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Detection of bark beetle-attacked spruce using computer-based image analysis Banner, Allen Vernon 1986

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DETECTION OF BARK BEETLE-ATTACKED SPRUCE USING COMPUTER-BASED IMAGE ANALYSIS by ALLEN VERNON BANNER B.Sc, Lakehead University, 1979 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L 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 T H E D E G R E E O F M A S T E R O F S C I E N C E in T H E F A C U L T Y O F G R A D U A T E STUDIES (Department of Forestry/Remote Sensing) We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F BRITISH C O L U M B I A September, 1986 ©Allen Vernon Banner, 1986 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission f o r extensive copying of t h i s thesis f o r s c h o l a r l y purposes may be granted by the head of my department or by h i s or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Forestry/Remote sensing The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date September 29, 1986 / Abstract The spruce beetle (Dendroctonus rufipennis Kirby) is the most destructive forest pest affecting mature spruce stands in British Columbia. A variety of responses to curtail the spread of bark beetle infestations exist. The responses, however, depend upon early detection of the infestations to minimize the cost of treatment and reduce losses of timber. It has been demonstrated that bark beetle-attacked spruce can be detected using visual interpretation of large scale colour infrared film (Churcher 1984; Churcher and McLean 1984; Murtha 1985; Murtha and Cozens 1985). These studies indicate that it is possible to distinguish attacked spruce, to some degree, by their visual colour in the photographs. The image intensities associated with trees in the photographs are profoundly in-fluenced by factors such as the viewer's position and shape of the tree as well as the "colour" of the tree. This thesis develops a computer-based image analysis technique-projected intensity triplet space-which can be used to interpret the attack condition of a tree regardless of shading effects due to its position in the photograph or its shape. The procedure is used to classify trees in a test photo according to three beetle attack categories-unattacked, current attack and old attack. The interpretation accuracy for trees which were unattacked, fully current attacked and old attacked was high (84, 68 and 89 percent respectively). The percentages of trees from the 1983 strip attacked and 1983 pitched-out ground data classes interpreted by the computer to be attacked were very low (22 and 6 percent). The poor results for the strip attacked and pitched-out trees were attributed to the lack of evident colour differences from unattacked trees in the photographs. In cases where there were visually evident colour differences, however, the technique was able to classify the attack status reliably. ii Contents Abstract ii Contents iii List of Tables v List of Figures v i Acknowledgements viii 1 Introduction 1 2 Background 5 2.1 The Spruce Beetle 5 2.2 Visual interpretation 6 2.3 Densitometric analysis 10 3 D a t a and facilities 13 3.1 The Study Area 13 3.2 Aerial photography 13 3.3 Field work 16 3.3.1 Flight line markers 16 3.3.2 Ground data collection 17 3.4 Laboratory work 17 3.4.1 Scanning of photographs 18 3.4.2 Software 19 iii 4 " I n t e n s i t y t r i p l e t s p a c e " 20 4.1 Considering several viewpoints 20 4.2 Red, green and blue trees 39 4.3 ITS and Ratioing 45 4.4 Hue, saturation and lightness 50 5 " P r o j e c t e d i n t e n s i t y t r i p l e t s p a c e " 54 5.1 The transformation 54 5.1.1 Identifying the "colour" 57 6 I m p l e m e n t a t i o n 63 6.1 Locating the convergence point 63 6.2 Interpreting attack status 66 6.3 Putting it together 67 7 M e t h o d o l o g y E v a l u a t i o n 73 7.1 The convergence point 73 7.2 Geometry independence 77 7.3 Gaussian smoothing 79 8 T h e te s t f r a m e 82 9 C o n c l u s i o n s 104 L i t e r a t u r e C i t e d 108 A S u m m a r y o f B a n n e r (1984) 112 A . l Methodology 112 A.2 Results and Discussion 113 B F l i g h t L i n e M a r k e r A s s e m b l y 130 C S u m m a r y o f S o f t w a r e 143 iv List of Tables 4.1 Computation of the central axis for the " T L " view of tree 119 36 6.1 Convergence points 66 7.1 Kruskal and Wallis test of distances from peaks to means 80 8.1 Interpretation results of test frame 84 A . l Median test of blue image intensities sampled from tree 50 115 A.2 Median test of green image intensities sampled from tree 50 116 A.3 Median test of red image intensities sampled from tree 50 117 A.4 Median test of blue image intensities sampled from tree 81 118 A.5 Median test of green image intensities sampled from tree 81 119 A.6 Median test of red image intensities sampled from tree 81 120 A.7 Median test of