i t h m 30 2.8b Sample b i n a r y c h a r a c t e r s t h i n n e d w i t h m o d i f i e d a l g o r i t h m 31 3.1 Examples of j u n c t i o n s w i t h r a d i a l i t y g r e a t e r than f o u r 36 3.2 L o c a l neighbourhood of an i l l e g a l J3 p i x e l P 41 3.3 L o c a l neighbourhood of a J3 p i x e l h a v i n g f i v e n e i g h b o u r s 41 3.4 L o c a l neighbourhood of an i l l e g a l J4 p i x e l P 42 3.5 C r i t i c a l p o i n t s of c h a r a c t e r images from Munson's d a t a and t h e i r 'analogue e q u i v a l e n t ' 45 i i x page 3.6 Images w i t h i d e n t i c a l g l o b a l f e a t u r e s t h a t a re ar e t o p o l o g i c a l l y i n e q u i v a l e n t 55 3.7 R e p r e s e n t a t i o n of c h a r a t e r 'A' b e f o r e p r u n i n g (a) and a f t e r p r u n i n g (b) 58 4.1 ARG d e s c r i p t i o n of c h a r a c t e r 'R' 65 4.2 D i f f e r e n t forms of a s i n g l e c h a r a c t e r h a v i n g the same t o p o l o g y 96 4.3 B l o c k diagram showing the f i n a l i m p l e m e n t a t i o n of the r e c o g n i z e r and i t s p o t e n t i a l f u t u r e developments 102 i x L i s t o f t a b l e s . T a ble page I . A t y p i c a l node d a t a t a b l e f o r c h a i n coded d i g a r p h r e p r e s e n t a t i o n of t h i n n e d a l p h a n u m e r i c c h a r a c t e r s . ..56 I I . Group c l a s s i f i c a t i o n of sample c h a r a c t e r s from Munson's d a t a 57 I I I . E q u i v a l e n c e between c h a i n coded d i g r a p h and ARG NDTs 72 IV. T a b l e showing the number of t o p o l o g i e s f o r each image i n a g i v e n p r e c l a s s i f i e d group and the d i c t i o n a r y s i z e of each group 101 V. T a b l e of r e c o g n i t i o n r a t e s f o r d i f f e r e n t c h a r a c t e r s . .101 X Acknowledgements. I would l i k e t o thank P r o f . M. P. Beddoes whose guidance and f i n a n c i a l s u p port i n the form of Research A s s i s t a n t s h i p has made t h i s t h e s i s p o s s i b l e , and t o P r o f . R. W. Donaldson f o r the use of Munson's d a t a . CHAPTER I INTRODUCTION. Machine r e c o g n i t i o n of h a n d p r i n t e d c h a r a c t e r s i s an ar e a of r e s e a r c h t h a t has been a c t i v e l y pursued by many r e s e a r c h e r s i n the f i e l d of p a t t e r n r e c o g n i t i o n and computer v i s i o n . The r e s u l t s of t h e s e a c t i v i t i e s a r e p r e s e n t e d i n the numerous r e p o r t s and p u b l i c a t i o n s on the s u b j e c t d a t i n g back t o over two decades. A study of t h i s e x t e n s i v e l i t e r a t u r e as w e l l as a summary of the problems, t e c h n i q u e s and performance of r e c o g n i z e r s f o r Roman l e t t e r s i s p r e s e n t e d by Suen et al. i n [ 1 ] . I n the p a s t , r e s e a r c h has been c o n c e n t r a t e d on both o n - l i n e and o f f - l i n e t e c h n i q u e s f o r c h a r a c t e r r e c o g n i t i o n . I n o n - l i n e c h a r a c t e r r e c o g n i t i o n , d a t a i n p u t t o the r e c o g n i z e r o c c u r s as i t i s g e n e r a t e d , such as w r i t i n g w i t h a l i g h t pen or on a d i g i t i z i n g t a b l e t . O n - l i n e r e c o g n i t i o n has l i m i t e d use and advantage because the r e c o g n i t i o n can be done under the s u p e r v i s i o n of the w r i t e r . I n p r e s e n t day r e s e a r c h , the main e f f o r t has been c o n c e n t r a t e d on o f f - l i n e c h a r a c t e r r e c o g n i t i o n which i s re g a r d e d as a more d i f f i c u l t problem. In o f f - l i n e r e c o g n i t i o n t h e o b j e c t i v e i s t o r e c o g n i z e c h a r a c t e r images such as p r i n t e d t e x t or w r i t t e n m a t e r i a l . As p r i n t , s c r i p t and paper remains the dominant media where i n f o r m a t i o n i s s t o r e d , the e f f i c i e n c y of e l e c t r o n i c d a t a p r o c e s s i n g can be improved by a more e f f i c i e n t i n t e r f a c e between the p r i n t or w r i t t e n m a t e r i a l and the d i g i t a l computer. T h e r e f o r e t h e advantages of a d i r e c t d a t a i n p u t i n t o computers v i a automated machine r e c o g n i t i o n p r o v i d e a s t r o n g m o t i v a t i o n and c h a l l e n g e t o r e s e a r c h e r s i n p a t t e r n r e c o g n i t i o n . Another important a p p l i c a t i o n of o f f - l i n e c h a r a c t e r r e c o g n i t i o n i s the development of a r e a d i n g a i d f o r the b l i n d . The advances made i n the m i c r o p r o c e s s o r t e c h n o l o g y , speech s y n t h e s i s and the i n c r e a s e d p o r t a b i l i t y of m i c r o p r o c e s s o r based machines have made the r e a l i z a t i o n of a p o r t a b l e r e a d i n g machine both t e c h n i c a l l y and e c o n o m i c a l l y a t t r a c t i v e . P r e s e n t l y the r e c o g n i t i o n of p r i n t e d and w r i t t e n m a t e r i a l has been r e s t r i c t e d t o the r e c o g n i t i o n of i n d i v i d u a l c h a r a c t e r s , e x c e p t f o r a meagre few [ 3 4 ] , t h a t have i n v e s t i g a t e d the p o s s i b i l i t y of word r e c o g n i t i o n . The main a c t i v i t i e s i n c h a r a c t e r r e c o g n i t i o n have now been d i v i d e d i n t o two main streams, a l p h a n u m e r i c c h a r a c t e r and Chinese or Japanese c h a r a c t e r r e c o g n i t i o n . A l t h o u g h i n t e r e s t i n g r e s u l t s have been r e p o r t e d i n the r e s e a r c h on the l a t t e r by M o r i et al. [ 5 ] , the work p r e s e n t e d i n t h i s r e s e a r c h p r o j e c t c o n c e r n s o n l y o f f - l i n e r e c o g n i t i o n of u n c o n s t r a i n e d h a n d p r i n t e d c h a r a c t e r s . A b r i e f summary of the b a s i c p r o c e d u r e s t h a t a r e i n v o l v e d i n a complete o p t i c a l c h a r a c t e r r e c o g n i z e r w i l l be g i v e n i n the f o l l o w i n g s e c t i o n as an i n t r o d u c t i o n t o the s u b j e c t as w e l l as t o p r o v i d e the f o u n d a t i o n f o r a f o r m a l d e s c r i p t i o n of the o b j e c t i v e s of t h i s r e s e a r c h . 1. B a s i c c h a r a c t e r r e c o g n i t i o n p r o c e s s . A l l t he v a r i o u s t e c h n i q u e s of computer c h a r a c t e r r e c o g n i t i o n can be viewed as c o m p r i s i n g of the f o l l o w i n g p r o c e s s e s ; image c a p t u r e and d i g i t i z a t i o n , c h a r a c t e r s e g m e n t a t i o n , p r e p r o c e s s i n g , image e x t r a c t i o n and r e c o g n i t i o n . These p r o c e s s e s a r e shown i n the b l o c k diagram of a t y p i c a l o p t i c a l c h a r a c t e r r e c o g n i z e r i n f i g u r e 1.1. D i g i t a l Computer Input Image Image Capture and D i g i t i z a t i o n Preprocessing Image or Feature Extract ion Recogni t ion Output - Character ident i t y . F i g . 1.1 B l o c k diagram of a t y p i c a l o p t i c a l c h a r a c t e r r e c o g n i t i o n p r o c e s s . The p r e s e n t t e c h n o l o g y t h a t i s a v a i l a b l e f o r use i n image c a p t u r e such as t h e charge d c o u p l e d d e v i c e s or h i g h r e s o l u t i o n TV cameras can p r o v i d e a h i g h q u a l i t y d i g i t i z e d image f o r computer p r o c e s s i n g . These images a r e o f t e n a c q u i r e d w i t h m u l t i l e v e l i n t e n s i t i e s . S i n c e c h a r a c t e r r e c o g n i t i o n i n v o l v e s b a s i c a l l y a b i n a r y image, s t a t e of the a r t d a t a a c q u i s i t i o n and d i g i t i z a t i o n i s u s u a l l y adequate. The main problem l i e s i n the subsequent p r o c e s s i n g of the image. C h a r a c t e r segmentation i s a d i f f i c u l t problem and few r e s e a r c h r e s u l t s a r e a v a i l a b l e . In most c a s e s f o r c e d s e gmentation [ 3 6 ] , based on a h e u r i s t i c a pproach i s used w i t h the p r o c e s s a p p l i e d r e c u r s i v e l y u n t i l a s u c c e s s f u l i d e n t i f i c a t i o n can be made. U n l e s s an h i g h l y e f f i c i e n t r e c o g n i z e r c a p a b l e of g u i d i n g t h i s r e c u r s i v e segmentation p r o c e s s i s a v a i l a b l e , segmentation u s i n g t h i s t e c h n i q u e w i l l remain a p a i n f u l l y slow p r o c e s s . T h i s dependence on the r e c o g n i t i o n p r o c e s s s u g g e s t s t h a t s e g m e n t a t i o n cannot be a c c o m p l i s h e d on a mere image p r o c e s s i n g l e v e l , i t must t a k e i n t o account the semantic c o n t e n t of the image. T h e r e f o r e one may be b e t t e r equipped t o s o l v e the problem i f the r e q u i r e m e n t s and t e c h n i q u e s of the subsequent r e c o g n i t i o n p r o c e s s has been b e t t e r e s t a b l i s h e d and u n d e r s t o o d . P r e p r o c e s s i n g i s an i m p o r t a n t s t e p towards s u c c e s s f u l r e c o g n i t i o n . The p r e p r o c e s s i n g r e q u i r e m e n t s of an image v a r i e s from one d e s i g n t o a n o t h e r as i t i s o f t e n d i c t a t e d by the r e c o g n i t i o n t e c h n i q u e used. For example, t e c h n i q u e s t h a t use image c o n t o u r s f o r shape d e s c r i p t i o n and i d e n t i f i c a t i o n r e q u i r e the image t o have w e l l d e f i n e d edges. W h i l e those t h a t r e l y on t h i n n i n g w i l l be s e n s i t i v e t o ' p i n - h o l e s ' i n the b i n a r y image which w i l l l e a d t o the t h i n n e d image h a v i n g s p u r i o u s c l o s e d l o o p s . A p a r t from t h e s e s p e c i a l i z e d f u n c t i o n s , p r e p r o c e s s o r s a r e g e n e r a l l y r e q u i r e d f o r p e r f o r m i n g b a s i c image enchancement f u n c t i o n s such as n o i s e f i l t e r i n g , s c a l i n g and image n o r m a l i z a t i o n . Image or f e a t u r e e x t r a c t i o n and r e c o g n i t i o n forms t h e c e n t r a l i s s u e s t h a t have been r e s e a r c h e d over the y e a r s . The numerous t e c h n i q u e s t h a t have been a p p l i e d t o r e c o g n i z e h a n d p r i n t e d and p r i n t e d a l p h a n u m e r i c c h a r a c t e r s i n d i c a t e t h e d i f f i c u l t y of the problem. T h e o r e t i c a l l y , c l a s s i f i c a t i o n can be made by e x t r a c t i n g d i s t i n g u i s h i n g f e a t u r e s from an i n p u t image and comparing these f e a t u r e s w i t h t h o s e of a known c l a s s of images. In p r a c t i c e t h i s i s a f o r m i d a b l e problem because h a n d p r i n t e d c h a r a c t e r s o f t e n c o n t a i n a wide range of d e f o r m a t i o n s . B e s i d e s , the performance of any r e c o g n i z e r w i l l u l t i m a t e l y be compared t o the human v i s u a l r e c o g n i t i o n system, the most e f f i c i e n t known. In the t h e o r e t i c a l approach t h e c h o i c e of f e a t u r e s a re o f t e n o p t i m i z e d s t a t i s t i c a l l y , t h e s e may not n e c e s s a r i l y be the same as the optimum f e a t u r e s o b t a i n e d from p s y c h o l o g i c a l c o n s i d e r a t i o n s , nor does t h e t h e o r e t i c a l r e c o g n i t i o n p r o c e d u r e t a k e s i n t o account t h e methodology i n v o l v e d i n the human r e c o g n i t i o n p r o c e s s . The p r e s e n t methods of image r e c o g n i t i o n a r e d e r i v e d from two main t h e o r i e s , the s t a t i s t i c a l or d e c i s i o n t h e o r e t i c [ 2 4 ] , and the s y n t a c t i c or l i n g u i s t i c [ 1 7 ] , [ 2 2 ] , a p p r o a c h . The s t a t i s t i c a l a p proach c o n s i s t s of a p a r a m e t r i c approach w h i c h i s based on the m o d e l l i n g of the b a s i c p r o c e s s t h a t g e n e r a t e s the i n p u t images and a p p l y i n g the l a r g e number of p r o b a b i l i t y a n a l y s i s t e c h n i q u e s t o c l a s s i f y an i n p u t ; and a n o n - p a r a m e t r i c approach t h a t c o n c e n t r a t e s on e x t r a c t i n g m u t u a l l y e x c l u s i v e f e a t u r e v e c t o r s from t h e image and r e l i e s on d i s c r i m i n a n t a n a l y s i s of t h e s e f e a t u r e v e c t o r s f o r c l a s s i f i c a t i o n . B o th methods have a c h i e v e d l i m i t e d s u c c e s s when a p p l i e d t o c h a r a c t e r r e c o g n i t i o n because the c h a r a c t e r g e n e r a t i o n p r o c e s s i n a t e x t cannot be a d e q u a t e l y m o d e l l e d and d i s c r i m i n a n t a n a l y s i s o f t e n r e q u i r e s the p r o c e s s i n g of v e c t o r m a t r i c e s of h i g h d i m e n s i o n a l i t y . The s y n t a c t i c approach t o p a t t e r n r e c o g n i t i o n i s d e r i v e d from the n a t u r a l languages t h a t a r e used i n the f i e l d of a r t i f i c i a l i n t e l l i g e n c e [ 3 0 ] , t o e n a b l e computers t o be engaged i n commonsense r e a s o n i n g and u n d e r s t a n d i n g language [ 2 5 ] . I n the s y n t a c t i c approach an image i s d e s c r i b e u s i n g a p i c t u r e d e s c r i p t i o n language (PDL) g e n e r a t e d by a p p l y i n g a s p e c i f i e d s e t of g r a m m a t i c a l r u l e s on a s e t of p r i m i t i v e symbols. R e c o g n i t i o n i s a c h i e v e d by p a r s i n g the r e s u l t i n g PDL g e n e r a t e d from an i n p u t t o d e t e c t the p r e s e n c e of s t r u c t u r e s i n t he PDL t h a t would r e s u l t i n i t s c l a s s i f i c a t i o n . T h i s approach r e s u l t s i n a r i c h e r d e s c r i p t i o n of a p a t t e r n because i t i s based on p a t t e r n p r i m i t i v e s ( t h e b a s i c i d e n t i f i a b l e u n i t i n t he image) i n s t e a d of j u s t some s c a l a r o r p r o b a b i l i t y measures. In s p i t e of i t s h i g h e r d e s c r i p t i v e c a p a b i l i t y , the s y n t a c t i c t e c h n i q u e has two main drawbacks. F i r s t l y , t he i n f e r e n c e of the grammar t h a t i s r e q u i r e d i n g e n e r a t i n g the PDL f o r c h a r a c t e r s images i s a d i f f i c u l t p r o c e s s . T h i s problem i s c o n v o l u t e d by the f a c t t h a t u n c o n s t r a i n e d h a n d p r i n t e d c h a r a c t e r s e x h i b i t c o n s i d e r a b l e v a r i a t i o n s i n shapes due t o d i f f e r e n t w r i t i n g s t y l e s as w e l l as d i s t o r t i o n s . T h e r e f o r e a number of g r a m m a t i c a l r u l e s may be r e q u i r e d f o r a s i n g l e c h a r a c t e r . T h i s p r e s e n t s a c o n s i d e r a b l e i n c r e a s e i n the c o m p u t a t i o n a l r e q u i r e m e n t s as the p a r s i n g a l g o r i t h m s f o r the PDLs a r e o f t e n complex o p e r a t i o n s . S e c o n d l y , the s y n t a c t i c approach t o r e c o g n i t i o n a l o n e l a c k s the c a p a b i l i t y of i n c o r p o r a t i n g c o n t e x t u a l i n f o r m a t i o n i n t o t h e r e c o g n i t i o n p r o c e s s . C o n t e x t u a l i n f o r m a t i o n a r e more r e a d i l y d e s c r i b e d by the use of s t a t i s t i c s as the p r o b a b i l i t y of o c c u r r e n c e of a p a r t i c u l a r c h a r a c t e r c o n d i t i o n e d upon the o b s e r v a t i o n of some o t h e r p r e c e d i n g c h a r a c t e r ( s ) . As a r e s u l t a t t e m p t s have been made t o combine both the s y n t a c t i c and s t a t i s t i c a l methods f o r p a t t e r n r e c o g n i t i o n [ 1 9 ] , 2. Problem d e f i n i t i o n - A statement of o b j e c t i v e s . From the o v e r v i e w of the methods t h a t a r e a v a i l a b l e f o r the d e s i g n of a c h a r a c t e r r e c o g n i z e r and the numerous number of t e c h n i q u e s t h a t have been a p p l i e d t o s o l v i n g the e q u a l l y numerous number of problems a s s o c i a t e d w i t h i t , one may ask i f the g o a l s of an automated c h a r a c t e r r e c o g n i t i o n machine have been r e a c h e d . O b v i o u s l y n o t , f o r t h e f o l l o w i n g r e a s o n s : P r e s e n t c h a r a c t e r r e c o g n i z e r s have been d e v e l o p e d m a i n l y f o r s p e c i a l i z e d u s e s , such as r e a d i n g from a s p e c i a l c h a r a c t e r s e t or p r i n t f o n t . R e s e a r c h on h a n d p r i n t e d c h a r a c t e r r e c o g n i t i o n has been m a i n l y i n v e s t i g a t i v e i n n a t u r e , c o n c e n t r a t i n g on working out t h e fundamental approaches t o t h e s o l u t i o n . R e c o g n i t i o n p r o c e d u r e s and the a s s o c i a t e d image p r o c e s s i n g r e q u i r e m e n t s used t o da t e a r e c o m p u t a t i o n a l l y i n t e n s i v e and u n a t t r a c t i v e f o r r e a l t i m e a p p l i c a t i o n s . C u r r e n t c h a r a c t e r r e c o g n i z e r s do not po s s e s s c o n t e x t u a l p r o c e s s i n g c a p a b i l i t i e s . In machine c h a r a c t e r r e c o g n i t i o n , an i n p u t may be u n i d e n t i f i a b l e because i t has an ambiguous shape. A human reader can u n c o n s c i o u s l y r e s o l v e t h i s a m b i g u i t y by r e f e r e n c e t o h i s g e n e r a l knowledge about the s p e l l i n g of a word or the se m a n t i c s of the c o n t e x t . An e f f i c i e n t c h a r a c t e r r e c o g n i z e r may be r e q u i r e d t o posses s t h i s c a p a b i l i t y i n o r d e r t o be an a c c e p t a b l e replacement f o r the human r e a d e r . The o b j e c t i v e of t h i s r e s e a r c h p r o j e c t i s t o d e s i g n a c h a r a c t e r r e c o g n i z e r f o r u n c o n s t r a i n e d h a n d p r i n t e d a l p h a n u m e r i c c h a r a c t e r s ( r e f e r r e d t o from here onwards s i m p l y as c h a r a c t e r r e c o g n i z e r ) t h a t w i l l p r o v i d e a s a t i s f a c t o r y performance w i t h r e s p e c t t o the f i r s t t h r e e c o n c e r n s g i v e n above. The d e s i g n i s aimed a t p r o d u c i n g a h i g h l y e f f i c i e n t t e c h n i q u e f o r the c o n t e x t f r e e r e c o g n i t i o n of u n c o n s t r a i n e d h a n d p r i n t e d c h a r a c t e r s t h a t i s s u i t a b l e f o r i m p l e m e n t a t i o n i n r e a l t i m e . Such a r e c o g n i z e r w i l l p r o v i d e the i m p o r t a n t knowledge i n r e c o g n i t i o n t e c h n i q u e s and can be used as a b a s i c r e c o g n i z e r f o r f u t u r e r e s e a r c h i n t o the problem of se g m e n t a t i o n , c o n t e x t u a l t e x t p r o c e s s i n g , p s y c h o l o g i c a l c o n s i d e r a t i o n s i n c h a r a c t e r r e c o g n i t i o n and the VLSI i m p l e m e n t a t i o n of a c h a r a c t e r r e c o g n i z e r i n p o r t a b l e u n i t s as an a i d f o r t h e b l i n d . As a f a i r l y s o p h i s t i c a t e d p r e p r o c e s s o r f o r the d i g i t i z e d image has been d e s i g n e d by Lunscher [ 3 3 ] , i n h i s M.A.Sc. r e s e a r c h p r o j e c t , the p r e s e n t d e s i g n w i l l t a k e as i t s i n p u t a b i n a r i z e d image of an i s o l a t e d c h a r a c t e r . I t w i l l emphasizes t e c h n i q u e s t h a t w i l l r e s u l t i n a l g o r i t h m s t h a t a r e f a s t and easy t o implement. S p e c i a l c o n s i d e r a t i o n s a r e g i v e n t o dec r e a s e d a t a m a n i p u l a t i o n and i n c r e a s e c o m p u t a t i o n a l speed. The f i n a l d e s i g n c o m p r i s e s of t h r e e main s t a g e s as shown i below. B1 nary Input Image F inal Preprocess ing (Image Thinning) Single class group Global Feature Detect, Image Extraction and Preclass 1 f i c a t i o n ARG Image Representat(on and Matching 1 >-2 >-Output - Character i d e n t i t y * U n i d e n t i f i a b l e character F i g . 1.2 B l o c k d i a g r a m of t h e f i n a l r e c o g n i z e r . Data r e d u c t i o n i s a c h i e v e d i n the f i r s t s t a g e by u s i n g a new t h i n n i n g a l g o r i t h m s p e c i a l l y a d a p t e d f o r t h i n n i n g a l p h a n u m e r i c c h a r a c t e r s . D e s i g n of t h i s t h i n n i n g a l g o r i t h m i s p r e s e n t e d i n d e t a i l i n c h a p t e r I I . The second s t a g e performs a f a s t p r e c l a s s i f i c a t i o n of the i n p u t image based on i t s t o p o l o g y . I t w i l l l a t e r be shown t h a t t h i s r e s u l t s i n a s u b s t a n t i a l r e d u c t i o n i n t h e e n t r o p y of t h e i n p u t image and i s a c r u c i a l s t e p towards h i g h speed r e c o g n i t i o n . D e s i g n of t h i s image e x t r a c t i o n , r e p r e s e n t a t i o n and p r e c l a s s i f i c a t i o n p r o c e d u r e s w i l l be g i v e n i n c h a p t e r I I I . Chapter IV d e s c r i b e s a c h a r a c t e r d e s c r i p t i o n t e c h n i q u e u s i n g a t t r i b u t e d r e l a t i o n a l graphs (ARGs). The t e c h n i q u e i s based on s i m p l e l o c a l f e a t u r e e x t r a c t i o n p r o c e d u r e s t h a t can be implemented v e r y e f f i c i e n t l y . F i n a l c l a s s i f i c a t i o n i s a c c o m p l i s h e d by matching t h i s ARG r e p r e s e n t a t i o n of a p r e c l a s s i f i e d image w i t h the ARGs of r e f e r e n c e images. A new graph m a t c h i n g p r o c e d u r e i s a l s o d e s i g n e d f o r t h i s purpose w i t h s u p e r i o r c o m p u t a t i o n a l c o m p l e x i t y compared t o c o n v e n t i o n a l graph matching schemes. 3. Data base. Munson's m u l t i - c o d e r a l p h a n u m e r i c c h a r a c t e r images [ 3 ] , a r e used f o r t e s t i n g and v e r i f y i n g the a l g o r i t h m s d e s i g n e d i n t h i s r e s e a r c h p r o j e c t . The d a t a c o n s i s t s of 24x24 b i n a r y images from 49 c o d e r s of c h a r a c t e r s from th e F o r t r a n I I language. Except f o r the s l a s h t o the l e t t e r Z and the c r o s s b a r s f o r the l e t t e r I , the images s i m u l a t e s u n c o n s t r a i n e d h a n d p r i n t e d a l p h a n u m e r i c c h a r a c t e r s . A random 1500 c h a r a c t e r s e t of images was s e l e c t e d f o r t e s t i n g the r e s u l t i n g r e c o g n i z e r . The o n l y c o n d i t i o n was t h a t the images w i t h p i n - h o l e s were e x c l u d e d . T h i s i s due t o the assumption t h a t t h e p r e p r o c e s s o r such as one d e s i g n e d by Lunscher w i l l remove p i n - h o l e n o i s e s . 11 CHAPTER I I FINAL PREPROCESSING AND DATA REDUCTION. 