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Colour manipulation of digital images Palmer, Patricia Jane Carmel 1982

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C.I COLOUR MANIPULATION OF DIGITAL IMAGES by PATRICIA JANE CARMEL PALMER B . S c , 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 , 1979 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Department of Computer S c i e n c e ) / We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d . THE UNIVERSITY OF BRITISH COLUMBIA A u g u s t , 1982 (c ) P a t r i c i a J a ne C a r m e l P a l m e r , 1982 I n 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 o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e 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 a n d s t u d y . I f u r t h e r a g r e e 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 o f 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 t h e h e a d o f my d e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f 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 n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f Computer Science The U n i v e r s i t y o f B r i t i s h C o l u m b i a 1956 Main Mall V a n c o u v e r , Canada V6T 1Y3 D a t e ^ k u u * ^ / : /r.  DE -6 (3/81) i i C u r r e n t l y , s t a n d a r d enhancement o f t h r e e - c h a n n e l c o l o u r d i g i t a l imagery i s n o t p e r f o r m e d i n a g e n e r a l f a s h i o n ; i t i s d e p e n d e n t on t h e p a r t i c u l a r c o l o u r d e v i c e u s e d t o d i s p l a y t h e i m a g e r y . By i n t r o d u c i n g a c o l o u r t r a n s f o r m a t i o n , t h e enhancement c a n be s t a n d a r d i z e d a n d t h e r e f o r e be d e f i n e d i n t e r m s o f o t h e r d e v i c e s . In a d d i t i o n , t h e c o l o u r t r a n s f o r m a t i o n can be d e f i n e d s u c h t h a t t h e p e r c e p t u a l a t t r i b u t e s o f c o l o u r a s s o c i a t e d w i t h an image a r e more e a s i l y m a n i p u l a t e d . The p u r p o s e o f t h i s work i s t o examine a v a r i e t y of s u c h c o l o u r t r a n s f o r m a t i o n s and implement a s u b s e t o f t h e s e on a c o l o u r CRT. Table of Contents 1. Introduction 1 2. Motivation for Colour Manipulation 3 3. Colour Science 8 3.1 Theoretical Development 8 3.2 Human Colour Matching 11 3.3 Grassman's Laws 12 3.4 Colour Spaces 13 CIE XYZ 14 CIE UVW 21 Dominant Wavelength, Purity & Luminance ... 23 NTSC YIQ 25 Other Examples 28 4. Implementation 36 4.1 Display Device 36 4.2 CIE XYZ 43 4.3 CIE UVW 47 4.4 Dominant Wavelength, Purity & Luminance 47 4.5 NTSC YIQ 49 4.6 Implementation Structure 50 5. Results 52 6. Conclusion 65 Bibliography 70 iv L i s t of Figures 1. Flow Diagram of Enhancement Technique 7 2. S e n s i t i v i t y of Rods and Cones 9 3. S e n s i t i v i t y of Three Pigments 10 4. Tristimulus Values for Equal Energy White 16 5. XYZ Coordinate System 18 6. (x,y) Chromaticity Diagram 18 7. Spectral Locus and Purple Line 20 8. Perceptual Differences on (x,y) Diagram 22 9. Perceptual Differences on (u,v) Diagram 24 10. D e f i n i t i o n of Dominant Wavelength and Purity 26 11. Munsell Colour System 29 12. Gamut of Inks and Dyes 29 13. Red-Green-Blue Colour Space 31 14. Cyan-Magenta-Yellow Colour Space 31 15. Chromaticity Gamuts on the (u,v) Diagram 38 16. Chromaticity Gamuts on the (x,y) Diagram 39 17. RGB Monitor Chromaticity Coordinates 41 18. Reference White Chromaticity Coordinates 41 19. Equidistant D i s t r i b u t i o n on the (x,y) Chromaticity Diagram 53 20. Equidistant D i s t r i b u t i o n on the (u,v) Chromaticity Diagram 54 21. Increasing Luminance with Constant Purity and Dominant Wavelength 56 22. Increased Purity with Constant Luminance and Dominant Wavelength 58 23. YIQ Axis Recombination 59 24. Portion of Landsat Image 61 25. Luminance Enhancement 62 26. Graduated Increase in Purity 63 27. Purity Enhancement 64 v i Acknowledgement I am grateful to my supervisor, Dr. R. J . Woodham, for his helpful suggestions and c r i t i c i s m s , as well as his f i n a n c i a l support. I also thank Dr. A. K. Mackworth for reviewing the work. 1 1. Introduction Multispectral d i g i t a l images are finding increasingly widespread use. Applications arise in many areas including forestry, agriculture, geology, oceanography, meteorology and planetary exploration. Once multispectral data i s acquired, i t i s t y p i c a l l y corrected for known or assumed radiometric and geometric d i s t o r t i o n s . The resulting image can be reproduced in hardcopy form or shown on a colour d i g i t a l image display system. A variety of d i g i t a l image processing techniques have been developed to accentuate p a r t i c u l a r features in an image and to better u t i l i z e the output medium in the hope that relevant information can be made more d i s t i n c t . These are known as image enhancement techniques. Currently, standard enhancement of three-channel colour d i g i t a l imagery i s not performed in a general fashion; i t i s dependent on the p a r t i c u l a r colour device used to display the imagery. By introducing a colour transformation, the enhancement can be standardized and therefore be defined in terms of other devices. In addition, the colour transformation can be defined such that the perceptual attributes of colour associated with an image are more eas i l y manipulated. The purpose of t h i s work i s to examine a variety of such colour transformations and implement a subset of these on a p a r t i c u l a r device: a colour CRT. Before describing the d e t a i l s and r e s u l t s of the work 2 (Chapters 4 and 5 respectively), motivation for the work and colour science background w i l l be presented (Chapters 2 and 3 respectively). Problems associated with the implementation of the technique are discussed in the conclusion (Chapter 6 ) . 3 2. M o t i v a t i o n f o r C o l o u r M a n i p u l a t i o n Human c o l o u r v i s i o n r e s p o n d s t o t h r e e u n d e r l y i n g c o l o u r d i m e n s i o n s of t h e s t i m u l u s . The maximum number of d a t a c h a n n e l s w h i c h c a n be v i s u a l l y i n t e r p r e t e d ( s i m u l t a n e o u s l y ) on t h e b a s i s of c o l o u r , i s t h e r e f o r e l i m i t e d t o t h r e e . C o l o u r image d i s p l a y d e v i c e s a r e g e n e r a l l y l i m i t e d t o t h r e e c h a n n e l s ; b l a c k and w h i t e d i s p l a y d e v i c e s a r e l i m i t e d t o one c h a n n e l . M u l t i s p e c t r a l s c a n n e r s c a n r e t u r n e l e v e n ( o r more) c h a n n e l s o f d a t a . C o n s e q u e n t l y , t h e r e i s o f t e n a need f o r c h a n n e l r e d u c t i o n . P r i n c i p a l component a n a l y s i s and r a t i o i n g a r e examples of s u c h r e d u c t i o n t e c h n i q u e s (see [DONKE76], [ S A B I N 7 8 ] ) . On t h e o t h e r hand, i f t h r e e d a t a c h a n n e l s a r e not a v a i l a b l e , i t may be a d v a n t a g e o u s t o p r o d u c e a d d i t i o n a l d a t a c h a n n e l s i n o r d e r t o b e t t e r u t i l i z e t h e c a p a c i t y o f human c o l o u r v i s i o n . P s e u d o - c o l o u r i n g i s s u c h a t e c h n i q u e ; i t i s m o t i v a t e d by t h e f a c t t h a t t h e eye c a n d i s t i n g u i s h many more c o l o u r s t h a n s h a d e s o f g r a y . By i n c r e a s i n g or d e c r e a s i n g t h e number o f d a t a c h a n n e l s , t h e s e enhancement t e c h n i q u e s a t t e m p t t o b e t t e r u t i l i z e t h e o u t p u t medium o r t h e human v i s u a l s y s t e m . The m o t i v a t i o n f o r t h i s work i s t h e enhancement o f t h r e e - c h a n n e l c o l o u r i m a g e r y , w i t h o u t i n c r e a s i n g o r d e c r e a s i n g t h e number o f c h a n n e l s . The i n p u t may a r i s e f r o m a v a r i e t y o f s o u r c e s . Examples i n c l u d e : t h r e e c h a n n e l s f r o m a m u l t i s p e c t r a l s c a n n e r , t h r e e c h a n n e l s from a c o l o u r v i d i c o n (TV) c a mera, p h o t o g r a p h i c d e n s i t i e s o f 4 three dye layers of a colour f i l m , three channels resulting from data compression, and combinations of multispectral, multitemporal and multisensor data. Many enhancement techniques which input and output a single channel of data ( i . e . , black and white images) have been developed. Gray-level enhancements, achieved by re d i s t r i b u t i o n of intensity values are an example of thi s technique. They are simple and e f f e c t i v e . Their use i s widespread. Different r e d i s t r i b u t i o n s have been implemented and found to have pa r t i c u l a r e f f e c t s : a uniform r e d i s t r i b u t i o n achieves greatest enhancement in areas where most frequently occurring p i x e l values are found, Gaussian r e d i s t r i b u t i o n emphasizes the t a i l s of the pi x e l value histogram (see [LILLE79] and [SABIN78]). A variety of other p o s s i b i l i t i e s for single-channel enhancement techniques e x i s t . Mathematically, a gray-level r e d i s t r i b u t i o n can be characterized as follows: C*(x,y) = f[ C(x,y) ] (1) The value of the pi x e l at location (x,y) in the new channel ( C ) i s dependent only on the pixe l value at that same location (x,y) in the o r i g i n a l channel (C). This equation describes only a limited class of single-channel enhancements. Extended to colour, these enhancements can be mathematically characterized as follows: 5 C r ' ( x , y ) = f r [ C r ( x , y ) , C g ( x , y ) , C b ( x , y ) ] C g ' ( x , y ) = f g [ C r ( x , y ) , C g ( x , y ) , C b ( x , y ) ] ( 2 ) C b ' ( x , y ) = f b [ C r ( x , y ) , C g ( x , y ) , C b ( x , y ) ] I n t h i s c a s e , t h e p i x e l v a l u e a t l o c a t i o n ( x , y ) i n e a c h new c h a n n e l ( C r ' , C g ' , C b ' ) i s d e p e n d e n t on t h e p i x e l v a l u e s a t t h a t same l o c a t i o n i n ( p o s s i b l y ) a l l t h r e e o r i g i n a l c h a n n e l s ( C r , C g , C b ) . E n h a n c e m e n t o f c o l o u r e d i m a g e s i s g e n e r a l l y a c c o m p l i s h e d by s e p a r a t e l y a p p l y i n g r e d i s t r i b u t i o n t e c h n i q u e s t o e a c h o f t h e t h r e e i n p u t c h a