blue image intensities sampled from tree 119 121 A.8 Median test of green image intensities sampled from tree 119 122 A.9 Median test of red image intensities sampled from tree 119 123 A.10 Median test of blue image intensities sampled from tree 262 124 A.11 Median test of green image intensities sampled from tree 262 125 A.12 Median test of red image intensities sampled from tree 262 126 A.13 Median test of blue image intensities sampled from tree 945 127 A.14 Median test of green image intensities sampled from tree 945 128 A.15 Median test of red image intensities sampled from tree 945 129 v List of Figures 1.1 Spruce beetle infestation in the Bowron River Valley 2 2.1 Normal colour ground photo of beetle-attacked spruce trees 7 2.2 Colour infrared ground photo of beetle-attacked spruce trees 8 3.1 Location of study site on Chapman Lake 14 3.2 Aerial view of Chapman Lake study site 15 4.1 Nine views of a normal or "red" tree (119) 21 4.2 Intensity triplet space for the " T L " view of tree 119 22 4.3 Intensity triplet space for the " T C " view of tree 119 23 4.4 Intensity triplet space for the " T R " view of tree 119 24 4.5 Intensity triplet space for the " M L " view of tree 119 25 4.6 Intensity triplet space for the " M C " view of tree 119 26 4.7 Intensity triplet space for the " M R " view of tree 119 27 4.8 Intensity triplet space for the " B L " view of tree 119 28 4.9 Intensity triplet space for the " B C " view of tree 119 29 4.10 Intensity triplet space for the "BR" view of tree 119 30 4.11 Intensity triplet space for all views of tree 119 32 4.12 Intensity triplet space for all normal trees 33 4.13 Stereogram of intensity triplet space for a "red" tree 35 4.14 Central axes for each view of tree 50 37 4.15 Central axes for all five normal trees 38 4.16 Intensity triplet space for a green tree 40 4.17 Intensity triplet space for a blue tree 41 4.18 Nine views of a green tree 42 4.19 Nine views of a blue tree 43 vi 4.20 Central axes for each view of a blue tree 44 4.21 Central axes for five green trees using pooled views for each tree 46 4.22 Central axes for five blue trees using pooled views for each tree 47 4.23 Convergence of central axes 48 4.24 Mean intensities and central axes for red, green and blue trees 49 4.25 Comparison of hue, saturation and lightness with intensity triplet space. . 51 4.26 Three points in a hypothetical calibrated intensity triplet space 53 5.1 Projected intensity triplet space 56 5.2 Projected intensity triplet space images 58 5.3 Gaussian smoothing of histograms 59 5.4 A PITS image smoothed at a values of 1, 3 and 9 61 5.5 Peaks associated with smoothed PITS images 62 6.1 Convergence points in relation to intensity triplet space 65 6.2 A "tan-coloured" current attacked tree 68 6.3 A current attacked tree which is "tan-coloured with green spots" 69 6.4 Decision boundaries and the training set 70 7.1 Points displaced around the convergence point 74 7.2 Effect of displacement of the projection viewpoint 76 7.3 Major peaks in PITS for the nine views of tree 119 78 8.1 Stereogram of the test frame 83 8.2 Photograph of test frame 91 8.3 Key to the unattacked trees 92 8.4 Peaks in PITS for the unattacked trees 93 8.5 Key to the current attacked trees 94 8.6 Peaks in PITS for the current attacked trees 95 8.7 Key to the old attacked trees 96 8.8 Peaks in PITS for the old attacked trees 97 8.9 Key to the 1983 pitched-out trees 98 8.10 Peaks in PITS for the 1983 pitched-out trees 99 8.11 Key to the 1983 strip attacked trees 100 8.12 Peaks in PITS for the 1983 strip attacked trees 101 8.13 Key to the old and mixed strip attacked trees 102 8.14 Peaks in PITS for the old and mixed strip attacked trees 103 vii B . l Sketch of tarp setup 133 B.2 Looking up at anchor trees prior to setup 134 B.3 Firing fishing line over crown 135 B .4 Pulling the anchor rope over a tree 136 B .5 Passing pulley rope through ring of the anchor rope 137 B.6 The anchor rope is pulled up with the pulley rope passed through it. . . . 138 B.7 The anchor rope is pulled close to the trunk of the tree 139 B .8 The tarp is hoisted using the pulley ropes 140 B.9 Looking up at anchor trees with tarp in place 141 B.10 Tarps can be suspended high in the canopy 142 viii Acknowledgements I would like to express sincere gratitude to the members of my committee-Dr. P. A. Murtha, Dr. R. J. Woodham and Dr. J . A . McLean-for their patience, guidance and support throughout the course of this thesis. I would also like to thank the many other people who have helped me while I have been completing this work. During the period of fieldwork, Tom Maher of Northwood Pulp and Timber Limited shared his wealth of experience and saved the day numerous times when things seemed to be coming apart at the seams. The fieldwork could not have been completed without the help of two really fine assistants: Rob Haley and Kevin Widen. Dr. H . Moeck of the Pacific