1 . I n t r o d u c t i o n . The use of t h i n n i n g f o r the purpose of d a t a r e d u c t i o n as w e l l as image t r a n s f o r m a t i o n of a b i n a r y c h a r a c t e r image i n t o one t h a t i s b e t t e r s u i t e d f o r more r i g o r o u s a n a l y s i s by d i g i t a l computers w i l l be p r e s e n t e d i n t h i s c h a p t e r . Such t r a n s f o r m a t i o n s a r e p a r t i c u l a r l y w e l l s u i t e d f o r images t h a t were meant t o be t h i n or l i n e d rawings i n the f i r s t p l a c e because i f t h i n n i n g r e s u l t s i n the r e t e n t i o n of the e s s e n t i a l c h a r a c t e r i s t i c s of t h e image then the o r i g i n a l image would have been reduced t o a form t h a t would l e n d i t s e l f more r e a d i l y t o g r a p h i c a l a n a l y s i s . An e a r l y e f f o r t t o o b t a i n the t h i n n e d or s k e l e t a l forms of a b i n a r y image was based on the median a x i s t r a n s f o r m a t i o n (MAT) [ 3 7 ] , which was d e s i g n e d f o r o b t a i n i n g t h e median a x i s or s k e l e t o n of an o b j e c t d e f i n e d on the c o n t i n u o u s or E u c l i d i a n p l a n e . More s u c c e s s f u l c l a s s i c a l t h i n n i n g a l g o r i t h m s o p e r a t e on t h e i n d i v i d u a l p i c t u r e e l e m e n t s , p i x e l s , and examine t h e i r r e l a t i o n s w i t h the r e s t of the p i x e l s and t h e i r complements i n t h e b i n a r y image w i t h r e s p e c t t o a c e r t a i n c o n n e c t i v i t y c r i t e r i a . The c o n n e c t i v i t y c r i t e r i a i s the s i n g l e most i m p o r t a n t and n e c e s s a r y c o n d i t i o n t h a t has t o be s a t i s f e d i f the t o p o l o g i c a l p r o p e r t i e s of an image a r e t o be p r e s e r v e d i n t h e t h i n n i n g p r o c e s s . T h i n n i n g a l g o r i t h m s have e v o l v e d around 12 d i f f e r e n t d e f i n i t i o n s of the c o n n e c t i v i t y c o n d i t i o n , the most p o p u l a r of which has been R o s e n f e l d ' s 4- and 8 - c o n n e c t i v i t y [ 3 8 ] , [ 3 9 ] , [ 4 0 ] . V a r i o u s s u c c e s s f u l t h i n n i n g a l g o r i t h m have been d e s i g n e d around t h i s concept of c o n n e c t i v i t y , a number of which have been w e l l summarized by S t e n t i f o r d [41] and Tamura [ 4 2 ] . These a l g o r i t h m s have been p r e d o m i n a n t l y p a r a l l e l a l g o r i t h m s i n t h a t t h e y r e q u i r e a s e q u e n t i a l e x a m i n a t i o n of a l l t he p i x e l s i n the image a t each i t e r a t i o n of the t h i n n i n g p r o c e s s . F u r thermore the p r o c e s s e s a r e d i r e c t i o n dependent [ 3 8 ] , t h a t i s each i t e r a t i o n w i l l r e q u i r e the a l g o r i t h m t o c o n s i d e r o n l y p i x e l s i n some s p e c i f i c l o c a t i o n ( s ) of the image such as t h e p i x e l s t h a t a r e t o the n o r t h , s o u t h , e a s t or west of the image i n o r d e r t o o b t a i n a s y m m e t r i c a l l y t h i n n e d s k e l e t o n . A l l t h e s e r e q u i r e m e n t s c o u p l e d w i t h the o f t e n n o i s y r e s u l t a n t t h i n n e d images made these c l a s s i c a l t h i n n i n g a l g o r i t h m s t o o slow f o r most r e a l t i m e a p p l i c a t i o n s . In t h i s c h a p t e r a new t h i n n i n g a l g o r i t h m f o r alphanumeric c h a r a c t e r s w i l l be d e s i g n e d . T h i s new a l g o r i t h m i s i n s p i r e d by the a l g o r i t h m of P a v l i d i s [ 4 3 ] , and w i l l i n c l u d e a d d i t i o n a l p r o c e s s i n g t o p r e s e r v e image c o n n e c t i v i t y and shape. a d d r e s s t h e problem of c r o s s o v e r s i n t h e d i g i t i z e d b i n a r y p a t t e r n . t r i m , on the f l y , redundant p i x e l s . The above m a t t e r s a r e c o n s i d e r e d t o be of prime importance i n c h a r a c t e r r e c o g n i t i o n . S e c t i o n 2 p r e s e n t s the b a s i c d e f i n i t i o n s fundamental t o t h e t h i n n i n g p r o c e s s and p r o v i d e s 13 the s p e c i f i c a t i o n s t h a t w i l l be c o n s i d e r e d e s s e n t i a l f o r a t h i n n i n g a l g o r i t h m f o r c h a r a c t e r r e c o g n i t i o n . S e c t i o n 3 g i v e s d e t a i l s of the t h i n n i n g a l g o r i t h m and d i s c u s s some of i t s c h a r a c t e r i s i t c s and the r e s u l t s of i t s a p p l i c a t i o n on some al p h a n u m e r i c c h a r a c t e r s . 2. B a s i c d i s c r e t e geometry and d e f i n i t i o n s . 2.1 B a s i c d e f i n i t i o n s . D e fn: 2.1.1 The local neighbourhood of the p i x e l P i s d e f i n e d as the 8 ne i g h b o u r s of the c e n t r a l l y l o c a t e d p i x e l P i n a 3x3 p i x e l window as shown i n f i g u r e 2.1. P4 P3 P2 P5 P PI P6 P7 P8 F i g . 2.1 P i x e l s P1-P8 a r e the l o c a l s n e i g h b o u r s of P. Defn: 2.1.2 . P i x e l s P1,P3,P5 and P7 a r e c a l l e d t he direct neighbours of P. D e f n : 2.1.3 P i x e l s P2,P4,P6 and P8 a r e c a l l e d the indirect neighbours of P. 14 Defn: 2.1.4 A sequence of p i x e l s S, c o n s i s t i n g of p i x e l s p n...p N i s J-connect ed i f p and p a r e l o c a l n e i g h b o u r s of and D-connect ed i f P j l _ 1 and 1 a r e d i r e c t n e i g h b o u r s of p k f o r 1 < k £ N-1. Defn: 2.1.5 The Is r e p r e s e n t i n g the o b j e c t body i n a b i n a r y image a r e I-c o n n e c t e d w h i l e i t s background r e p r e s e n t e d by 0s a r e D-connected. T h i s i m p l i e s t h a t the 7's i n c l u d e the o b j e c t b o u n d a r i e s w h i l e t h e 0's r e p r e s e n t i n g the background do n o t . T h i s d e f i n i t i o n f o r b i n a r y images s a t i s f i e s t he J o r d a n ' s c u r v e theorem f o r d i g i t a l c u r v e s [ 4 0 ] , which s t a t e s t h a t the complement of a s i m p l e c l o s e d c u r v e C has e x a c t l y two components, one i n s i d e C and one o u t s i d e , and C i s the common boundary between t h e s e two components. T h e r e f o r e , u n l e s s o t h e r w i s e s p e c i f i e d , the above d e f i n i t i o n of c o n n e c t i v i t y w i l l be assumed when r e f e r r i n g t o b i n a r y images i n the r e s t of t h i s t h e s i s . 2.2 S p e c i f i c a t i o n s f o r t h i n n e d images. I t has been assumed i n the p r e v i o u s c h a p t e r t h a t the i n p u t image i s a b i n a r y image of an i s o l a t e d a l p h a n u m e r i c c h a r a c t e r , whose g a u s s i a n type n o i s e has been f i l t e r e d by a p r e p r o c e s s i n g s t a g e and the b i n a r y image a c c u r a t e l y r e p r e s e n t s the 2 - d i m e n s i o n a l image i n t e n d e d by t h e w r i t e r . The t h i n n i n g a l g o r i t h m must reduce t h i s i n p u t i t s s k e l e t a l or t h i n n e d form h a v i n g t h e c h a r a c t e r i s t i c s : image t o f o l l o w i n g 1. The c o n n e c t i v i t y of the d i g i t a l image must be p r e s e r v e d . 2. A r c s or branches of t h e t h i n n e d images must be of s i n g l e p i x e l t h i c k n e s s except a t the l o c a l neighbourhood of an i n t e r s e c t i o n of two or more bra n c h e s . 3. The a n g u l a r c h a r a c t e r i s t i c s of t h e image, s p e c i f i c a l l y a t or near p o i n t s of i n t e r s e c t i o n s must be c o n s i s t e n t w i t h the o r i g i n a l image. For example a concave a r c h opening eastward must t h i n t o a concave l i n e opening e a s t w a r d and not a meandering or f o r k e d l i n e opening e a s t w a r d . 4. The r e s u l t a n t t h i n n e d images must not c o n t a i n any f a l s e b r a n c h e s . That i s , a b r a n c h e x i s t s i n t h e - t h i n n e d image o n l y i f the i n p u t image shows the p h y s i c a l e x i s t e n c e of such a f e a t u r e . T h i s i s d e s i r a b l e so as not t o add f a l s e t o p o l o g i c a l i n f o r m a t i o n t o the image due t o n o i s y t h i n n i n g p r o c e d u r e s . 5. The t h i n n i n g p r o c e s s must be f a s t . I t must be s u i t a b l e f o r s e q u e n t i a l p r o c e s s i n g i n r e a l t i m e as the image i s a c q u i r e d or s u i t a b l e f o r i m p l e m e n t a t i o n i n a m u l t i p r o c e s s o r e n v i r o m e n t . P a v l i d i s a l g o r i t h m p r o v i d e s s o l u t i o n s t o the c h a r a c t e r i s t i c s 2, 4 and 5. But i t f a i l s i n t h e f o l l o w i n g r e s p e c t s : The a l g o r i t h m does not p r e s e r v e c o n n e c t i v i t y i n a l l 1 6 p o s s i b l e c a s e s . I d e a l r i g h t a n g l e s a r e not t h i n n e d c o n s i s t e n t l y i n t h a t the r e s u l t i n g a n g l e s i n the t h i n n e d image depend on the or d e r the p i x e l s a r e scanned. No n o i s e branch t r i m m i n g p r o c e d u r e s have been suggested nor were t h e r e any a n a l y s i s on the ty p e s of i n t e r s e c t i o n s t h a t w i l l r e s u l t from the t h i n n i n g p r o c e s s . These problems w i l l be r e c t i f i e d i n the new or m o d i f i e d t h i n n i n g a l g o r i t h m t h a t i s g i v e n i n the f o l l o w i n g s e c t i o n s . 3. D e s i gn r u l e s f o r the m o d i f i e d t h i n n i n g a l g o r i t h m . 3.1 D e f i n i t i o n s f o r t he t h i n n i n g a l g o r i t h m . The f o l l o w i n g d e f i n i t i o n s p r o v i d e the b a s i c r u l e s f o r the t h i n n i n g p r o c e s s . Defn: 3.1.1 The contour p i x e l s of an image i s the s e t of / p i x e l s t h a t have a t l e a s t ONE d i r e c t neighbour which i s a 0. Contour p i x e l s a r e l a b e l e d 2 as they a r e found. Defn: 3.1.2 A c o n t o u r p i x e l i s multiple i f i t s a t i s f i e s any ONE of the two f o l l o w i n g c o n d i t i o n s : (a) . I t has a t most ONE non-zero n e i g h b o u r . (b) . I t s l o c a l neighbourhood conforms t o e i t h e r ONE of the t h r e e masks shown i n f i g u r e s 2 . 2 ( i - i i i ) o r thos e o b t a i n e d from them by m u l t i p l e s of 90° r o t a t i o n s . M u l t i p l e p i x e l s a r e l a b e l e d 3 as they a r e found and a r e 17 NOT removable. ( i ) . A A A 0 P 0 where a t l e a s t ONE of A B B B and ONE of B i s nonzero. ( i i ) . A A A A P 0 A 0 B ( i i i ) . where a t l e a s t ONE of A and B i s non-zero. where A i s non-zero and a t l e a s t ONE of C i s z e r o F i g . 2.2 L o c a l neighbourhood of a m u l t i p l e p i x e l P D e f n : 3.1.3 A c o n t o u r p i x e l i s tentatively multiple i f i t s a t i s f i e s any ONE o f the f o l l o w i n g c o n d i t i o n s : (a) . I t has no n e i g h b o u r s l a b e l e d /. (b) . I t s neighbourhood conforms t o t h e mask shown i n f i g u r e 2.3 or t h o s e o b t a i n e d from them by m u l t i p l e s of 90° r o t a t i o n s . T e n t a t i v e l y m u l t i p l e p i x e l s a r e l a b e l e d 4 as they a r e found. where a t l e a s t ONE of A , B and C must be non- z e r o and D >= 2. I f both C's ar e non-zero then A and B can be a n y t h i n g . A A C 0 P D B B C F i g . 2.3 L o c a l n e ighbourhood of a t e n t a t i v e l y m u l t i p l e p i x e l P . 18 Defn: 3.1.4 A t e n t a t i v e l y m u l t i p l e p i x e l i s removable i f i t s a t i s f i e s ONE of the f o l l o w i n g t h r e e c o n d i t i o n s : (a) . I t s 5-neighbour ( P 5 ) i s z e r o and i t s 1-neighbour ( P I ) i s m u l t i p l e or t e n t a t i v e l y m u l t i p l e . (b) . I t s 3-neighbour (P3) i s z e r o and i t s 6-neighbour (P6) i s m u l t i p l e or t e n t a t i v e l y m u l t i p l e and i t does • not have a neighbour l a b e l e d removable by c o n d i t i o n ( a ) . (c) . I t s l o c a l neighbourhood conforms t o any ONE of the masks shown i n f i g u r e s 2 . 4 ( i — i i i ) o r t h o s e o b t a i n e d from them by m u l t i p l e s of 90 ° r o t a t i o n s . T e n t a t i v e l y m u l t i p l e p i x e l s a r e l a b e l e d 5 as they a r e found. 0 B 0 B P 0 0 0 0 X 0 0 B P 0 A 0 0 A 0 0 B P 0 X 0 0 ( i ) ( i i ) ( i i i ) F i g . 2.4 L o c a l neighbourhood of t e n t a t i v e l y m u l t i p l e p i x e l s t h a t a r e r e m o v a b l e 1 . W i t h B = 3 or 4, A >0 and i s not l a b e l e d removable by c o n d i t i o n s (a) or ( b ) . X i s don't c a r e . 1 T h i s t e n t a t i v e l y m u l t i p l e p i x e l s c o r r e s p o n d s t o t h e type 2 e x t r a p i x e l s t o be c l a s s i f i e d i n the l a t e r p a r t of t h i s s e c t i o n . 19 The mask ( i i ) i n f i g u r e 2.2 d i f f e r s from the P a v l i d i s ' d e f i n i t i o n s i n t h a t the p i x e l B i s d e f i n e d t o be B>0 i n s t e a d of B=2. T h i s i s n e c e s s a r y t o p r e s e r v e c o n n e c t i v i t y i f s e q u e n t i a l i m p l e m e n t a t i o n i s used, t h a t i s the p i x e l s a re scanned from l e f t t o r i g h t , t o p t o bottom. T h i s i s obvi o u s because i f B i s s i t u a t e d a t the t o p r i g h t hand c o r n e r of the l o c a l neighbourhood of P and has been l a b e l e d m u l t i p l e then P w i l l have t o be m u l t i p l e t o p r e s e r v e c o n n e c t i v i t y . Mask ( i i i ) of f i g u r e 2.2 i s a d d i t i o n a l t o the masks of the o r i g i n a l a l g o r i t h m . The mask i s i n c l u d e d t o improve the c o r n e r c h a r a c t e r i s t i c s of an i d e a l T - j u n c t i o n as s t i p u l a t e d i n the s p e c i f i c a t i o n s . These p o i n t s can b e s t be i l l u s t r a t e d by the s e q u e n t i a l i m p l e m e n t a t i o n of the o r i g i n a l and m o d i f i e d a l g o r i t h m t o the t e s t image of f i g u r e 2.5, the o u t p u t s a t the end of each i t e r a t i o n of the a l g o r i t h m s a r e shown i n f i g u r e s 2.6a and 2.6b. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . 1 1 1 ! i i i i 1 1 1 1 . 1 1 1 1 1 1 1 1 1 1 1 . 1 1 1 . 1 1 1 1 1 1 1 1 . 1 1 . 1 1 1 1 1 1 1 1 . 1 1 1 . 1 1 1 1 1 1 1 1 . 1 1 1 . 1 1 1 1 1 1 1 1 . 1 1 1 1 . 1 1 1 1 1 1 1 1 . 1 1 1 . 1 1 1 1 1 1 1 1 . 1 1 1 1 1 1 1 1 1 1 1 . 1 1 1 1 1 1 1 1 1 1 1 . 1 1 1 1 1 . 1 1 1 1 1 1 1 1 . 1 1 1 1 1 1 1 ' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . F i g . 2.5 T e s t image. 20 0 0 c 0 0 0 0 0 0 c 0 r 0 c 0 0 c c o C 0 0 0 0 0 0 0 0 0 0 0 0 0 ? 0 0 0 0 c 0 0 ? c c c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c c 0 0 0 0 0 0 0 c c 0 c 0 0 0 r. c 2 2 2 2 2 2 2 7 J 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 c 0 0 0 0 0 0 0 0 c c c 0 0 o c 0 2 1 1 1 1 i 1 1 1 1 1 1 1 2 0 0 0 0 0 r> 0 0 2 2 5 3 3 3 3 3 3 3 3 3 s 2 2 c 0 0 0 0 0 c 0 2 , , 1 2 2 2 2 2 ^ 2 2 1 1 1 2 0 0 0 0 0 0 c 0 2 1 4 0 0 0 c 0 0 0 0 0 4 1 2 0 0 c 0 r\ 0 G 0 2 2 0 0 0 0 0 0 0 0 0 2 1 i 2 0 0 0 0 0 0 0 0 5 4 0 0 0 0 0 0 0 0 0 0 0 5 4 0 c 0 0 0 0 e c 2 1 \ 2 0 2 2 2 0 0 0 0 0 2 1 1 2 C 0 0 0 0 0 0 0 5 4 0 0 0 0 0 0 0 c 0 0 0 s d 0 0 0 0 0 0 r, 2 1 2 0 2 1 1 2 0 0 0 0 2 1 1 2 0 0 0 0 0 0 0 0 5 4 0 0 0 3 3 0 0 0 0 0 0 s 4 0 0 0 0 0 0 0 0 2 t 2 0 2 2 2 3 0 c 0 0 2 1 1 2 0 0 0 0 0 0 0 0 5 4 0 c 0 0 0 3 0 0 0 0 0 5 4 0 c c 0 0 0 0 0 2 1 1 2 0 0 C 0 0 s 4 5 0 2 1 1 1 S 4 5 0 0 0 c 0 5 4 0 0 0 0 0 0 0 s 0 0 0 2 t 5 0 5 0 0 0 c 0 2 1 2 0 0 0 0 0 s 4 4 0 2 1 1 1 4 4 4 0 0 0 0 0 5 4 0 0 0 0 0 0 0 3 4 c 0 2 1 A 3 4 4 0 0 0 0 2 2 0 0 2 4 3 4 c 0 0 2 1 1 2 o o o o 0 0 0 0 5 4 0 0 0 0 3 3 s 0 0 0 0 5 4 0 0 0 0 0 0 0 0 2 t 1 2 0 2 1 2 0 4 0 0 0 2 1 1 2 0 0 0 0 0 0 0 0 5 4 0 0 0 3 0 0 4 0 0 0 0 5 4 0 c 0 0 0 0 0 0 2 1 2 0 2 1 2 0 0 0 0 0 2 1 t 2 0 0 0 0 0 0 0 0 5 4 0 0 0 3 0 0 0 0 0 0 0 5 4 0 0 0 0 0 0 0 0 2 2 0 2 1 2 0 0 0 0 0 2 1 i 2 0 0 0 0 0 0 0 0 5 4 0 0 0 3 0 0 0 0 0 0 0 5 4 0 0 0 0 0 0 0 0 2 1 2 0 2 1 1 2 2 2 2 0 2 1 1 2 0 0 0 0 0 0 0 0 s 4 0 0 0 5 4 0 0 0 0 0 0 4 c 0 c 0 0 0 0 0 2 1 2 0 2 1 1 i 1 1 2 0 2 t 1 2 0 0 0 0 0 0 0 0 5 4 0 0 0 5 4 3 3 3 0 0 0 5 a 0 0 0 0 0 0 0 c 2 1 t 2 0 2 2 2 2 2 2 2 0 2 1 1 2 0 0 0 0 o 0 0 0 s 4 0 0 0 0 0 0 0 0 0 0 0 5 4 0 0 0 c c 0 0 0 2 t 2 0 0 0 0 0 0 0 0 0 2 1 I 2 0 0 0 0 0 0 0 0 5 4 0 c 0 0 c c 0 0 £ 0 0 5 4 0 0 c 0 0 0 0 c 2 1 2 0 0 0 0 0 0 0 0 2 1 1 1 2 0 0 0 0 0 0 c 0 5 4 0 0 0 0 0 0 0 0 0 0 2 1 2 0 c 0 0 0 0 c c 2 1 2 2 2 2 0 2 2 2 1 i 1 i 2 0 0 0 0 0 0 0 0 2 1 s 0 0 0 c 0 0 0 0 5 1 1 2 c 0 0 0 0 0 0 c 2 1 1 1 1 1 2 0 2 1 1 1 1 t 1 2 o o o o 0 0 0 0 2 2 4 3 3 3 0 0 0 3 3 4 2 2 2 0 0 0 0 c 0 0 0 2 2 2 2 2 2 2 2 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c 0 0 0 0 0 0 0 0 o o o o 0 0 0 0 0 0 0 0 0 0 0 c 0 0 0 0 0 0 C c c 0 0 0 (a) 1st i terat1on (b) 2nd 1terat ion 0 c c 0 0 0 o c ^ 0 0 0 0 c 0 C 0 0 0 o o o o 0 0 0 c 0 c 0 0 0 c 0 0 0 0 0 c c 0 c 0 C 0 ? 0 0 0 0 0 c c c c 0 0 0 0 0 0 0 0 0 c o o o o 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 0 £ 0 0 0 C 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 c 5 3 0 0 0 0 0 0 0 0 0 3 3 0 0 o o o 1 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 c 0 3 0 o o o o 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 o o o o 1 1 0 0 0 0 0 3 0 0 0 3 3 0 0 0 0 0 0 0 3 0 o o o o 1 1 1 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 0 3 0 o o o o 1 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 o o o o 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 3 3 0 0 0 S 3 3 3 3 0 * 1 1 1 1 1 0 0 0 0 0 3 0 0 0 0 3 3 0 0 0 0 0 0 3 0 o o o o 1 1 1 0 0 0 0 0 3 0 0 0 3 0 0 3 0 0 0 0 0 3 0 o o o o 1 y 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 3 0 o o o o 1 1 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 3 0 o o o o 1 1 1 0 0 0 0 0 3 0 0 0 0 3 0 0 0 0 0 0 0 3 0 o o o o 1 1 ( 1 0 0 0 0 0 3 0 0 0 0 5 3 3 3 0 0 0 0 3 0 o o o o 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 c 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 o o o o 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 3 0 0 o o o o 1 1 0 0 0 0 0 3 0 0 0 c 0 0 0 0 0 0 3 4 0 0 o o o o 1 1 1 0 0 0 0 0 0 3 3 3 3 0 0 0 3 3 3 0 0 0 0 o o o o 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o o o o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o o o o (c) 3rd i t e r a t i o n . (d) Final Image. F i g . 2.6a Test image t h i n n i n g w i t h o r i g i n a l P a v l i d i s a l g o r i t h m . Remark: The image i n each of t h e i t e r a t i o n s i n f i g u r e s 2.6(a) and (b) c o r r e s p o n d s t o the image a f t e r the t e s t s f o r c o n d i t i o n s i n d e f n . 3.1.4. T h i s c o r r e s p o n d s t o the end of s t e p 5 i n a l g o r i t h m A 1 . 6uiuuxq^ patjtpoui a m 6uxsn 6UT.UUTU.} a6eun ^saj, q9*2 *&TJ a 6 e w i t e u i j ( p ) i i i i i i i . i i 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 l 1 l l 0 0 0 0 0 0 0 0 c c c 0 0 0 c c c c 0 0 0 0 0 0 I 0 0 0 0 0 0 s c 0 0 0 0 0 0 0 0 0 0 c 0 0 0 0 0 " i 0 0 0 0 0 0 c 0 0 0 0 0 0 0 0 0 0 0 c 0 0 0 0 0 I 0 0 0 0 0 e 0 0 0 0 0 0 0 0 0 0 0 0 c 0 0 c 0 0 0 0 0 0 0 c 0 0 0 0 0 0 0 0 0 0 0 0 c 0 0 0 0 0 1 0 0 0 0 0 c 0 0 0 0 e c c 9 0 0 0 0 c 0 0 0 0 0 I 0 0 0 0 0 c 0 0 0 0 0 0 0 r s 0 0 0 c 0 0 0 0 0 1 1 0 0 0 0 0 c 0 0 0 0 0 0 0 0 c 0 0 0 c 0 0 0 0 0 i i 0 0 0 0 0 c 0 0 0 0 0 0 0 0 c 0 0 0 c 0 0 0 0 0 I i 0 0 0 0 0 c 0 0 0 0 0 0 0 0 c 0 0 0 c 0 0 0 0 0 i 0 0 0 0 0 c 0 0 0 0 0 c e c 0 0 0 0 e 0 0 0 0 0 1 0 c c c t c 0 0 0 € c 0 0 0 0 0 0 0 c 0 0 0 0 0 i 0 0 0 0 0 c 0 0 0 0 0 c 0 0 0 0 0 0 c 0 0 0 0 0 I 0 0 0 0 0 c 0 0 0 0 0 0 c 0 0 0 0 0 c 0 0 0 0 0 I k 0 0 0 0 0 c 0 0 0 0 0 0 0 c c 0 0 0 c 0 0 0 0 0 I 0 0 0 c 0 c 0 0 0 0 0 0 0 0 0 0 0 0 c 0 0 0 0 0 I 0 0 0 0 0 c 0 0 0 0 0 0 0 0 0 0 0 0 E 0 0 0 0 0 I 0 0 0 0 0 0 c s 0 0 0 0 0 0 0 0 0 V s 0 0 0 0 0 > 1 1 0 0 0 0 0 0 0 r c c e c c c c c c 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 z 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c 0 0 0 0 0 0 0 0 0 0 u o t i B j e i i p u j ( q ) U O I } S l ( e ) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 z c z z z z z 0 e t : z z z : z 0 0 0 0 0 0 0 z \ i I I t I z 0 z I i I V \ z 0 0 0 0 0 0 0 z i I 1 z c c 0 z I z z I I 1 z 0 0 0 0 0 0 0 z i I c 0 0 0 0 0 0 0 0 z I I z 0 0 0 0 0 0 0 z t t z 0 0 0 0 0 0 0 0 0 z I i z 0 0 0 0 0 0 0 z t 1 z 0 z t z z z z z 0 z I 1 z 0 0 0 0 0 0 0 z i I z 0 z t t t \ z 0 z 1 z 0 0 0 0 0 0 0 z i z 0 z z z z t t z 0 z 1 I z 0 0 0 0 0 0 0 z i i z 0 0 0 0 0 z I z 0 z t I z 0 0 0 0 0 0 0 z x 1 z 0 0 0 0 0 z \ z 0 z k I z 0 0 0 0 0 0 0 z i i z 0 0 0 s 0 z z 0 z k t z 0 0 0 0 0 0 0 z i L z 0 0 0 » c e z 0 0 z 1 z 0 0 0 0 » * » t * I z 0 » » 9 0 0 0 0 0 z ^ i z 0 0 0 0 9 » s I i z 0 s » c 0 0 0 0 0 z 1 1 z 0 0 0 0 0 0 0 z V z 0 0 0 0 c z z z 0 z I I z 0 0 0 0 0 0 0 z t 4 z 0 0 0 0 z t z 0 z I t z 0 0 0 0 0 0 0 z t i z 0 0 0 0 0 z z z 0 z i I z 0 0 0 0 0 0 0 z i z 0 0 0 0 0 0 0 0 0 z I I z 0 0 0 0 0 0 0 z i I 1 : z z z £ c c z z t 1 I z 0 0 0 0 0 0 0 z I I 1 i I I I V i I t L 1 z 0 0 0 0 0 0 0 z z z z z z z c z z z z : z z z z 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22 I t i s c l e a r t h a t the c o n n e c t i v i t y of the c e n t r a l p i e c e of t h e t e s t image i s p r e s e r v e d by the m o d i f i e d a l g o r i t h m but not t h e o r i g i n a l a l g o r i t h m f o r the reason g i v e n above. A l e s s a p p a r e n t d i f f e r e n c e between the two r e s u l t i n g t h i n n e d images a r e the t o p r i g h t hand c o r n e r and the T - j u n c t i o n on the r i g h t edge of the image. F i r s t l y the t o p r i g h t hand c o r n e r e x i b i t s a smoother r o l l - a r o u n d c h a r a c t e r i s t i c w i t h the m o d i f i e d a l g o r i t h m and a l s o the T - j u n c t i o n i s b e t t e r p r e s e r v e d . T h i s i s c o n s i d e r e d d e s i r a b l e f o r the purpose of c h a r a c t e r d e s c r i p t i o n because i f t o p o l o g i c a l p o i n t s such as j u n c t i o n s as w e l l as c e r t a i n n o n - t o p o l o g i c a l p o i n t s such as the c o r n e r s a r e t o be used t o p r o v i d e a g l o b a l d e s c r i p t i o n of the image then t h e s e p o i n t s must be w e l l d e f i n e d and e a s i l y d e t e c t a b l e . T h i s i s a c h i e v e d t h r o u g h the a d d i t i o n of mask ( i i i ) i n f i g u r e 2.2. Note t h a t a l t h o u g h the mask improves the i n t e r p r e t a b i l i t y of c o r n e r s and j u n c t i o n s , r e s u l t i n g i d e a l r i g h t a n g l e c o r n e r s a r e o n l y w e l l behaved but not a b s o l u t e l y c o n s i s t e n t . T h i s can be seen by t h e number of p i x e l s r e q u i r e d t o t u r n the d i f f e r e n t r i g h t a n g l e c o r n e r s i n the f i n a l image. S o l u t i o n t o t h i s w i l l r e q u i r e s e l e c t i v e t h i n n i n g from d i f f e r e n t d i r e c t i o n s w hich i s s l o w . B e s i d e s , t h i s dependence on s c a n n i n g o r d e r i s due t o the d e f i n i t i o n 3.1.4(a) and (b) d e s i g n e d t o reduce branches of t h i c k n e s s 2 t o s i n g l e p i x e l t h i c k , by removing one of t h e two t e n t a t i v e l y m u l t i p l e p i x e l s . T h i s i s i l l u s t r a t e d by the two v e r t i c a l s i d e s of t h e t e s t image i n f i g u r e 2.6b. D i f f e r i n g s e l e c t i o n s of which p i x e l t o remove g i v e r i s e t o i d e a l r i g h t a n g l e c o r n e r s d i f f e r i n g by a t most one p i x e l . I f t h i s c o r n e r c h a r a c t e r i s t i c i s n o n - e s s e n t i a l the mask need not be used. The second d i f f e r e n c e between the two a l g o r i t h m s l i e s i n the t y p e s of e x t r a p i x e l s t h a t are not r e q u i r e d f o r c o n n e c t i v i t y but a r e p r e s e r v e d by the a l g o r i t h m s . We can c l a s s i f y t h e s e p i x e l s i n t o two t y p e s : Type 1. E x t r a p i x e l s o c c u r i n g i n p l a c e s where a p h y s i c a l j u n c t i o n j u n c t i o n e x i s t s , e.g. 0 1 0 1 1 1 0 0 0 Type 2. E x t r a p i x e l s o c c u r i n g i n p l a c e s o t h e r than where a p h y s i c a l j u n c t i o n e x i s t s , e.g. 0 0 1 0 OR 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 These e x t r a p i x e l s c o u l d be removed by p o s t - t r i m m i n g r o u t i n e s . However, depending on r e q u i r e m e n t s not a l l t h e s e e x t r a p i x e l s a r e u n d e s i r a b l e . In t h i s case e x t r a p i x e l s of t y p e one i s the d i r e c t consequence of the mask i n f i g u r e 2 . 