n n e l s . S u c h e n h a n c e m e n t s c a n be c h a r a c t e r i z e d a s f o l l o w s : C r ' ( x , y ) = f r [ C r ( x , y ) ] C g ' ( x , y ) = f g [ C g ( x , y ) ] ( 3 ) C b ' ( x , y ) = f b [ C b ( x , y ) ] T h i s i s a n e n h a n c e m e n t o f t h e RGB s p a c e o f t h e p a r t i c u l a r d i s p l a y d e v i c e . S u c h a t e c h n i q u e c a n n o t be c o n s i d e r e d a g e n e r a l c o l o u r r e d i s t r i b u t i o n b u t o n l y a s p e c i a l c a s e o f e q u a t i o n ( 2 ) . T h e r e a r e two m a j o r d i s a d v a n t a g e s i n a p p l y i n g e n h a n c e m e n t t e c h n i q u e s d i r e c t l y t o a s e t o f R , G , B a x e s . F i r s t , t h e c o l o u r s d e f i n e d a s R , G , a n d B v a r y f r o m d e v i c e t o d e v i c e a n d t h u s t h e e n h a n c e m e n t t e c h n i q u e s d e s c r i b e d by e q u a t i o n (3 ) a r e d e v i c e - d e p e n d e n t . A l t h o u g h t h e RGB s p a c e o f a d i s p l a y d e v i c e may be s i m p l e t o wo rk w i t h , i t i s n o n s t a n d a r d . S e c o n d , humans do n o t p e r c e i v e c o l o u r s d i r e c t l y i n t e r m s o f t h e a m o u n t s o f p a r t i c u l a r c o l o u r s o f w h i c h t h e y a r e c o m p o s e d ( i . e . , t h o s e c o r r e s p o n d i n g t o t h e 6 R, G and B axes). No matter how a colour image i s produced, through photographic, electronic or other means, i t s colour- can be perceived by a human observer only in terms of the human colour v i s u a l parameters: hue, saturation and brightness. Hue i s that attribute of colour perception which allows c l a s s i f i c a t i o n as red, orange, yellow, etc. Saturation i s that attribute of colour perception which allows c l a s s i f i c a t i o n from pastel through intense. Brightness i s that a t t r i b u t e of colour perception which allows c l a s s i f i c a t i o n as equivalent to white, l i g h t gray, through black. Therefore, standardized colour spaces based on perceptual attributes seem more appropriate. A more general method of enhancing colour d i g i t a l imagery would be to transform the image into a new space with these desired properties and perform the r e d i s t r i b u t i o n in t h i s new space. Transformation back to the o r i g i n a l space would be required in order to display the enhanced image. A flow diagram of this operation is given below (figure 1). Note however, that the enhancement described i s not a complete generalization of equation (2), since each new channel i s enhanced independently of the other. The technique could be completely generalized by performing some type of three-dimensional r e d i s t r i b u t i o n in the new space. 7 R Colour Inverse R G -> Transform -> Enhancement -> Colour -> G B Transform B Figure 1. Flow Diagram of Enhancement Technique. The o r i g i n a l and f i n a l axes (R, G, and B) are a r b i t r a r y . They are motivated by p r a c t i c a l considerations r e l a t i n g to the output medium (for example the phosphors of a CRT or the dye layers of colour f i l m ) . They need not correspond to the colours perceived as red, green and blue. In the case of colour f i l m , for example, they might correspond to cyan, magenta and yellow. One goal of t h i s work i s to investigate standard methods of defining colour so that colour operations can be performed more consistently on d i f f e r e n t colour devices. Although such devices w i l l generally produce d i f f e r e n t colour gamuts, d e f i n i t i o n of the union and intersection of their gamuts should provide for a method of dealing with t h i s problem. A second goal i s to examine alternate colour spaces which are more d i r e c t l y related to the human colour v i s u a l parameters than the RGB space. Some such colour spaces w i l l be implemented in order to determine whether they display the perceptual q u a l i t i e s that the space was designed to capture, and hence whether they are suitable for such enhancement techniques. 8 3. Colour Science Colour allows the observer to distinguish objects due to the spectral composition of their radiant energy independent of their s i z e , shape and structure. Colour perception i s an att r i b u t e of b i o l o g i c a l v i s i o n systems. Consequently, any computer-based system which attempts to describe and distinguish colours as people do must ultimately rely on a model of human colour perception. Therefore, relevant properties of human colour v i s i o n w i l l be surveyed to provide a basis for a description of colour s p e c i f i c a t i o n schemes which follows. 3.1 Theoretical Development Human vision i s dependent on the electromagnetic energy entering the eye. Two types of c e l l s in the eye are l i g h t - s e n s i t i v e : rods and cones. They are sensitive to the limited region of the electromagnetic spectrum (from 400 to 700 nanometers) known as the v i s i b l e region. The response curves of these c e l l s within the v i s i b l e region are simi l a r , although that of the rods is shifted s l i g h t l y towards the shorter wavelengths (see figure 2). At low l i g h t l e v e l s , bleaching of a photo-pigment within the rod c e l l s occurs. This bleaching does not provide for the sensation of colour. At higher l i g h t l e v e l s , the cones respond. Cones provide for colour v i s i o n . Three photo-sensitive pigments with peak absorptions in diff e r e n t 9 blue WAVELENGTH (nm.) Figure 2. S e n s i t i v i t y of Rods and Cones The s o l i d curve represents daylight v i s i o n (cones). The dashed curve represents night v i s i o n (rods) and i l l u s t r a t e s the s h i f t toward the blue spectrum when the eye i s adapted to low luminance conditions. These are known respectively as the photopic and scotopic luminosity curves and are used when radiant power i s converted to luminous power. (from [ J U D D 7 7 ] ) . 10 Figure 3. S e n s i t i v i t y of Three Pigments The three cone pigments have peak absorptions in the 445 (a), 540 (b) and 570 (c) nanometer region. The sum of these responses give the photopic luminosity curve (see s o l i d curve in figure 2). Note the overlap in the three curves (from [PRITC77]). 11 regions of the v i s i b l e spectrum have been found within the cones (see figure 3). Notice that the response curves of these pigments overlap s u b s t a n t i a l l y . It i s not understood how such responses produce the subjective sensation of colour. However, many theories of colour perception have been proposed. 3.2 Human Colour Matching The colour matching c a p a b i l i t i e s of an individual can be determined using a set of three monochromatic l i g h t s in the red, green and blue regions of the v i s i b l e spectrum. Two patches are viewed: a patch formed by a mixture of the three coloured l i g h t s each of which is controlled by the i n d i v i d u a l , and a test patch. A "match" i s obtained when the individual can no longer distinguish between the two patches. It has been found that an individual with normal colour v i s i o n can match almost any test patch by adjusting the quantities of the three coloured l i g h t s . I f , in addition, the individual i s allowed to add l i g h t s (from the three) to the test patch, a match can always be obtained. This phenomenon is c a l l e d tri-chromatic colour matching and can be explained in terms of the three photo-sensitive pigments in the cones of the r e t i n a . If colours are analyzed solely by these three receptors, any d i s t r i b u t i o n of l i g h t which e l i c i t s the same response as that of a sample from each of the three 12 receptors w i l l be perceived as the same colour. Thus samples with widely d i f f e r e n t spectral d i s t r i b u t i o n s may appear the same colour. This explains why most test patches can be matched by simple addition of the three l i g h t s . However, i t does not explain why certain colours cannot be matched unless l i g h t s are added to the test patch. This can be explained by the overlap in s e n s i t i v i t y of the three photo-sensitive pigments (see figure 3). The receptors cannot be i n d i v i d u a l l y stimulated. Therefore, no matter what choice of coloured l i g h t s , there always exist c e r t a i n responses which cannot be produced. Addition of coloured l i g h t to the test patch can be viewed as canceling out the unwanted response, thus producing the desired response. Addition of l i g h t to the test patch i s therefore considered a subtraction from the mixture of coloured l i g h t s , even though such a process i s not physically possible. The tri-chromatic theory of colour matching appears to f i t well with the known physiology of the eye. 3.3 Grassman's Laws Pri n c i p l e s which describe the colour matching c a p a b i l i t i e s of a human observer with normal colour v i s i o n are well known. They were determined experimentally by Herman Grassman in 1854. In summary: 13 1. The eye distinguishes hue, saturation and brightness. (Hue, saturation and brightness are perceptual terms. Dominant wavelength, purity and luminance are the corresponding psychophysical terms which can be quant i t a t i v e l y measured.) 2. The luminance (Y) of a colour mixture equals the sum of the individual colour luminance values: Yt = Y1 + Y2 + Y3 + ... . 