Forest Research Centre supplied a crossbow for putting up the flight line markers. I owe much to the other people working at the Laboratory for Computational Vision-graduate students, faculty and staff. The people at the Lab, together with the facility itself, provide a learning and research environment which is truly first class. In particular, I would like to thank Marc Majka, Francois Dumoulin and Detlef Heiss for their help and friendship. Frank Pronk, the L C V System Manager for most of the time I was working there, seemed to have limitless patience with those who were not so wise in the w a y s of UNIX-thankyou. Nedenia Krajci digitized the photographs-all 83 of them-and made Figure B . l look great! The funding for this thesis was provided by B . C . Science Council Grant #47 (RC-6 and RC-8), a B . C . Science Council G R E A T Award and a B .C . Forest Products Limited Fellowship in Forest Resource Management. ix Chapter 1 Introduction The spruce beetle (Dendroctonus rufipennis Kirby) is the most destructive forest pest affecting mature spruce stands (including white spruce (Picea glauca (Moench) Voss) and Engelmann spruce (Picea engelmannii (Parry) ) in British Columbia. In 1982, the spruce beetle was recognized as the foremost forest pest in the Prince George Forest Region and second only to the Mountain Pine Beetle (Dendroctonus ponderosae Hopkins) in the Kamloops, Nelson and Prince Rupert Forest Regions (Anon 1982). When their populations are allowed to reach epidemic proportions, spruce beetles are capable of killing millions of cubic metres of timber per year (Figure 1.1). A variety of responses to curtail the spread of bark beetle infestations exist rang-ing from pheromone baiting and single-tree disposal to large-scale clearcutting. Any response, however, hinges on early detection of infestations to reduce losses of timber and minimize the cost of treatment. The essense of the problem was expressed by Dyer and Hodgkinson (1981): "The infested trees that are visible after changing colour are mainly a sal-1 Figure 1.1: Spruce beetle infestation in the Bowron River Valley. This is a colour infrared photograph of a well established infestation. The "green" trees in this colour infrared photo-graph are all dead and have lost their foliage. Trees which look red in the photograph have foliage which appears green in real life. 2 vage problem, not a beetle problem, because most of the beetles have gone before this timber is detected, made accessible and harvested. If only the green infested material gave off smoke, we would find the means to treat it immediately." Several studies have been conducted using visual analysis of colour infrared pho-tographs for early detection of bark beetle-attacked spruce. The results have been promising. Murtha and Cozens (1985) reported on a comparison of results and cost of a photographic approach versus traditional ground-based assessment. Both techniques provided "similar and acceptable results" but the cost of the ground-based approach was five times that of using photographs. Based upon studies by Murtha (1985), Churcher and McLean (1984) and Churcher (1984), human interpreters seem capable of distinguishing attacked and unattacked spruce, to some extent, on the basis of their overall colour in colour infrared photographs. In general, unattacked trees appear red, current attacked trees appear tan-coloured and old attack appears green or blue. The overall aim of this thesis is to investigate the use of digital image analysis tech-niques for detection of current bark beetle-attacked spruce using digitized large scale colour infrared photographs. Digital images derived from large scale photographs can provide fine spatial detail with many pixels per tree. However, much of the variation in the image intensities is due to factors such as the position in the photograph where a tree is imaged and changes in 3 surface orientation of the tree's foliage. There is little quantitative information available regarding the images other than the image intensities themselves. In particular, there is no quantitative information regarding the positions of the light source and camera or the shapes of trees. This information is instrumental for computing the "shading" component of the image intensities. In this thesis, sampled image intensities are converted to "projected intensity triplet space" to capture the "colour" of the intensities but remove the "shading". The tech-nique is used for the implementation of a computer-based procedure to interpret the bark beetle-attack status of individual trees sampled from an image. A test frame with a mix-ture of unattacked, pitched-out, strip attacked, fully current attacked, and old attacked spruce is used to demonstrate the effectiveness of the approach. Background information on the spruce beetle and a review of studies using visual interpretation and densitometric analysis are presented in Chapter 2. Chapter 3 outlines the data acquisition and resources used for the analysis. Chapter 4 introduces "intensity triplet space". Trees with visually distinctive colours in the photographs-red, green and blue-are used to illustrate the characteristics of intensity triplet space. In Chapter 5, these observations are used to develop "projected intensity triplet space" as a technique to distinguish "colour" in digitized photographs. Chapter 6 presents an implementation of the approach to classify sampled trees as unattacked, current attack or old attack. The methodology is evaluated in Chapter 7. The results of the test frame are presented in Chapter 8. Chapter 9 gives the conclusions. 