2 ( i i i ) . T h e r e f o r e o n l y e x t r a p i x e l s of t ype 2 need t o be removed. Comparing p i x e l P ( r e p r e s e n t i n g t y p e 2 e x t r a p i x e l ) i n t h e masks i n f i g u r e 2.4 and those of f i g u r e 2.2 24 f o r m u l t i p l e p i x e l s , i t i s o b v i o u s t h a t type 2 e x t r a p i x e l s can never q u a l i f y as m u l t i p l e p i x e l s . T h e r e f o r e t hey a r e p r e s e r v e d o n l y as p o s s i b l e t e n t a t i v e l y m u l t i p l e p i x e l s . As such they can be removed on the f l y by e x amining o n l y t h o s e t e n t a t i v e l y m u l t i p l e p i x e l s t h a t a r e not c o n s i d e r e d removable by c o n d i t i o n s (a) and (b) i n d e f i n i t i o n 3.1.4. T h i s i s done t h r o u g h the i n t r o d u c t i o n of c o n d i t i o n (c) i n the same d e f i n i t i o n . T h i s method p r e s e n t s a c o n s i d e r a b l e amount of time s a v i n g s compared t o u s i n g a p o s t - t r i m m i n g p r o c e d u r e . S i n c e the c o n d i t i o n s i n d e f i n i t i o n 3.1.4 has t o be checked i n the o r d e r ( a ) , (b) and ( c ) , (see A l o g r i t h m A1) c o n d i t i o n 3.1.4(c) i s checked o n l y i f a t e n t a t i v e l y m u l t i p l e p i x e l does not s a t i s f y c o n d i t i o n s 3.1.4(a) or ( b ) . 3.2 I m p l e m e n t a t i o n of t h i n n i n g a l g o r i t h m and t e s t r e s u l t s . The t h i n n i n g a l g o r i t h m was implemented i n P a s c a l on the PDP11/23 minicomputer system. The p r o c e d u r e i n v o l v e s s c a n n i n g the image s e q u e n t i a l l y s t a r t i n g from the t o p l e f t c o r n e r of t h e image and l a b e l s the p i x e l s a c c o r d i n g t o the a l g o r i t h m g i v e n below. 25 A l g o r i t h m A l . 1. For each 1 p i x e l do t e s t f o r c o n t o u r p i x e l as i n d e f n . 3.1.1; l a b e l c o n t o u r p i x e l s 2; 2. For each 2 p i x e l do i f p i x e l s s a t i s f i e s c o n d i t i o n 3.1.2(a) then r e l a b e l p i x e l as 3 e l s e i f p i x e l s a t i s f i e s c o n d i t i o n 3.1.2(b) then r e l a b e l p i x e l as 3; 3. For each 2 p i x e l do i f p i x e l s a t i s f i e s c o n d i t i o n 3.1.3(a) then r e l a b e l p i x e l as 4 e l s e i f p i x e l s a t i s f i e s c o n d i t i o n 3.1.3(b) then r e l a b e l p i x e l as 4; 4. For each 4 p i x e l do i f p i x e l s a t i s f i e s c o n d i t i o n 3.1.4(a) then r e l a b e l p i x e l as 5; 5. F o r each r e m a i n i n g 4 p i x e l do i f p i x e l s a t i s f i e s c o n d i t i o n 3.1.4(b) then r e l a b e l p i x e l as 5 e l s e i f p i x e l s a t i s f i e s c o n d i t i o n 3.1.4(c) then r e l a b e l p i x e l as 5; 6. s e t a l l 2 and 5 p i x e l s t o 0; s e t a l l 3 and 4 p i x e l s t o 7; 7. Repeat s t e p s 1 t o 6 u n t i l a l l c o n t o u r p i x e l s a r e m u l t i p l e or t e n t a t i v e l y m u l t i p l e . 2 There a r e a v a r i e t y of ways the same a l g o r i t h m can be implemented i n r e a l t i m e a p p l i c a t i o n s . P a v l i d i s has suggested a p i e c e m e a l approach where f i v e 8 - b i t r e g i s t e r masks a r e used t o r e p r e s e n t t h e e i g h t n e i g h b o u r s of P and the whole frame i s 2 T h i s c o n d i t i o n i s d i f f e r e n t from ' a l l p i x e l s a r e m u l t i p l e or t e n t a t i v e l y m u l t i p l e ' . The l a t t e r case w i l l not r e s u l t i n program t e r m i n a t i o n i f a p a t t e r n of the t y p e shown below e x i s t s . 0 3 0 3 1 3 0 3 0 26 s u b d i v i d e d and p r o c e s s i n s m a l l s e c t i o n s by a number of p r o c e s s o r s . T h i s approach i s not s u i t a b l e i n r e a l t i m e c h a r a c t e r r e c o g n i t i o n a p p l i c a t i o n s as p r o c e s s s y n c h r o n i z a t i o n r e q u i r e m e n t s w i l l slow down the a l g o r i t h m . For c h a r a c t e r r e c o g n i t i o n p i e c e m e a l t h i n n i n g i s not n e c e s s a r y because the c h a r a c t e r can be e f f e c t i v e l y r e p r e s e n t e d and t h i n n e d i n a 24x24 frame s i z e as shown by t h e Munson's c h a r a c t e r images, f o u r of which i s g i v e n i n f i g u r e 2.7. The t h i n n e d images of t h e s e c h a r a c t e r s w i l l s t i l l c o n t a i n w e l l d e f i n e d f e a t u r e s which w i l l e n a b l e c l a s s i f i c a t i o n t o be made. I n s t e a d , the a l g o r i t h m can be implemented s e q u e n t i a l l y i n hardware u s i n g an 8 - b i t r e g i s t e r f o r each mask ( e x c l u d i n g 90° r o t a t i o n s ) and a s i n g l e 8 - b i t s c r a t c h pad r e g i s t e r t o r e p r e s e n t the the n e i g h b o u r s of t h e p i x e l b e i n g t e s t e d . Each t e s t i s p e r f ormed by comparing the s c r a t c h pad r e g i s t e r w i t h an a p p r o p i a t e r e g i s t e r mask and each 90° mask r o t a t i o n i s e q u i v a l e n t t o a 2 - b i t c y c l i c s h i f t of the c o n t e n t s of the s c r a t c h pad r e g i s t e r . In t h i s a pproach o n l y s i m p l e c o n t r o l c i r u i t s a r e r e q u i r e d . As each o p e r a t i o n can be performed whenever 3 or more l i n e s of the image becomes a v a i l a b l e , v e r y h i g h speed o p e r a t i o n can be a c h i e v e d i f s e v e r a l of t h e s e u n i t s each w i t h i t s own s c r a t c h pad r e g i s t e r i s p i p e l i n e d and f a b r i c a t e d u s i n g V L S I . 1500 b i n a r y c h a r a c t e r images from Munson's c h a r a c t e r d a t a were t h i n n e d w i t h t h e a l g o r i t h m . The r e s u l t i n g t h i n n e d images m a i n t a i n i n g most i f not t h e a l l t h e shape a t t r i b u t e s of t h e 27 i n p u t c h a r a c t e r . Four of t h e s e images are shown i n f i g u r e 2.7 w i t h t h e i r t h i n n e d v e r s i o n s by u s i n g b oth P a v l i d i s and m o d i f i e d a l g o r i t h m g i v e n i n f i g u r e s 2.8a and 2.8b. For the images t h i n n e d w i t h P a v l i d i s a l g o r i t h m , shown i n f i g u r e 2.8a, c o n n e c t i v i t y i s not p r e s e r v e d i n images 'A', 'R' and 'X', and image 'B' has a redundant p i x e l a t the r i g h t hand c o r n e r of the bottom c u r v e of 'B'. On the o t h e r hand, a l l images t h i n n e d w i t h t h e m o d i f i e d a l g o r i t h m have p r e s e r v e d c o n n e c t i v i t y w i t h o u t any t ype 2 e x t r a p i x e l s . T h i s i s an i m p o r t a n t f e a t u r e 1 f o r images where f e a t u r e e x t r a c t i o n i n v o l v e s b r a n c h t r a c k i n g and e x t r a p i x e l s w i l l s i g n a l the p r e s e n c e of an i n t e r s e c t i o n of two or more bra n c h e s . E x t r a p i x e l s a t the j u n c t i o n can be f u r t h e r s o r t e d i n t o t h o s e b e l o n g i n g t o the d i f f e r e n t branches meeting t o form the j u n c t i o n . These a r e the t o p o l o g i c a l a t t r i b u t e s of the c h a r a c t e r t h a t can be brought out v e r y e f f e c t i v e l y by the t h i n n i n g a l g o r i t h m , t h u s c o n t r i b u t e s v i t a l i n f o r m a t i o n t h a t can be used f o r p r e c l a s s i f i c a t i o n (or c l a s s i f i c a t i o n ) . 4. D i s c u s s i o n . The t h i n n i n g a l g o r i t h m p r e s e n t e d has been d e s i g n e d t o be used as a f i n a l p r e p r o c e s s o r f o r a r e a l t i m e c h a r a c t e r r e c o g n i z e r . The d e s i g n i n v o l v e s t e s t s of l o c a l 3x3 c l u s t e r s of p i x e l s w h i c h a r e r e l a t i v e l y f a s t and s i m p l e t o make. E x p e r i m e n t s have been made u s i n g Munson's c o l l e c t i o n of h a n d w r i t t e n c h a r a c t e r s , and t h e s e show t h a t t h e shape c h a r a c t e r i s t i c s as judged by the eye a r e w e l l p r e s e r v e d . 28 T y p i c a l t h i n n e d c h a r a c t e r s a r e g i v e n i n f i g u r e 2.8b. These may be compared t o the same s e t of c h a r a c t e r s t h i n n e d w i t h P a v l i d i s ' a l g o r i t h m i n f i g u r e 2.8a. The new a l g o r i t h m c l e a n s up the e x t r a p i x e l s t h a t a r e not r e q u i r e d f o r c o n n e c t i v i t y but a r e p r e s e n t i n images t h i n n e d w i t h P a v l i d i s ' a l g o r i t h m as can be seen i n the bottom c u r v e of image 'B' i n f i g u r e 2.8a, and i n the rounded bottom r i g h t hand c o r n e r of the t e s t image i n f i g u r e 2.6a. Breaks i n c o n n e c t i v i t y a r e a l s o e l i m i n a t e d , l e a v i n g c o n t i n u o u s p a r t s of the c h a r a c t e r as a sequence of c onnected one p i x e l o u t l i n e s . A g a i n g e o m e t r i c p r o p e r t i e s , e s p e c i a l l y a t c o r n e r s a r e w e l l p r e s e r v e d by the a l g o r i t h m . T h i s t h i n n i n g a l g o r i t h m i s t h e r e f o r e an e x c e l l e n t f i n a l p r e p r o c e s s o r f o r b i n a r y c h a r a c t e r images. From the t h i n n i n g of Munson's d a t a , i t i s o b s e r v e d the number of image p i x e l s a r e reduced by 60 t o 70 p e r c e n t i n the m a j o r i t y of the c a s e s . L e a v i n g a s k e l e t a l image t h a t c o n t a i n a l l t h e e s s e n t i a l c h a r a c t e r i s t i c s of the c h a r a c t e r , as seen i n the examples i n f i g u r e 2.8b. The s p e c i f i c c h a r a c t e r i s t i c s such as the c o n t i n u o u s c u r v e s of s i n g l e p i x e l t h i c k n e s s and the w e l l behaved i n t e r s e c t i o n s a r e i m p o r t a n t f e a t u r e s i n the t h i n n e d images which w i l l be e x p l o i t e d i n the subsequent r e c o g n i t i o n p r o c e s s . These f e a t u r e s w i l l be d i s c u s s e d i n g r e a t e r d e t a i l i n the next c h a p t e r . •e^ep s.uosunw UIOJJ saa^oejeqD Aaeutq axduies L'Z 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I I 0 0 0 o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 t I 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 1 I I 0 0 0 0 0 0 0 1 I I 0 0 0 0 0 0 0 0 0 0 0 I 1 0 0 0 0 0 0 0 I t 1 I 0 0 0 0 0 0 0 0 0 0 0 0 I 1 0 0 0 0 0 1 I I I 0 0 0 0 0 0 0 o 0 0 0 0 0 t I 1 0 0 0 I 1 I I I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 1 I 0 I > 1 I I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 1 I 1 I 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 I I 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 1 I 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 L 1 1 I I I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I > 1 1 I 1 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 I I I I i I 1 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 I I I 0 1 I I 1 0 0 0 0 0 0 0 0 0 0 0 0 0 t 1 I I I 0 0 0 1 I 1 I 1 0 0 0 0 0 0 0 0 0 0 t i I 1 I L 0 0 0 I 1 I t 0 0 0 0 0 0 0 0 0 0 0 0 1 I 0 0 0 0 0 0 0 I I I I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . a. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 t I O O O O I I 0 O O 0 0 0 0 0 0 0 0 0 0 0 0 1 1 I O O 0 O I 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 I I 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 1 I O O O O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 I 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 I I I I 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 I I I I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 I I I I I 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 I I 1 I I I 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 I I 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 I 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 I 1 0 1 0 0 0 O O O 0 0 0 0 0 0 0 0 0 0 1 1 I I 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 I I I 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 1 1 1 I I 1 0 0 0 1 I 1 1 1 I 1 I I 0 0 1 1 I 1 1 1 1 1 1 1 0 0 1 1 1 I 0 0 0 0 0 0 0 0 1 I 1 0 0 0 0 0 0 0 0 0 I 1 I 0 0 0 0 0 0 0 0 0 I I I 1 0 0 0 0 0 0 0 0 1 1 I 0 0 0 0 0 0 0 0 0 0 1 I 0 0 0 0 0 0 0 0 0 0 1 I 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 I 1 1 t 1 0 0 0 0 0 0 1 I 1 1 I 0 0 0 0 0 0 I 1 1 I 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 I 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 I 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 o 0 0 0 0 0 0 1 I 1 0 0 0 0 0 0 0 0 0 0 0 0 .a. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 l l l l l l l l l O O O 1 1 1 1 1 1 1 1 1 1 0 0 l l l l l l l l l O O O l l l O l l l l t O O O I I 1 0 0 0 0 0 0 0 0 0 I I 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 I I 1 0 0 0 0 0 0 0 0 0 I 1 1 0 0 0 0 0 0 0 0 0 1 I 1 0 1 0 1 0 0 0 0 0 I I I I I 1 0 0 0 0 0 0 I t l l l l O O O O O O 1 1 1 1 1 1 0 0 0 0 0 0 0 1 I 0 0 0 0 0 0 0 0 0 0 1 i O O O O O O O O O 0 1 I 1 0 0 0 0 0 0 0 0 0 1 I 1 0 0 0 0 0 0 0 0 0 1 I 1 0 0 0 0 0 0 0 0 0 1 I 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0.0 1 1 I 1 0 1 I I 1 1 1 1 1 1 1 I o l l l l l l l O O O O O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 I I 0 0 0 0 0 0 0 0 0 0 I 1 0 0 0 0 0 0 0 0 0 0 1 I 0 0 0 0 0 0 0 0 0 0 I 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 I 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 I 1 1 1 0 0 0 0 0 0 0 I 1 I I 1 0 0 0 0 0 0 0 I 1 I 1 1 0 0 0 0 0 0 0 0 1 0 I 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 1 1 t 0 0 0 0 0 0 0 0 1 I 1 I 0 0 0 0 0 0 0 0 1 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 I 1 1 0 0 0 0 1 I 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 I 1 I 0 0 0 0 0 0 0 0 0 I 1 0 0 0 0 0 0 0 0 0 0 t 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 I 1 I 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 I 1 0 0 0 0 0 0 0 0 0 1 I 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o 0 0 0 0 62 . 1 . 1 . 1 . 1 . . . . 1 . . . 1 1 1 1 1 . 1 . I . 1 . 1 1 . 1 . 1 . 30 i . . 1 1 1 1 1 . 1 1 1 1 . . . 1 1 i . . . . i . i 1 . . . 1 1 1 . 1 1 1 1 1 . . . . 1 1 . . . i 1 . . . 1 . . . . i i i . i i 1 i 1 i 1 11 1 1 1 1 1 1 . 1 1 1 1 1 1 1 1 . . . 1 1 . 1 1 1 1 . . 1 . 1 i . . . 1 1 . . . i i . . i i . i i . . 1 i . . . i . . . i i . . . . 1 1 1 1 1 i 1 . . . i 1 . . 1 . . . 1 . . . i . i . i F i g . 2.8a Sample b i n a r y c h a r a c t e r s t h i n n e d w i t h o r i g i n a l P a v l i d i s ' a l g o r i t h m . 1 . . . . . . 1 . 1 . . . . 1 . . . 1 1 . 1 . . . 1 . 1 . . . . 1 . . 1 . . . . 1 . . 1 . . . . 1 . . 1 . . . . 1 . 1 1 1 1 1 1 . . 1 . . 1 . . . . . . 1 . . . . . . . 1 . . . . . . . 1 . . . . . . . 1 . . . . . . 1 . . . . . . . 1 . . . . . . . 1 . . . . 1 1 1 1 1 1 . . 1 . . . . 1 1 . 1 1 1 1 . 1 . . . . 1 1 1 1 1 . . . 1 . . . 1 1 . . . 1 1 1 . 1 1 1 1 1 . . . . 1 1 . . . 1 1 . . . 1 . . . . 1 1 1 . 1 1 1 1 1 1 1 1 1 1 1 . . . 1 . . 1 . 1 1 . . 1 . . F i g . 2.8b Sample b i n a r y c h a r a c t e r s t h i n n e d w i t h m o d i f i e d t h i n n i n g a l g o r i t h m . CHAPTER I I I IMAGE EXTRACTION, REPRESENTATION AND PRECLASSIFICATION. 1. I n t r o d u c t i o n . One of the fundamental problems f a c i n g the s u c c e s s f u l d e s i g n of r e a l t i m e c h a r a c t e r r e c o g n i t i o n machines or image r e c o g n i t i o n machines i n g e n e r a l , has been the e f f e c t i v e r e p r e s e n t a t i o n of the i n p u t images i n a format s u i t a b l e f o r e f f i c i e n t p r o c e s s i n g on a d i g i t a l computer. In many p a t t e r n r e c o g n i t i o n problems, t h i s p r o c e s s i s synonymous w i t h the f e a t u r e s e l e c t i o n and d e f i n i t i o n problem, where a t t e m p t s a r e made t o f i n d a f e a t u r e or c o m b i n a t i o n of f e a t u r e s t h a t can be u n i q u e l y i d e n t i f i e d as a d i s t i n g u i s h i n g f e a t u r e b e l o n g i n g t o a g i v e n c l a s s of image. In both the s y n t a c t i c and s t a t i s t i c a l approach t o r e c o g n i t i o n a v a r i e t y of t e c h n i q u e s f o r f e a t u r e s e l e c t i o n have been d e v i s e d and a survey of t h e s e t e c h n i q u e s have been made by Hanakata [ 4 7 ] , and P a v l i d i s [ 4 8 ] . Some of thos e t e c h n i q u e s t h a t have been a p p l i e d t o c h a r a c t e r r e c o g n i t i o n a r e ; image c o n t o u r d e s c r i p t i o n s and a n a l y s i s [ 6 ] , [ 1 0 ] , s t r o k e v e c t o r sequences [ 1 2 ] , p o l y g o n a l a p p r o x i m a t i o n t o shapes [ 2 3 ] , [ 4 9 ] , and s p e c i a l l y d e f i n e d shapes such as a r c s , s p u r s , e t c . [ 3 ] , [ 1 1 ] . The l a r g e number of d i f f e r e n t t y p e s of f e a t u r e s used t o date i n d i c a t e s t h a t t h e r e has not been a s i n g l e f e a t u r e or s e t of f e a t u r e s t h a t can be c o n s i d e r e d e s s e n t i a l f o r c h a r a c t e r shape d e s c r i p t i o n . I n s t e a d the f e a t u r e s e l e c t i o n p r o c e s s i s based 33 o n l y on the d e s i g n e r ' s i n t i m a t e knowledge of the t r a i n i n g s e t of d a t a , w i t h the s e l e c t e d f e a t u r e s s u b j e c t e d t o a g e n e r a l s e t of c r i t e r i a such a s : f e a t u r e i n v a r i a n c e t o r i g i d body motion , i e . t r a n s l a t i o n , r o t a t i o n and d i l a t i o n , maximum n o i s e r e j e c t i o n . maximum d i s c r i m i n a t o r y i n f o r m a t i o n c o n t e n t , low c o s t of e x t r a c t i o n . T h i s approach t o f e a t u r e s e l e c t i o n and image d e s c r i p t i o n has two main d i s a d v a n t a g e s . F i r s t l y , the t e c h n i q u e l a c k s f l e x i b i l i t y , because i n p r a c t i c e shape d i s t o r t i o n i s more o f t e n e l a s t i c i n n a t u r e and the use of g e o m e t r i c p r o p e r t i e s f o r shape d e s c r i p t i o n w i l l r e s u l t i n a r e c o g n i t i o n a l g o r i t h m t h a t w i l l p e r f o r m p o o r l y when a p p l i e d t o u n c o n s t r a i n e d h a n d p r i n t e d c h a r a c t e r s . S e c o n d l y , i n r e a l t i m e o p e r a t i o n s , once s e l e c t e d the f e a t u r e s may be the o n l y i n f o r m a t i o n e x t r a c t e d from the i n p u t image t h a t i s a v a i l a b l e f o r r e c o g n i t i o n , u n l e s s one i s ready t o s t o r e s e v e r a l frames of images i n o r d e r t o re s c a n them i f no c l a s s i f i c a t i o n can be made on the f i r s t t r y . N a t u r a l l y t h i s w i l l a l s o i n c r e a s e the amount of s t o r a g e r e q u i r e d and reduce the r e c o g n i t i o n r a t e as f e a t u r e e x t r a c t i o n i s o f t e n a time consuming p r o c e d u r e . The d e s c r i p t i o n and e x t r a c t i o n t e c h n i q u e p r e s e n t e d i n t h i s c h a p t e r w i l l overcome the above problems by u s i n g a two st a g e c h a r a c t e r d e s c r i p t i o n and e x t r a c t i o n p r o c e s s . The f i r s t s t a g e i n v o l v e s the i d e n t i f i c a t i o n of t o p o l o g i c a l p o i n t s such 34 as j u n c t i o n s (of r a d i a l i t y 2 & 3 ) , i s o l a t e d p o i n t s , e n d p o i n t s and c l o s u r e s . These p o i n t s a r e c a l l e d t o p o l o g i c a l p o i n t s of the image by v i r t u e of t h e i r i n v a r i a n c e t o e l a s t i c d e f o r m a t i o n s . J u n c t i o n s of r a d i a l i t y 2 and 3, e n d p o i n t s and s i n g l e p o i n t s a r e a l s o the c r i t i c a l p o i n t s of a t h i n n e d image because they can be i d e n t i f i e d as p o s s i b l e nodes of the image from the g r a p h i c a l p o i n t of view. These t o p o l o g i c a l f e a t u r e s d e s c r i b e t h e g l o b a l p r o p e r t i e s of the image and w i l l be r e f e r e d t o as g l o b a l f e a t u r e s . The second s t a g e i n v o l v e s the t r a c k i n g and e x t r a c t i o n of the t h i n n e d image by t r e a t i n g the t h i n n e d image as a graph, w i t h nodes r e p r e s e n t e d by the c r i t i c a l p o i n t s and l i n k s by the c h a i n codes of the branches between nodes. These g l o b a l f e a t u r e s (nodes) t o g e t h e r w i t h the c h a i n coded l i n k s c o n t a i n s the complete d e s c r i p t i o n of the image. The g l o b a l f e a t u r e s a r e used f o r image p r e c l a s s i f i c a t i o n , an i m p o r t a n t s t e p i n h i g h speed r e c o g n i t i o n e s p e c i a l l y i f the number of p o s s i b l e d i s t o r t i o n s i n the image can be enormous. G l o b a l f e a t u r e s s e p a r a t e images i n t o d i f f e r e n t groups based on t h e i r t o p o l o g y and a r e t h e r e f o r e i n v a r i a n t t o e l a s t i c d e f o r m a t i o n s . Thus l e a v i n g the f i n a l r e c o g n i t i o n a l g o r i t h m the t a s k of r e s o l v i n g d i f f e r e n c e s i n t h e shapes of o n l y a s m a l l s u b s e t of t h e t o t a l p o s s i b l e image v a r i a t i o n s . The r e m a i n i n g p a r t of t h i s c h a p t e r i s d i v i d e d i n t o t h r e e s e c t i o n s . S e c t i o n 2 p r o v i d e s the d e t a i l s f o r the g l o b a l f e a t u r e d e f i n i t i o n , d e t e c t i o n and e x t r a c t i o n p r o c e s s . S e c t i o n 3, the t r a c k i n g a l g o r i t h m and d a t a s t r u c t u r e s and f i n a l l y s e c t i o n 4, the d i s c u s s i o n on the r e s u l t s of a p p l y i n g the t e c h n i q u e t o the t h i n n e d Munson's c h a r a c t e r images. 2. Image D e f i n i t i o n . 2.1 B a s i c c o n c e p t s - d i s c r e t e c u r v e geometry and g r a p h . The f o l l o w i n g d e f i n i t i o n s p r o v i d e the b a s i c c o n c e p t s fundamental t o the d e t e c t i o n of g l o b a l f e a t u r e s and the r e p r e s e n t a t i o n of graphs i n the d i s c r e t e p l a n e . Defn. 2.1.1 An e n d p o i n t ( f r e e end) i s a p i x e l t h a t has o n l y ONE n e i g h b o u r . Defn. 2.1.2 A j u n c t i o n i s a s i n g l e p o i n t i n the d i g i t a l f i e l d where two or more c u r v e s touch or i n t e r s e c t . The j u n c t i o n p i x e l p r o v i d e s c o n n e c t i v i t y f o r a l l c u r v e s i n t e r s e c t i n g a t the j u n c t i o n . P r o p o s i t i o n 2.1a. The r a d i a l i t y of a j u n c t i o n i s the number of c u r v e s r a d i a t i n g from a j u n c t i o n . The most common type of j u n c t i o n b e i n g the t r i - r a d i a l ( J3) and q u a d - r a d i a l (J4) j u n c t i o n s . As d e f i n e d i n 2.1.2, the d e f i n i t i o n i s o n l y a p p l i c a b l e t o J3s and J 4 s i n the d i s c r e t e p l a n e . T h i s l i m i t a t i o n i s the c h a r a c t e r i s t i c of the d i s c r e t e p l a n e because u n l i k e the c o n t i n u o u s p l a n e j u n c t i o n s w i t h r a d i a l i t y g r e a t e r than f o u r cannot be r e p r e s e n t e d by a s i n g l e p o i n t but by a c o l l e c t i o n of p o i n t s . F i g u r e s 3.1a and 3.1b i l l u s t r a t e s t h i s p o i n t . Both p a t t e r n s i n f i g u r e 3.1 has a c o l l e c t i o n of non-zero p o i n t s which cannot be t h i n n e d any f u r t h e r i f image c o n n e c t i v i t y i s t o be m a i n t a i n e d . A c l o s e r i n s p e c t i o n w i l l show t h a t p a t t e r n s 3.1a and 3.1b a r e formed as a r e s u l t of f i v e and e i g h t i n t e r s e c t i n g c u r v e s r e s p e c t i v e l y . To d e s c r i b e each one of t h e s e s i t u a t i o n s u n i q u e l y i n the d i s c r e t e p l a n e i s n o n t r i v i a l , t h e r e f o r e we w i l l not a t t e m p t t o c l a s s i f y them. T h i s w i l l not p r e s e n t any c o n s i d e r a b l e l i m i t a t i o n on the image d e s c r i p t i o n t e c h n i q u e because j u n c t i o n s w i t h r a d i a l i t y g r e a t e r than f o u r a r e r a r e i n n a t u r e and i n f a c t none was e n c o u n t e r e d i n t h e 1500 random samples from Munson's c h a r a c t e r d a t a . 