3. Suppose A, B, C-and D are colours. If A = B, C = D then A + C = B + D. If A = B + C then B = A - C. If A = B, B = C then A = C. [PRITC77] 3.4 Colour Spaces Grassman's laws state that three independent quantities are necessary and s u f f i c i e n t to specify colour and that colour quantities add l i n e a r l y . Therefore, i t i s convenient to represent colour as a three-dimensional vector space. In such a space, a p a r t i c u l a r colour i s represented as the coefficents of the linear sum of three basis vectors. Many such colour spaces have been developed. Generally, these f a l l into one of two categories. The coordinate axes of the f i r s t type consist of the intensity of three colours. Any three colours may be chosen provided none can be matched by a mixture of the 1 4 other two. Such colours are known as primaries. Colour t e l e v i s i o n displays rely on t h i s type of system; the three phosphors determine the set of primaries. The second type of coordinate system i s more cl o s e l y related to perceptual quantities. It consists of a brightness axis and two chrominance axes. Various colour atlases rely on t h i s type of colour space. However, any set of axes may be chosen provided they are independent. CIE XYZ In an attempt to standardize colour d e f i n i t i o n and measurement, the Commission Internationale de l'Eclairage (CIE) introduced, in 1931, a colour system based on a standard (or average) observer and three reference s t i m u l i . Once matching functions for the standard observer were determined experimentally, the set of reference stimuli was chosen. There were two main considerations in the choice of the primaries. F i r s t , i t was desired that a l l colours be reproducible by an additive combination of the primaries. Such real primaries, as mentioned e a r l i e r , do not e x i s t . Experiments have shown that there are always colours which cannot be produced by the mixture of three coloured l i g h t s . Second, i t was desired that luminance (brightness) be easily s p e c i f i e d . Non-physical primaries known as X, Y and Z were chosen 15 to s a t i s f y these constraints. Only positive amounts of X, Y and Z are required to reproduce a l l colours. Hence, the primaries are non-physical or imaginary. The X, Y and Z tristimulus values for the standard observer and an equal-energy white stimulus are shown in figure 4. (An equal-energy stimulus i s one for which the rate of energy emitted per unit wavelength i s equal throughout the v i s i b l e spectrum, [CONRA80].) The values of the colour matching functions (x(x), y(x), z(x.)) at a p a r t i c u l a r wavelength y i e l d the amount of the X, Y and Z primaries required to produce the spectrum colour corresponding to that wavelength. Y represents luminance; the y(X.) colour matching function i s the photopic luminosity curve. The tristimulus values required to match a sample may be found by integrating the spectral' energy d i s t r i b u t i o n of the sample (E(x.)) with the colour matching functions (refer to equation 4). For self-luminous samples, the spectral energy d i s t r i b u t i o n i s defined by the source i t s e l f . For transparent or opaque objects the spectral energy d i s t r i b u t i o n i s related to the spectral transmittance or reflectance and the radiant energy incident on the object. The non-physical primaries, X, Y and Z, form the coordinate axes of the CIE XYZ colour space. A p a r t i c u l a r (4) 16 t o < > ZD _ l 13 cc A i T - -// / / — • WAVELENGTH (nm.) Figure 4. Tristimulus Values for Equal Energy White The values are expressed in terms of the CIE 1931 standard observer and the XYZ primaries. Note that the y(X.) colour matching function i s the photopic luminosity curve (from [NEAL73]). 17 colour i s represented as the sum of three vectors, one in each of the X, Y and Z d i r e c t i o n s , with magnitudes proportional to the corresponding tristimulus values (see figure 5). The chromaticity coordinates (x,y,z) are defined as the r e l a t i v e amounts of each of the primaries (the r a t i o of the appropriate tristimulus value and the sum of the tristimulus values): x = X X + Y + Z y = Y (5) X + Y + Z Z = Z X + Y + Z (X,Y,Z) are t r i s t i m u l u s values; (x,y,z) are chromaticity coordinates. (Although there are only two degrees, of freedom to the chromaticity coordinates, i t i s convenient to include the t h i r d equation for later calculations.) Projection of the unit plane (X+Y+Z=1) on the XY plane y i e l d s the (x,y) chromaticity diagram (see figure 6). The set of colours produced by monochromatic stimuli from the v i s i b l e region and mixtures of monochromatic stimuli from two endpoints of this region form a cone which bounds the re a l colours. Those colours which l i e outside the cone are referred to as imaginary. The X, Y and Z primaries are examples of such imaginary colours; they f a l l outside t h i s cone. It i s s u f f i c i e n t , however, to consider the chromaticity point of a colour to determine i f i t i s r e a l . Projection of monochromatic stimuli from the v i s i b l e 18 c = (Xc.Y c .Z c) Figure 5. XYZ Coordinate System An arb i t r a r y colour C i s defined as a sum of three vectors, (Xc,Yc,Zc), each in the d i r e c t i o n of one of primaries. Figure 6. (x,y) Chromaticity Diagram The (x,y) chromaticity diagram i s formed by the projection of the unit plane in XYZ tristimulus space onto the XY plane. Therefore, the intersection I of an a r b i t r a r y colour C with the unit plane, i s projected back onto the XY plane to form the (x,y) chromaticity coordinates. 19 region onto the chromaticity diagram y i e l d s a curved l i n e -the "spectral locus". Projection of the mixture of the monochromatic stimuli corresponding to the two ends of the v i s i b l e region onto the chromaticity diagram yi e l d s a straight l i n e - the "purple l i n e " . The spectral locus and purple l i n e are shown in figure 7. Together they form an enclosed area. If the chromaticity point of a sample f a l l s outside this area, the sample i s imaginary. If i t f a l l s within or on the boundary of t h i s area, i t i s r e a l . The entire cone f a l l s within the positive quadrant of the XYZ colour space. For real colours, therefore, the tristimulus values X, Y, Z, are always p o s i t i v e . The CIE XYZ system thus provides simple expression and manipulation of colour quantities according to the desired standards. Acceptance of the CIE 1931 standard observer and coordinate system has been extensive [JUDD75], However, some discrepancies between the tristimulus values predicted by the standard observer and those obtained by actual observers have been found. Hence, new colour matching functions were defined in 1964. These supplement the o r i g i n a l colour matching functions. For small f i e l d viewing (one to four degrees at the eye of the observer) the CIE 1931 functions are s u f f i c i e n t ; for larger viewing angles, the CIE 1964 functions are recommended. Consideration of the d i s t r i b u t i o n of perceived colours i s not included in the CIE XYZ system. Reference coordinates were chosen for ease in expressing colour 20 M r Figure 7. Spectral Locus and Purple Line CIE 1931 (x,y) chromaticity diagram showing spectral locus, purple l i n e and equal energy white stimulus E. 21 mixing information and representation of luminance. It i s not surprising, therefore, that the d i s t r i b u t i o n of perceived colours i s non-uniform on the CIE XYZ chromaticity diagram (see figure 8). Discrepancies of twenty to one have been found [WRIGH69]. A variety of schemes have been proposed to red i s t r i b u t e the perceived colours more evenly. CIE UVW The CIE UVW space i s a b i - l i n e a r transform of the CIE XYZ space which was designed to provide a perceptually more uniformly d i s t r i b u t e d chromaticity diagram. The relationship between the chromaticity coordinates i s defined as follows: u = 4x / (12y - 2x + 3) (6a) v = 6y / (I2y - 2x + 3) (6b) The colour matching function for V i s the same as that of Y. Since (u,v) and V are known, the UVW tristimulus values can be determined using the set of equations for the chromaticity coordinates (see equation 5): v/V yields the sum of the tristimulus values; substituting back into the equations for u and w yi e l d s values for U and W. Similar to the CIE XYZ system, the V stimulus represents luminance; the U and W stimulus a f f e c t only chrominance. Discrepancies between perceptual differences and physical 22 Figure 8. Perceptual Differences on (x,y) Diagram The l i n e s indicate chromaticity differences of the same degree of p e r c e p t a b i l i t y (from [JUDD75]). 23 distances on the (u,v) chromaticity diagram, in comparison to the (x,y) chromaticity diagram, are small. These differences are at most four to one and for the most part are only two to one [WRIGH69], on the (u,v) chromaticity diagram (see figure 9). Although no linear projection of the chromaticity diagram i s adequate to provide a perceptually uniform chromaticity diagram, choice of di f f e r e n t reference primaries i s c l e a r l y advantageous. Dominant Wavelength, Purity & Luminance Using the chromaticity coordinates defined by the CIE XYZ and UVW systems, dominant wavelength (the psychophysical equivalent to saturation) and purity (the psychophysical equivalent to hue) can be defined. These d e f i n i t i o n s are based on the chromaticity diagram. The dominant wavelength "S" of a colour "C" is calculated by projecting a l i n e from white "W" through C u n t i l i t intersects the spectral locus or purple l i n e (refer to figure 10). If the projection of the a r b i t r a r y colour intersects the purple l i n e rather than the spectral locus, as i s the case with C (refer to figure 10), the complementary dominant wavelength "S'c" is calculated by projecting the l i n e in the opposite d i r e c t i o n u n t i l i t intersects the spectral locus. Intersection with the spectral locus yields a wavelength value. Purity i s 24 0.4 5510 ^V. C — O O-gi J 550 5^ o ° > ^ 5 o—o o—o cPP: < f o—o o—o o-590 . ^ oi -o o—o t 1 J> •650 nm 4 9 0 \ ] I I S ) y o-o O-O O-o c < J n 460ntiv\ 1 n • 0.3 0.4 u Figure 9. Perceptual Differences on (u,v) Diagram The li n e s (representing those of figure 8) indicate chromaticity differences of the same degree of pe r c e p t a b i l i t y (from [JUDD75]). 25 represented by the r a t i o of the lengths of two vectors: the vector from W to C, "WC", divided by the dominant wavelength vector "WS" (refer to figure 1 0 ) . In the case of C , purity i s s i m i l a r l y defined as the r a t i o : WC / WS'. Using t h i s algorithm, dominant wavelength and purity can be derived from the CIE tristimulus values for either the XYZ or UVW system. (Note that luminance i s d i r e c t l y defined in both of these systems.) An alternate representation, consisting of luminance, purity and dominant wavelength, i s thus provided. This alternate representation i s more d i r e c t l y related to the parameters of human vi s u a l perception. NTSC YIQ Unlike the imaginary primaries used in the CIE systems, colour reproduction systems such as colour t e l e v i s i o n must rely on real primaries. The National Television System Committee (NTSC) defined standards for colour t e l e v i s i o n transmission signals based on a set of phosphors and an illuminant. This coordinate system consists of a luminance axis and two colour difference axes. The luminance component (equivalent to Y) i s a weighted sum of the red, green and blue signals generated by a camera at the scene. A black and white image can be 26 Figure 10. De f i n i t i o n of Dominant Wavelength and Purity This d e f i n i t i o n i s provided in terms of the (x,y) chromaticity diagram. However, the corresponding d e f i n i t i o n holds for the (u,v) chromaticity diagram, (from [CONRA80]). 