4 Chapter 2 Background 2.1 T h e Spruce Beetle The biology of the spruce beetle and consequent forest management implications are given in detail by Schmid and Frye (1977). A brief summary of considerations which will have a direct bearing on analysis to follow is presented here. Mature spruce beetles bore beneath the bark of host trees to create egg galleries. They introduce a blue staining fungus (Ceratocystis spp). Sapwood colonization by the fungus and subsequent larval feeding in the phloem halts translocation of water and nutrients through part or all of the stem. Successful attack around the full circumference of the bole leads to complete death of the tree or "full attack". The attack may only stop translocation around part of the circumference leaving a "strip attacked tree". The tree may resist the attack by exuding pitch. The beetle is repelled or drowned in pitch and the influence of the fungus is restricted. While such a "pitched-out" tree may survive the attack, it may still show strain symptoms. 5 Schmid (1976) describes the changes in crown appearance undergone by attacked spruce based upon detailed observations of three trees over a period of three years. The crown does not discolour evenly. Instead, needles discolour in clusters to give the crown a "mottled green-yellow green" appearance (Figures 2.1 and 2.2). A n attacked tree will maintain a predominantly green appearance for a long period. The discoloured needles fall off during storms leaving a thinner, but still green, crown behind. Schmid (1976) observed that older needles, furthest from the branch tips, fell in the first summer. The steady thinning of the crown eventually gives the tree a "gray cast" by exposing bare branches. The life cycle of the spruce beetle is variable from one to three years. Population trends are generally related to environmental conditions such as mean summer temper-ature (Schmid 1976; Churcher 1984). Individually, however, each beetle develops at its own rate giving a mixture of life cycles in a particular population. Similarly, the deterioration of attacked trees is variable. Massey and Wygant (1954) found that needles had dropped off one year after attack. Schmid (1976) found that 65 to 70 percent of the needles were still on attacked trees at the beginning of the third summer. 2.2 Visual interpretation The use of aerial photographic surveys and visual interpretation of photographs for detection and evaluation of bark beetle attack is well established. Heller and Bean 6 Figure 2.1: Normal colour ground photo of beetle-attacked spruce trees. Visually apparent strain symptoms on a spruce which is fully attacked (left) and one in which the beetles have been pitched out (right). Examples of yellow discolouration or "flagging" are indicated by arrows. The photograph was taken at approximately 2:00 p.m., September 15, 1983. Figure 2.2: Colour infrared ground photo of beetle-attacked spruce trees. The same trees as in Figure 2.1 are shown. Again, note the yellow nagging indicated by the arrows. The photograph was taken at approximately 2:00 p.m., September 15, 1983. 8 reported on the use of black and white infrared film for detecting "faded pine trees" in 1951. By 1959, Heller et al. were advocating the use of colour film (Ektachrome Aero) rather than panchromatic film for detecting southern pine beetle damage. Some of the previous work has focussed on the assessment of damage and has concen-trated on the development of efficient sampling and survey designs to estimate mortality. A n overview of some of these surveys is given in Heller and Ulliman (1983). Other work has focussed on detection of current attacked trees with the aim of being able to determine the locale of the beetle population and taking measures to prevent the spread of the infestation. It has been demonstrated that it is possible to use visual interpretation of large scale colour infrared photographs to discriminate trees which are i j currently attacked by the Douglas-fir beetle (Dendroctonus pseudotsugae Hopk.) (Hall 1981), mountain pine beetle (Hobbs 1983; Hobbs and Murtha 1984) and spruce beetle (Murtha 1985; Murtha and Cozens 1985). Murtha and