1 I 0 1 0 0 0 1 0 0 0 1 0 1 0 0 • 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 / ,., N F i g . 3.1 Examples of j u n c t i o n s w i t h r a d i a l i t y g r e a t e r than f o u r . 0 0 1 0 1 0 1 1 0 0 1 1 1 1 1 (b) 1 1 1 1 1 1 0 1 0 S 37 Defn. 2.1.3 A c h a i n coded d i g r a p h G, c o n s i s t s of a s e t of nodes Q={ N } i=1..k t o g e t h e r w i t h a s e t U whose members a r e i o r d e r e d p a i r s of nodes each w i t h a c h a i n coded branch f o r m i n g the d i r e c t e d l i n k between the node p a i r . That i s U . . = {(N . ,N j ), D } , 1 S i , j > k. where D={d , ...d } f o r a branch m p i x e l s l o n g and i m d €. {1,2,3,4,5,6,7,8}, the Freeman's d i r e c t i o n s shown below. 4 3 2 6 7 8 Defn.2.1 .4 A branch or l i n k i s a c o n n e c t e d p a t h or sequence of p i x e l s , s i n g l e p i x e l t h i c k between two nodes whose members a r e r e p r e s e n t e d by Freeman's c h a i n codes. The l e n g t h of the branch m, i s e q u a l t o the number of c h a i n code elements r e q u i r e d t o r e p r e s e n t the branch e.g. node 2 w i t h m = 9, and D = 122211882 Node 1 i s c a l l e d the node of o r i g i n and node 2 the d e s t i n a t i o n node. 38 Defn. 2.1.5 A s i m p l e c l o s u r e ( r e f e r r e d t o here as j u s t c l o s u r e ) e x i s t s i f a c l o s e d p a t h can be t r a c e d by e x i t i n g a node from a branch and r e t u r n i n g t o the same node v i a a d i f f e r e n t branch w i t h o u t e n c l o s i n g a n other such c l o s e d p a t h . T h i s d e f i n i t i o n can b e s t be i l l u s t r a t e d by the examples shown below. P r o p o s i t i o n 2.1b. A l o o p or s l i n g i s a s p e c i a l c a s e of a c l o s u r e w i t h o n l y one b r a n c h . Loops a r e c h a r a c t e r i z e d by the f a c t t h a t they a r e formed by a br a n c h h a v i n g t h e same node of o r i g i n and d e s t i n a t i o n . L i k e t h e E u l e r number [ 5 0 ] , a w e l l known t o p o l o g i c a l p r o p e r t y r e l a t i n g t h e number of o b j e c t b o d i e s and h o l e s i n a 2-D image, c l o s u r e i s a t o p o l o g i c a l p r o p e r t y of a l i n e image. The p r e s e n c e o f c l o s u r e s i n a t h i n n e d image i n d i c a t e s the p r e s e n c e of c y c l e s i n i t s d i g r a p h r e p r e s e n t a t i o n . I t w i l l be shown l a t e r t h a t c l o s u r e s can be r e a d i l y o b t a i n e d from t h e i n p u t image d u r i n g the image e x t r a c t i o n p r o c e s s , t h u s a v o i d i n g t h e use of l e n g h t y a l g o r i t h m s t o d e t e c t t h e p r e s e n c e of c y c l e s i n d i g r a p h s . No. of c l o s u r e s = 2 2 39 So f a r the co n c e p t s from t o p o l o g y have been used l i b e r a l l y i n the d e f i n i t i o n s and d i s c u s s i o n s w i t h o u t q u a l i f i c a t i o n . As have been p o i n t e d out e a r l i e r the d i s c r e t e p l a n e does not have the same p r o p e r t i e s of the c o n t i n u o u s p l a n e . N e v e r t h e l e s s the a m b i g u i t i e s t h a t may a r i s e from the d i s c r e t e r e p r e s e n t a t i o n can be r e s o l v e d by b e a r i n g i n mind t h a t the images a r e o r i g i n a l l y c o n t i n u o u s and the p r o p e r t i e s r e f e r e d t o can be viewed as t h a t of the e q u i v a l e n t image i n the c o n t i n u o u s p l a n e . One of the most im p o r t a n t p r o p e r t y t h a t w i l l be used i n the d e s i g n of c h a r a c t e r r e c o g n i t i o n a l g o r i t h m s i s the concept of homeomorphism or t o p o l o g i c a l e q u i v a l e n c e . Two graphs or l i n e images A and B a r e s a i d t o be t o p o l o g i c a l l y e q u i v a l e n t i f t h e r e i s a one t o one mapping of p o i n t s from one image t o ano t h e r and v i c e v e r s a , w i t h such mapping b e i n g c o n t i n u o u s . That i s two p o i n t s c l o s e t o g e t h e r or a d j a c e n t i n one image are mapped i n t o two p o i n t s c l o s e t o g e t h e r or a d j a c e n t i n the o t h e r image. P i c t u r e s q u e l y , two images a r e t o p o l o g i c a l l y e q u i v a l e n t i f one image can be o b t a i n e d by e l a s t i c a l l y deforming the o t h e r w i t h o u t any c u t s b e i n g made. Examples of the s e c o n c e p t s i n t o p o l o g y and the t o p o l o g y of d i s c r e t e images can be found i n r e f e r e n c e s [ 4 4 ] , [ 5 4 ] , [ 5 6 ] . 2.2 G l o b a l f e a t u r e d e t e c t i o n and e x t r a c t i o n . F o l l o w i n g the above d e f i n i t i o n s we can now s p e c i f y the g l o b a l f e a t u r e s of a t h i n n e d alphanumeric c h a r a c t e r as j u n c t i o n s of t y p e J 3 and J 4 , e n d p o i n t s ( E p ) , s i n g l e p o i n t s 40 (Sp) and the number of c l o s u r e s . These f e a t u r e s can be d e t e c t e d and e x t r a c t e d from the. t h i n n e d images by examining t h e i r l o c a l neighbourhood f o r the e x i s t e n c e of c e r t a i n b i t p a t t e r n s i n a manner s i m i l a r t o the t h i n n i n g a l g o r i t h m p r e s e n t e d i n c h a p t e r I . T h i s i s c o n s i s t e n t w i t h the s t r a t e g y f o r f a s t p r o c e s s i n g t h a t i s used i n the d e s i g n of the t h i n n i n g a l g o r i t h m and i n f a c t can share the same d e d i c a t e d hardware i f VLSI i m p l e m e n t a t i o n i s t o be used. The g l o b a l f e a t u r e d e t e c t i o n p r o c e d u r e f o r a t h i n n e d b i n a r y image ( c o n s i s t i n g of 1's and 0's) i s based on the f o l l o w i n g d e f i n i t i o n s of c r i t i c a l p o i n t s 1 : 1. A p i x e l P i s c a l l e d an s i n g l e p o i n t i f i t has no non-zero n e i g h b o u r s . S i n g l e p o i n t s a r e l a b e l e d 9 as they a r e found. 2. A p i x e l P i s c a l l e d an e n d p o i n t i f i t has e x a c t l y ONE non-zero n e i g h b o u r . E n d p o i n t s a r e l a b e l e d 2 as they a r e found. 3. A p i x e l P i s t r i - r a d i a l (J3) i f i t s a t i s f i e s any ONE of the two c o n d i t i o n s below. ( a ) . I t has e x a c t l y t h r e e non-zero n e i g h b o u r s and does not have a l o c a l neighbourhood of any ONE of the c o n f i g u r a t i o n s shown i n f i g u r e 3.2 or those o b t a i n e d 1 C r i t i c a l p o i n t s a r e g l o b a l f e a t u r e s t h a t can be viewed as nodes i n t h e t h i n n e d image. 41 from them by m u l t i p l e s of 9 0 ° r o t a t i o n s , A A 1 A P 1 A A A A 1 1 A P A A A A where ONE of A i s n o n - z e r o . F i g . 3.2 L o c a l ne ighbourhood of an i l l e g a l J3 p i x e l P. ( b ) . I t has e x a c t l y f i v e ne ighbours and a neighbourhood of the c o n f i g u r a t i o n shown in f i g u r e 3.3 or those o b t a i n e d from them by m u l t i p l e s of 9 0 ° r o t a t i o n s . A 0 A A P 0 A 0 A where A>0 F i g . 3.3 L o c a l ne ighbourhood of a J3 p i x e l P hav ing f i v e n e i g h b o u r s . 4. A p i x e l P i s q u a d - r a d i a l (J4) i f i t has e x a c t l y four ne ighbours and does not have any ONE of the c o n f i g u r a t i o n s shown i n f i g u r e 3.4 or those o b t a i n e d from 42 them by m u l t i p l e s of 90° r o t a t i o n s A A A B P B B B B B A B 0 P 0 C A C where A>0, ONE of B and ONE of C i s non-zero. F i g . 3.4 L o c a l neighbourhood of an i l l e g a l J4 p i x e l P. J3 p i x e l s and J4 p i x e l s a r e l a b e l e d as 3s and 4s as they a r e found. These d e f i n i t i o n s f o r J3 and J4 a r e not n e c e s s a r i l y the o n l y p o s s i b l e ones t h a t w i l l unambiguously d e f i n e the j u n c t i o n s of a t h i n n e d image i n the d i s c r e t e p l a n e . T h i s i s because as d e f i n e d a 4-way j u n c t i o n i n the c o n t i n u o u s p l a n e w i l l not n e c e s s a r i l y map i n t o a s i m p l e J4 but p o s s i b l y i n t o d i f f e r e n t c o m b i n a t i o n s of J 3 s and J 4 s back t o back. In the absence of j u n c t i o n s w i t h r a d i a l i t y g r e a t e r than f o u r i t can e a s i l y be v e r i f i e d by examining the p o s s i b l e p e r m u t a t i o n s of the l o c a l neighbourhood of a p i x e l i n a 3x3 p i x e l window t h a t the d e f i n e d J3 and J4 w i l l unambiguously l a b e l a l l p o s s i b l e c o m b i n a t i o n s of t r i - r a d i a l and q u a d - r a d i a l j u n c t i o n s , p r o v i d e d t h a t back t o back j u n c t i o n p i x e l s a r e p e r m i t t e d and c o n s i d e r e d as two j u n c t i o n s s e p a r a t e d by a br a n c h of u n i t p i x e l l e n g t h . Examples of some c h a r a c t e r images whose g l o b a l f e a t u r e s have been l a b e l e d can be seen i n f i g u r e 3.5. F i g u r e s 3.5a-c a r e images from Munson's d a t a but f i g u r e 3.5d i s a s i m u l a t e d image 43 showing the worst p o s s i b l e case t h a t can a r i s e f o r a q u a d - r a d i a l j u n c t i o n . The analogue e q u i v a l e n c e of these images were o b t a i n e d by drawing c o n t i n u o u s c u r v e s t o the t h i n n e d images. The number of c l o s u r e s i n an image can be o b t a i n e d from the number of d i s j o i n t p i e c e s and the number of c r i t i c a l p o i n t s p r e s e n t i n the image. The number of d i s j o i n t p i e c e s can be o b t a i n e d d u r i n g the image or graph t r a c k i n g p r o c e s s which i s g i v e n i n a l g o r i t h m A2. For a c o n t i n u o u s l i n e image i t i s easy t o v e r i f y t h a t the e m p i r i c a l f o r m u l a of e q u a t i o n 3.2.1 g i v e s the c o r r e c t number of c l o s u r e s i n the image. C = l/2( 0 + 27 + 2p - a ) (3.2.1) where a = No. of e n d p o i n t s . j3 = No. of J 3 s . 7 = No. of J 4 s . p = No. of d i s j o i n t p i e c e s . Because of the non-unique mapping from the c o n t i n u o u s t o the d i s c r e t e c a s e , u s i n g the number of J3 s and J 4 s o b t a i n e d from the d i s c r e t e r e p r e s e n t a t i o n of the image i n e q u a t i o n 3.2.1 w i l l y i e l d an e r r o r n e o u s r e s u l t . However, i f a p a i r of back t o back j u n c t i o n i s viewed as a d i s c r e t e r e p r e s e n t a t i o n of a s i n g l e j u n c t i o n formed from two j u n c t i o n s t h a t have merged i n t h e c o n t i n u o u s p l a n e , ( d e s p i t e the f a c t t h a t a u n i t p i x e l b ranch i s c o n s i d e r e d t o e x i s t i n i t s d i s c r e t e r e p r e s e n t a t i o n ) than some of the branches would be l o s t i n 44 t h i s merger. For a d i s c r e t e image w i t h a J3 and J4 back t o back t h e s e two j u n c t i o n s share a common b r a n c h , i n o t h e r words an e q u i v a l e n t branch i s l o s t i n i t s analogue image. S i m i l a r l y , f o r two J 4 s back t o back two branches are s h a r e d or l o s t i n i t s analogue v e r s i o n . T h e r e f o r e e q u a t i o n 3.2.1 can be m o d i f i e d so t h a t the c o r r e c t c l o s u r e count i n the image can be o b t a i n e d by u s i n g the j u n c t i o n s d e f i n e d i n i t s d i s c r e t e v e r s i o n . T h i s i s done by i n t r o d u c i n g two o f f s e t v a r i a b l e s ; o f f s e t l , the number of J3-J4 p a i r s and o f f s e t 2 , the number of J4-J4 p a i r s found i n the d i s c r e t e image. These o f f s e t s a r e e a s i l y o b t a i n e d through the use of c o u n t e r s i n the t r a c k i n g a l g o r i t h m 2 . The m o d i f i e d e q u a t i o n i s then g i v e n as C = 1/2( /5 + 27 + 2p -a - o f f s e t l - 2 x o f f s e t 2 ) • • ••••(3»2*2)« T h i s completes the d e s c r i p t i o n of the d e t e c t i o n p r o c e d u r e s f o r the c r i t i c a l p o i n t s and c l o s u r e s . Note t h a t the g l o b a l f e a t u r e s d e f i n e d do not i n c l u d e f e a t u r e s such as 2-way j u n c t i o n s , p o i n t s of i n f l e c t i o n , maximas and minimas. These p o i n t s a r e n o n t o p o l o g i c a l p o i n t s and t h e i r p r e s e nce i n an image a r e somewhat s u b j e c t i v e and d i f f i c u l t t o d e f i n e . B e s i d e s t h e i r p r o p e r t i e s would be b e t t e r u t i l i z e d i f used i n the l a t t e r s t a g e of the r e c o g n i t i o n p r o c e s s t o d i f f e r e n t i a t e between images h a v i n g the same t o p o l o g y . 2 More p r e c i s e l y o f f s e t l i s i ncremented once e v e r y time a n o n t e r m i n a l J3 node i s e n c o u n t e r e d as a n e i g h b o u r of a J4 node or v i c e v e r s a . 0 f f s e t 2 i s incremented once e v e r y time a n o n t e r m i n a l J4 node i s e n c o u n t e r e d as a n e i g h b o u r of another J4 node. F i g . 3.5 C r i t i c a l p o i n t s of c h a r a c t e r images from Munson's da t a and t h e i r 'analogue e q u i v a l e n t ' . 46 3. Image E x t r a c t i o n . 3.1 Data s t r u c t u r e . The d a t a s t r u c t u r e used t o r e p r e s e n t a c h a i n coded d i g r a p h not o n l y must be e c o n o m i c a l i n i t s memory r e q u i r e m e n t s but must a l s o be s u i t a b l e f o r h a n d l i n g a b s t r a c t d a t a w i t h f a s t a c c e s s t i m e . T h i s i s m a i n l y because the r e c o g n i t i o n p r o c e d u r e s i n g e n e r a l i n v o l v e r e p e a t e d a c c e s s t o d i f f e r e n t v a r i a b l e s of the image. I f r e c o g n i t i o n i s t o be performed i n r e a l t i m e , the type of d a t a s t r u c t u r e w i l l p l a y a key r o l e i n d e t e r m i n i n g the r e c o g n i t i o n speed. B e s i d e s t h e c h a r a c t e r images when r e p r e s e n t e d by i t s d i g r a p h w i l l be s u b j e c t e d t o g r a p h i c a l a n a l y s i s which i n v o l v e s the use of graph t r a v e r s a l a l g o r i t h m s . T h e r e f o r e t h e da t a s t r u c t u r e used must be one t h a t p e r m i t s • r a p i d a c c e s s from one node t o a n o t h e r as w e l l as a l l o w i n g some form of r e l a t i o n s h i p t o e x i s t between nodes. The most s u i t a b l e d a t a s t r u c t u r e f o r the above r e q u i r e m e n t s i s the p o i n t e r i m p l e m e n t a t i o n of l i n k e d l i s t s f o r d i g r a p h s . U s i n g two p o i n t e r s a s e a r c h a l g o r i t h m can move fo r w a r d or backward from a g i v e n node as w e l l as d e l e t e or i n s e r t nodes from the l i s t w i t h ease. The c h a i n coded d i g r a p h r e p r e s e n t a t i o n of an image can be s t o r e d as a l i n k e d l i s t formed by l i n k i n g the node d a t a t a b l e (NDT) t h a t i s c r e a t e d f o r each node found i n the image. Each NDT c o n t a i n s the a t t r i b u t e s of the node such as node number, j u n c t i o n t y p e , l o c a t i o n and c h a i n codes of the branches a s s o c i a t e d w i t h the node. S t a t u s r e g i s t e r s or f l a g s a r e a l s o i n c l u d e d t o p r o v i d e 4 7 d i f f e r e n t s t a t u s i n f o r m a t i o n about each node. T a b l e I shows the c o n t e n t of a t y p i c a l NDT. 3.2 Image e x t r a c t i o n and s p u r i o u s branch p r u n i n g p r o c e d u r e . Image e x t r a c t i o n i s b a s i c a l l y a t r a n s f o r m a t i o n of the t h i n n e d image i n t o i t s d i g r a p h . The t r a n s f o r m a t i o n i s a c c o m p l i s h e d by t r a c k i n g and e x t r a c t i n g the c h a i n codes of the branches ( l i n k s ) between the nodes ( c r i t i c a l p o i n t s ) of the image t h a t have been d e t e c t e d and l a b e l e d by the proc e d u r e g i v e n i n s e c t i o n 2. In o r d e r t o t r a c k t h e s e branches s u c c e s s f u l l y , the t r a c k i n g p r o c e d u r e must observe the f o l l o w i n g r u l e s : 1. S t a r t i n g from a node. When the f i r s t p i x e l of a branch has been i d e n t i f i e d by p r o c e d u r e ' t r a c k ' , a l l o t h e r '1' n e i g h b o u r s of the node must be t e m p o r a r i l y i g n o r e d or s u p p r e s s e d u n t i l the next p i x e l i n the branch has been i d e n t i f i e d . 2. P r o c e d u r e ' t r a c k ' must check a l l the n e i g h b o u r s of the c u r r e n t branch p i x e l f o r the p r e s e n c e of c r i t i c a l p o i n t p i x e l s (nodes) b e f o r e i d e n t i f y i n g the next '1' p i x e l (hence the next code) of the b r a n c h . 3. R e l a b e l a l l p i x e l s i n a branch whose code has been e x t r a c t e d t o 9. 4. The next p i x e l of a branch i s i d e n t i f i e d by f o l l o w i n g i t s '1's c o n n e c t i v i t y . 5. Branch t e r m i n a t i o n o c c u r s when a new c r i t i c a l p o i n t p i x e l i s found or a c r i t i c a l p o i n t i s found a f t e r the branch 48 code has a l e n g t h of g r e a t e r than two. Lemma: A l l branches of a t h i n n e d b i n a r y image whose j u n c t i o n s a r e unambiguously d e f i n e d and l a b e l e d by the pr o c e d u r e i n s e c t i o n 2 can be s u c c e s s f u l l y t r a c k e d by u s i n g r u l e s 1 t o 5. P r o o f : Only e n d p o i n t s and j u n c t i o n s of type J3 or J4 have bra n c h e s . S i n c e branches have s i n g l e p i x e l t h i c k n e s s they can be t r a c k e d by f o l l o w i n g i t s 1's c o n n e c t i v i t y . . The r e s t of the pro o f l i e s i n the c o r o l l a r y t o d e f i n i t i o n 2.1.2. That i s , i f a p i x e l has more than two n e i g h b o u r s then i t must e i t h e r be a j u n c t i o n p i x e l (J3 or J4) or i t has a t l e a s t one j u n c t i o n p i x e l as i t s n e i g h b o u r . T h i s g u a r a n t e e s a branch t e r m i n a t i o n i n a n o t h e r c r i t i c a l p o i n t . H aving e s t a b l i s h e d a v i a b l e b r a n c h t r a c k i n g p r o c e d u r e , the r e s t of the image e x t r a c t i o n i n v o l v e s t r a c k i n g the branches and l i n k i n g the nodes whose NDT's have been c r e a t e d p r e v i o u s l y by the f e a t u r e d e t e c t i o n and d e f i n i t i o n p r o c e s s . The image e x t r a c t i o n f o l l o w s a depth f i r s t graph t r a v e r s a l t e c h n i q u e u s i n g the f o l l o w i n g r u l e s : 1. P i c k a c o n v e n i e n t node and c a l l t h i s the r o o t node. T h i s node i s taken t o be the bottom r i g h t - m o s t node by the A l g o r i t h m A2. 2. S t a r t i n g w i t h the r o o t node as the p r e s e n t node, t r a c k and e x t r a c t the c h a i n code of any branch t h a t i s found s t a r t i n g from the e a s t e r l y (Freeman's 1) d i r e c t i o n and moving c o u n t e r c l o c k w i s e . I f a branch t r a c k e d l e a d s t o an e n d p o i n t or a node t h a t has p r e v i o u s l y been v i s i t e d ( t e r m i n a l node) then the branch i s c a l l e d a s u b l i n k . The c h a i n code f o r t h i s s u b l i n k i s s t o r e d and i t s a s s o c i a t e d p o i n t e r s e t t o p o i n t t o the n o n t e r m i n a l node. Branch s e a r c h i n g and t r a c k i n g c o n t i n u e s a t t h i s p r e s e n t node. I f a branch t r a c k e d l e a d s t o a J3 or J4 t h a t has not been p r e v i o u s l y v i s i t e d ( n o n t e r m i n a l node) then the branch i s c a l l e d a main l i n k . The c h a i n code f o r t h i s main l i n k i s s t o r e d a t the p r e s e n t node and the new n o n t e r m i n a l node found i s taken as the new p r e s e n t node. The f o r w a r d p o i n t e r and backward p o i n t e r of the new and p r e v i o u s p r e s e n t nodes a r e then s e t . T r a v e r s a l c o n t i n u e s i n t h i s manner u n t i l the a l g o r i t h m can go no deeper, t h a t i s a l l branches from a p r e s e n t node have been t r a c k e d . Then the a l g o r i t h m b a c k t r a c k s t o the l a s t node t h a t was used as the p r e s e n t node and the p r o c e s s c o n t i n u e s . The t r a v e r s a l i s complete when the p r o c e s s b a c k t r a c k s t o the r o o t node and a l l branches of the r o o t node has been t r a c k e d . In t h i s approach the p r o c e s s i s gu a r a n t e e d t o t e r m i n a t e a f t e r t r a c k i n g a l l the nodes b e l o n g i n g t o the graph w i t h the chosen r o o t node. Upon t e r m i n a t i o n of each t r a v e r s a l the e x t r a c t i o n a l g o r i t h m must check f o r the p r e s e n c e of o t h e r d i s j o i n t p i e c e s or i s o l a t e d c l o s u r e s i n the image t h a t has not been t r a c k e d ( e x t r a c t e d ) . D i s j o i n t p i e c e s can be d e t e c t e d by c h e c k i n g i f a l l the nodes i n the image have been v i s i t e d by 50 the t r a c k i n g a l g o r i t h m . O t h e r w i s e a new u n v i s i t e d node w i l l be t a k e n as the new r o o t node and t r a c k i n g of the d i s j o i n t p i e c e s can be a c c o m p l i s h e d i n the same way as above. I s o l a t e d c l o s u r e s a r e c i r c u l a r p a t t e r n s of s i n g l e p i x e l t h i c k and t h e r e f o r e has no nodes. The presence of t h e s e p a t t e r n s are d e t e c t e d by c h e c k i n g t h a t a l l 1's p i x e l s i n the image have been t r a c k e d . I s o l a t e d c l o s u r e s when found can be t r a c k e d by f i r s t t a k i n g i t s top l e f t m o s t p o i n t (or any p o i n t v i a a c o n s i s t e n t c h o i c e ) and l a b e l i t as a s p e c i a l node of type ' c l o s e d ' . Then the same t r a c k i n g p r o c e d u r e s g i v e n above can be a p p l i e d t o e x t r a c t i t s c h a i n code. The r e s u l t of t h i s e x t r a c t i o n p r o c e d u r e i s one or more l i n k e d l i s t s of NDTs, each d e s c r i b i n g g r a p h i c a l l y p a r t of or the whole t h i n n e d image of an a l p h a n u m e r i c c h a r a c t e r . T h i s d e s c r i p t i o n of the image may s t i l l c o n t a i n n o i s e i n the form of s p u r i o u s branches t h a t may be p r e s e n t due t o the t h i n n i n g p r o c e s s or d e l i b e r a t e l y i n t r o d u c e d as a r e s u l t of d i f f e r e n t w r i t i n g s t y l e s . These n o i s e branches can be pruned by merely i n s p e c t i n g the nodes (NDTs i n the l i n k e d l i s t ) f o r s u b l i n k s t h a t t e r m i n a t e i n e n d p o i n t s w i t h a l e n g t h of say l e s s than 5% of t h e t o t a l number of non-zero p o i n t s i n the image. T h i s user programmable p r u n i n g parameter i s an advantage because i t a l l o w s the a l g o r i t h m t o be tuned or a d j u s t e d t o o p e r a t e o p t i m a l l y under d i f f e r e n t n o i s e c o n d i t i o n s . P r u n i n g a l s o r e s u l t i n a change t o the t ype of j u n c t i o n t h a t forms the node. For example, a J3 node w i t h one branch pruned w i l l mean t h a t the j u n c t i o n no l o n g e r q u a l i f i e s as a node and t h e r e f o r e 51 the l i n k e d l i s t s t r u c t u r e w i l l have t o be r e v i s e d . T h i s i s e q u i v a l e n t t o a node d e l e t i o n from the l i s t w i t h the c h a i n code of the main l i n k of the d e l e t e d node j o i n e d t o the c h a i n code of the main l i n k of i t s p r e d e c e s s o r . Such d e l e t i o n can be done v e r y e a s i l y w i t h a two way l i n k e d l i s t s t r u c t u r e - . The b a s i c p r o c e d u r e s f o r g l o b a l f e a t u r e d e t e c t i o n and image e x t r a c t i o n i s p r e s e n t e d i n A l g o r i t h m A2. F i g u r e s 2.7a and 2.7b shows the t h i n n e d image of c h a r a c t e r 'A' a f t e r g l o b a l f e a t u r e d e t e c t i o n , i t s e q u i v a l e n t c h a i n coded d i g r a p h and i t s image s t a t i s t i c s both b e f o r e and a f t e r p r u n i n g . 