27 formed d i r e c t l y from th i s component or i t can be combined with the colour difference signals to form a coloured image. It i s known that the resolving power of the eye i s better for patterns with luminance contrast rather than hue or saturation contrast, and that i t becomes harder to evaluate hue as the size of an object under consideration i s decreased in comparison to the f i e l d of view. Therefore, the luminance component i s assigned the greatest channel bandwidth of the three axes and i s transmitted in more d e t a i l . The colour difference components are formed by f i r s t subtracting the luminance component from the red and green signals. Because the resolving power of the eye for colour variations along certain axes (orange-cyan) i s better than others (purple-green), the difference axes are rotated. They l i e along the orange-cyan (I) and purple-green (Q) axes. The I component i s transmitted with greater bandwidth than the Q component to account for their r e l a t i v e importance in perception. They are calculated as follows: [k1(R-Y), k1k2(B-Y)] cos© sin© •sin© cos© = [I,QJ I = k1(R-Y)cos© - k1k2(B-Y)sin© Q = k1(R-Y)sin© + k1k2(B-Y)cos© (7) Where © = 33°; k1 = 1/1.14; k2 = 1/1.78; [BOOTH79] 28 e r o t a t e s the c o l o u r - d i f f e r e n c e axes t o the p r e f e r r e d orange-cyan, p u r p l e - g r e e n a x e s . k1 and k2 o p t i m i z e the bandwidth c o n s t r a i n t s on t h e t r a n s m i t t e d s i g n a l . Both p h y s i o l o g i c a l p r o p e r t i e s of the eye and c o d i n g c o n s t r a i n t s were i m p o r t a n t c o n s i d e r a t i o n s i n development of the NTSC YIQ system. Other Examples The c o l o u r spaces which have a l r e a d y been p r e s e n t e d were implemented f o r t h i s t h e s i s . Many o t h e r c o l o u r systems e x i s t . To p r o v i d e a b e t t e r i d e a of the c h a r a c t e r i s t i c s which a r e used i n the r e p r e s e n t a t i o n of c o l o u r , s i x more c o l o u r spaces w i l l be' b r i e f l y examined. I f a p p l i c a b l e , reasons why the spaces were not implemented a r e a l s o mentioned. 1) M u n s e l l The M u n s e l l system i s used t o e v a l u a t e r e f l e c t i v e - s u r f a c e c o l o u r . S e t s of M u n s e l l " c h i p s " ( p i e c e s of paper r e g u l a r l y v a r y i n g i n c o l o u r ) form the M u n s e l l book of c o l o u r . These c h i p s a r e compared t o the sample i n o r d e r t o f i n d the n e a r e s t match. U s i n g the c h i p , the c o l o u r sample i s s p e c i f i e d . The axes of t h i s c y l i n d r i c a l c o o r d i n a t e system a r e shown i n f i g u r e 11. They c o n s i s t of hue, chroma ( s a t u r a t i o n ) and v a l u e ( b r i g h t n e s s ) . V a l u e i s Hue Figure 11. Munsell Colour System 0.0 0.2 0.4 x Figure 12. 0.6 0.8 Gamut of Inks and Dyes (from [NEAL73]) 30 the central axis. Hue i s the angle about the central axis. Chroma is the r a d i a l distance. The Munsell system i s well-known and is used in a wide variety of applications. However, because i t i s based on r e f l e c t i v e rather than luminous samples, the relationship between an RGB monitor and the Munsell system i s d i f f i c u l t to define. The gamut of pigments, paints and dyes currently available i s much smaller than that of an RGB monitor (see figure 12). The Munsell system i s not suitable for this RGB monitor work because, in general, not a l l of the colour gamut of an RGB monitor i s defined in the Munsell space. However, i f a non-luminous display was u t i l i z e d (for example photographic p r i n t s ) , a system based on r e f l e c t i v e samples such as the Munsell system, would be appropriate. 2) Cyan-Magenta-Yellow The three "subtractive" primaries (cyan, magenta and yellow) provide an inverse to the RGB monitor space (see figures 13 and 14). These primaries are used in colour photography. Each primary forms a dye layer which subtracts either red, green or blue l i g h t (respectively); hence the term subtractive. Therefore, the amount of dye produced in a pa r t i c u l a r layer is inversely proportional to the amount of coloured l i g h t , of the associated primary, which i s allowed to pass through that layer. Transformations between the two spaces is simple (assuming that the axes are l i n e a r l y scaled between zero and one): 31 a n ' B L U E . Gf\E£N yellow b l a c k magenta. F i g u r e 13. R e d - G r e e n - B l u e C o l o u r Space - • ' R E D YELLOW MAGENTA * CYAN F i g u r e 14. C y a n - M a g e n t a - Y e l l o w C o l o u r Space 32 [ c y a n , m a g e n t a , y e l l o w ] = [1,1,1] - [ r e d , g r e e n , b l u e ] However, b e c a u s e o f t h e i r symmetry, r e d i s t r i b u t i o n o f a x e s a f t e r t r a n s f o r m a t i o n t o t h e c y a n - m a g e n t a - y e l l o w s p a c e f o l l o w e d by t r a n s f o r m a t i o n back t o t h e RGB s p a c e , y i e l d s t h e same r e s u l t as r e d i s t r i b u t i o n o f axe s i n t h e o r i g i n a l RGB s p a c e . Hence, f o r t h e enhancement t e c h n i q u e s d e v e l o p e d i n t h i s t h e s i s , t h e c y a n - m a g e n t a - y e l l o w s p a c e i s not a d v a n t a g e o u s . 3) U*V*W* U s i n g t h e UVW c o l o u r s p a c e a s a b a s i s , t h e C I E l a t e r d e f i n e d a u n i f o r m c o l o u r s o l i d i n an a t t e m p t t o p r o v i d e a s t a n d a r d method f o r d e s c r i b i n g c o l o u r d i f f e r e n c e s . The U*V*W* s y s t e m i s d e f i n e d a s f o l l o w s : U* = 13 W* (u - u') V* = 13 W* (v - v') W* = 25 V 1 / 3 > - 17 Where 1 <= v <= 100 u and v a r e t h e c h r o m a t i c i t y c o o r d i n a t e s o f t h e sample; u' and v' a r e t h e c h r o m a t i c i t y c o o r d i n a t e s o f t h e g r a y a x i s . V i s t h e l u m i n a n c e o f t h e sample. The d i f f e r e n c e between two c o l o u r s , (Au,Av,Aw) and (Bu,Bv,Bw), i s d e f i n e d as t h e i r E u c l i d e a n d i s t a n c e i n t h r e e - d i m e n s i o n a l s p a c e : ( (Au - B u ) 2 + (Av - B v ) 2 + (Aw - B w ) 2 ) V* (8) However, some a d j u s t m e n t must be made i f t h e c o l o u r s a r e w i d e l y s e p a r a t e d . Under t h e s e c o n d i t i o n s , b r i g h t n e s s i s 33 not as important in colour discrimination. Therefore, the (Aw - Bw)2 factor in equation 8 i s often weighted by a constant less than one. Colour discrimination becomes easier as the brightness of two samples i s increased. This phenomenon i s captured mathematically: U* and V* are proportional to W*. The CIE chose th i s transformation of the UVW system because of i t s s i m p l i c i t y and because there were indications that i t provided uniformity, but the system has met with only limited success [JUDD7 5]. This colour space, as well as the next two examples, attempt to provide perceptual uniformity. In a l l three cases, one axis i s based on the CIE d e f i n i t i o n of luminance and i s therefore related to brightness. The other two axes however, are not defined in terms of perceptual quantities. To examine the usefulness of these spaces would therefore require a three-dimensional operation. The form of such operations are not immediately obvious. However, the claimed attributes of these colour spaces appear to be extremely well suited to image enhancement. 4) Cube Root The cube-root colour coordinate system developed by Glasser, McKinney, R e i l l e y and Schnelle also attempts to provide perceptual uniformity [WYSZE67]. It consists of similar axes: a lightness axis (L*) and two chromaticity axes (a* and b*). It i s defined in terms of the CIE XYZ t r i s t i m u l u s values: 34 L* = 25.29G1'3 - 18.38 a* = Ka(R1/3 - G 1 / 3) b* = Kb (G 1 / 3 - B 1 / 3) Where R = 1.02X, G = Y, B = 0.847Z Ka = 106.0, Kb = 42.43 This system i s noteworthy because of i t s good approximation to the spacing provided by the Munsell system and i t s r e l a t i v e s i m p l i c i t y . The difference between two colours i s defined as t h e i r Euclidean distance in colour space. 5) Hunter The CIE TJ*V*W* and Cube Root systems attempt to provide uniform colour spaces. Another example is the Hunter system, which consists of a lightness axis (L) and two chromaticity axes (a,b). The system i s defined in terms of the CIE XYZ tristimulus values expressed in percent: L = 1 0Y a = 17.5 * (1,02X - Y) Y b = 7.0 * (Y - 0.847Z) Y L, a and b are measured d i r e c t l y by the Hunter photoelectric colour difference meter. The difference between two colours i s again defined as t h e i r Euclidean distance in colour space. Because perceptually uniform spaces are important for colour control, many such systems 35 have been d e v e l o p e d ; b u t none has been t o t a l l y s u c c e s s f u l . The s e a r c h c o n t i n u e s f o r i m p r o v e d methods o f e v a l u a t i n g c o l o u r d i f f e r e n c e s . 6) L u t h e r - N y b e r g The L u t h e r - N y b e r g c o l o u r s o l i d p r o v i d e s a more a b s t r a c t r e p r e s e n t a t i o n of c o l o u r . I t d e f i n e s new c h a r a c t e r i s t i c s o f c o l o u r (two c o l o u r moments and c o l o u r w e i g h t ) i n t e r m s o f t h e C I E XYZ t r i s t i m u l u s v a l u e s : Moment 1 = -X + Y Moment' 2 = -Z - Y C o l o u r Weight = X + Y + Z T h i s c o l o u r s p a c e i s d e s c r i b e d i n more d e t a i l by [ARENS67]. The c o l o u r s y s t e m s w h i c h have been d i s c u s s e d r e p r e s e n t o n l y a f r a c t i o n o f t h o s e i n t h e l i t e r a t u r e . F o r f u r t h e r r e f e r e n c e , t h e r e a d e r i s d i r e c t e d t o [JUDD75] and [WYSZE67]. B o t h p r o v i d e i n - d e p t h s t u d i e s o f c o l o u r sc i e n c e . 