McLean (1981) introduced the concept of a "normal standard tree" which serves as an "in-photo-standard" of a healthy tree with which other trees may be compared. The normal trees are defined on the basis of an "even-medium magenta hue" and "lack of noticeable damage symptoms". Murtha (1985) demonstrated that successfully attacked spruce display a series of strain symptoms as the tree's condition deteriorates. He found that the initial symptoms are changes in a "variagated magenta" pattern within the foliage of unattacked trees. Interpretation of the pattern requires knowledge of the tree's shape since the mottling results from variations between new foliage at the branch tips and older foliage away from 9 the tips. Some of the more advanced symptoms, however, involve distinct departures in overall colour from the typical magenta of an unattacked or "normal" spruce. These include "tan-magenta" (IIIOa-T), "whitish or off-white" (IIIOb-H) and partially defoliated trees (LID) which appear green. Churcher and McLean (1984) and Churcher (1984) outlined a simpler key for inter-preting bark beetle-attacked spruce. Using colour infrared film, healthy trees appear "red", attacked trees appear "red-brown" to "brown". Dead trees are described as "hav-ing no foliage". These would appear blue (Murtha 1972). To some extent, therefore, it seems possible to distinguish attacked trees on the basis of their "colour" on colour infrared film. 2.3 Densitometric analysis Densitometric analysis of colour infrared film has been used to assess its potential for de-tection of bark beetle-attacked spruce (Churcher 1984), pine (Hobbs 1983) and Douglas-fir (Hall 1981; Hall et al. 1981; Hall et al. 1983). The work has been based upon use of a MacBeth TR-524 Transmission Reflection Densitometer (Anon. 1975) with subsequent analysis using standard statistical tests of the density measurements and their ratios. The results of densitometric analysis did not appear to be as good as those of visual interpretation of the same film. Churcher (1984) stated that "densitometry does not add significant information" to visual analysis. Hobbs (1983) concluded that densito-metric analysis was "complicated and, in the light of the visual interpretation results, 10 unnecessary." Hall (1981) stated that the attacked trees "exhibit a marked colour change" which was "consistent in all successfully attacked trees." However, the results of densitometric analysis did not reflect the consistency. Three papers using the same data but different statistical analyses claimed to distinguish 67 percent (Hall 1981), 50 percent (Hall et al. 1981), and 60 percent (Hall et al. 1983) of the attacked trees. Hobbs (1983) attributed the poor results of densitometric analysis to variation in the data: "The results of one-way analysis of variance between each of the attack cat-egories showed little difference between the film response values and their ratios for each of the attack categories. The standard deviation about the mean was generally so large that significant differences did not exist between most of the attack categories." Churcher (1984) commented that "while the average variation of densitometric read-ings for one given tree crown at one dye-layer was 5%, it was as high as 35% in some cases." He attributed the variation to the large (1 mm) aperture of the MacBeth den-sitometer. He explained that "not only would the tree crown be measured, but limbs, bark and possibly surface vegetation could be included." However, image intensities are not only affected by surface material, but also by shape, illumination, shadow, viewing direction and path effects. Slight movement of the film between replications of readings with the MacBeth den-11 sitometer could produce differences in the amount of contained shadow within the tree's image visible to the aperture of the densitometer, thereby changing the recorded "film response value." Similarly, a slight shift of the film so that the aperture fell more on the side of a tree crown in the image than a previous reading would produce variation in the "film response value" due to effects of a change in the orientation of the foliage imaged in the two points of the photograph. Banner (1984) used a median test to demonstrate that statistically significant dif-ferences could be produced by sampling intensities using different views of the same tree from overlapping photographs.1 The significant differences were not likely due to changes in the foliage from one view of the tree to another. They were primarily caused by variations in image intensity resulting from the changes in camera position for the different views. Ratios of dye-layer densities have been used to reduce the variability inherent in the densitometric data. The technique received mixed reviews regarding its effectiveness. Hall found that "the ratios had a much smaller range within each class" (Hall 