4. Image P r e c l a s s i f i c a t i o n . A graph based image d e f i n i t i o n and e x t r a c t i o n has been d e s i g n e d based on d e s c r e t e image t o p o l o g y . The a l g o r i t h m i s implemented i n P a s c a l on the PDP 11/23 minicomputer. A l i s t of g l o b a l f e a t u r e s was chosen based on e n g i n e e r i n g knowledge of c h a r a c t e r shapes. These f e a t u r e s a r e used t o form t h e 25 groups of the p r e c l a s s i f i e r . When t e s t e d w i t h 1000 c h a r a c t e r s i t i s found t h a t 108 d i s t i n c t v a r i a t i o n s i n the shapes of t h e 26 c h a r a c t e r s were c l a s s i f i e d i n t o the 25 d i f f e r e n t g roups. The l a r g e s t of t h e s e groups c o n t a i n 22 c l a s s e s w h i l e some groups such as Group I , IV, V, e t c . c o n t a i n o n l y a s i n g l e c l a s s or c h a r a c t e r t y p e . These s i n g l e c l a s s groups w i l l r e s u l t i n the d i r e c t r e c o g n i t i o n of the c h a r a c t e r s w i t h o u t f u r t h e r p r o c e s s i n g as shown i n the b l o c k diagram of f i g u r e 1.2. 52 4.1 Input e n t r o p y r e d u c t i o n due t o p r e c l a s s i f i c a t i o n . To measure the e f f e c t i v e n e s s of t h i s p r e c l a s s i f i e r , we w i l l c a l c u l a t e i t s e f f e c t i v e n e s s i n r e d u c i n g the e n t r o p y H of the i n p u t , where H i s d e f i n e d a s , H = - I p l o g 2 p i i i w i t h p the a priori p r o b a b i l i t y of each c h a r a c t e r . Assuming i a l l 26 c h a r a c t e r s as e q u a l l y p r o b a b l e , then the t o t a l e n t r o p y ( u n c e r t a i n t y ) of an image a t the i n p u t of the p r e c l a s s i f i e r i s 4.7 b i t s ( = l o g 2 2 6 ) . A f t e r p r e c l a s s i f i c a t i o n , the i n p u t t o the f i n a l c l a s s i f i e r w i l l be from a known group. Hence i f we assume t h a t the c h a r a c t e r s i n each group a r e a g a i n e q u a l l y p r o b a b l e , then the t o t a l e n t r o p y of an i n p u t t o the f i n a l c l a s s i f i e r can be c a l c u l a t e d s i m i l a r l y and w i l l depend on which group i t b e l ongs t o . The e n t r y H i n t a b l e I I shows the G t o t a l e n t r o p y of an image from each group. I t can be seen t h a t the t o t a l e n t r o p y of an image from any group i s s m a l l e r than t h a t of an image a t the i n p u t of t h e p r e c l a s s i f i e r . To o b t a i n a more r e a l i s t i c average r e d u c t i o n i n e n t r o p y by the p r e c l a s s i f i e r , one has t o c o n s i d e r the d i s t r i b u t i o n of the i n p u t c h a r a c t e r s over the 25 g r o u p s . T h i s can be done by making use of the p e r c e n t a g e d i s t r i b u t i o n f i g u r e s g i v e n i n the A% column of t a b l e I I . C o n s i d e r a b a t c h of 100 c h a r a c t e r images, r e p r e s e n t i n g a t o t a l e n t r o p y of 470 b i t s a t the i n p u t of t h e p r e c l a s s i f i e r . Then from th e A% f i g u r e f o r Group I I X , we can say t h a t on t h e average 16 of t h e s e i n p u t images w i l l be c l a s s i f i e d as b e l o n g i n g t o Group I I X . These 16 images from 53 Group I I X w i l l have a t o t a l e n t r o p y of 64 b i t s when p r e s e n t e d as i n p u t t o the f i n a l c l a s s i f i e r . P e r f o r m i n g s i m i l a r c a l c u l a t i o n s f o r the images c l a s s i f i e d i n t o a l l the o t h e r groups and summing, we o b t a i n a t o t a l e n t r o p y a f t e r p r e c l a s s i f i c a t i o n of 330 b i t s . T h e r e f o r e p r e c l a s s i f i c a t i o n has r e s u l t e d i n an average e n t r o p y r e d u c t i o n of 140 b i t s (1.4 b i t per i n p u t ) or 30%. The 30% average e n t r o p y r e d u c t i o n a c t u a l l y r e f l e c t s a v e r y e f f e c t i v e p r e c l a s s i f i e r because the above e v a l u a t i o n i s based on a human o b s e r v e r ' s p e r c e p t i o n of the problem. That i s t o i d e n t i f y one of the 26 p o s s i b l e c h a r a c t e r s i r r e s p e c t i v e of i t s s t y l e , shape or f o n t . I d e a l l y , one would l i k e t o be a b l e t o d e s i g n a r e c o g n i t i o n system t h a t c o u l d p e r f o r m the t a s k of r e c o g n i z i n g a c h a r a c t e r t o the same l e v e l of s o p h i s t i c a t i o n as the human re a d e r but t h i s i s not p o s s i b l e a t the p r e s e n t s t a t e of a r t . I n s t e a d i n machine r e c o g n i t i o n , the c l a s s i f i c a t i o n i s based on image s t r u c t u r e s and the r e l a t i o n s between these s t r u c t u r e s t h a t d e f i n e i t s shapes. T h e r e f o r e from the machine's p o i n t of v i e w, the problem i s not s i m p l y t o i d e n t i f y one of the 26 p o s s i b l e c h a r a c t e r s but t o i d e n t i f y one of the t o t a l number of shapes t h a t can be formed from the 26 c h a r a c t e r s . Each c h a r a c t e r i s now not t r e a t e d as a s i n g l e c l a s s by i t s e l f but c o m p r i s e s of a number of c l a s s e s depending on the number of t o p o l o g i c a l v a r i a t i o n s i n i t s shape. From the d a t a we have i d e n t i f i e d 108 p o s s i b l e v a r i a t i o n s i n the shapes of t h e s e c h a r a c t e r s , so t o the r e c o g n i t i o n machine t h i s r e p r e s e n t s an i n i t i a l i n p u t image e n t r o p y of 6.75 b i t s 54 ( = l o g 2 l 0 8 ) . From t h i s p o i n t of v i e w, th e p r e c l a s s i f i e r has an average e n t r o p y r e d u c t i o n of 51%. 5. D i s c u s s i o n . O b v i o u s l y i n p u t image e n t r o p y r e d u c t i o n i s not the o n l y g a i n from u s i n g the p r e c l a s s i f i e r . Another i m p o r t a n t r e s u l t of t h i s t e c h n i q u e i s t h a t images a r e grouped such t h a t images i n d i f f e r e n t groups a r e t o p o l o g i c a l l y n o n e q u i v a l e n t . U n f o r t u n a t e l y , the c o n v e r s e cannot be s a i d f o r a l l images w i t h i n a g i v e n group f o r two r e a s o n s . The f i r s t i s the i n e x a c t r e p r e s e n t a t i o n of analogue images i n the d i s c r e t e p l a n e . For j u n c t i o n s w i t h r a d i a l i t y g r e a t e r than 4, the s h a r e d branch i n a back t o back node would be a t t a c h e d t o a d i f f e r e n t node depending on the branch p o s i t i o n and t h e o r d e r the nodes a r e v i s i t e d . S e c o n d l y , a l t h o u g h the g l o b a l f e a t u r e s a r e d e f i n e d as t o p o l o g i c a l p o i n t s , t h e s e p o i n t s a l o n e are i n s u f f i c i e n t t o u n i q u e l y s p e c i f y t o p o l o g i c a l e q u i v a l e n c e . The e x t r a i n f o r m a t i o n t h a t i s needed i s the c u r v e c o n t i n u i t y or o r d e r of c o n n e c t i v i t y , which i s not used i n t h e p r e c l a s s i f i c a t i o n of the images. T h e r e f o r e images w i t h i n each group may have common g l o b a l f e a t u r e s but a r e not n e c e s s a r i l y t o p o l o g i c a l l y e q u i v a l e n t as i l l u s t r a t e d by the two images i n f i g u r e 3.6 below. 55 F i g . 3.6 Images w i t h i d e n t i c a l g l o b a l f e a t u r e s tha t are t o p o l o g i c a l l y i n e q u i v a l e n t . N e v e r t h e l e s s , i f the o r d e r of c o n n e c t i v i t y or c o n t i n u i t y i s c o n s i d e r e d as l o c a l v a r i a t i o n s i n the image than p r e c l a s s i f i c a t i o n does r e s u l t i n a g r o s s s e p a r a t i o n of images i n t o groups wi th commom g l o b a l f e a t u r e s as r e f l e c t e d by the en tropy r e d u c t i o n . More i m p o r t a n t l y , p r e c l a s s i f i c a t i o n a l l o w s v a r i a t i o n s i n l o c a l f e a t u r e s can be examined in g r e a t e r d e t a i l in a s eparate p r o c e s s tha t w i l l r e s u l t i n the f i n a l r e c o g n i t i o n . Such a p r o c e s s i s g i v e n in the next c h a p t e r . 56 Table I . A t y p i c a l node data t a b l e f o r chain coded digraph r e p r e s e n t a t i o n of thinned alphanumeric c h a r a c t e r s . CONTENTS: Abv. I n i t i a l Value Node number Node-no. 0 June. t y p . JT ** Coordinate (I , J ) (0,0) Forward p o i n t e r fwdptr N i l Backward p o i n t e r bkptr N i l Integer s ta tus o r d e r , l k , M l 0 ,0 ,0 Main l i n k code M a i n - l i n k 0. .0 s u b l i n k l code s u b - l i n k 1 0. .0 subl ink2 code s u b - l i n k 2 0. .0 sub l ink3 code s u b - l i n k 3 0. .0 s u b l i n k l p t r . subptr1 N i l sub l ink2 p t r . subptr2 N i l sub l ink3 p t r . subptr3 N i l Remarks: 1. Node number i s the order the nodes are found. 2 . Order i s the order the nodes are v i s i t e d by during the e x t r a c t i o n process. Therefore once v i s i t e d a node w i l l have an order of > 0 . 3 . Lk and Ml are used to i n d i c a t e the number of s u b l i n k s and mainlink attached to a node. 4. Subptrs are used t o i n d i c a t e the t e r m i n a l nodes of s u b l i n k s , these information are required by the pruning procedures. 57 T a b l e I I . Group c l a s s i f i c a t i o n of sample c h a r a c t e r s data from Munson's d a t a . GROUP. GLOBAL FEATURES A% CHARACTERS. H SP. J 3 . J 4 . SP. c . G I 0 0 0 0 1 3.0 0 0 II 0 2 0 0 2 1 .2 0,B 1 .00 III 1 1 0 0 1 5.8 D , G , 0 , P , Q , S 2.59 IV 1 1 1 0 2 0.1 Q 0 V 1 1 2 0 2 0.2 Q 0 VI 1 2 1 0 2 0.1 B 0 VII 1 3 0 0 2 1 .8 B , 0 , Q 1 .59 IIX 2 0 0 0 0 16.0 B , C , D , G , J , L , M , N ,0 4.00 P , R , S , U , V , W , 2 IX 2 0 1 0 1 0.3 R 0 x 2 0 2 0 1 4.5 Q 0 XI 2 1 1 0 1 8.0 P .Q .R 1 .59 XII 2 2 0 0 1 6.0 A , B , D , G , P , Q , R , J 3.00 XIII 2 4 0 0 2 0.2 B 0 XI V 3 1 0 0 0 28.2 B , C , D , E , F , G , H , I , J , L ,M 4.46 N , P , Q , R , S , T , U , V , W , Y , Z XV 3 1 1 0 1 0.1 A 0 XVI 3 3 0 0 1 0.2 A , B , G , Q , R 2.32 XVII 4 0 0 0 0 0.3 G , J , T 1 .59 XIIX 4 0 1 0 0 0.2 Q,x 1 .00 XIX 4 0 2 0 0 0.3 K 0 XX 4 1 1 0 0 0.5 K , X 1 .00 XXI 4 2 0 0 0 20.8 B , E , F , G , H , I , J , K ,M 4.00 N , P , R , T , W , X , Z XXII 4 2 1 0 1 0.1 A 0 XXIII 4 4 0 0 2 0.3 A 0 XXIV 5 1 1 0 0 0.2 H 0 XXV 5 3 0 0 0 1.6 A , E , H , M , N , W , X , Z 3.00 Remarks: 1. Ep,J3,J4,Sp and C a r e t h e number of e n d p o i n t s , J 3 s , J 4 s , s i n g l e p o i n t s and c l o s u r e s found i n the image. 2. A % i s the p e r c e n t a g e d i s t r i b u t i o n o f i n p u t images over t h e d i f f e r e n t g r oups. 3. H r i s the t o t a l e n t r o p y of an image from the group. 26 2i 1 3 1 1 1 1 © E q u i v a l e n t d i g r a p h . Chain c o d e d l i n k s : Ml H2 M3 SI S2 S3 332333233 233323446666 7777 4 1111 567767676 © Ml M2 SI «'S2 © E q u i v a l e n t diagraph. Chain coded l i n k s . Ml - 332333233 M2 - 2333234466667777 51 - 1111 52 - 567767676 Image s t a t i s t tea before pr-unnlng: Totel no. of p i x e l s * 39 Total no. of nodes • 6 Es • 3. 03 • 3 J4 • 0. Sp • O Number of pieces - 1. O f f s e t l - O. 0 f f s e t 2 • 0 Number of closures • 1 Node^no - 6 , Order - 1 Junction type : Es. coord:(23,15) Associated branches :-Main_11nk : 332333233 : next node no - 4 Node_no - 4 . Order - 2 Junction type : J3. coord:(14,17) Associated branches :-«a1n_llnk : 233323446666 : next node no - 2 Node_no - 2 . Order - 3 Junction type : J3. coord:(10.13) Associated branches :-Main_link : 7777 : next node no - 3 Sut>_l1nk[1] : 4 : terminal node no - 1 Nodervo - 3 , Order - S JuncTlon type : J3, coord: ( 14 . 13 ) Associated branches :-Sub 11nk[1] : 1111 : term1na1 node no - 4 Sub -1Infc[2) : 967767676 : terminal node no - 5 Image s t a t i s t i c s a f t e r prunnmg: Total no. of p i x e l s » 38 Total no. of nodes * 4 Es • 2. J3 • 2 J4 - 0 Number of pieces • 1, O f f s e t l • 0. 0 f f s e t 2 - 0 Number of closures • 1 Sp Node_no - 6 . Order - 1 Junction type : Es. coord:(23.15) Associated branches :-Mam li n k : 332333233 : next node no - 4 _no - 4 . Order - 2 Junction type : J3. coord:(14.17) Associated branches :-Maln_11nk : 2333234466667777 : next node no - 3 Node_no - 3 , Order - 5 Junction type : J3. coord:(14,13) Associated branches :-Sub_1lnk(1] . 1111 : terminal node no - 4 Sub~11nkl2] : S67767676 : terminal node no - 5 (a) (b) F i g . 2.7 R e p r e s e n t a t i o n of c h a r a c t e r 'A* b e f o r e p r u n i n g (a) and a f t e r p r u n i n g ( b ) . ALGORITHM A2. In p u t : Thinned b i n a r y image of an al p h a n u m e r i c c h a r a c t e r . Output: L i n k e d l i s t g r a p h i c a l r e p r e s e n t a t i o n of i n p u t image w i t h s p u r i o u s n o i s e branches removed. Root node of the graph i s c a l l e d base and any a u x i l i a r y graphs (subgraphs) p r e s e n t i n the image have t h e i r r o o t nodes c a l l e d s u b - b a s e [ l ] t o s u b - b a s e [ p i e c e s - 1 ] . BEGIN { main } 1 . For each '1' p i x e l Do check and l a b e l p i x e l s t h a t s a t i s f y any one of the c o n d i t i o n s 1 t o 4 i n s e c t i o n 2.2; 2. For each c r i t i c a l p o i n t found by s t e p 1 Do (a) . c r e a t e an NDT; (b) . E n t e r node a t t r i b u t e s of the new NDT, i e . node-no., j u n c t i o n type and c o o r d i n a t e s . 3. No. of p i e c e s := 0; 4. S e l e c t an NDT whose j u n c t i o n t y p e i s not an Sp and c a l l i t base; 5. Track and s t o r e g r a p h i c a l i n f o r m a t i o n of the image u s i n g the r u l e s i n s e c t i o n 3.2. T r a c k i n g p r o c e s s i n c l u d e s : (a) . I n c r e m e n t i n g c o u n t e r s o f f s e t l and o f f s e t 2 as a p p r o p i a t e . (b) . R e l a b e l a l l branch p i x e l s t h a t has been t r a c k e d as 9. (c) . L i n k the NDTs t r a c k e d a c c o r d i n g t o depth f i r s t t r a v e r s a l . 6. p i e c e s := p i e c e s + 1 ; 7. I f a l l nodes o t h e r than Sps have been v i s i t e d t h e n goto 8 e l s e B e g i n (a) , p i c k an u n v i s i t e d node o t h e r than an Sp and c a l l i t sub b a s e t p i e c e s ] (b) . r e p e a t s t e p s 5 t o 7 u n t i l a l l nodes t h a t a r e not Sps have been v i s i t e d . End. 8. c a l c u l a t e c l o s u r e u s i n g e q u a t i o n 3.2.2; c o n t . 60 9. I f t h e r e a r e any 1 1 ' p i x e l s l e f t i n the image then B e g i n (a) , c r e a t e a new NDT w i t h j u n c t i o n t y p e 'closed'and c a l l i t s u b - b a s e [ p i e c e s ] . (b) . t r a c k and s t o r e c h a i n code of l o o p . (c) . c l o s u r e := c l o s u r e + 1; (d) . p i e c e s := p i e c e s + 1; (e) . r e p e a t s t e p 9 u n t i l a l l '1' p i x e l s i n the image has been t r a c k e d . End. 10. F o r each NDT Do { p r u n i n g } (a) , remove each s u b l i n k t h a t t e r m i n a t e s a t an endpoint w i t h l e n g t h l e s s than some s p e c i f i e d minimum. (b) . update NDT e n t r i e s and p o i n t e r s as a p p r o p i a t e . END { ma i n }. 61 CHAPTER IV FINAL IMAGE CLASSIFICATION. 1. I n t r o d u c t i o n . Graphs have been used e x t e n s i v e l y f o r m o d e l l i n g r e l a t i o n s h i p s between d a t a o b j e c t s i n a l a r g e v a r i e t y of problems encountered i n computer s c i e n c e , mathematics and e n g i n e e r i n g . C o n s e q u e n t l y , a l a r g e number of r e s u l t s and a l g o r i t h m s p e r t a i n i n g t o g r a p h i c a l a n a l y s i s a r e a v a i l a b l e , [56] t o [ 6 2 ] . With the i n c r e a s e d demand f o r s o l v i n g h i g h l y complex problems on the d i g i t a l computer, a number of h i g h l y s p e c i a l i z e d graphs have been d e v e l o p e d from c o n v e n t i o n a l graph t h e o r i e s . One such graph i s the A t t r i b u t e d R e l a t i o n a l Graph (ARG), used i n s y n t a c t i c p a t t e r n r e c o g n i t i o n t o r e p r e s e n t s t r u c t u r a l and r e l a t i o n a l i n f o r m a t i o n of g i v e n p a t t e r n s [ 6 0 ] , A re v i e w of the b a s i c ARG w i l l be g i v e n i n the next s e c t i o n and the p a t t e r n d e f o r m a t i o n models t h a t can be r e p r e s e n t e d by the ARG a r e p r e s e n t e d t o g e t h e r w i t h the d i s t a n c e or c o s t measures f o r p a t t e r n d e f o r m a t i o n s . The main o b j e c t i v e of the r e v i e w on the ARG i s t o show i t s p o t e n t i a l a p p l i c a t i o n i n c h a r a c t e r r e c o g n i t i o n . B e f o r e such an a p p l i c a t i o n i s p o s s i b l e i t has t o be shown t h a t c h a r a c t e r images can be d e s c r i b e d r e a d i l y by an ARG. T h e r e f o r e s e c t i o n 3 i s devoted t o the d e s i g n of a t r a n s f o r m a t i o n which w i l l map a c h a i n coded d i g r a p h r e p r e s e n t a t i o n of a t h i n n e d c h a r a c t e r image r e p r e s e n t e d by i t s nodes and c h a i n codes of 62 i t s branches (as g i v e n i n c h a p t e r I I I ) t o an ARG d e s c r i p t i o n . I t w i l l be shown t h a t such t r a n s f o r m a t i o n i s e f f e c t i v e l y a l o c a l f e a t u r e e x t r a c t i o n p r o c e s s where ' i n t e r e s t i n g ' s t r u c t u r a l and r e l a t i o n a l a t t r i b u t e s are e x t r a c t e d from the c h a i n coded d i g r a p h . The r e s u l t i s a ARG d e s c r i p t i o n of the image which p r o v i d e s both the s t r u c t u r a l and r e l a t i o n a l i n f o r m a t i o n t h a t i s n e c e s s a r y f o r a s y n t a c t i c ( l i n g u i s t i c ) c l a s s i f i c a t i o n of the image. One of the main drawbacks i n u s i n g graphs f o r t h e purpose of computer r e c o g n i t i o n has been the c o m p l e x i t y t h a t i s i n v o l v e d i n graph matching or graph isomorphism. I n g e n e r a l , graph matching belongs t o a c l a s s of n o n d e t e r m i n i s t i c p o l y n o m i a l - t i m e (NP) complete problem where the o p t i m a l s o l u t i o n i s o b t a i n e d b a s i c a l l y by t r y i n g a l l p o s s i b i l i t i e s . Such an approach i s c o m p u t a t i o n a l l y v e r y e x p e n s i v e . A more w i d e l y a c c e p t e d and p r a c t i c a l approach i s t o use a h e u r i s t i c m atching p r o c e d u r e . A h e u r i s t i c matching a l g o r i t h m i s one t h a t can q u i c k l y produce a good but not n e c e s s a r i l y an o p t i m a l s o l u t i o n i n most i f not a l l the c a s e s . S e c t i o n 4 i s d e v o t e d t o the d e s i g n of such an a l g o r i t h m , c a l l e d the r e f e r e n c e g u i d e d i n e x a c t matching p r o c e d u r e . T h i s a l g o r i t h m i s shown t o g i v e a h i g h r e c o g n i t i o n r a t e w i t h Munson's c h a r a c t e r d a t a when used w i t h the p r e c l a s s i f i e r d e s i g n e d i n c h a p t e r I I I . 63 2. A t t r i b u t e d R e l a t i o n a l Graph - An I n t r o d u c t i o n . 2.1 B a s i c d e f i n i t i o n and t e r m i n o l o g y . The approach to ARG f o r m u l a t i o n and d e f i n i t i o n tha t i s taken here i s c l o s e l y r e l a t e d to the work of T s a i and Fu [ 6 0 ] . D e f n . 2.1.1 An ARG over a set of node and branch l a b e l s V„ U V D i s a 4-tuple.. G = ( N , B , u , e ) where N = { a j \ i : [ l , N ] } a f i n i t e set of nodes . B = W j \ J : [ 1 r n B J CI NxN i s a set of o r d e r e d p a i r s of d i s t i n c t e lements in N c a l l b r a n c h e s . u(a>\i:[1,N]) = V N = { n , , n 2 . . . . n N } i s c a l l e d the node i n t e r p r e t e r . e ( 7 \ j : [ l , n _ ]) = V D = { b , , b 2 , . . . . b „ } i s c a l l e d a branch 3 ** " n B i n t e r p r e t e r . D e f n . 2.1.2 For each element i n N , the c o r r e s p o n d i n g node l a b e l (n j \ i : [ l , N ] ) denotes a p a t t e r n p r i m i t i v e and i s a 2 - t u p l e . M ( a i ) = = ( s i , ^ i ) , i : [ l , N ] . where s^ i s a s y n t a c t i c symbol . x. i s a semantic v e c t o r d e n o t i n g a set of l o c a l f e a t u r e s . 64 Semantic v e c t o r s d e s c r i b e the c h a r a c t e r i s t i c f e a t u r e s p e r t a i n i n g t o the s y n t a c t i c symbol and t o g e t h e r they d e s c r i b e a p a t t e r n p r i m i t i v e . For the case where the semantic v e c t o r i s a n u l l s e t or s i m p l y not d e f i n e d , then we have a c o n v e n t i o n a l node whose symbol i s s^. For our purpose of u s i n g ARGs f o r c h a r a c t e r d e s c r i p t i o n and r e c o g n i t i o n , the node s y n t a c t i c symbols chosen must be of the type t h a t denotes the t o p o l o g i c a l p r o p e r t i e s of the image f o r r e a s o n s which w i l l become apparent i n s e c t i o n 2.2. Defn. 2.1.3 S i m i l a r l y f o r each element 7 j i n B, the c o r r e s p o n d i n g branch l a b e l (b j \ j : [ l , n B ]) denotes a r e l a t i o n a l p r i m i t i v e and i s a 2 - t u p l e . e ( 7 j > = b j = ( U l k , ^ ), l , k : [ l , N ] , j : [ l , n B ]. where U l k = ^ n l n k ^ fc^e b r a n c f t s y n t a c t i c symbol, and i s a p a i r of node l a b e l s n^ and n^ whose r e l a t i o n i s d e s c r i b e d by the branch semantic v e c t o r . As an example f i g u r e 4.1 i l l u s t r a t e s the ARG d e s c r i p t i o n of a sample c h a r a c t e r 'R'. De f n. 2.1.4 An ARG G' i s a d e f o r m a t i o n of a n o t h e r ARG G i f f t h e r e e x i s t a t r a n s f o r m a t i o n h such t h a t : h: G'-^ G and h~ 1: G —*• G' . 65 Input image. Nodes:-N = U | l 0 2 , 0 ) I a , , O i , o 6 } 1 Branches : -B = {71 -72 .73 . 7 . .75 r7« )• ARG Representa t ion . where i i (o , ) s NODE 1 = (s,,X u(a2) B NODE 2 = ( s 2 , x u(a3) = NODE 3 •= ( s , , x <i(a,) NODE 4 = (s,,x u(a%) NODE 5 = (s s ,x « ( a « ) = NODE 6 = is, ,x « ( 7 i ) = b, - ( 0 1 2 .>i> • ( T i ) b 2 = (U 2 3 ' ^ ^ *<7,> = b , = e<7.) B b. = ( u 3 4 , * . ) t ( 7 i ) •S b s •= ( u 3 5 . „ > « ( > • ) b . « ( u 4 6 , , « > F i g . 4.1 ARG d e s c r i p t i o n of c h a r a c t e r 'R'. Remarks: D e t a i l d e s c r i p t i o n of th e s y n t a c t i c symbol ' s' and semantic v e c t o r s x and y used f o r c h a r a c t e r d e s c r i p t i o n w i l l be g i v e n i n s e c t i o n 3. 