36 4. I m p l e m e n t a t i o n In t h i s c h a p t e r , p r o p e r t i e s o f t h e p a r t i c u l a r d i s p l a y d e v i c e a r e e x a m i n e d and t r a n s f o r m a t i o n p a i r s f o r e a c h o f t h e c o l o u r s p a c e s i m p l e m e n t e d a r e d e r i v e d . I n a d d i t i o n , a s h o r t d i s c u s s i o n o f t h e i m p l e m e n t a t i o n i s i n c l u d e d . 4.1 D i s p l a y D e v i c e The d i s p l a y d e v i c e u s e d i n t h i s s t u d y i s a s t a n d a r d RGB c o l o u r t e l e v i s i o n m o n i t o r . I n d e p e n d e n t r e d , g r e e n and b l u e p h o s p h o r guns a r e d i g i t a l l y c o n t r o l l e d . The f u l l a n a l o g r a n g e o f e a c h o f t h e guns i s a p p r o x i m a t e d by d i s c r e t e s t e p s . In t h i s c a s e , t h e s e s t e p s (256) a r e p e r c e p t u a l l y s m a l l enough t o be c o n s i d e r e d a n a l o g . The e n t i r e gamut of t h e RGB m o n i t o r c o n s i s t s of a l l p o s s i b l e c o m b i n a t i o n s o f t h e d i s c r e t e l e v e l s o f e a c h of t h e p h o s p h o r guns ( i . e . , 2 5 6 3 c o l o u r s ) . T h i s number i s v e r y l a r g e and c o n s i s t s o f many more c o l o u r s t h a n a r e a c t u a l l y d i s t i n g u i s h a b l e on t h e d i s p l a y m o n i t o r . The c h r o m a t i c i t y c o o r d i n a t e s o f t h e p h o s p h o r s i n an RGB m o n i t o r d e t e r m i n e i t s c h r o m a t i c i t y gamut. B e c a u s e s u c h s y s t e m s r e l y on p h y s i c a l l y r e a l i z a b l e p r i m a r i e s , some c o l o u r s c a n n o t be p r o d u c e d . T h e o r e t i c a l l y , t h e c h r o m a t i c i t y gamut can be m a x i m i z e d by m a x i m i z i n g t h e a r e a o f t h e t r i a n g l e formed by t h e c h r o m a t i c i t y p o i n t s o f t h e t h r e e p r i m a r i e s , p r o v i d e d t h e c h r o m a t i c i t y d i a g r a m i s 37 p e r c e p t u a l l y u n i f o r m . C h o o s i n g m o n o c h r o m a tic s t i m u l i r e p r e s e n t e d by t h e two e n d p o i n t s o f t h e p u r p l e l i n e , and a n o t h e r m o n o c h r o m a t i c s t i m u l u s i n t h e g r e e n r e g i o n t h u s m a x i m i z e s t h e c h r o m a t i c i t y gamut. F i g u r e 15 shows a s e t of t h r e e m o n o c h r o m a t i c s t i m u l i w h i c h i n c l u d e a much l a r g e r c h r o m a t i c i t y gamut t h a n t h a t o f b o t h t h e NTSC p r i m a r i e s and t h e p r i m a r i e s of t h e m o n i t o r u s e d i n t h i s s t u d y . C h o i c e o f t h e t h r e e p h o s p h o r s i s not b a s e d s o l e l y on t h e i r c h r o m a t i c i t y gamut. The r a n g e i n b r i g h t n e s s p r o v i d e d by t h e t h r e e p h o s p h o r s must a l s o be c o n s i d e r e d . A t r a d e o f f between c h r o m a t i c i t y gamut and b r i g h t n e s s must be made. S t a n d a r d p h o s p h o r s d e f i n e d by NTSC i l l u s t r a t e t h i s c ompromise; t h e y do not p r o d u c e t h e w i d e s t c h r o m a t i c i t y gamut p o s s i b l e . The p h o s p h o r s of t h e m o n i t o r u s e d i n t h i s s t u d y have s i m i l a r c h a r a c t e r i s t i c s ( s e e f i g u r e s 15 and 1 6 ) . C o n f l i c t i n g c o n s t r a i n t s f u r t h e r r e d u c e t h e gamut of c o l o u r s w h i c h c a n be p r o d u c e d by a RGB m o n i t o r . The gamut o f an RGB m o n i t o r forms a p a r a l l e l o p i p e d s u b s p a c e i n t h e CIE XYZ s p a c e . U n i t s a l o n g t h e s u b s p a c e a x e s may, however, be n o n - u n i f o r m b e c a u s e t h e i n t e n s i t y o f l i g h t e m i t t e d i s a n o n l i n e a r f u n c t i o n o f t h e v o l t a g e a p p l i e d t o t h e p h o s p h o r s . The l u m i n a n c e i s a p p r o x i m a t e l y p r o p o r t i o n a l t o t h e s q u a r e o f t h e v o l t a g e . The s l o p e o f t h e l i n e o b t a i n e d from p l o t t i n g t h e l o g a r i t h m o f t h e l u m i n a n c e a g a i n s t t h e l o g a r i t h m o f t h e v o l t a g e ( a p p r o x i m a t e l y two) i s known as t h e gamma. Such n o n l i n e a r i t i e s o f t h e r e d , g r e e n and b l u e p h o s p h o r s may be 38 u. F i g u r e 15. C h r o m a t i c i t y Gamuts on t h e (u,v) Diagram The c h r o m a t i c i t y gamut of the m o n i t o r used i n t h i s t h e s i s ( s o l i d l i n e ) , t h a t of the NTSC p r i m a r i e s ( l i n e c o n s i s t i n g of s h o r t d a s h e s ) , and t h a t of monochromatic p r i m a r i e s chosen t o i n c r e a s e the c h r o m a t i c i t y gamut ( l i n e c o n s i s t i n g of l o n g dashes) a r e shown here i n terms of the (u,v) c h r o m a t i c i t y diagram. A l s o i n c l u d e d i s the w h i t e p o i n t used: D6500. 39 F i g u r e 16. C h r o m a t i c i t y Gamuts on the (x,y) Diagram The c h r o m a t i c i t y gamut of the m o n i t o r used i n t h i s t h e s i s ( s o l i d l i n e ) , and t h a t of the NTSC p r i m a r i e s (dashed l i n e ) a r e shown here i n terms of the (x,y) c h r o m a t i c i t y diagram. A l s o i n c l u d e d i s the w h i t e p o i n t used: D6500. 40 corrected by hardware. If not, a look-up table (gamma correction table) can be implemented in software [SMITH78]. By systematically varying the voltage and measuring the luminance, the gamma-correction table can be experimentally determined. Although each of the red, green and blue phosphors have di f f e r e n t gamma correction factors, the standard index used in colour t e l e v i s i o n industry i s 2.2 for each of the phosphors [HUNT75]: Luminance = Channel V o l t a g e 2 ' 2 (9) Provided gamma correction has been performed, the RGB monitor can be thought of as a linear device. The phosphor chromaticity coordinates and the white point ( i . e . , the chromaticity and luminance of the colour generated by the maximum RGB values) of the pa r t i c u l a r RGB monitor are generally used to derive the transformation between the RGB monitor space and a standardized space (such as the CIE XYZ or CIE UVW spaces). These coordinates can be determined experimentally using a photometer and a colorimeter. It i s important that the phosphor chromaticity, the white point and the gamma be accurately determined to ensure r e l i a b l e and consistent results are obtained. This procedure i s described by [MEYER80]. The chromaticity coordinates of the R, G and B phosphors of the part i c u l a r RGB monitor used in th i s study, in terms of the CIE XYZ colour space are: 41 X y R .628 .346 G .268 .588 B .150 .070 Figure 17. RGB Monitor Chromaticity Coordinates (These are plotted in figures 15 and 16). They were obtained from the manufacturer. However, measuring these values d i r e c t l y would be a more desirable method of obtaining them, since a number of factors (such as age and temperature) may effect phosphor chromaticity. The chromaticity coordinates of the reference white used in th i s study (D6500), in terms of the CIE XYZ colour space are: X y D6500 .3127 .3291 Figure 18. Reference White Chromaticity Coordinates (It i s plotted in figures 15 and 16). D6500 i s used because i t has replaced illuminant C as the reference white for colour monitors in industry [NEAL73]. When a colour CRT i s aligned to a reference white, the monitor i s adjusted so that equal colour inputs y i e l d a white, gray or black display. The photopic luminosity curve given in figure 2 i l l u s t r a t e s that the luminance values of individual wavelengths for equal energy white vary 42 considerably. Less red and blue than green i s required to produce a white. This implies that the f u l l scale red and blue luminances are much smaller than the f u l l scale green luminance of a colour CRT. (This fact i s i l l u s t r a t e d mathematically by the r e l a t i v e weighting of the R, G and B axes in the calculation of luminance (CIE "Y"). The green c o e f f i c i e n t i s much larger than that of the blue and red.) The monitor used in th i s study requires gamma correction, since t h i s operation i s not performed i n t e r n a l l y . A much simpler approach than that of actually measuring the luminance of each of the phosphors i s taken to correct t h i s problem. The standard gamma factor assumed in the colour t e l e v i s i o n industry (2.2) i s used to modify each of the RGB channels. This correction i s performed by software rather than hardware. Two ways to perform such a gamma correction technique are: via a lookup table through which the integral values are passed before they are displayed (such a lookup table could be stored in the display device i t s e l f ) ; or by a n a l y t i c a l l y performing the correction on the data before i t i s converted to integral values for display. The former method requires l i t t l e computation as the lookup table, v a l i d for a l l three RGB channels of any image, need only be calculated once. However, because the d i s t r i b u t i o n of the large RGB values is compressed (since large input values are mapped closer together) and the d i s t r i b u t i o n of the smaller RGB values i s expanded (since small input values 43 are mapped farther apart), the output range for each channel i s reduced. The 256 input l e v e l s are mapped to 184 output lev e l s ( i . e . , a reduction of 28%). The possible number of colour combinations i s thus reduced from 256 3 to 1 84 3 ( i . e . , by 63%). Although the l a t t e r method i s computationally much more expensive, i t allows the entire range of output values to be accessed. However, this technique i s useful only i f the data i s real in nature; otherwise, i t simply degenerates to the former technique. Because the colour transformations are a l l defined in terms of real values, the l a t t e r technique i s used to produce the images presented in t h i s thesis. 