1981; Hall et al. 1981; Hall et al. 1983). According to Churcher (1984), ratioing reduced the variability "slightly" in some cases and "greatly" in others. From her comments quoted above, it is clear that Hobbs (1983) did not feel that ratioing reduced the variability sufficiently. *A summary of the methodology and results related to this discussion are given i n Appendix A. 12 Chapter 3 Data and facilities 3.1 The Study Area A n active spruce beetle infestation at Chapman Lake near Smithers, B .C . was chosen as the study site (Figure 3.1). Tree species composition of the 10 hectare site was primarily Engelmann spruce with a small aspen (Populus tremuloides Michx.) and lodgepole pine (Pinus contorta Dougl.) component. Ground assessments conducted in August, 1983 indicated that up to one third of the stems were currently attacked. 1 Figure 3.2 shows an aerial view of the study site. 3.2 Aerial photography Aerial photographs were acquired by Integrated Resources Photography Limited of Van-couver, B . C . on September 10, 1983 between 12:10 and 12:50 Pacific Daylight Saving 1 Preliminary ground assessment data supplied by T. Maher, Northwood Pulp and Timber Limited, Prince George, B.C. 13 Figure 3.1: Location of study site on Chapman Lake. 14 Figure 3.2: Aerial view of Chapman Lake study site. Coloured tarps used to identify flight lines are visible at both ends of the study site (indicated by arrows). 15 Time. Two wingtip Vinten 70-mm cameras (Williams 1978) with 75-mm lenses (3 inch), Wratten 12 and CC20M filters, and Kodak Aerochrome Infrared 2443 (CIR) film were used. The requested flight parameters also included an approximate scale of 1:2500, forward overlap of 80 percent, and sidelap (from one flight line to its neighbour) of 60 percent. The 75 millimetre lenses were used to ensure that a significant camera viewangle effect would result in the photographs. The high degree of overlap was requested to provide multiple photographic views of each tree in the study site. 3.3 Field work 3.3.1 Flight line markers Coloured tarps were suspended between trees at the beginning and end of each flight line (Figure 3.2). The tarps were placed such that the pilot would have an unobstructed view of the tarps at both ends of a flight line as he approached the line during photo acquisition. The tarps for each line were a distinct colour to provide rapid identification of the matching tarps for any particular line. The assembly procedure is given in detail in Appendix B. The marker assembly was labour intensive and time consuming, taking an average of one day to set up each tarp. However, a system to provide highly visible flight line markers was essential for obtaining the required amount of overlap between flight lines. In this respect, the tarps were very 16 effective. 3.3.2 Ground data collection Ground data for 1128 trees was collected in October, 1983. Trees having no foliage were checked to confirm that they were old attack. If so, they were not given identification numbers and no further data was collected for them. Trees with foliage were inspected for attack status, presence of cones, general crown colour, shape and condition. Those with full and vigorous foliage and which showed no visible evidence of stress were identified as "potential normal" trees. The presence of small trees which could be confused in the photographs with a tallied tree were noted. 3 . 4 Laboratory work All analyses were conducted at the UBC Laboratory for Computational Vision (LCV). The primary equipment of the Laboratory used for this thesis included: • a DEC VAX 11/780 computer • an O P T R O N I C S C-4500 colour film scanning digitizer • a Raster Technologies Model One/25 image display workstation Other input and output peripheral devices were also used. 17 3.4.1 Scanning of photographs Scanning of the 70-mm colour infrared transparencies was done using the O P T R O N I C S C-4500 colour film scanning digitizer. Eighty-three 70-mm colour infrared transparen-cies were scanned using a 50 pm aperture and 0 to 2D range. " D " represents "density" or "optical density" which is an expression of the opacity of film. Density is defined by the formula D = log 1 0 ^ where T is the percentage of light transmitted through the film. A density of 0 is equivalent to 100 percent transmission and would be represented by a digital value of 255. A density of 2 represents 1 percent transmission and would result in a digital value of 0. During scanning, three successive scans through colour separation filters record the intensities of the red, green and blue transmission components (Deigan 1981). Three eight-bit digital images are produced for each transparency. The three images may be displayed on a C R T by assigning the blue, green and red colour guns to the respective digital images producing a visual impression similar to viewing the original photograph. Hence, the three images will be hereafter referred to as the blue, green and red images according to this assignment. At a scale of 1:2500, a 50 p,m aperture yields a ground resolution of |ra x |m per pixel. The number of pixels per tree ranged from about 200 to over 2500 and averaged about 900. 