66 2.2 ARG d e f o r m a t i o n models. C o n s i d e r an ARG G' = (N' ,B' , / u ' , e' ) o b t a i n e d from G =(N,B,ji,e) by a t r a n s f o r m a t i o n h~1. By s u i t a b l y d e f i n i n g h such t h a t o n l y a p a r t i c u l a r component of G i s p e r m i t t e d t o be deformed, s e v e r a l d e f o r m a t i o n models can be o b t a i n e d . These models can be c a t e g o r i z e d i n t o t h r e e main t y p e s , namely; non-graph p r e s e r v i n g , graph p r e s e r v i n g and t o p o l o g y p r e s e r v i n g d e f o r m a t i o n s . Non-graph p r e s e r v i n g d e f o r m a t i o n r e s u l t s when h i s such t h a t N#N', B*B', u*u' and e*e'. T h i s means t h a t G' can be c o m p l e t e l y a d i f f e r e n t graph from G as none of the p r i m i t i v e s p r e s e n t i n G' and G may have any common p r o p e r t i e s . As such, t h i s t y p e of d e f o r m a t i o n i s of l i t t l e i n t e r e s t i n p a t t e r n r e c o g n i t i o n . Graph p r e s e r v i n g d e f o r m a t i o n r e s u l t s when h i s such t h a t N=N', B=B', u*n' and e*e'. Here the two graphs G and G' have i d e n t i c a l number of nodes and branches but d i f f e r s i n t h e i r node and bra n c h i n t e r p r e t a t i o n s . T h i s i m p l i e s t h a t b o t h s t r u c t u r a l and r e l a t i o n a l d e f o r m a t i o n s t o t h e nodes and branches can e x i s t . I n o t h e r words, the t y p e s of nodes, branches and c o n n e c t i o n o r d e r of t h e ARG a r e s u b j e c t e d t o change by h. Topology p r e s e r v i n g d e f o r m a t i o n (TPD) can be c o n s i d e r e d as a s u b c l a s s of the graph p r e s e r v i n g d e f o r m a t i o n . L e t G' be a t o p o l o g y p r e s e r v e d d e f o r m a t i o n of an ARG (TPD-ARG) G and h be the a s s o c i a t e d t r a n s f o r m a t i o n . Then h i s d e f i n e d t o have the T f o l l o w i n g p r o p e r t i e s : 67 h : G ' ( N ' , B ' , M ' , e ' ) • G (N, B , M , e ) • w i t h 1 . N = N'. 2. B = B ' . 3. G i v e n t h a t node l a b e l s n' i n G' and n i n G i s such h m n t h a t n' — n then m n u'(a ) = n' = ( s , x ' ) and m m m uia ) = n = ( s , x ). m,n :[ 1 , N ] . n n n 4. S i m i l a r l y g i v e n t h a t b ranch l a b e l s b' i n G' and b h P q i n G i s such t h a t b' — b then P q e' (7 ) = b' = (U' , y ) and p p ml p e ( 7 ) = b = (U , , y ) . q q nk q where U' , = (n' n' ). m,l : [ l , N ] ml m l and U , = (n n, ). n,k :[ 1 , N ] . nk n k h h g i v e n t h a t n' — n and n ' , — n , . m n 1 k The f i r s t and second p r o p e r t i e s a r e r e q u i r e d f o r graph p r e s e r v a t i o n . The t h i r d p r o p e r t y s t a t e s t h a t i n a TPD-ARG the node s y n t a c t i c symbol ' s ' remains unchanged. T h i s i s o n l y p o s s i b l e i f the ARG node s y n t a c t i c symbols chosen a re of the ty p e t h a t i n d i c a t e the t o p o l o g i c a l p r o p e r t i e s of the image. T h i s i s t h e r e f o r e the c o n d i t i o n f o r the e x i s t e n c e of TPD-ARG. For the ARG d e s c r i p t i o n of t h i n n e d c h a r a c t e r images, the c r i t i c a l p o i n t s ( t o p o l o g i c a l p o i n t s ) d e f i n e d i n the l a s t c h a p t e r a r e used as the node s y n t a c t i c symbols. In the d e f o r m a t i o n s above we have assumed t h a t the nodes a r e deformed i n d e p e n d e n t l y of each o t h e r . T h i s same assumption w i l l not be 68 p r a c t i c a l f o r branch a t t r i b u t e s because the branches are c o n s t r a i n e d a t t h e i r ends by nodes. The d e f o r m a t i o n s of the branches or r e l a t i o n a l a t t r i b u t e s can o n l y be d e f i n e d i f the d e f o r m a t i o n of t h e i r end nodes a r e known. Hence t h e c o n d i t i o n s h h n' — » . n and n' —T-*- n i n (4) above. T h i s c o n d i t i o n i s m n 1 k not r e s t r i c t e d t o TPD-ARGs but must a p p l y t o a l l graph p r e s e r v i n g ARG d e f o r m a t i o n s . TPD-ARGs a r e of s p e c i a l i n t e r e s t i n c a s e s where a p r e c l a s s i f i e r i s used t o p e r f o r m a g l o b a l c l a s s i f i c a t i o n and s o r t i n p u t s i n t o groups of t o p o l o g i c a l l y e q u i v a l e n t images. Then the TPD-ARG model can be used t o c o n c e n t r a t e on the l o c a l or n o n t o p o l o g i c a l f e a t u r e s of the images i n each group and s y n t a c t i c a l l y d i s t i n g u i s h one image from the o t h e r . 2.3 D e f o r m a t i o n d i s t a n c e measures f o r ARG. S i m i l a r i t y ( o r d i s s i m i l a r i t y ) between two ARGs can be i n f e r r e d w i t h t h e used of some q u a n t i t a t i v e measures such as the p r o b a b i l i t y or d i s t a n c e measures. P r o b a b i l i t y measure o f t e n t a k e s the form of h y p o t h e s i s t e s t i n g , such as the maximum l i k e l i h o o d c r i t e r i a or the B a y e s i a n c o n d i t i o n a l p r o b a b i l i t y . A l t h o u g h the s t a t i s t i c a l t h e o r y i s r i c h w i t h r e s u l t s i n p r o b a b i l i t y a n a l y s i s , t hey a r e based on the ass u m p t i o n t h a t the u n d e r l y i n g b e h a v i o u r i n the d i s t r i b u t i o n of t h e i n p u t s can be e s t i m a t e d or m o d e l l e d . For the case of u n c o n s t r a i n e d h a n d w r i t t e n c h a r a c t e r s i t i s e x t r e m e l y d i f f i c u l t t o i n f e r t h i s d e f o r m a t i o n p r o b a b i l i t y r e l i a b l y from the samples, t h e r e f o r e o t h e r measures a r e p r e f e r r e d . 69 D i s t a n c e measures a r e d e f i n e d as the c o s t i n c u r r e d as a consequence of t r a n s f o r m i n g one ARG i n t o a n o t h e r . When used w i t h t h e s y n t a c t i c a p p r o a c h t o r e c o g n i t i o n t h i s measure i s e x t r e m e l y i n f o r m a t i v e and t h e e s s e n t i a l p a r t of a s u c c e s s f u l d e s i g n i s t o append t h e c o r r e c t p e n a l t y f o r each t r a n s f o r m a t i o n . The d e s i g n of t h i s c o s t f u n c t i o n f o r a s p e c i f i c a p p l i c a t i o n i s an a r e a of r e s e a r c h i n i t s own r i g h t . C o s t measures can range from s i m p l e v a l u e s f o r each type of d e f o r m a t i o n t o complex c o n s i d e r a t i o n s i n v o l v i n g the p s y c h o l o g i c a l a s p e c t s of human r e c o g n i t i o n of d i s t o r t e d images. For a g e n e r a l g r a p h p r e s e r v i n g d e f o r m a t i o n , the c a l c u l a t i o n of t h e d e f o r m a t i o n d i s t a n c e between G' and G where h G' * G i s d e f i n e d as f o l l o w s : d(G',G) = w,I d ( n \ ,n. ) + w 2Z d(b' . , b . \ t T , ,U ) i 1 1 j ] ] ml nk • •• • • • (4«2»13) • where d ( n ' . ,n. ) i s t h e c o s t of o b t a i n i n g node l a b e l n'. from 1 1 i n. by h~ 1 l d(b* . ,b.\ U' , ,U , ) i s the c o s t of o b t a i n i n g branch 3 ] N ml nk l a b e l b' . from b. by /i" 1 g i v e n t h a t U' , , the end 3 3 ml node p a i r of b'. i s o b t a i n e d from U , t h e end nodes 3 nk of b. by the same t r a n s f o r m a t i o n . 1 w1 and w 2 can be n o r m a l i z i n g c o n s t a n t s or w e i g h t s . 70 P r o p e r t i e s of d e f o r m a t i o n d i s t a n c e . 1. d(G',G) = d(G,G'), symmetry. 2. a. Node d e f o r m a t i o n d i s t a n c e i s composed of two components, the s y n t a c t i c and semantic d e f o r m a t i o n components. d ( n ' . ,n £ ) = d ( s * i ,s. ) + d ( x V ) V i . b. Branch or r e l a t i o n a l d e f o r m a t i o n d i s t a n c e i s the d e f o r m a t i o n d i s t a n c e of i t s semantic v e c t o r y s u b j e c t e d t o the c o n d i t i o n t h a t t h e i r end nodes are t r a n s f o r m e d a c c o r d i n g l y . T h i s i s i n acc o r d a n c e t o the g e n e r a l p r o p e r t y (4) f o r h i n s e c t i o n 2.2. For conve n i e n c e we s h a l l r e f e r t o t h i s c o n d i t i o n as the f e a s i b i l i t y c o n d i t i o n . d ( b ' j ,bj ) = d{(y' j ,y^ ) \ f e a s i b i l i t y c o n d i t i o n } . 3. d(G',G) i s NOT a m e t r i c because of c o n d i t i o n (c) below. That i s g i v e n t h a t G,, G 2 and G 3 a r e t h r e e ARGs such t h a t h i fi2 G 2 > G, and G 3 — * G 2, then (a) d(G,,G 2) £ 0, e q u a l i t y i f f G,= G 2. (b) d ( G 1 r G , ) = d ( G 2 , G 2 ) = d ( G 3 , G 3 ) = 0. (c) d(G 3,G,) ^ d ( G 2 , G 1 ) + d ( G 3 , G 2 ) . For a TPD-ARG, the s y n t a c t i c symbol remains unchanged, t h e r e f o r e d ( s ' j , s . )=0 and e q u a t i o n 4.2.1a s i m p l i f i e s t o d T (G',G) = w ^ d U ^ rac. ) + W j E d t t ^ ' j ,>>j ) \ f e a s i b i l i t y c o n d i t i o n } (4.2.1b). From e q u a t i o n s 4.2.1, r e c o g n i t i o n by ARG matching reduces t o the problem of f i n d i n g a match between the i n p u t and r e f e r e n c e ARGs t h a t w i l l produce the minimum d e f o r m a t i o n d i s t a n c e . 3. T r a n s f o r m a t i o n of c h a i n coded d i g r a p h t o ARG. B e f o r e the a n a l y t i c a l t e c h n i q u e s d e v e l o p e d f o r the ARGs i n s e c t i o n 2 can be a p p l i e d t o t h e t h i n n e d c h a r a c t e r images, a t r a n s f o r m a t i o n must be d e s i g n e d t o t r a n s f o r m the c h a i n coded d i g r a p h d e s c r i p t i o n of t h e images g i v e n i n the l a s t c h a p t e r t o t h e i r ARG d e s c r i p t i o n s . A l t h o u g h t h i s d e s i g n i s aimed a t d e s c r i b i n g c h a r a c t e r images, the concept can be a p p l i e d g e n e r a l l y t o any t h i n n e d image t h a t can be d e s c r i b e d g r a p h i c a l l y . The t r a n s f o r m a t i o n i s a r e w r i t i n g and r e f o r m a t t i n g p r o c e s s of t h e g r a p h i c a l d a t a t h a t r e p r e s e n t s the d i g r a p h . The main o b j e c t i v e i s the e x t r a c t i o n of l o c a l f e a t u r e s i n the image t h a t a r e u s e f u l f o r c l a s s i f i c a t i o n and r e j e c t i n g redundant or e x c e s s i n f o r m a t i o n . T h i s l o c a l f e a t u r e s e l e c t i o n s t a g e i s where the r e c o g n i t i o n machine examines the f i n e r d e t a i l s of the geometry of the images t h a t have been p r e - s o r t e d and does the f i n a l c l a s s i f i c a t i o n . S i n c e the t r a n s f o r m a t i o n o p e r a t e s on the g r a p h i c a l d a t a e x t r a c t e d from the image the p r o c e s s can be f a c i l i t a t e d by a w e l l d e s i g n e d d a t a s t r u c t u r e . U s i n g the l i n k e d l i s t r e p r e s e n t a t i o n f o r the c h a i n coded d i g r a p h t h a t i s g i v e n i n c h a p t e r I I I the mapping can be a c c o m p l i s h e d by r e w r i t i n g the da t a i n t h e node d a t a t a b l e s (NDTs) f o r each graph, the 72 e q u i v a l e n c e between t h e i r NDTs i s shown t a b l e I I I below. The r e s u l t of the t r a n s f o r m a t i o n i s a l i n k e d l i s t r e p r e s e n t a t i o n of an ARG C h a i n coded d i g r a p h NDT. ARG NDT. J u n c t i o n t y p e . —»• Node s y n t a c t i c symbol. C o o r d i n a t e . —> Node semantic v e c t o r . P o i n t e r s & node no. —»• Branch s y n t a c t i c symbol (denotes l i n k a g e o r d e r ) . M a i n - l i n k & s u b l i n k c h a i n — * Branch semantic v e c t o r . codes. T a b l e I I I . E q u i v a l e n c e between c h a i n coded d i g r a p h and ARG NDTs. 3.1 R e w r i t i n g node p r i m i t i v e s . As i n d i c a t e d i n the p r e v i o u s s e c t i o n s , i n o r d e r t o use the TPD-ARG d e f o r m a t i o n model the node s y n t a c t i c symbols must be the node j u n c t i o n t y p e s ( c r i t i c a l p o i n t s ) , so no r e w r i t i n g i s r e q u i r e d . The node s y n t a c t i c symbols f o r the t h i n n e d c h a r a c t e r s a r e Ep, J 3 , J 4 , Sp and ' c l o s e d ' , c o r r e s p o n d i n g t o the j u n c t i o n t y p e s d e f i n e d i n the l a s t c h a p t e r . The c o o r d i n a t e s of a g i v e n node marks i t s p r e c i s e l o c a t i o n i n the d i s c r e t e f i e l d . For s i m p l i c i t y , we d i v i d e the image frame i n t o 73 9 e q u a l a r e a r e g i o n s as shown below. aa ba ca ab bb cb ac be cc T h i s e q u a l a r e a d i v i s i o n has been done a r b i t r a r i l y and more complex s p a t i a l d i v i s i o n can be used i f i t i s d e s i r e d depending on the c h a r a c t e r i s t i c s of t h e image. The node semantic v e c t o r i s d e f i n e d as a v a r i a b l e p a i r d e n o t i n g the l o c a t i o n of t h e node i n t h e image frame and i s a n o n t o p o l o g i c a l p r o p e r t y of the image. x {aa,ab,ac , ba,bb,be ,ca , c b , c c } . 3.2 R e w r i t i n g branch ( r e l a t i o n a l ) p r i m i t i v e s . Branch p r i m i t i v e t r a n s f o r m a t i o n i s more i n v o l v e d than node p r i m i t i v e t r a n s f o r m a t i o n because b r a n c h p r i m i t i v e s c o n t a i n t h e b u l k of the i n f o r m a t i o n on t h e l o c a l f e a t u r e s t h a t w i l l be used f o r f i n a l c l a s s i f i c a t i o n . T h i s i n f o r m a t i o n i s e x t r a c t e d e n t i r e l y from the c h a i n coded l i n k s of the d i g r a p h d e s c r i p t i o n . Branch p r i m i t i v e t r a n s f o r m a t i o n i s a c h i e v e d i n two p a r t s , the e x t r a c t i o n of the s y n t a c t i c symbol and the semantic v e c t o r . In the l i n k e d NDT l i s t r e p r e s e n t a t i o n , the branch s y n t a c t i c symbol can be r e a d i l y o b t a i n e d from the p o i n t e r s . 74 For c o n v e n i e n c e a new n o t a t i o n f o r the s y n t a c t i c symbol w i l l be i n t r o d u c e d . U s i n g the node numbers ( i n t e g e r s ) t o r e p r e s e n t node l a b e l s n^ , the s y n t a c t i c symbol f o r a branch between two nodes 1 and k where 1 and k a r e two s i n g l e d i g i t i n t e g e r s w i l l be denoted as U l k . The i n t e g e r s 1 and k a r e no l o n g e r used as s u b s c r i p t s and l , k : [ 1,8], That i s , not more than a maximun of e i g h t nodes a r e e x p e c t e d from t h e ARG d e s c r i p t i o n of a h a n d p r i n t e d c h a r a c t e r . Branch p r i m i t i v e s a r e now w r i t t e n a s : b. = (Ulk,;/. ). where U l k denotes the end nodes of the branch w i t h node 1 as the node of o r i g i n and node k the d e s t i n a t i o n node. The t r a n s f o r m a t i o n of the c h a i n coded l i n k s t o the semantic v e c t o r y i s an important one. Here the problem i s c o n c e r n e d w i t h t h e s e l e c t i o n of c u r v e f e a t u r e s as the components of the branch semantic v e c t o r must c o n t a i n i n f o r m a t i o n on the shape of the c u r v e t h a t forms the branch between t h e two nodes i n q u e s t i o n . A commonly used s o l u t i o n i s t o a n a l y s e t h e c h a i n codes and d e c l a r e the branch as h a v i n g one of a number of p r e d e f i n e d shapes. The d i f f i c u l t i e s e n c o u n t e r e d i n t h i s approach a r e two f o l d ; f i r s t l y , the d i f f i c u l t y i n d e t e r m i n i n g the t y p e s of shape t h a t s h o u l d be chosen f o r t h e g i v e n problem and s e c o n d l y the p r o c e s s of shape e x t r a c t i o n and i d e n t i f i c a t i o n from t h e image i s o f t e n time consuming. These two problems a r e not independent and i t i s w e l l known t h a t more complex shapes a r e c a p a b l e of more d e t a i l d e s c r i p t i o n but a r e a l s o more c o s t l y t o e x t r a c t . In f a c t the c u r v e f e a t u r e s e l e c t i o n problem can be approached from two r e l e v a n t p o i n t s of v i e w , a m a t h e m a t i c a l and p s y c h o l o g i c a l v i e w p o i n t . In t h i s d e s i g n we w i l l use th e s e two c o n s i d e r a t i o n s t o o b t a i n i n t u i t i v e l y the shape f e a t u r e s such t h a t t hey are b o t h w e l l d e f i n e d m a t h e m a t i c a l l y and a l s o e s s e n t i a l t o the g e n e r i c d e s c r i p t i o n of a l p h a n u m e r i c c h a r a c t e r s . T a k i n g t h i s approach, we d e f i n e the b r a n c h semantic v e c t o r v. f o r branch b. of l e n g t h m. a s : 3 I D y. = (L . ,0 1 . ,0 2 . ) (4.3.1 ). 3 3 3 3 3 where L_. denotes the l e n g t h a t t r i b u t e of the b r a n c h , denotes the c u r v a t u r e a t t r i b u t e of the b r a n c h . 3 0 1 . and 62 . a r e the Freeman's d i r e c t i o n s 1 d e n o t i n g t h e 3 3 b r a n c h e x i t d i r e c t i o n from the node of o r i g i n and e n t r y d i r e c t i o n a t the d e s t i n a t i o n node. 3.2.1 L e n g t h a t t r i b u t e (L) d e f i n i t i o n and e x t r a c t i o n . I f T i s the t o t a l number of p i x e l s i n the t h i n n e d image and m the l e n g t h of a b r a n c h , then t h e l e n g t h a t t r i b u t e of the branch i s d e f i n e d a s : 1Freeman's d i r e c t i o n s a r e i n t e g e r s d e n o t i n g the d i r e c t i o n s shown: 4 3 2 1 76 L = Sh i f m<T/2 0. < Me i f T/20<m<3T/10. Lg i f m>3T/lO. (4.3.2) . The symbols Sh, Me and Lg denotes th e t h r e e l e n g t h a t t r i b u t e s of the b ranch namely; s h o r t , medium l e n g t h and l o n g . These c a t e g o r i e s a r e d e c i d e d upon s o l e l y by the number of c h a i n code elements r e q u i r e d t o d e f i n e t h e branch and the t o t a l number of p i x e l s t h a t i s i n the image, t h e r e f o r e L i s independent of branch d i r e c t i o n . 3.2.2 C u r v a t u r e a t t r i b u t e (*) d e f i n i t i o n and e x t r a c t i o n . G i v e n t h a t {d 1,d 2,....d } i s the Freeman's c h a i n code f o r the b r a n c h , then we d e f i n e a t o t a l i n c r e m e n t a l c u r v a t u r e 4> a s : m-i Z 6. 0 , m> 1 . m= 1 . • •••• • »(4»3»3) w i t h 6. the i n c r e m e n t a l c u r v a t u r e ( i n degrees) i n moving from one component of the code t o another a s : 6. = I 4 5 ( d i + 1 - d . ) , 4 5 ( d i + 1 - d . " 8 ) , 45(8 - | d i + 1 " * . | ) f -4 < ( d i + 1 - d . ) < 4. ( d i + 1 - d . ) > 4. ( d i + 1 - d i ) < -4 (4.3.4) The i n c r e m e n t a l a n g l e 6^ i s the a n g u l a r change i n s t e p s of 45° i n moving from one code of the branch t o the next w i t h the a n t i c l o c k w i s e r o t a t i o n t a k e n as the +ve d i r e c t i o n of a n g u l a r change. 5^ i s not d e f i n e d f o r ( d ^ + 1 - d j )=±4 because i t 77 cannot e x i s t in a proper c h a i n code for a b r a n c h . Assume tha t the Freeman's c h a i n code for d ^ _ 1 and d^ are as shown below, 3 4 n ! 2 *; * l 7 then the next code d ^ + 1 can take any v a l u e s denoted by the d o t t e d arrows except where ( d ^ + 1 - d^ ) = ± 4 i f the c h a i n code i s not to b a c k t r a c k on i t s e l f . T h e r e f o r e in a proper c h a i n code (d £ + 1 - d^ ) = ± 4 does not e x i s t and 6^  i s bounded i n the i n t e r v a l - 1 8 0 ° < 8 i < + l 8 0 ° . The branch c u r v a t u r e a t t r i b u t e * i s d e f i n e d as one of the f i v e d i f f e r e n t curve shapes d e f i n e d f o r f i v e d i f f e r e n t types of t o t a l i n c r e m e n t a l c u r v a t u r e s t h a t are c o n s i d e r e d e s s e n t i a l f o r the d e s c r i p t i o n of c h a r a c t e r shapes . These f i v e c u r v a t u r e types are d e s i g n a t e d C 1 f C 2 , C 3 , C t t and C 5 where * = (c, f or - 4 5 ° < * ^ 4 5 ° . C 2 f o r 4 6 ° < * < 9 0 ° or - 4 6 ° < * < - 9 0 ° . < C 3 f o r 9 1 ° < $ < 2 7 0 ° or -91 ° < 4 > < - 2 7 0 ° . C , f o r $ > 2 7 0 ° or * < - 2 7 0 ° . C« * (4 3 5) * C 5 d e f i n e s a s p e c i a l shape of the form ' / V " \ ' tha t i s o f t e n present i n c h a r a c t e r s B , M and W. A curve i s d e c l a r e d a C 5 i f the t o t a l i n c r e m e n t a l c u r v a t u r e $ i s £ 9 0 ° and i n moving from one node of the branch to the o t h e r , $ f i r s t reaches a v a l u e of £ 1 3 5 ° then £ 4 5 ° be fore t a k i n g a f i n a l v a l u e of >90°. By d e f i n i t o n C,, C 2, C 3 f and C„ a r e symmetric w h i l e $ i s a n t i s y m m e t r i c w i t h r e s p e c t t o branch d i r e c t i o n . That i s , i f A and B are two end nodes of the branch then the $ o b t a i n e d from the c h a i n code e x t r a c t e d w h i l e moving from A t o B and the $ o b t a i n e d from the c h a i n code e x t r a c t e d by moving from B t o A ( r e v e r s e c h a i n codes) w i l l o n l y d i f f e r i n s i g n , w h i l e the c u r v a t u r e a t t r i b u t e s t o C« w i l l remain unchanged. For example, i f a branch h a v i n g node 1 as i t s node of o r i g i n and node 2 i t s d e s t i n a t i o n node and i t s c h a i n code g i v e n a s ; 87888123 then 4> = 45(- 1 +1+0 + 0+1 +1 +1 ) = 135°. and * = C 3. R e v e r s i n g the r o l e of the node of o r i g i n and d e s t i n a t i o n the r e v e r s e d c h a i n c o d e 2 f o r the same branch i s : 76544434 w i t h $ = 45(-1-1-1+0+0-1+1) = -135°. and * = C 3. T h i s p r o p e r t y i s i m p o r t a n t because c u r v a t u r e a t t r i b u t e s Ci t o Co i s independent of which end of the branch one b e g i n s i n e x t r a c t i n g i t s c h a i n codes. U n f o r t u n a t e l y C 5 do not have such a p r o p e r t y and a r e v e r s e c h a i n code have t o be g e n e r a t e d i n o r d e r t o t e s t f o r C 5. However t h i s need not be done f o r a l l 2The r e v e r s e c h a i n code {d' , ,d' 2,....d' } of { d 1 f d 2 f . . . . d } can be o b t a i n e d u s i n g the r e l a t i o n shown below: d' . = I (d, m-i + 1 + 4)Mod 8, (d, m-i + 1 + 4)Mod 8 > 0 . 8, o t h e r w i s e . branches because C 5 s are c h a r a c t e r i s e d by the f a c t that t h e i r f i n a l t o t a l i n c r e m e n t a l c u r v a t u r e i s > 9 0 ° , so o n l y those branches tha t have t h i s c h a r a c t e r i s t i c s need to have t h e i r r e v e r s e c h a i n codes generated and checked for C 5 type of c u r v a t u r e . 3 . 2 . 3 D e f i n i t i o n and e x t r a c t i o n of 0 1 and Q2. Given tha t {d,,d 2,....d } i s the Freeman's c h a i n code for a branch whose node of o r i g i n i s node 1 and d e s t i n a t i o n node i s node 2, we d e f i n e i t s e x i t and e n t r y d i r e c t i o n s a s : For m£4 For m < 4 0 1 = d,. 62 = d (4. 3.6b) . m F o r branches whose l e n g t h i s g r e a t e r than 4, the average d i r e c t i o n o b t a i n e d from the two end codes are u s e d . T h i s w i l l g i v e a b e t t e r e s t i m a t e of the a c t u a l e x i t and e n t r y d i r e c t i o n s . N a t u r a l l y , 0 1 and 62 w i l l be a f f e c t e d by branch d i r e c t i o n r e v e r s a l , the s i t u a t i o n where the r o l e of the node of o r i g i n and node of d e s t i n a t i o n i s i n t e r c h a n g e d . L e t b , = ( U 1 2 , ( L , , 8 } ! , 6 2 ,) ) be the p r i m i t i v e for a branch whose node r = r(d,+ d 2 ) / 2 l , Id,- d 2| < 4. < ([(d,+ 62)/2\+ 4)Mod 8 , |d,- d2|> 4. 80 of o r i g n i s node 1 and d e s t i n a t i o n node i s node 2. b 2 = ( U 2 1 , ( L 2 , * 2 , 6 1 2 i 9 2 2 ) ) be the p r i m i t i v e f o r the branch formed by r e v e r s i n g the r o l e of the o r i g i n and d e s t i n a t i o n nodes. Then from s e c t i o n 3.2.2, L , = L 2 and • i = * 2 w i l l remain unchanged but the e x i t and e n t r y d i r e c t i o n s of the o r i g i n a l and r e v e r s e d branch w i l l be r e l a t e d by; 0 1 ( 0 2 ,+4)Mod 8, 8, » 2 2 = [ ( 0 i 1+4)Mod 8, 1 8, (0 2!