4.2 CIE XYZ The transformation between the RGB monitor space and the CIE XYZ space i s determined by the phosphor chromaticities and the reference white of the RGB monitor. Let the R, G and B primaries (Pr,Pg,Pb) be defined in terms of the CIE XYZ tristimulus values: Pr = Xr + Yr + Zr Pg = Xg + Yg + Zg Pb = Xb + Yb + Zb Assuming that the primary outputs are l i n e a r l y related to the voltage applied (Vr,Vg,Vb), the CIE XYZ tristimulus values are defined as follows: 44 X = Pr«xr-Vr + Pg«xg-Vg + Pb«xb-Vb Y = Pr-yr«Vr + Pg«yg«Vg + Pb«yb«Vb Z = Pr«zr«Vr + Pg-zg«Vg + Pb«zb«Vb ( x i , y i and z i , i 6 {r,g,b}, are the chromaticity coordinates of the phosphors.) In matrix form: X Pr •xr Pg • xg Pb'xb Vr Y = Pr •yr Pg-yg Pb«yb Vg Z Pr • zr Pg • zg Pb« zb Vb In expanded matrix form: xr xg xb yr yg yb zr zg zb Pr 0 0 0 Pg 0 0 0 Pb Vr Vg Vb (10) Let xr xg xb xr yg yb zr zg zb Then, = C Pr 0 0 0 Pg 0 0 0 Pb X Vr Y = T Vg Z Vb = p CP = T C i s the phosphor chromaticity matrix; i t i s constant for a pa r t i c u l a r device. P i s a tristimulus constant matrix; i t can be determined by requiring that the output for equal (normalized) channel voltages, be a p a r t i c u l a r (normalized) illuminant. T i s the transformation matrix from the RGB monitor space to the CIE XYZ space. Let Sw be the tristimulus values of the white point of 4 5 the RGB mon i t o r and i t s l u m i n a n c e , Yw, be n o r m a l i z e d t o one. (The luminance of X and Z a r e z e r o by d e f i n i t i o n . ) G iven t h a t Yw = 1, Sw can be e x p r e s s e d i n terms of known v a l u e s ( i . e . , c h r o m a t i c i t y c o o r d i n a t e s ) i n t h e f o l l o w i n g way: Sw = Xw Yw Zw U s i n g the d e f i n i t i o n of c h r o m a t i c i t y c o o r d i n a t e s , ( r e f e r t o e q u a t i o n 5 ) , Sw can be r e w r i t t e n : Sw = (Xw+Yw+Zw) xw yw zw P r e m u l t i p l y i n g t h i s e q u a t i o n by Yw/Yw and s i m p l i f y i n g (Xw+Yw+Zw)/Yw t o 1/yw y i e l d s : Sw = Yw/yw xw yw zw S u b s t i t u t i n g back, (YW=1) g i v e s Sw i n terms of the c h r o m a t i c i t y c o o r d i n a t e s : Sw = 1/yw xw yw zw (11) S u b s t i t u t i n g the n o r m a l i z e d r e f e r e n c e w h i t e ( e q u a t i o n 11) and the n o r m a l i z e d c h a n n e l v o l t a g e s (Vr=Vg=Vb=1) back i n t o e q u a t i o n 10 y i e l d s : 46 xw Pr 0 0 1 1/yw yw = C 0 Pg 0 1 zw 0 0 Pb 1 Simplifying and solving for the tristimulus constants: 1/yw xw Pr xw Pr yw = C Pg 1/yw C"1 yw = Pg zw Pb zw Pb Thus the tristimulus constant matrix (P) and the transformation matrix from the RGB monitor space to the CIE XYZ space (T), can be calculated. (The basis of th i s derivation i s from [NEAL73].) The inverse transformation, as with a l l the linear transforms described in th i s paper, i s calculated by inverting the o r i g i n a l transformation matrix. Since three independent quantities are required to produce f u l l colour, the transformations should always be non-singular and therefore i n v e r t i b l e . However, the implementation does check that each transformation i s i n v e r t i b l e and that i t i s not i l l - c o n d i t i o n e d . The transformation matrix from RGB to XYZ (for tristimulus values) based on the RGB monitor phosphors and illuminant D6500 i s : 0. 47658 0. 29896 0. 1 7463 R X 0. 26257 0. 65593 0. 08149 G = Y 0. 01973 0. 1 6064 0. 90805 B Z 47 4.3 CIE UVW The CIE UVW colour space i s a linear transformation of the CIE XYZ space. Given the transformation from (x,y) to (u,v) chromaticity coordinates (refer to equations 6a and 6b), derivation of the transformation matrix proceeds exactly the same as for the CIE XYZ transformation matrix. Again, the reverse transformation i s determined by inverting the transformation matrix. The transformation matrix from RGB to UVW (for tristimulus values) based on the RGB monitor phosphors and illuminant D6500 i s : 0. 31772 0. 19931 0. 1 1642 R U 0. 26257 0. 65593 0. 081 49 G — V 0. 16544 0. 91474 0. 48895 B w 4.4 Dominant Wavelength, Purity & Luminance This system i s examined in two ways. F i r s t , the dominant wavelength spectrum i s generated while maintaining constant purity and luminance. This i s implemented using a table of chromaticity coordinates corresponding to the spectral locus at 10 nm wavelength intervals from 410 nm to 700 nm. Intermediate i n t e g r a l wavelength values are determined using linear interpolation. Based on each wavelength, chromaticity coordinates with the desired purity are determined. This i s accomplished by finding the roots of a quadratic equation. Recall that purity i s a r a t i o of l i n e segments which are defined in terms of the 48 chromaticity diagram: ttie l i n e segment between a colour and the white point, and the l i n e segment from the point formed by the projection of the previous l i n e (from the white point through the colour) to the spectral locus and the white point. Since the two endpoints of the l a t t e r l i n e and one endpoint of the former l i n e are known, as well as the r a t i o of the lengths of these two l i n e s , the missing endpoint can be determined using a quadratic equation. The root closest to the point on the spectral locus i s chosen. Using the luminance and the chromaticity coordinates, the tristimulus values for either the XYZ or UVW system are obtained. These are then transformed to RGB (as described in the previous sections). The other method of examining the space i s through the enhancement of purity. In t h i s case, an RGB image i s transformed, via XYZ or UVW, into chromaticity coordinates and luminance ( i . e . , x,y,Y or u,v,V). The purity of the image i s increased by a l t e r i n g the chromaticity coordinates such that each point's distance from the white point i s increased. In terms of the chromaticity diagram, a l l points are projected outwards from the white point (excluding those equal to the white point which remain unaltered), and hence have increased purity. The equations of the three l i n e s corresponding to the chromaticity t r i a n g l e of the RGB monitor are used to ensure that the maximum purity i s not exceeded (and hence ensures that points are not undefined as a result of the operation). 49 Purity need not be calculated; a constant length i s added to each l i n e . This a l l e v i a t e s problems of specifying the spectral locus. However, a quadratic equation must be solved in order to determine the new chromaticity coordinates ( i . e . , theendpoint of the l i n e with adjusted length). Three endpoints of two l i n e s plus the length of both l i n e s are known in thi s case. After the chromaticity coordinates are altered to provide increased purity, a transformation back to the tristimulus values ( i . e . , XYZ or UVW) i s performed. These values are then transformed back to RGB (as described in the previous sections). 4 . 5 NTSC YIQ Recall that the NTSC system i s based on a luminance axis (Y) and two rotated colour difference axes (I and Q). Transformations between the YIQ space and the NTSC standard RGB monitor have been developed based on a reference white (illuminant C) for use in the t e l e v i s i o n industry. However, since the system was adopted, s i g n i f i c a n t changes have occurred in both the phosphors generally used in colour monitors and the normalizing white [NEAL73]. Therefore, derivation of the NTSC transformation i s re-examined to develop a transformation based on the appropriate chromaticity values. The luminance component has already been derived based 50 on illuminant D6500 and the RGB monitor phosphors. See equation 7 for ca l c u l a t i o n of the colour difference components. Note that R, G and B values refer to the NTSC standard monitor, therefore a transformation from the pa r t i c u l a r RGB monitor space to the NTSC standard RGB monitor space i s also necessary. Since both are linear transformations, they can be concatenated into a single operation by multiplying the two transformations together. The reverse transformation i s calculated by inverting the transformation matrix. The transformation matrix from RGB to YIQ (for tristimulus values) based on the RGB monitor phosphors and illuminant D6500 i s : .0.26257 0.65593 0.35628 -0.12339 0.03747 -0.34633 4.6 Implementation Structure In order to provide p o r t a b i l i t y between RGB monitors with d i f f e r e n t chrominance and/or luminance s p e c i f i c a t i o n s as well as to provide user convenience (assuming that the user seldom changes the chrominance and luminance s p e c i f i c a t i o n s ) , one program calculates the c o e f f i c i e n t s for a l l of the linear transformations. This program need be run only when the user wishes to change the luminance and/or the chrominance s p e c i f i c a t i o n s . It requests the chromaticity coordinates of the phosphors and the white 0.08149 -0.24619 0.26565 R Y G = I B Q 51 point of the RGB monitor. From these, the c o e f f i c i e n t s of the linear transformations are calculated. These c o e f f i c i e n t s are stored in a f i l e which i s subsequently read by the test programs. The transformations are performed a n a l y t i c a l l y in this implementation. However, other alternatives may be more appropriate under di f f e r e n t circumstances. For example, a faster method might include the use of lookup tables. These tables could be pre-calculated and stored, thus reducing the transformation operation to simple lookup. Some approximation to the f u l l RGB set i s p r a c t i c a l in the implementation of such a lookup technique. (Recall that 2563 RGB combinations exist.) This approximation should be based on perceptual differences rather than simply d i g i t a l differences. These methods were not chosen because of the greater overhead in storage for the tables as well as the limited use of the program. 