18 In contrast, the 1 mm aperture of the MacBeth densitometer used in previous studies would measure a circular area about 2.5m in diameter on the ground at a scale of 1:2500. Three measurements were taken using the MacBeth by Hobbs (1983) and Churcher (1984). The density measurements were averaged to provide one "pixel" for the analysis. The number of measurements taken by Hall (1981) were not specified. Further details regarding the characteristics of the O P T R O N I C S C-4500 scanner may be found in Heiss (1985) and Deigan (1981). Additional information regarding the fundamentals of densitometry may be found in Scarpace (1978). 3.4.2 Software Existing L C V software was employed and other software was developed to sample images, view the data and implement the technique to classify the attack status of trees in the photographs. A list of the programs and a brief description of each is provided in Appendix C. 19 Chapter 4 "Intensity triplet space'5 4 .1 Considering several viewpoints1 "Intensity triplet space" (ITS) is a histogram giving the frequency of each triplet in a 3-dimensional space in which the axes are defined by the range of possible intensity values in the three images (blue, green and red) of a colour digital image. The distribution of data in ITS is dependent upon the film and scanner calibration of the sampled image. Figure 4.1 shows multiple views of a "red" tree (number 119). The different views were obtained using overlapping ground coverage from adjacent 70-mm photo frames. This tree is "normal" or unattacked. However, for this discussion, the important point is that it appears red to a human interpreter. Figures 4.2 to 4.10 are graphic representations of the distribution of image intensities in intensity triplet space for each of the views of tree 119. Intensity triplet space has been depicted by slicing the space along the red axis and 1 T h i s section uses results originally presented in Banner (1984). The relevant discussion is repeated here due to limited availability of the original paper. 20 Figure 4.1: Nine views of a normal or "red" tree (119). Partitions in composite images are identified according to position: vertically: horizontally: - " T " for top - " L " for left - «M" for middle " " C " for center - " B " for bottom " " R " f o r r i S h t For example, the tree in the top left corner will be identified as being the " T L " view. 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K m : | I f ("| I I I ES s 3 8 CO 26 I I I I I 1 I I I 1 I I I I I I 8 raaa I 1 1 1 I 1 1 | I I I | I I I 8 03 | I I I | I I I 8 K33W I 1 1 1 I 1 - " a i-a s r § 5 11111111 11111111 -2 a -3 a I 1111 11 I 8 H33W J I I I | M I E-3 s 3 s I I I I I I I I 8 K33BO | l I I [ l I I 8 M33tia F3 8 3 CD CD 11 1 1 I 1 1 g -3* 3 8 -3 2 11111111 E-3» 3 I 1 1 1 I : g F3? 3 I 1 1 1 I 1 1 1 g 3 I I I I I I I I 8 KZ3U9 ' e H i 3 8 I 1 1 1 I 1 E-3« 3 8 I ' 1 1 I 1 1 1 8 K3MO -8 g r3 = 3 8 1-8 11 11 j 111 8 «n» I " 1 1 1 1 8 N U B -3S 3 c r3 11111111 -3 B ! 1 E-3» K p T T T T T T T 3 NEW F 8 I 3 11111111 1-8 g -3 z 3 8 j I I I j I I I : F3? 8 I I I j I I I tcaa 8 8 •3 5 L3 S 3 r i i f i i i 1111111 3 s i 3 11111111 -3 B I I I I I I I I E-3i 3 8 CD o CD O cd: CD " a •1—( w CD CD IH tlf l 27 I I I I I I I I BLUE 298 II I I II I I > S U C Zflfl a to IB In RED I I I | I I I | 0 BLUE 255 IB to 13 In RED I I I [ I I I | 0 BLUE 156 24 to 31 h RED -I I I | I I I | I to 38 In RED I I I j I I I j BLUE sas 40 to 47 In RED I I I | I I I | 0 BLUE 255 40 to 59 in RED I I I | I I I j SLUE 266 58 to 83 h RED I I I | I I I | •4 to 71 In HEP I I I j I I I | 0 BLUE 236 72 to 78 h RED I I I | I II | 0 BLUE 255 80 to 87 In RED I I I | I I I ) BLUE 155 88 to 95 h RED " I " 1 ! o sue at n to 103 h RED I I I | I I I | o BUJC ass 104 to 111 In RED I I I | I I I | ) aujc lis 112 to I K ki RCO I I I | I I I | 0 BLUE 255 120 to 127 In RED (si 00 I I I | I I I | 0 B U C 250 120 to ISO In RED I I I | I I I | » B U Z »S 13B to 143 h RED I I I | I I I | 0 K iJE 295 144 to 191 In RED I I I | I I I | 0 BLUE 256 132 to 13t In RED I I I | I I I | 0 B U C 236 100 to 137 In RED I I I | I I I | t UE a ISO to 170 In RED I I I | I I I | > BUJE 235 170 to 103 In RED I I I | I I I | 0 BLUE 253 104 to 1S1 In RED I I I | I I I | 0 S U E 290 1B2 to I M In RED 200 to 207 h RED I I I | I I I | 206 to 215 tn RED I I I | I I I | 0 BLUE 2 » 218 to 223 tn RED I I I [ I I I | 0 BLUE 259 224 to 231 In RED I 1 I | I M | 0 flLUC 255 232 to 238 h RED I I I j I I I | 0 BLUE 259 240 to 247 Ln RED I I I j I I I | D BLUE 259 248 to 259 tn RED Figure 4.8: Intensity triplet space for the "BL" view of tree 119. 