+4)Mod 8 > 0. o t h e r w i se. (0 1,+4)Mod 8 > 0. o t h e r w i se. • • • • • (4.3.7) E.g. For the c h a i n codes b, = 87888123, u s i n g e q u a t i o n s 4.3.6a we o b t a i n e d 0 1, = 8 and 6 2 , = 3. The c h a i n codes f o r the r e v e r s e branch i s b 2 = 76544434. The e x i t and e n t r y d i r e c t i o n f o r t h i s r e v e r s e branch can be c a l c u l a t e d i n two ways. (a) . U s i n g e q u a t i o n s 4.3.6a and branch b 2 ' s c h a i n codes we o b t a i n e d 0 1 2 = 7 and 6 2 2 = 4. (b) . U s i n g e q u a t i o n s 4.3.7 and the e x i t and e n t r y d i r e c t i o n s 0 1, and 0 2, of branch b, we o b t a i n e d 0 1 2 = (3 + 4)Mod 8 = 7 . and 0 2 = ( 8 + 4 ) M o d 8 = 4 . The e q u a t i o n i s e x t r e m e l y u s e f u l i n matching a branch of one ARG t o a branch of an o t h e r ARG whose branch a t t r i b u t e s had 81 been o b t a i n e d from the c h a i n code which i s t r a c k e d i n the r e v e r s e d i r e c t i o n . S i n c e the l e n g t h and c u r v a t u r e a t t r i b u t e s remain unchanged, matching can s t i l l p r o c e e d by u s i n g e q u a t i o n s 4.3.7 t o c o r r e c t the d i r e c t i o n codes of the r e v e r s e b r a n c h w i t h o u t r e s o r t i n g t o g e n e r a t i n g i t s r e v e r s e c h a i n c o d e s . B e s i d e s the c h a i n codes may not be a v a i l a b l e a f t e r the b r a n c h t r a n s f o r m a t i o n . In t h i s s e c t i o n the t e c h n i q u e f o r t r a n s f o r m i n g a c h a i n coded d i g r a p h t o an ARG has been d e v e l o p e d . The d e s i g n has been based m a i n l y on two i m p o r t a n t a s p e c t s . F i r s t l y , the a n a l y s i s a v o i d s u s i n g complex shape d e s c r i p t o r s ; i t doesn't become i n v o l v e d i n s t a t i s t i c a l f e a t u r e o p t i m i z a t i o n but t a k e s a s y n t a c t i c approach t o e x t r a c t f e a t u r e s t h a t have s t r o n g s y m b o l i c meanings. S e c o n d l y , t h e f e a t u r e s a r e d e f i n e d such t h a t they can be e x t r a c t e d e a s i l y from the e x i s t i n g d a t a . F e a t u r e s t h a t a r e i n v a r i a n t t o branch r e v e r s a l can h e l p reduce the amount of e x t r a c t i o n t i m e . B a s i c a l l y the t r a n s f o r m a t i o n t u r n s a d i g r a p h d e s c r i p t i o n of a d i s c r e t e image i n t o a more n a t u r a l d e s c r i p t i o n w i t h the node semantic v e c t o r s g i v i n g i n f o r m a t i o n on the l o c a t i o n of th e nodes i n the image and t h e branch a t t r i b u t e s t h e i r r e l a t i o n s h i p s . I n t h i s r e s p e c t we have o b t a i n e d s y m b o l i c a l l y a r i c h e r d e s c r i p t i o n of t h e c h a r a c t e r and so performs t h e f i n a l r e c o g n i t i o n based on t h i s d e s c r i p t i o n . The t y p e s of shape used i n t h e d e s c r i p t i o n can be d e r i v e d t h r o u g h p s y c h o l o g i c a l s t u d i e s on the human v i s u a l system [13] thus a d d i n g t o the d e s c r i p t i o n an a s p e c t which cannot be m o d e l l e d m a t h e m a t i c a l l y . As an i l l u s t r a t i o n of the a p p l i c a t i o n of the t h e o r i e s t h a t has been p r e s e n t e d as w e l l as an i n t r o d u c t i o n t o the next s e c t i o n , we c o n c l u d e t h i s s e c t i o n w i t h two examples. Example 1 shows the ARG d e s c r i p t i o n of a c h a r a c t e r from Munson's d a t a t h a t i s o b t a i n e d by t r a n s f o r m i n g from i t s c h a i n coded d i g r a p h and example 2 shows the c a l c u l a t i o n of the d i s t a n c e measure between two ARGs. Example 1 ; T r a n s f o r m a t i o n of the d i g r a p h r e p r e s e n t a t i o n of 'R' i n t o an ARG r e p r e s e n t a t i o n . Input Image. Digraph R e p r e s e n t a t i o n . t i i i t i . 1 1 . i . . i i . . t o« (5,23) 7 i • 556, m, • 3. - 77766777. n, • 8. 7 , - 1 1 1 2 1 22233445555, m, -7. • 2, m, • 1. It - 87777778, m, . 8. 7t - 323232332 1 , m, • 10. t o t a l no. of p i x e l s T . 46. a, (12, 22) 16. Nodes: Branches: 1 - ( J 3 , b a ) , b , - ( U 1 2 , ( M e . C i , 5 , 6 ) ) 2 « ( E p , b a > , b , « ( U l 3 , ( M e , C i , 7 , 7 ) ) 3 « ( J 3 , b b ) , b , « ( U 3 l , ( L g , C 3 , 1 , 5 ) ) 4 - ( J 3 , b b ) , b , - « ( U 4 3 , ( S h . d ,2 ,2 ) ) 5 « ( E p , c c ) , b 5 « ( U 4 5 , ( M e , C i , 8 , 8 ) ) 6 - ( E p , a c ) , b , « ( U 6 4 , ( M e , C 2 , 3 , 2 ) ) Sample c a l c u l a t i o n s . u(a6) = Node 6 = ( s s , x 6 ) = ( E p , a c ) . where s y n t a c t i c symbol i s Ep and c o o r d i n a t e (5,23) maps i n t o s e c t o r a c . «(7s> - b 6 = ( V6A,(L*,*$,0%S.02B > w i t h L 6 = Me s i n c e T/20<m s<3T/l0. * 6 = I 6. = (-1+1-1+1-1+1+0-1-1)45 * -90°. e\ = [1/2(3+2)1= 3 and 9*, = fl/ 2 ( 2 + 1 ) " u 2. 8 4 Example 2. : T h i s example i l l u s t r a t e s how the d i s t a n c e between the two ARGs shown below can be c a l c u l a t e d . For the moment we assume t h a t the f e a s i b i l i t y of matching the nodes and branches of the two ARGs have been checked and they a r e matched a c c o r d i n g t o t h e i r l a b e l s (node numbers & b r a n c h s u b s c r i p t s ) . ARC of "A'. 1 - (Ep.be) b, - (U21,(Sh.Cl,7,7) ) 2 * (J3,be> b, • (042,(Me,Ci,3,4)) 3 - (J3,bb) b, • (U23,(Me,CI,7,7)) 4 - (Bp.cb) b, • (U34,(Me.Ci,1.I)) 5 - (Ep.ac) b, > (D35,(Me,C1,6,6)) 6 • (Ep.cc) b ( • (U64,(Me,Ci,3,4>) ARG of (Ep, ba ) b - , • (C2';' ,(Me,C2,1,7 i i 2' • (J 3 , ba ) b ' i • (U4,2' ,(Me,C2,3,5)) 3' • <J3,bb) b-, • <U2'3' ,(Me.Ci,7,7)) 4 ' • (Ep.cb) b' . . (U3'4' , (Me , C I , 6 , l ) ) 5' • (Ep.bc) b' , • (U3'5' ,(Me,C2,6,7)) 6' > (Ep,ac) b'. • (U4'6' ,(Me,C2,1,6)) Given that the tr a n s f o r m a t i o n * T i s such that the branch and node semantic vector components have the f o l l o w i n g deformation d i s t a n c e s : Por nodes: d(a,b)-3, d<b,c)«3, d(a,c)>7. Por branches: 1. Length a t t r i b u t e s : - . d(Sh,Me)«2, d(Me,Lg)-2, d(Sh,Lg)>B. 2. Curvature a t t r i b u t e s : -d(Ct,C2)-2, d(Cl,C3)-4, d(C1.C4)-16, d(C1,C5)-l6, d(C2,C3)>2. d(C2,C4)-8, d(C2,C5)»B, d(C3,C4)-2, d(C3.C5)-B, d(C4.C5)-B. 3. 4" and E x i t and entry d i r e c t i o n s have a di s t a n c e of 2 for every 45° of deformation. eg. d(l,2)«2. d(i,3>»4, d(l,4)-6 d<1.5>-8, d(l,6)«6, d(l,7).4, d(l,8)-2, d(2,3)-2, d(2,4)-4 e t c . . •,•1 and »,•!. D i s t a n c e c a l c u l a t i o n s : d(B,A) «= Z (node d e f o r m a t i o n d i s t a n c e ) + Z (branch d e f o r m a t i o n d i s t a n c e ) = (0+0+0+0+3+7) + (8+4+0+2+4+6) = 34. e.g. d(node 6 ' ,node 6 ) » d(c,c) + d ( a r c ) - 7 + 0 - 7. d ( b ' c , b 6 ) - d(Me,Me) • d(C2,C1) + d t * 1 , * 1 ' ) + d ( 0 2 , 0 2 ' ) . cont Note t h a t node 6 i s matched t o node 6' and node 4 t o node 4' so U64 and U 4 ' 6 ' d e s c r i b e a p a i r of matched branches b 6 and b 6 ' w i t h one b r a n c h t r a c k e d i n the r e v e r s e d i r e c t i o n w i t h r e s p e c t to t h e i r end nodes as i n d i c a t e d by t h e i r s y n t a c t i c symbols. In o r d e r t o match these two branches we have t o use e q u a t i o n 4.3.7 t o c o r r e c t 0 1 and 62 of any one of the branch b e f o r e m a t c h i n g . C o r r e c t i n g 0 1 and 82 of b 6 ' we r e w r i t e i t s branch p r i m i t i v e as b' 6 = (US' 4',(Me,C2,2,5)). T h e r e f o r e the branch d e f o r m a t i o n d i s t a n c e i s c a l c u l a t e d a s : d(Me,Me) = 0. d(C1,C2) = 2. d(3,2) = 2. d(4,5) = 2. T h e r e f o r e d ( b 6 , b ' 6 ) = 0+2+2+2 = 6. 86 4 . ARG M a t c h i n g . 4.1 Concept of r e f e r e n c e g u i d e d m a t c h i n g . As have been mentioned e a r l i e r , c o n v e n t i o n a l graph isomorphism belongs t o a c l a s s of NP-complete problems and the s o l u t i o n i s o b t a i n e d u s i n g an e x h a u s t i v e b l i n d s e a r c h . To a v o i d u s i n g such a time consuming s e a r c h p r o c e d u r e , a h e u r i s t i c ARG matching scheme i s d e s i g n e d by making use of the known i n f o r m a t i o n about the images t h a t a r e b e i n g matched. T h i s i n f o r m a t i o n i s a v a i l a b l e as a r e s u l t of p r e c l a s s i f i c a t i o n as w e l l as from the r e f e r e n c e ARG i t s e l f . S p e c i f i c a l l y , p r e c l a s s i f i c a t i o n d e t e r m i n e s the t y p e s of nodes and hence the s y n t a c t i c symbols of the nodes t h a t a r e p r e s e n t i n t h e image. T h e r e f o r e i t i s o n l y r e q u i r e d t o match the i n p u t ARG w i t h the r e f e r e n c e ARGs of the same group ( c o n s i s t i n g of images w i t h the same f i x e d number and type of no d e s ) . I n c h a p t e r I I I , i t i s shown t h a t not a l l images i n a g i v e n group a r e t o p o l o g i c a l l y e q u i v a l e n t . But by u s i n g a d i c t i o n a r y of r e f e r e n c e c h a r a c t e r ARGs f o r each group t h a t c o n s i s t s of ARGs f o r each type of t o p o l o g y t h a t a c h a r a c t e r i n the group can have, then t h e f i n a l r e c o g n i t i o n i n v o l v e s o n l y the matching of t o p o l o g i c a l l y e q u i v a l e n t images. That i s , the f i n a l r e c o g n i t i o n i n v o l v e s the matching of ARGs u s i n g the TPD-ARG model and t h e t r a n s f o r m a t i o n s d e v e l o p e d i n s e c t i o n 3. Another source of i n f o r m a t i o n t h a t can be used t o guide the m a t c h i n g procedure can be o b t a i n e d from t h e r e f e r e n c e ARG i t s e l f . By e x p r e s s i n g the r e f e r e n c e ARG as a d i r e c t e d graph, 87 the ARG can be t r a v e r s e d i n an o r d e r l y manner and matching between the i n p u t and the r e f e r e n c e can be g u i d e d a l o n g by the r e f e r e n c e ARG and a c c o m p l i s h e d i n two main s t e p s . 1. O b t a i n a b e s t match between the nodes of the i n p u t ARG and r e f e r e n c e ARG. M a t c h i n g w i l l p roceed i f and o n l y i f a match can be found f o r e v e r y node i n the r e f e r e n c e and i n p u t ARG. 2. P e r f o r m a depth f i r s t t r a v e r s a l of the r e f e r e n c e ARG. For each s t e p of t h i s t r a v e r s a l f i n d an e q u i v a l e n t s t e p i n the i n p u t ARG by c h e c k i n g the f e a s i b i l i t y of making such a s t e p between the p a i r ( s ) of nodes i n the i n p u t image t h a t has been matched t o the node p a i r i n the r e f e r e n c e ARG t h a t i s i n v o l v e d i n the s t e p . For each f e a s i b l e s t e p found i n the i n p u t ARG, c a l c u l a t e the d e f o r m a t i o n d i s t a n c e between the branch i n v o l v e d and the r e f e r e n c e branch t r a v e r s e d . The f e a s i b l e e q u i v a l e n t branch y i e l d i n g the minimum d i s t a n c e i s taken as the best matched bra n c h . A l t h o u g h s t e p s 1 and 2 shows o n l y the g e n e r a l concept of the r e f e r e n c e g u i d e d matching p r o c e d u r e i t s u f f i c e s i n showing the importance of the r o l e p l a y e d by the d a t a s t r u c t u r e i n the r e c o g n i t i o n a l g o r i t h m . The l i n k e d l i s t d a t a s t r u c t u r e d e s c r i b e d i n c h a p t e r I I I has e n a b l e d the c h a i n coded d i g r a p h t o be t r a n s f o r m e d i n t o a d i r e c t e d ARG by t r a n s f o r m i n g o n l y the c o n t e n t s of t h e NDTs w h i l e p r e s e r v i n g i t s l i s t s t r u c t u r e . T h i s makes i t easy f o r the matching a l g o r i t h m t o check t h e branches a t t a c h e d t o each node of t h e i n p u t image ARG by s i m p l y c h e c k i n g t h e c o n t e n t s of i t s NDT i n s t e a d of s c a n n i n g a l l the 88 branches and i d e n t i f y i n g t h e i r end nodes. S t e p 2 r e v e a l s t h a t the r e f e r e n c e g uided matching p r o c e d u r e r e q u i r e s the r e f e r e n c e ARG t o be a d i r e c t e d ARG. However, the l i n k e d l i s t r e p r e s e n t a t i o n of the d i r e c t e d ARG cannot be s t o r e d i n permanent memory as the p o i n t e r s w i l l become m e a n i n g l e s s and t h u s the d a t a s t r u c t u r e d e s t r o y e d . A s l i g h t m o d i f i c a t i o n has t o be made t o the r e f e r e n c e ARGs by r e p l a c i n g t h e i r p o i n t e r s by the node numbers of the nodes p o i n t e d by the p o i n t e r s . The r e f e r e n c e ARG can then be s t o r e d by s t o r i n g t h e i r m o d i f i e d NDTs. These NDTs ar e read back b e f o r e matching and t h e i r s t r u c t u r e s r e s t o r e d . Note t h a t the r e f e r e n c e ARGs i n each group have the same number of NDTs, t h e r e f o r e they can be c o n v e n i e n t l y s t o r e d i n a s e q u e n t i a l format i n the group d i c t i o n a r y w i t h the most f r e q u e n t l y o c c u r i n g c h a r a c t e r s i n the group p l a c e d i n f r o n t of the l i s t . T h i s h e l p s t o improve the average matching time because i f a p e r f e c t match i s found e a r l i e r than an i n p u t ARG do not have t o be matched w i t h t h e r e s t of the c h a r a c t e r s i n the d i c t i o n a r y . Another i m p o r t a n t p o i n t t o note here i s t h a t the r e f e r e n c e ARGs can be a c q u i r e d i n the same manner as any o t h e r i n p u t ARGs. T h e r e f o r e the same a l g o r i t h m can be used t o c r e a t e the d i c t i o n a r y or the r e c o g n i t i o n a l g o r i t h m can be made i n t o an i n t e l l i g e n t a l g o r i t h m t h a t i s c a p a b l e of l e a r n i n g new or s p e c i a l c h a r a c t e r s by a c t i v a t i n g a s p e c i a l r o u t i n e t h a t can p l a c e the new ARG i n t o the p r o p e r group d i c t i o n a r y . 89 4.2 D i s t a n c e m a t r i x and r e f e r e n c e g u i d e d i n e x a c t m a t c h i n g . The r e f e r e n c e g u i d e d matching of ARGs can be a c c o m p l i s h e d v e r y e f f i c i e n t l y by u s i n g an ARG d i s t a n c e m a t r i x (DM). C o n s i d e r a group of ARGs w i t h N nodes. We form a DM of s i z e NxN w i t h the rows r e p r e s e n t i n g the r e f e r e n c e nodes and columns r e p r e s e n t i n g the unknown nodes as shown below. Ref. nodes ( I ) unknown nodes ( J ) N x N The r e s u l t a n t d i s t a n c e between the unknown and the r e f e r e n c e ARGs can be c a l c u l a t e d w i t h the a i d of t h i s DM i n two s e p a r a t e s t e p s . 1. DM g e n e r a t i o n and f i l l i n g t h r o u g h node m a t c h i n g . 2. DM r e d u c t i o n t h r o u g h f e a s i b i l i t y t e s t and branch m a t c h i n g . U s i n g the DM, the complete ARG matching p r o c e d u r e can best be e x p l a i n e d t h r o u g h the f o r m a l p r e s e n t a t i o n of i t s a l g o r i t h m A3. 90 A l g o r i t h m A 3 : R e f e r e n c e Guided I n e x a c t M a t c h i n g . Input : L i n k e d l i s t of NDTs r e p r e s e n t i n g the d i r e c t e d r e f e r e n c e ARG and a l i n k e d l i s t of NDTs r e p r e s e n t i n g the ARG of i n p u t image. Output : T o t a l d e f o r m a t i o n d i s t a n c e between the Re f e r e n c e ARG and i n p u t ARG. Let ' I ' s r e p r e s e n t the node numbers of the r e f e r e n c e ARG and 'J's r e p r e s e n t the node numbers of the i n p u t (unknown) ARG each h a v i n g N nodes. 1 . I n i t i a l i z e DM of s i z e NxN t o z e r o ; d ( I n p u t ARG, Ref. ARG) := 0; 2. { s t e p s 2 t o 4 f i n d t he best match between the nodes of the i n p u t and r e f e r e n c e ARGs } For r e f . node I := 1 t o N Do For unknown node J := 1 t o N Do Begin I f node J s y n t a c t i c symbol = node I s y n t a c t i c symbol then c a l c u l a t e d ( n l f n j ) ; I f d(n f ,nj ) = 0 then DM (I , J ) := 1 e l s e i f d ( n x ,n, ) £ t h r e s h o l d l 1 then DM(I,J) := 0 e l s e DM(I,J) := d ( n x , n 3 ) End; 3. F o r I := 1 t o N Do Begin keep the minimum non-zero e n t r y of each row and s e t the r e s t t o z e r o ; I f a row w i t h a l l z e r o e n t r i e s i s d e t e c t e d then goto s t e p 10 End; 4. For J := 1 t o N Do If column J has no non-zero e n t r y then Begin For I := 1 t o N Do Begin I f node J s y n t a c t i c symbol = node I s y n t a c t i c symbol then c a l c u l a t e d ( n I f n 3 ) ; I f d ( n x , n j ) = 0 then DM(I,J) := 1 e l s e i f d ( n i , n T ) £ t h r e s h o l d l then DM(I,J) := 0 e l s e DM(I,J) := d ( n x , n 3 ) End; c o n t . 1 t h r e s h o l d l = node d e f o r m n a t i o n t h r e s h o l d above which we c o n s i d e r the d e f o r m a t i o n t o be unr e a s o n a b l e so the match i s not c o n s i d e r e d a p o s s i b l e match. 91 For J := 1 t o N Do Begin keep the minimum non-zero e n t r y of each column and s e t the r e s t t o z e r o ; I f a column w i t h a l l z e r o e n t r i e s i s d e t e c t e d then goto s t e p 10 End; End; 5. Ref. node I := r o o t node of d i r e c t e d Ref. ARG ; 6. { f e a s i b i l i t y check and branch matching } For J := 1 t o N Do Begin I f DM(I,J) > 0 then Repeat Le t I ' be an end node a s s o c i a t e d w i t h an o u t g o i n g branch from node I ; r e s e t b f l a g ; db := t h r e s h o l d 2 2 ; Begin For J ' := 1 t o N Do I f DM(I',J') > 0 then Begin I f a branch e x i s t s between nodes J J ' of the Unknown ARG { f e a s i b i l i t y s a t i s f i e d } then i f ( d ( b r a n c h J J ' , b r a n c h I I ' ) < t h r e s h o l d 2 and d ( b r a n c h J J ' , b r a n c h l I ' ) < bd) then Begin db := d ( b r a n c h J J ' , b r a n c h I I ' ) ; s e t b f l a g End; End; I f b f l a g s e t then DM(I,J) := DM(I,J) + db e l s e B e g in DM(I,J) := 0 { node p a i r I & J i s not a f e a s i b l e match so i s e l i m i n a t e d }; goto nn End; End; U n t i l a l l o u t g o i n g branches of Ref. node I have been t e s t e d and matched; nn : End; 7. check row I and keep the minimum non-zero e n t r y of the row and s e t the r e s t t o z e r o ; I f a l l z e r o s i n the row i s d e t e c t e d then goto s t e p 10; c o n t . 2 T h r e s h o l d 2 i s the branch d e f o r m a t i o n t h r e s h o l d above which we c o n s i d e r the d e f o r m a t i o n as u n r e a s o n a b l e and so the match i s not c o n s i d e r e d f e a s i b l e 8. I := next node of the depth f i r s t t r a v e r s a l of the Ref. ARG; 9. Repeat s t e p s 5 t o 8 u n t i l t r a v e r s a l of the Ref.ARG i s co m p l e t e d ; g o t o 11; 10. No match between the two ARGs i s p o s s i b l e ; g o t o l 2 ; 11. F o r I := 1 t o N Do Fo r J := 1 t o N Do d.(Input ARG, Ref. ARG) := d d n p u t ARG, Ref.ARG) + D M ( I , J ) ; 12. End. Remarks: In t h e d i s t a n c e m a t r i x , z e r o e n t r i e s a r e used t o i n d i c a t e 'no match' w h i l e '1's i n d i c a t e p e r f e c t l y matched nodes. S t e p s 2 and 3 i n d e n t i f i e s t h e i n p u t node(s) t h a t g i v e s the b e s t match f o r each r e f e r e n c e node. T h i s i s a row dominated node matching where p r i o r i t y i s g i v e n t o f i n d i n g a be s t match f o r each row ( r e f . node). As a r e s u l t i t i s p o s s i b l e t h a t a l t h o u g h e v e r y r e f e r e n c e node may have a b e s t match, t h e r e may be i n p u t nodes w h i c h a r e not matched t o any r e f e r e n c e node a t a l l . T h i s s i t u a t i o n shows up i n the DM as columns w i t h a l l z e r o e n t r i e s w h i l e e v e r y row has a t l e a s t one non-zero e n t r y . T h i s problem i s r e s o l v e d i n s t e p 4 which e n s u r e s t h a t a t t e m p t s a r e made t o f i n d a be s t match f o r a l l i n p u t nodes as w e l l . F o r two ARGs w i t h i d e a l l y matched nodes, t h e r e w i l l be a one t o one matching between the r e f e r e n c e and the i n p u t nodes. The i d e a l l y matched DM s h o u l d t h e r e f o r e have e x a c t l y one '1' 93 i n each row and column. For n o n - i d e a l but n e v e r t h e l e s s b e s t matched c a s e s , the b e s t matched nodes are d e s i g n a t e d by the c o r r e s p o n d i n g elements i n the DM t a k i n g the v a l u e s of the d e f o r m a t i o n d i s t a n c e s between the two nodes. In t h i s case i t i s p o s s i b l e t h a t t h e r e c o u l d be more than one minimum non-zero e n t r y i n a row or column. For the m a j o r i t y of such c a s e s these m u l t i p l e b e s t matches w i l l be e l i m i n a t e d a f t e r the f e a s i b i l i t y t e s t and branch matching i n s t e p s 5 t o 9. In the r a r e cases where t h e s e m u l t i p l e best matches s t i l l e x i s t a f t e r the complete ARG matching then they w i l l c o n t r i b u t e t o an i n c r e a s e i n the r e s u l t a n t d e f o r m a t i o n d i s t a n c e . T h e r e f o r e ' i n e x a c t ' matchings y i e l d a more c o n s e r v a t i v e measure of the d e f o r m a t i o n d i s t a n c e . 4.2.1 C o m p u t a t i o n a l c o m p l e x i t y . The c o m p u t a t i o n a l c o m p l e x i t y f o r the ARG matching c o m p r i s e s of the time r e q u i r e d t o match the nodes and the time r e q u i r e d t o make a f e a s i b i l i t y t e s t and branch matching. Suppose t h e matching a l g o r i t h m i s used t o match an i n p u t ARG of N nodes w i t h a r e f e r e n c e of M nodes. The f i r s t p a r t of the matching p r o c e s s c o n s i s t s of f i n d i n g the b e s t match f o r the nodes. L e t c, be the time r e q u i r e d t o match one node. Then t o f i n d the b e s t match f o r a l l the r e f e r e n c e nodes t a k e s c,MN t i m e . In o r d e r t o ensure t h a t a l l t h e i n p u t nodes g e t s a b e s t match ( s t e p 4) r e q u i r e s i n the worst case another c,MN t i m e , g i v i n g the t o t a l time r e q u i r e d f o r node matching as 2ciMN. 94 The second p a r t of the matching p r o c e s s i n v o l v e s the f e a s i b i l i t y t e s t and branch m a t c h i n g . In the r e f e r e n c e guided m a t c h i n g p r o c e s s , f o r each r e f e r e n c e branch t r a v e r s e d a f e a s i b i l i t y t e s t i s made and a branch d e f o r m a t i o n d i s t a n c e c a l c u l a t e d i f the match i s f e a s i b l e . The number of such t e s t s p e r f o rmed f o r each r e f e r e n c e branch depends on the number of i n p u t nodes t h a t a r e matched t o the r e f e r e n c e node p a i r i n v o l v e d . In terms of the DM, t h e number of t e s t s performed depends on t h e number of non-zero elements i n the two rows c o r r e s p o n d i n g t o the two r e f e r e n c e nodes i n v o l v e d . T h e r e f o r e t o o b t a i n an i n d i c a t i o n of the time c o m p l e x i t y , we can use a h y p o t h e t i c a l worst case where th e DM i s a f u l l m a t r i x of non-zero e l e m e n t s . ( T h i s s i t u a t i o n cannot o c c u r i n the DM f o r m a t c h i n g the ARGs of c h a r a c t e r s because i t r e q u i r e s e v e r y node t o match each o t h e r ) . L e t c 2 be the time r e q u i r e t o p e r f o r m a f e a s i b i l i t y t e s t and a branch matching and k be the average number of o u t g o i n g branches f o r each r e f e r e n c e node. Suppose f o r each r e f e r e n c e node a f e a s i b i l i t y t e s t and branch matching i s done f o r each one of the k o u t g o i n g b r a n c h e s . T h i s w i l l t a k e c 2 * N time as each t e r m i n a l node of an o u t g o i n g r e f e r e n c e b r a n c h has N i n p u t nodes matched t o i t . S i n c e the r e f e r e n c e node i t s e l f has N i n p u t nodes matched t o i t then the time t a k e n t o c o m p l e t e l y check t h e f e a s i b i l i t y and match the o u t g o i n g branches from each r e f e r e n c e node i s c 2 * N 2 . W i t h a r e f e r e n c e ARG of M nodes th e h y p o t h e t i c a l w orst c a s e c o m p u t a t i o n f o r the second p a r t of t h e m a t c h i n g p r o c e s s i s c 2*MN 2. Thus th e t o t a l worst c a s e r e f e r e n c e g u i d e d matching 95 time i s 2c,MN+c 2fcMN 2. From t h e h i g h e r c o m p l e x i t y of the b r a n c h a t t r i b u t e s compared t o t h e nodes a t t r i b u t e s i t i s o b v i o u s t h a t c 2 i s much g r e a t e r than c,. In the ARG r e p r e s e n t a t i o n of h a n d p r i n t e d c h a r a c t e r s t h e maximum number of branches a node can have i s d e f i n e d as 4, t h e r e f o r e k=2 i s a r e a s o n a b l e e s t i m a t e f o r the average number of o u t g o i n g branches per node. U s i n g t h i s a ssumption we can s i m p l i f y the worst case time r e q u i r e d f o r matching t o 2 C 2 M N ( N + 1 ) or a time c o m p l e x i t y of 0 ( M N ( N + 1 ) ) . For t o p o l o g i c a l l y e q u i v a l e n t images M=N, so the time c o m p l e x i t y becomes 0 ( N 2 ( N + 1 ) ) . T h i s t i m e c o m p l e x i t y i s e x t r e m e l y f a v o u r a b l e compared t o t h e s t a t e space approach f o r matching ARGs [61] which r e q u i r e s a t i t s b e s t 0(N*) time or the p o l y n o m i a l , f a c t o r i a l or even e x p o n e n t i a l time c o m p l e x i t i e s f o r o t h e r c o n v e n t i o n a l graph isomorphisms [ 6 2 ] . 