52 5. Results In t h i s chapter, a number of pictures which i l l u s t r a t e the colour spaces implemented for this thesis are presented. The appropriate way to display the results of this work is on the colour CRT for which i t was intended. However, such a medium i s not p r a c t i c a l in t h i s case. Therefore, colour negative f i l m exposed by a video-printer i s used to reproduce the r e s u l t s . The gamut of colours which can be produced by the f i l m i s quite d i f f e r e n t from that which can be produced by the CRT. In addition, the method of colour production is d i f f e r e n t for f i l m and CRT. No compensation i s made for these differences. However, for the purposes of presentation i t was f e l t that this reproduction technique was adequate. The f i r s t two pictures i l l u s t r a t e the d i s t r i b u t i o n of the (x,y) and (u,v) chromaticity diagrams. Figure 19 shows equidistant d i s t r i b u t i o n on the (x,y) chromaticity diagram. Figure 20 shows equidistant d i s t r i b u t i o n on the (u,v) chromaticity diagram. Luminance i s constant (and equal) in both pictures. The four separate bands have constant purity. The top band has the smallest purity; the bottom band has the largest purity. Undefined values are represented as black. The pictures are generated by c a l c u l a t i n g the chromaticity coordinates with the desired purity at single nanometer wavelength i n t e r v a l s . These chromaticity coordinates are resampled to represent equal distance on either the (x,y) or the (u,v) diagram. 53 F i g u r e 19. E q u i d i s t a n t D i s t r i b u t i o n on t h e ( x , y ) C h r o m a t i c i t y D i a g r a m T h i s image i s g e n e r a t e d by r e s a m p l i n g t h e c h r o m a t i c i t y c o o r d i n a t e s ( w i t h t h e a p p r o p r i a t e p u r i t y ) of e a c h d o m i n a n t w a v e l e n g t h , so t h a t t h e s e c o o r d i n a t e s a r e e q u a l l y s p a c e d on t h e ( x , y ) c h r o m a t i c i t y d i a g r a m . Luminance i s c o n s t a n t i n a l l f o u r bands ( a t 0 .30). P u r i t y i s c o n s t a n t w i t h i n e a c h band. The p u r i t y i s i n c r e m e n t e d by 0.10 a t t h e s t a r t of e a c h new band. The t o p band has a p u r i t y o f 0.25; t h e b o t t o m band has a p u r i t y of 0.55. 54 F i g u r e 20. E q u i d i s t a n t D i s t r i b u t i o n on t h e (u,v) C h r o m a t i c i t y D i a g r a m T h i s image i s g e n e r a t e d by r e s a m p l i n g t h e c h r o m a t i c i t y c o o r d i n a t e s ( w i t h t h e a p p r o p r i a t e p u r i t y ) o f e a c h dominant w a v e l e n g t h , so t h a t t h e s e c o o r d i n a t e s a r e e q u a l l y s p a c e d . o n t h e (u,v) c h r o m a t i c i t y d i a g r a m . Luminance i s c o n s t a n t i n a l l f o u r bands ( a t 0.30). P u r i t y i s c o n s t a n t w i t h i n e a c h band and i s i n c r e m e n t e d by 0.10 a t t h e s t a r t o f e a c h new band. The t o p band has a p u r i t y o f 0.25; t h e b o t t o m band has a p u r i t y o f 0.55. 55 Subsequently, the sampled chromaticity coordinates along with the luminance i s translated into XYZ or UVW. tri s t i m u l u s space and f i n a l l y to RGB. Notice that the (x,y) diagram i s strongly dominated by green. Blue and red are represented by much smaller areas. This i s in agreement with pictures representing the (x,y) diagram presented in the l i t e r a t u r e (see [CHAMB80]). The (u,v) diagram i s more uniformly d i s t r i b u t e d . Red, green and blue are represented by nearly equal area. This supports the claim that the (u,v) chromaticity diagram i s more uniformly d i s t r i b u t e d than the (x,y) diagram. Also notice that as purity i s increased, the f i r s t values which become undefined in figure 19 are those in the green region; the f i r s t values which become undefined in figure 20 are in the same green region, followed by those at the extreme ends of the spectrum. If the chromaticity gamut of the monitor and the white point is plotted on the (x,y) diagram, (as in figure 16) i t i s evident that the maximum purity which can be produced by the monitor i s at a minimum in the wavelengths from approximately 500nm to 520nm. This corresponds to the green region. S i m i l a r l y , i f the gamut of the monitor and the white point i s plotted on the (u,v) diagram, (as in figure 15) i t i s evident that the maximum purity which can be produced by the monitor i s minimal in the same green region, as well as at both ends of the spectrum. These observations support both the implementation and the design of the systems. 56 F i g u r e 2 1 . I n c r e a s i n g Luminance w i t h C o n s t a n t P u r i t y and Dominant W a v e l e n g t h T h i s image i s g e n e r a t e d by s a m p l i n g t h e c h r o m a t i c i t y c o o r d i n a t e s o f t h e dominant w a v e l e n g t h s ( w i t h t h e a p p r o p r i a t e p u r i t y ) a t e q u a l dominant w a v e l e n g t h i n t e r v a l s . T h e s e a r e t r a n s l a t e d i n t o RGB s p a c e u s i n g t h e d e s i r e d l u m i n a n c e v a l u e . P u r i t y i s c o n s t a n t i n a l l f o u r bands ( a t 0 . 2 5 ) . Luminance i s c o n s t a n t w i t h i n e a c h band and i s i n c r e m e n t e d by 0.15 a t t h e s t a r t o f e a c h band. The t o p band has a l u m i n a n c e o f 0.20; t h e bottom band has a l u m i n a n c e o f 0.65. 57 The next picture, (figure 21), i l l u s t r a t e s constant purity and equally d i s t r i b u t e d dominant wavelengths, with increasing luminance. It i s generated in terms of the (u,v) chromaticity diagram. Each band has constant luminance. The top band has least luminance; the bottom band has greatest luminance. Perceptually, each successive band shows an increase in brightness. Therefore, i t seems that the numerical d e f i n i t i o n of luminance has captured a value which i s related to brightness. Notice that the f i r s t values which become undefined as the luminance i s increased are those in the blue region of the spectrum. This i s due to the fact that the f u l l scale blue luminance of the CRT is less than that of the f u l l scale green and red (see sections 4.1 and 4.2). The picture in figure 22 i l l u s t r a t e s constant luminance and equally d i s t r i b u t e d dominant wavelengths, with increasing p u r i t y . It i s generated in terms of the (u,v) chromaticity diagram. The top band has smallest purity; the bottom band has greatest purity. Perceptually, each successive band appears to have less white mixed with i t - the bands become less "pastel" or more "intense". The numerical d e f i n i t i o n of purity, therefore, also seems to have captured the perceptual quality of inte r e s t . Similar to figure 20, the f i r s t values which become undefined as the purity i s increased are those in the green region. Figure 23 shows an experiment performed on the YIQ system. The RGB image is transformed to YIQ and the 58 F i g u r e 22. I n c r e a s e d P u r i t y w i t h C o n s t a n t Luminance and Dominant W a v e l e n g t h T h i s image i s g e n e r a t e d by s a m p l i n g t h e c h r o m a t i c i t y c o o r d i n a t e s o f t h e dominant w a v e l e n g t h s ( w i t h t h e d e s i r e d p u r i t y ) a t e q u a l dominant w a v e l e n g t h i n t e r v a l s . T h e s e a r e t r a n s l a t e d i n t o RGB s p a c e u s i n g t h e a p p r o p r i a t e l u m i n a n c e v a l u e . Luminance i s c o n s t a n t i n a l l f o u r bands ( a t 0.40). P u r i t y i s c o n s t a n t w i t h i n e a c h band and i s i n c r e m e n t e d by 0.10 a t t h e s t a r t o f e a c h new band. The t o p band has a p u r i t y o f 0.10; t h e b o t t o m band has a p u r i t y o f 0.40. F i g u r e 23. YIQ A x i s R e c o m b i n a t i o n The RGB image i s t r a n s f o r m e d t o YIQ and t h e f o l l o w i n g s e t s o f a x e s a r e t r a n s f o r m e d back t o RGB: YIQ, Y I , YQ, and Y ( a s l a b e l l e d ) . 60 f o l l o w i n g s e t s of a x e s a r e t r a n s f o r m e d back t o RGB: YIQ, Y l , YQ and Y (as l a b e l l e d i n t h e d i a g r a m ) . R e c a l l t h a t I r e p r e s e n t s t h e o r a n g e - c y a n a x i s ; Q r e p r e s e n t s t h e p u r p l e - g r e e n a x i s ; and Y r e p r e s e n t s l u m i n a n c e . I t i s e v i d e n t t h a t e a c h a x i s i s c a p t u r i n g t h e s e a p p r o p r i a t e l y . The r e m a i n i n g p i c t u r e s i l l u s t r a t e a t t e m p t s t o enhance m u l t i s p e c t r a l d i g i t a l i m a g e r y b a s e d on t h e s e c o l o u r d e f i n i t i o n s . F i g u r e 24 i s t h e p o r t i o n o f t h e L a n d s a t s c e n e , (imaged May 13, 1975), u s e d i n t h e s e e x a m p l e s . Bands 4, 5 and 7 a r e a s s i g n e d b l u e , g r e e n and r e d r e s p e c t i v e l y . F i g u r e 25 shows an enhancement o f t h e l u m i n a n c e component of t h e YIQ s y s t e m . A l i n e a r r e d i s t r i b u t i o n o f t h i s a x i s has been p e r f o r m e d i n t h e manner d e s c r i b e d by f i g u r e 1. F i g u r e 26 shows f o u r g r a d u a t e d enhancements o f p u r i t y . In e a c h s u c c e s s i v e band, p u r i t y i s i n c r e a s e d by a c o n s t a n t amount. The a x i s d e s c r i b i n g p u r i t y has been r e d i s t r i b u t e d i n t h e manner d e s c r i b e d by f i g u r e 1. I m p l e m e n t a t i o n o f t h i s t e c h n i q u e i s d e s c r i b e d i n s e c t i o n 4.4. Based on t h e s e s a m p l e s , t h e d e s i r e d i n c r e a s e i n p u r i t y i s c h o s e n . F i g u r e 27 shows t h e e n t i r e image en h a n c e d by t h e a p p r o p r i a t e i n c r e a s e d p u r i t y . 61 F i g u r e 24. P o r t i o n o f L a n d s a t Image Imaged May 13, 1975. Bands 4, 5, and 7 a r e d i s p l a y e d i n b l u e , g r e e n , and r e d r e s p e c t i v e l y . The image i s n o t e n h a n c e d . 62 F i g u r e 25. Luminance Enhancement A l i n e a r r e d i s t r i b u t i o n o f t h e Y a x i s i n t h e YIQ s p a c e has been p e r f o r m e d on t h e L a n d s a t image p r o v i d e d i n f i g u r e 24. 63 F i g u r e 26. G r a d u a t e d I n c r e a s e i n P u r i t y The p u r i t y o f t h e t o p q u a r t e r of t h e L a n d s a t image p r o v i d e d i n f i g u r e 24 has been s u c c e s s i v e l y i n c r e a s e d by 0.020. The p u r i t y of t h e t o p band i s i n c r e a s e d by 0.005; t h a t of t h e b o t t o m band by 0.065. 64 F i g u r e 27. P u r i t y Enhancement The p u r i t y o f t h e L a n d s a t image p r o v i d e d i n f i g u r e 24 has been i n c r e a s e d by 0.035. 65 6. Conclusion The techniques implemented in th i s study u t i l i z e standard colour spaces. This requires the d e f i n i t i o n of transformations between a p a r t i c u l a r RGB monitor colour space and the standard colour spaces. These transformations are determined by specifying the chrominance and luminance of the RGB monitor in terms of a standard colour space: the CIE XYZ system. The transformation between the colour space of the RGB monitor and t h i s system can then be calculated. Because the other standard colour spaces can be defined in terms of the CIE XYZ system, they are also ( i n d i r e c t l y ) s p e c i f i e d by th i s transformation. However, there are a number of problems associated with t h i s procedure. One fundamental assumption of this technique i s that the conditions under which the CIE standards are obtained are similar to the conditions under which the monitor i s viewed. However, the two stimuli viewed by a standard CIE observer are of similar shape and si z e . In addition, the angular size of the viewing f i e l d and ambient l i g h t are s t r i c t l y c ontrolled. These c r i t e r i a are not met under normal viewing conditions of the monitor. Notwithstanding these comments, the CIE system currently appears to provide the best technique to define the RGB monitor space. Ca l i b r a t i o n of the RGB monitor presents another problem. The chrominance and luminance are not measured d i r e c t l y from the monitor at the time the image i s 66 displayed. (Recall that the phosphor chromaticities obtained from the manufacturer and the chromaticity of the standard illuminant D6500 are u t i l i z e d . In addition, a standard gamma correction factor i s used for a l l three RGB channels.) This undoubtedly introduces error in the transformations. In general, however, the phosphor response on a monitor screen d i f f e r s from point to point and varies with temperature and age. Therefore, absolute c a l i b r a t i o n of an RGB monitor - a shadow mask CRT - i s d i f f i c u l t , and is not repeatable over time. A more stable medium i s desirable. Better results are l i k e l y with a colour f i l m writer which uses a single output source and a more consistent medium. Extension of the transformations to d i f f e r e n t media is not straightforward. The gamut of colours which can be produced by film ( i . e . , dyes), for example, i s quite d i f f e r e n t from that that which can be produced by an RGB monitor (refer to figure 12). In terms of the CIE (x,y) diagram, the dyes and pigments gamut i s irregular; a relat i o n s h i p between the gamuts of the two media i s d i f f i c u l t to define. Although the chromaticity gamuts produced by two RGB monitors generally d i f f e r , their difference i s usually smaller and i s much more e a s i l y defined. The gamut of an RGB monitor on the CIE (x,y) diagram i s represented by a tr i a n g l e determined by i t s phosphors. Hence the relationship between the chromaticity gamuts of two RGB monitors can be defined in terms of two 67 t r i a n g l e s . The d e f i n i t i o n of standardized colour operations must therefore include consideration of the colour gamuts of the various media. Although these problems e x i s t , the results of t h i s work show that alternate standard colour spaces, which capture perceptual q u a l i t i e s , can be implemented on a CRT. Therefore these are better suited to enhancement than the RGB colour space of a p a r t i c u l a r device. Future work must be car r i e d out to determine what type of enhancements are most successful. Only two examples of enhancements are given here, one of luminance, the other of purity. Enhancement in these alternate colour spaces i s not straight-forward. Even extension of standard black and white enhancement techniques ( i . e . , l i n e a r , uniform or normal r e d i s t r i b u t i o n of axes) to linear transformations of the RGB space, introduce complications. Once a three-channel coloured image i s transformed to a standard colour space, r e d i s t r i b u t i o n , (similar to the techniques which have been developed for single channel imagery) can be performed. However, simply ensuring that the values of each of the axes are within the maximum and minimum values of that p a r t i c u l a r axis for the defined RGB space before the enhancement operation i s performed, does not ensure that the point i s defined in the RGB space after the enhancement operation i s performed. Consider a linear transformation of the RGB space, for example. The axes of the new space are defined in such a way as to e n t i r e l y 68 enclose the RGB monitor space. Thus a l l points in the RGB monitor space l i e in a parallelopiped within the new space. However, the parallelopiped ( i . e . , the RGB monitor space) generally does not f i l l t h i s new space. The volume of the parallelopiped i s related the number of points which are defined after the enhancement i s performed. In terms of the number of points which remain defined, the o r i g i n a l RGB monitor parallelopiped i s optimal (for example, the o r i g i n a l RGB monitor space or the cyan-yellow-magenta space) since no points can be mapped out of the RGB space; a parallelopiped with a-much smaller volume than that of the rectangle defining the new colour space may map many points outside the RGB space. Offs e t t i n g and scaling of the RGB axes appears to be a simple solution to th i s problem, however, such an operation i s device dependent (an enhancement of the RGB space) and therefore i s inappropr i a t e . A possible solution to t h i s problem i s to map the three-dimensional RGB space onto the desired alternate colour space and determine the intersection of the two. The enhancement could then be based on the space common to both s o l i d s . Assuming that the RGB space f a l l s e n t i r e l y within the alternate colour space, and that the alternate space i s a linear transformation of the RGB space, the volume to be enhanced can be determined by examining the eight vertices of the parallelopiped occupied by the RGB space. However, i f the alternate space is a non-linear 69 t r a n s f o r m a t i o n of the RGB space, d e t e r m i n i n g the i n t e r s e c t i o n of the two volumes may be more c o m p l i c a t e d . A l t h o u g h b r i g h t n e s s i s g e n e r a l l y r e p r e s e n t e d as a l i n e a r f u n c t i o n of the RGB m o n i t o r space, hue and s a t u r a t i o n a r e g e n e r a l l y r e p r e s e n t e d as more c o m p l i c a t e d , n o n - l i n e a r f u n c t i o n s . E x t e n d i n g the b l a c k and w h i t e enhancement t e c h n i q u e s t o the s e c o l o u r a t t r i b u t e s may t h e r e f o r e be i n a p p r o p r i a t e . More s u c c e s s f u l enhancements w i l l l i k e l y be a c h i e v e d by b a s i n g the t e c h n i q u e s on p a r t i c u l a r c o l o u r a t t r i b u t e s . I n t h i s way, the c h a r a c t e r i s t i c s of d i f f e r e n t c o l o u r spaces can be e x p l o i t e d . The g r e a t v a r i e t y of c o l o u r spaces which have been d e v e l o p e d o f f e r many p o s s i b i l i t i e s . B i b l i o g r a p h y [ARENS67] A r e n s , Hans C o l o u r Measurement F o c a l P r e s s , London 1967 [BOOTH79] B o o t h , K e l l o g g S. " T u t o r i a l : Computer G r a p h i c s " I . E . E . E . Computer S o c i e t y 1979 [CHAMB80] C h a m b e r l i n , C o l o u r , I t s  A p p l i c a t i o n Heyden & Son 1980 G. J . And Measurement, D. G. C h a m b e r l i n C o m p u t a t i o n , and L t d . , London [CONRA80] C o n r a c R a s t e r C o n r a c C o v i n a 1 980 D i v i s i o n , C o n r a c C o r p o r a t i o n G r a p h i c s Handbook D i v i s i o n , C o n r a c C o r p o r a t i o n , C a l i f o r n i a [FINK57] F i n k , D o n a l d G. T e l e v i s i o n E n g i n e e r i n g Handbook M c G r a w - H i l l Book Co. 1957 [HERBS67] H e r b s t r e i t , J a c k W. and H. P o u l i q u e n " I n t e r n a t i o n a l S t a n d a r d s F o r C o l o r T e l e v i s i o n " I . E . E . E . S p e c t r u m , pp. 104-111 March, 1967 [HUNT75] Hunt, R. W. G. The R e p r o d u c t i o n of C o l o u r i n P h o t o g r a p h y , P r i n t i n g and T e l e v i s i o n H a l s t e a d P r e s s , U. S. A. 1975 [JOBL078] J o b l o v e , G e o r g e H. and D o n a l d G r e e n b e r g " C o l o r S p a c e s F o r Computer G r a p h i c s " Computer G r a p h i c s , pp. 20-25 A u g u s t , 1978 [JUDD75] J u d d , Deane B. and G u n t e r W y s z e c k i C o l o r i n S c i e n c e , B u s i n e s s and I n d u s t r y J o h n W i l e y & Sons I n c . , New York 1975 [ L I L L E 7 9 ] L i l l e s a n d , Thomas M. and R a l p h W. K i e f e r Remote S e n s i n g and Image I n t e r p r e t a t i o n J o h n W i l e y & Sons I n c . , New York 1979 [MEYER80] Meyer, G a r y W. and D o n a l d P. G r e e n b e r g " P e r c e p t u a l C o l o r S p a c e s F o r Computer G r a p h i c s Computer G r a p h i c s , Volume 14, Number 3, pp. 254-261 J u l y , 1980 [NEAL73] N e a l , C. B a i l e y " T e l e v i s i o n C o l o r i m e t r y F o r R e c e i v e r E n g i n e e r s I . E . E . E . T r a n s a c t i o n s on B r o a d c a s t T e l e v i s i o n and R e c e i v e r s , pp. 149-161 A u g u s t , 1973 [PRATT78] P r a t t , W i l l i a m K. D i g i t a l Image P r o c e s s i n g J o h n W i l e y & Sons I n c . , New York 1978 [PRITC77] P r i t c h a r d , D. H. "U.S. C o l o r T e l e v i s i o n F u n d a m e n t a l s : A Review" SMPTE J o u r n a l , Volume 86, pp. 819-828 November, 1977 [PRITC80] P r i t c h a r d , D. H. and J . J . G i b s o n "Worldwide C o l o r T e l e v i s i o n S t a n d a r d s -S i m i l a r i t i e s and D i f f e r e n c e s " SMPTE J o u r n a l , Volume 89, pp. 111-120 F e b r u a r y , 1980 [SABIN78] S a b i n s , F l o y d F. J r . Remote S e n s i n g P r i n c i p l e s and I n t e r p r e t a t i o n W. H. Freeman and Company, San F r a n c i s c o 1 978 [SMITH78] S m i t h , A l v y Ray " C o l o r Gamut T r a n s f o r m P a i r s " Computer G r a p h i c s , pp. 12-19 A u g u s t , 1978 [WRIGH69] W r i g h t , W. D. The Measurement o f C o l o u r Adam H i l g e r L t d . , London 1969 [WYSZE67] W y s z e c k i , G u n t e r and W. S. S t i l e s C o l o r S c i e n c e , C o n c e p t s and Methods, Q u a n t i t a t i v e D a t a and F o r m u l a s J o h n W i l e y & Sons I n c . , New York 1967 

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