5. F i n a l r e c o g n i z e r i m p l e m e n t a t i o n and performance. 5.1 F i n a l r e c o g n i z e r i m p l e m e n t a t i o n . The d i s c u s s i o n on the ARG matching g i v e n above com p l e t e s t h e p r e s e n t a t i o n of the d e s i g n f o r t h e t h r e e main s t a g e s of t h e f i n a l r e c o g n i z e r as d e p i c t e d i n f i g u r e 1.2. In the i m p l e m e n t a t i o n of the r e c o g n i z e r the a l g o r i t h m s A1, A2 and A3 form the b a s i c t h r e e s t a g e s of t h e r e c o g n i t i o n p r o c e s s . As t h e s e p r o c e s s e s have been p r e s e n t e d i n d e t a i l i n t h e p r e v i o u s s e c t i o n s what remain t o be d i s c u s s e d i n the f i n a l i m p l e m e n t a t i o n a r e the f o r m a t i o n of the group d i c t i o n a r i e s and 96 the d e r i v a t i o n of the d e f o r m a t i o n t r a n s f o r m a t i o n h T Group d i c t i o n a r i e s f o r the r e c o g n i z e r a r e formed by ex a m i n i n g 1000 samples from Munson's d a t a . These c h a r a c t e r images were t h i n n e d and a f t e r p r e c l a s s i f i c a t i o n the r e s u l t i n g c h a i n coded r e p r e s e n t a t i o n of the images a r e t r a n s f o r m e d i n t o t h e i r ARG d e s c r i p t i o n s u s i n g the t r a n s f o r m a t i o n g i v e n i n s e c t i o n 3. The c h a r a c t e r s i n each group a r e examined and the t o p o l o g i e s of each c h a r a c t e r i n the group i d e n t i f i e d . T a b l e IV shows the number of t o p o l o g i e s each c h a r a c t e r i n the group i s observ e d t o have and the t o t a l number of r e f e r e n c e ARGs r e q u i r e d i n each group d i c t i o n a r y . I d e a l l y , the number of r e f e r e n c e c h a r a c t e r ARGs i n each group s h o u l d e q u a l t o t h e sum of the t o t a l number of t o p o l o g i e s of each c h a r a c t e r i n the group. In t a b l e IV t h i s i s not the case because a c h a r a c t e r h a v i n g a s i n g l e t o p o l o g y may appear t o be f a i r l y d i f f e r e n t v i s u a l l y . T h i s i s i l l u s t r a t e d i n f i g u r e s 4.2a and b below. (a) (b) F i g u r e 4.2. D i f f e r e n t forms of a s i n g l e c h a r a c t e r h a v i n g the same t o p o l o g y . 97 These d i f f e r e n t forms a r e taken i n t o c o n s i d e r a t i o n by the ARG i n i t s node semantic v e c t o r which i n d i c a t e s the p o s i t i o n of the nodes. The changes i n the node p o s i t i o n of t h e c h a r a c t e r s i n t h e s e c a s e s a r e not due t o n o i s e or d e f o r m a t i o n s but are d e l i b e r a t e as a r e s u l t of d i f f e r e n t w r i t i n g s t y l e s . For the r e c o g n i t i o n of u n c o n s t r a i n e d h a n d p r i n t e d c h a r a c t e r s , the group d i c t i o n a r y s h o u l d i n c l u d e d c h a r a c t e r s w i t h t h e s e d e l i b e r a t e s h i f t s i n node p o s i t i o n s . O t h e r w i s e the matching w i l l r e s u l t i n an u n n e c e s s a r y p e n a l t y on t h e s e images which a r e n o r m a l l y a c c e p t a b l e . By t a k i n g t h i s i n t o c o n s i d e r a t i o n we o b t a i n e d a t o t a l o f 231 r e f e r e n c e c h a r a c t e r ARGs a r r a n g e d i n t o the d i f f e r e n t group d i c t i o n a r i e s as shown i n t a b l e IV. The b l o c k diagram of t h i s f i n a l r e c o g n i z e r i s shown i n s o l i d l i n e s i n f i g u r e 4.3. The f i n a l r e c o g n i z e r uses the same d e f o r m a t i o n t r a n s f o r m a t i o n h as t h a t g i v e n i n example 2. T h i s t r a n s f o r m a t i o n i s o b t a i n e d i n t u i t i v e l y t h r o u g h the o b s e r v a t i o n of the samples t h a t were used i n d e r i v i n g the d i c t i o n a r y . As such, t h e d i s t a n c e s appended t o the d i f f e r e n t f e a t u r e d e f o r m a t i o n s a r e not n e c e s s a r i l y optimum. The optimun d e f o r m a t i o n t r a n s f o r m a t i o n s h o u l d be o b t a i n e d t h r o u g h e x p e r i m e n t a l s t u d i e s where d i f f e r e n t f e a t u r e s a r e s y s t e m a t i c a l l y deformed, and t h e s e v e r i t y (hence r e l a t i v e d i s t a n c e ) f o r each type of d e f o r m a t i o n i n f e r r e d from the r e l a t i v e d i f f i c u l t i e s f o r human s u b j e c t s t o r e c o g n i z e the r e s u l t a n t c h a r a c t e r s . T h i s type of a n a l y s i s i s h i g h l y i n v o l v e d and i s not performed i n t h i s r e s e a r c h . For t h i s e x p e r i m e n t , 98 t h e h e u r i s t i c a l l y d e r i v e d t r a n s f o r m a t i o n of example 2 i s an adequate e s t i m a t e f o r h and t h i s i s c o n f i r m e d by the performance r e s u l t s g i v e n below. 5.2 Performance w i t h Munson's c h a r a c t e r d a t a . The matching a l g o r i t h m i s implemented i n P a s c a l on the PDP 11/23 minicomputer and the Vax 11/750 r u n n i n g i n the PDP c o m p a c t i b i l i t y mode. 1511 samples from Munson's da t a a r e used as i n p u t s t o the r e c o g n i z e r u s i n g the same d e f o r m a t i o n t r a n s f o r m a t i o n h t h a t i s g i v e n i n example 2. 1382 of thes e i n p u t images were c o r r e c t l y i d e n t i f i e d g i v i n g an o v e r a l l r e c o g n i t i o n r a t e of 9 1 . 4 6 % . T h i s r e c o g n i t i o n r a t e i s the d i r e c t r e c o g n i t i o n r a t e w i t h o u t s u b s t i t u t i o n s . There was no need f o r s u b s t i t u t i o n s i n t h i s c a s e because 97% of the f a i l u r e s were due t o m i s r e c o g n i t i o n and not due t o f a i l u r e on the p a r t of the r e c o g n i z e r t o make an i d e n t i f i c a t i o n . The low pe r c e n t a g e of u n i d e n t i f i a b l e images i m p l i e s t h a t the t h i n n i n g , g l o b a l f e a t u r e d e t e c t i o n and matching p r o c e d u r e s have performed e x c e e d i n g l y w e l l . T h i s i s because i f t h i n n i n g has not been a b l e t o g i v e o u t p u t s w i t h t h e d e s i r e d f e a t u r e s or the g l o b a l f e a t u r e d e t e c t i o n , e x t r a c t i o n and p r e c l a s s i f i c a t i o n p r o c e d u r e s cannot s u c c e s s f u l l y p r o c e s s a l l the p o s s i b l e t o p o l o g i e s , then the r e c o g n i t i o n p r o c e s s would have f a i l e d a t th e p r e c l a s s i f i c a t i o n s tage r e s u l t i n g i n a h i g h e r p e r c e n t a g e of u n i d e n t i f i a b l e c h a r a c t e r s . L i k e w i s e the f a i l u r e of the matc h i n g p r o c e d u r e t o match a l l t h e images w i t h the r e f e r e n c e c h a r a c t e r s would have i n c r e a s e d the p e r c e n t a g e of u n i d e n t i f i a b l e c h a r a c t e r s . L i k e w i s e t h e f a i l u r e o f the 99 m atching p r o c e d u r e t o match a l l t h e images w i t h the r e f e r e n c e c h a r a c t e r s would have i n c r e a s e d t h e p e r c e n t a g e of u n i d e n t i f i a b l e c h a r a c t e r s . T h e r e f o r e the f i r s t c o n c l u s i o n t h a t can be drawn from the r e s u l t i s t h a t the experiment has c o n f i r m e d t h a t the r e c o g n i z e r can p e r f o r m as d e s i g n e d over the wide range of e x p e c t e d i n p u t images as r e p r e s e n t e d by Munson's d a t a . The breakdown of the r e c o g n i t i o n r a t e s f o r the i n d i v i d u a l c h a r a c t e r s a r e g i v e n i n t a b l e V, which shows t h a t the most d i f f i c u l t c h a r a c t e r s t o i d e n t i f y c o r r e c t l y a r e the U's and V s w i t h a r e c o g n i t i o n r a t e of 77.3% and 80% r e s p e c t i v e l y . T h i s i s not s u r p r i s i n g c o n s i d e r i n g t h a t t h e s e two c h a r a c t e r s e x i b i t a h i g h degree of a m b i g u i t y e s p e c i a l l y f o r t h e U's t h a t a r e w r i t t e n w i t h o u t a ' t a i l ' ( U- ). The low r e c o g n i t i o n r a t e s between t h e s e two c h a r a c t e r s have been i n v e s t i g a t e d by Suen and S h i l l m a n [ 1 4 ] . T h e i r e xperiment had shown t h a t human r e c o g n i t i o n r a t e s f o r thes e two c h a r a c t e r s a r e o n l y 86.8% and 95.9% r e s p e c t i v e l y . In t h i s e x p e r i m e n t , o t h e r p o o r l y r e c o g n i z e d c h a r a c t e r s a r e M, N, and G where a h i g h degree of a m b i g u i t y e x i s t between t h e s e c h a r a c t e r s and H, W and C r e s p e c t i v e l y . Examples of some of t h e s e ambiguous c h a r a c t e r s a r e shown i n f i g u r e 4.4. The pr e s e n c e of ambiguously shaped c h a r a c t e r s i n d i c a t e s t h a t i n t h e c o n t e x t f r e e r e c o g n i t i o n of i s o l a t e d u n c o n s t r a i n e d h a n d p r i n t e d a l p h a n u m e r i c c h a r a c t e r s t h e r e i s an upper l i m i t t o t h e r e c o g n i t i o n r a t e because the c h a r a c t e r shapes o v e r l a p and c r e a t e a m b i g u i t i e s which cannot be r e s o l v e d based on the e x a m i n a t i o n of the s i n g l e c h a r a c t e r . 100 A m b i g u i t i e s of the s e n a t u r e have been r e s e a r c h e d by B l e s s e r et al [13] and f i g u r e 4.5 shows the a m b i g u i t y m a t r i x f o r h a n d p r i n t e d a lphanumeric c h a r a c t e r s as c o m p l i e d by B l e s s e r . In o r d e r t o a c h i e v e a h i g h r e c o g n i t i o n r a t e , f u t u r e r e s e a r c h has t o i n c l u d e c o n t e x t u a l i n f o r m a t i o n i n t o the r e c o g n i t i o n p r o c e s s or employ p s y c h o p h y s i c a l t e c h n i q u e s t o o b t a i n p s y c h o l o g i c a l l y based f e a t u r e s f o r d e s c r i b i n g c h a r a c t e r shapes. Suen [14] i l l u s t r a t e s t h i s p o i n t i n h i s r e p o r t where r e c o g n i t i o n r a t e s of over 94% f o r the U's and V s can be o b t a i n e d . In t h e d e s i g n of t h i s f i n a l r e c o g n i z e r , the components of the semantic ( f e a t u r e ) v e c t o r s x and y a r e d e r i v e d i n t u i t i v e l y and the c h a r a c t e r d e f o r m a t i o n t r a n s f o r m a t i o n h used i s a l s o T d e r i v e d h e u r i s t i c a l l y w i t h o u t any d e t a i l c o n s i d e r a t i o n on the s e v e r i t y of each d e f o r m a t i o n w i t h r e s p e c t t o i t s r e c o g n i t i o n . That i s , t h e way each t y p e of d e f o r m a t i o n a f f e c t s t h e r e c o g n i t i o n of the c h a r a c t e r . F u r t h e r more, the w e i g h t e d d i s t a n c e measure i s p o o r l y u t i l i z e d when w1 and w2 a r e taken as 1. These parameters s h o u l d be c a r e f u l l y o b t a i n e d u s i n g a r e l i a b l e s e t of sample c h a r a c t e r s i n the d e s i g n of a p r a c t i c a l c h a r a c t e r r e c o g n i z e r . T a k i n g t h e s e f a c t o r s i n t o c o n s i d e r a t i o n , the r e c o g n i t i o n r a t e of 91.46% i s ind e e d h i g h 3 and i t s u f f i c e s i n c o n f i r m i n g the m e r i t of t h i s d e s i g n approach t o u n c o n s t r a i n e d h a n d p r i n t e d a l p h a n u m e r i c c h a r a c t e r r e c o g n i t i o n . 3Compared t o Munson's e x p e r i m e n t a l r e s u l t of 85% [ 3 ] , o b t a i n e d by u s i n g edge masks t o d e t e c t shape f e a t u r e s and c l a s s i f i e d on the b a s i s of the r e s u l t a n t f e a t u r e v e c t o r s o b t a i n e d . 101 T a b l e IV. Table showing the number of t o p o l o g i e s f o r each image i n a g i v e n p r e c l a s s i f i e d group and the d i c t i o n a r y s i z e of each group. GROUP CHARACTERS T C . TD. I 0(1 1 0 II 0(1 >,B(2) ) , G ( 1 ) , 0 ( 1 ) , P ( 1 ) , Q ( 1 ) , S ( 1 ) 2 3 III D(1 6 1 1 IV Q(1 1 0 V Q(1 1 0 VI B(1 1 0 VII B( 1 ) , 0 (1 ) ,Q(1 ) 3 7 IIX B( 1 0(1 ) ,C(1 ) , D ( 1 ) , G ( 1 ) , J ( 1 ) , L ( 1 ) , M ( 1 ) ,N( 1 ) ) , P ( 1 ) , R ( 1 ) , S ( 1 ) , U ( 1 ) , V ( 1 ) , W ( 1 ) , Z ( 1 ) 16 32 IX R(1 1 0 X Q(1 1 0 XI P(1 ) ,Q(2 ) ,R(2 ) 3 8 XII A(1 ) , B ( 1 ) ,D ( 1 ) , G ( 1 ) , P ( 1 ) , Q ( 1 ) , R ( 1 ) , J ( 1 ) 8 24 XIII B(1 1 0 XIV B(1 J(1 T(1 ) , C ( 1 ) ,D ( 1 ) , E ( 1 ) , F ( 1 ) , G ( 1 ) , H ( 1 ) , 1 ( 1 ) ) , L ( 1 ) ,M ( 1 ) , N ( 1 ) , P ( 1 ) , Q ( 1 ) , R ( 1 ) , S ( 1 ) ) , U ( l ) , V ( l ) , W ( l ) , y ( l ) , Z ( l ) 22 58 XV A(1 1 0 XVI A(1 ) , B ( 1 ) , G ( 1 ) , Q ( 1 ) , R ( 1 ) ) , J ( 1 ) , T ( 1 ) 5 8 XVII G(1 3 3 XIIX Q d ) ,X(1) 2 2 XIX K(1 1 0 XX K(1 ) ,X(1) 2 7 XXI B(1 M(1 ) , E ( 1 ) , F ( l ) , G ( l ) , H ( l ) , I ( 1 ) , J ( 1 ) , K ( 1 ) ) , N ( 1 ) , P ( 1 ) , R ( 1 ) , T ( 1 ) , W ( 1 ) , X ( 1 ) , Z ( 1 ) 16 52 XXII A(1 1 0 XXIII A(1 1 0 XXIV H(1 1 0 XXV A(1 ) , E ( 1 ) , H ( 1 ) , M ( 1 ) , N ( 1 ) , W ( 1 ) , X ( 1 ) , Z ( 1 ) e 16 R e m a r k s : T C » T o t a l n u m b e r o f d i f f e r e n t c h a r a c t e r s i n t h e g r o u p . T D • T o t a l n u m b e r o f r e f e r e n c e c h a r a c t e r s f o r t h e g r o u p . N u m b e r o f t o p o l o g i e s o b s e r v e d f o r e a c h c h a r a c t e r i s g i v e n i n b r a c k e t s b e s i d e e a c h c h a r a c t e r . T a b l e V. Table of r e c o g n i t i o n r a t e s f o r d i f f e r e n t c h a r a c t e r s . A - 93.75% F - 96.88% K - 90 .91% P - 96.83% u - 77.27% Z - 90.16% B - 90.57% G - 88 .10% L - 94.44% Q - BB.09% V - 80.00% c - 95.24% H - 92.31% M - 84.21% R - 92.59% W - 92 .10% D - 92.31% 1 - 93.75% N - 87.72% s - 95.65% X - 90 .91% E - 93 .10% J - 90 .91% 0 - 90.00% T - 97.37% y - 89.33% cha * n Digi t ized Input Image 1>-V Preprocessor and SegmentatIon i i B1 nary Input Image Global feature detect and Image E x t rac t(on digraph Th inn i ng Prun1ng Preclass-if teat Ion ARG Trans-forms t t on. Pruning Parameter ARG ARG Matching. 0 ictlonary setup Group Diet ionarles Control Block 1 Variable weights deformat ton threshoIds Ex ternaI inputs U n i d e n t i f i a b l e character Character i d e n t i t y F i g . 4.3 Bl o c k diagram showing the f i n a l i m p l e m e n t a t i o n of the r e c o g n i z e r and p o t e n t i a l f u t u r e developments. o 1 03 i i i i l i i i i i i i i i 1 i i i P < D ) H I H ) D ( O ) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 ( D ) t 1 1 1 1 1 1 1 1 1 1 1 U ( V ) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 K ( I ) F i g . 4.4 Examples of some c h a r a c t e r s t h a t were m i s r e c o g n i z e d . Remarks: The i n c o r r e c t i d e n t i f i c a t i o n of each c h a r a c t e r i s g i v e n i n b r a c k e t s . 104 A B C D E F 6 H 1 J K L M N 0 p Q R s T U V w X Y z A A k £ e K r. A\ H • n R V B f) B R D B E H M 6 B 0 R S 2 C R C C E c r r C I c c C c L O 0 6 0 C 0 E p 0 D 0 D D D E B E E E F. & r I tr- li • F c r <• F A C 0 F F X F: i: c F r * /-6 B r , & G ft O P o Q S o 0 H H H H H u H H W u \l w V 1 r r i t: I. I X JL I Z J j : J < 0 a J r J 7 1 K H c p: & H C < K K w K T 1/ Y w Y L £ li i: 6 u L L L L L M n H K M N ft M Y N H H W N N V A/ V 0 • 0 c 0 n o O a 0 D a P y O P /» B C D P F P (0 0 P 0 R ? T 0 n 0 c 0 O a Q 0 0 Q 9 u \J R R R D Q H k ft N P R Q R H V V S S c S I s <>' $ s T r r T T T T L T V T -V T U o t> o u J u L U V) 0 u u u V V V C U J Y U V li \j V V Y V V w M W ~> o u V w V X K M T * K Y i 1 \ V Y V X X Y e V I 7 r > s V T V V X Y z 2 z 1 L 1s V w 1 2 F i g . 4.5 M a t r i x showing a m b i g u i t i e s and o v e r l a p s i n the shapes of c h a r a c t e r s (from [ 1 3 ] ) . 105 CHAPTER V CONCLUSION AND FUTURE DEVELOPMENTS. In t h i s t h e s i s , the d e s i g n of a c h a r a c t e r r e c o g n i z e r f o r u n c o n s t r a i n e d h a n d p r i n t e d alphanumeric c h a r a c t e r s i s p r e s e n t e d . The r e s u l t a n t r e c o g n i z e r as g i v e n i n the b l o c k diagram of f i g u r e 4.3 e x h i b i t s the f o l l o w i n g c h a r a c t e r i s t i c s : E f f i c i e n t d a t a r e d u c t i o n by t h i n n i n g . The t h i n n i n g p r o c e d u r e r e s u l t s i n images w i t h w e l l p r e s e r v e d shapes and c o n t a i n f e a t u r e s e s s e n t i a l f o r a g r a p h i c a l r e p r e s e n t a t i o n of the images, a c o n v e n i e n t form f o r r i g o r o u s a n a l y s i s by d i g i t a l computers. E f f e c t i v e image e x t r a c t i o n and p r e c l a s s i f i c a t i o n based on image t o p o l o g y . T h i s p r e c l a s s i f i c a t i o n s t a g e a c h i e v e d two i m p o r t a n t r e s u l t s t h a t have e l u d e d o t h e r d e s i g n s ; ( i ) I t p r o v i d e s an e f f e c t i v e method f o r h a n d l i n g the wide range of e l a s t i c d e f o r m a t i o n s t h a t e x i s t i n c h a r a c t e r images and p e r m i t s the t o p o l o g y and geometry of the images t o be examined more e f f e c t i v e l y i n s e p a r a t e p r o c e d u r e s w i t h o u t i n t e r f e r e n c e . ( i i ) I t r e s u l t s i n a s u b s t a n t i a l r e d u c t i o n of the e n t r o p y of the i n p u t image and p r o v i d e s t h e n e c e s s a r y c o n d i t i o n s t h a t a r e e s s e n t i a l t o the d e s i g n of h i g h speed r e c o g n i t i o n a l g o r i t h m s . Use of ARG graph d e s c r i p t i o n t e c h n i q u e s i n c r e a s e s the d e s c r i p t i v e c a p a b i l i t y of the a l g o r i t h m s and e n a b l e s more complex shapes t o be p r o c e s s e d by the d i g i t a l computer. 1 E f f i c i e n t and f a s t matching t e c h n i q u e s f o r t o p o l o g i c a l l y e q u i v a l e n t graphs. Use of s i m p l e a r i t h m e t i c and l o g i c e x p r e s s i o n s f o r image p r o c e s s i n g t h a t can be implemented a t h i g h speed u s i n g V L S I . These a r e some of the c h a r a c t e r i s t i c s t h a t were demonstrated i n the c o u r s e of the d e s i g n and i n the l a s t c h a p t e r w i t h Munson's d a t a . In f a c t the d e s i g n e d r e c o g n i z e r has f a r more p o t e n t i a l than t h a t r e a l i z e d so f a r . The f u l l p o t e n t i a l of t h i s r e c o g n i z e r can o n l y be brought out through f u r t h e r r e s e a r c h i n t o the s p e c i f i c t y p e s of images t h a t a r e be r e c o g n i z e d so t h a t the o p t i m a l c h o i c e can be made f o r the l o c a l f e a t u r e a t t r i b u t e s , d e f o r m a t i o n t r a n s f o r m a t i o n s and w e i g h t s . T h i s p o i n t can b e s t be i l l u s t r a t e d by a d i s c u s s i o n on the p o t e n t i a l s f o r f u t u r e developments t h a t can be seen as a n a t u r a l e x t e n s i o n of t h i s d e s i g n . These a r e a s of developments a r e c h a r a c t e r segmentation and c o n t e x t u a l p r o c e s s i n g . A r e l i a b l e s e g m e n t a t i o n p r o c e d u r e w i l l have t o be a c l o s e d - l o o p p r o c e s s where the r e s u l t of each segmentation attempt can be f e d back and used t o improve the a c c u r a c y of the next a t t e m p t . T h i s i s the b a s i c r e q u i r e m e n t of r e c u r s i v e s e g m e n t a t i o n . In the d e s i g n e d r e c o g n i z e r , the i n f o r m a t i o n f o r feedback i s a v a i l a b l e from two s o u r c e s , the p r e c l a s s i f i e r and t h e o u t p u t from ARG matching ( f i n a l c l a s s i f i e r ) . S i n c e the most time consuming p r o c e s s i s t h e f i n a l c l a s s i f i e r , an i n p u t t h a t does not meet the t o p o l o g i c a l r e q u i r e m e n t s of known c h a r a c t e r s does not have t o go t h r o u g h the matching p r o c e d u r e . B e s i d e s t h i n n i n g and p r e c l a s s i f i c a t i o n can be performed a t h i g h speed w i t h the a i d of hardware, so t h i s d e s i g n w i l l u n d o u b t e d l y be a s u i t a b l e c h o i c e f o r use i n r e a d i n g machines t h a t u t i l i z e s r e c u r s i v e s e g m e n t a t i o n . The use of c o n t e x t i n p a t t e r n r e c o g n i t i o n can occur a t many d i f f e r e n t l e v e l s [ 2 6 ] , In s i n g l e c h a r a c t e r r e c o g n i t i o n the main use of c o n t e x t u a l i n f o r m a t i o n w i l l be t o t a c k l e the problem of d i s a m b i g u a t i o n and e r r o r c o r r e c t i o n . As mentioned p r e v i o u s l y , c o n t e x t u a l i n f o r m a t i o n can be o b t a i n e d and e x p r e s s e d e f f e c t i v e l y by s t a t i s t i c a l means. The use of ARG d e s c r i p t i o n f o r c h a r a c t e r images i n the d e s i g n a l l o w s one t o combine the s t a t i s t i c a l and s y n t a c t i c t e c h n i q u e s . For example, d e f o r m a t i o n of a p a r t i c u l a r f e a t u r e v e c t o r component (say c u r v a t u r e or l e n g t h ) may a f f e c t the r e c o g n i t i o n of some c h a r a c t e r s more than o t h e r s . T h i s d i f f e r e n c e i n s e n s i t i v i t y t o s p e c i f i c d e f o r m a t i o n s can be t a k e n i n t o c o n s i d e r a t i o n i n the d e s i g n by i n t r o d u c i n g w e i g h t s t o i n d i v i d u a l f e a t u r e v e c t o r components i n a d d i t i o n t o t h e node and branch w e i g h t i n g s . These w e i g h t s can be changed under program c o n t r o l so t h a t d i f f e r e n t w e i g h t s a r e used when an i n p u t i s matched w i t h d i f f e r e n t r e f e r e n c e c h a r a c t e r s . S i m i l a r l y , c o n t e x t u a l i n f o r m a t i o n can be used t o improve the r e c o g n i t i o n r a t e of a m biguously shaped c h a r a c t e r s . T h i s can be a c c o m p l i s h e d u s i n g dynamic w e i g h t s t o b i a s the d e f o r m a t i o n d i s t a n c e when matching w i t h d i f f e r e n t r e f e r e n c e c h a r a c t e r s . 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