6Z 0 CD CO I .1 I I I I I I .1111111 tr 3 5-8 s s SE — o — se t 11111 11111 1 1 1 1 1 1 1 1 r a »6-,i i ' i ' ' i i h-11 • • 11 GREEN g 1 ' ' I ' ' ' I CD GO r-»- 3 E-11111111 1 1 11 1 1 11 B *E 8 - '. ;£E s i-1 1 11 1 1 11 11111 1/1 •a o CD O tr CD I i i i I s 2 I i i I i i i I I I i I I 3£E C R E E N g I I I I I I I I 8 •E-3 j I I I I I I I 8 tr 3 « CREEN g i i i 1 i i i I CREEN g I I 1 I I I I I CREEN I I I t I I I I I td q < CD 3 i s g B M -GREEN g | I I I I 1 I 1 G R E E N g ' ' • I ' ' ' I s 8 g i 1 i ' i ' 11 ' ' I ' E 11111 CD CD s I-B » J O R E E N g I I I I I I I I St » aEE ' 1 1 1 1' i r 5 SE i 1111111 s * eq C R E E N g 11111111 CO C R E E N g ' ' ' I ' ' I I » CREEN g 1 I I I I 1 I I 8 fr 51-C R E E N | t I 1 I t I i S CREEN g I I 1 I I 1 1 OS CD CD L O 4 t—' CD 00 X) o CD O •1 CD td CD 3 3 s i SE CREEN g 3 EE I I ' I ' ' I 1 ' ' I I ' I ' I s S-9 M CHEN g ' ' 1 1 I 1 1 I 5 s I-WttEH g I J J J ) J J J » £-3 3 a i • 1111 • i s * SE i si 11111111 » s fi-ts-11111111 8 s SE 3 8-a SE 3 a-1 i I I 11111 is J j 1111111 a *EE 8 r 5 5-11111111 8 a-a E-s -I 1 1 I I I I I 8 -! 5 E CftEZN g J I i J J 1 i 8 = SE i »E i . 111 ;s-GREEN g i I i i i I S i - 1 I i i i I 3 CREEK g I 1 I I 1 t I I i i 11 11 i I a r J E i 8 . CREEN g i i i I i i i I S 2 EE GREN g i i I i i i I -i CD CD & 8 t s i i I i i i I a a-a SE S 8 i 1111111 EE 11111 8 us-I I I I I I I I CO CREEN g I I I I ' ' ' I CREEN ] I I I I I I I I CREEN g ' I ' I ' ' I I CREEN g I I I I I 1 I I laying the slices out in a tabular format. Each slice represents an interval of eight intensity levels in the original image. Green and blue intensity values vary within each scattergram and the red intensity varies from one scattergram to the next. The darkness of the plotted points indicates the relative number of pixels found in the original image having a particular combination of intensity ranges. For example, any pixels in the original image having a combination of blue intensity between 160 and 167, green intensity between 128 and 135, and a red intensity of 216 to 223, would contribute to the darkness of one point in intensity triplet space. The number of pixels sampled with such a combination determines the darkness at that point. Backlit original images have proportionately more low intensities with few or no high intensity values. Frontlit original images have high as well as low intensities but have a greater frequency of high intensity values. Sampling from different areas of a photographic frame is equivalent to altering the viewing direction and will influence the image intensities regardless of any changes in surface reflectances. Hence, sampling from different portions of a photo frame will intro-duce unexplained variation when intensities are used to directly infer differences in the reflectance of surfaces. In Figure 4.11, the data for all nine views of tree 119 have been pooled together. The pooled data shows that the sampled intensity values lie within a well-defined "envelope" or portion of intensity triplet space even with changes in the viewer's position. In Figure 4.12, the data for all of the normal trees have been pooled. The "envelope" in ITS appears to be generally consistent for the other normal trees as well as tree 119. 31 3 i E-11111111 a 8" sS-• ' ' i ' ' • i 8" ;E^ i M 1 1 1 1 1 TO c -I a CD Ul I 6"= ORED* g I I I I I I I [ Ei GREEN I I I I ' I t s \IZ-5„j GREEN g I I I I I I I I I 1 I I I 1 t I OREEN g ' I ' 1 I I ' I 5E-E i 1 1 ' ' i 11111111 W •a o CD O 6 E-3 1 gJ i i i I i i i I CREN g I I I I I t I I CREEN g 1 I I I t 1 I 1 » Ed \ 3 I-GREEN g I I I 1 I I I I i I I I I f I I 3 !E-CREEN g I I I I I I I I :&i GREEN g ' I ' I ' I I I CREEN g 1 I I I I 1 I I <i 3 O H i B 1 s s I ' I I I I ' s s . J ' ' ' I ' ' ' I CD CD CD a* 3 ? i i i I i i i I . o -a » sE-' 11111 I 5 E I I I I I I I I I I I I I I I I q CREEN g CREEN g CREEN g 3 raw 3 raw ° 3 KEW ° 3 N33W ° | I I I | I I I 3 raw -8 " fl H I B s 1 1 1 1 1 I I 1 I I". • I I 8 wwa 11111111 g E-aS : 1 -as 11111111 8 raw | I I I | I I I g raw | I I I | I I I ' | I I I | I I I 8 raw | I I I | I I I H 5 B s F a 8 j-S s S | I I I | I I i 8 K 3 S O I I I | I I I K33W E-a« t 8 I I I I I I I I I I I I I I I I' 8 raw F ag E 3 * B 111111 r -31= 11111111 -a a -3B > R -3 8 B 8 « 1 a* 8 I 1 1 1 I 1 1 8 raw | I I I | I I I r l 8 s 8 I 1 1 I 1 1 E3 i " 1 1 M 1 1 8 raw | I I I | I I I 8 raw •« g -3 2 B 8 - o *~ -3? s 8 | I I I | I I I I I I I I I -a a -3 s B 33 B o 3 I I I I I I I I -3 s r» a fi I I II [ I I I 3 2 | I I I j I I I S N33H8 | I 1 I | I I 1 g -3 S 11111111 F 8g E 3 ? 8 Ui CD cu ed r H o ed u o «4-l CD o ccS a CO cu r—< CH • r H r H Ui CJ CD CD r H 33 In Figure 4.13, the distribution of intensities sampled from the " T L " view of tree 119 is shown as a stereogram. A central axis, or the first principal component, of the distribution has been computed and superimposed in the figure. From the discussion so far, the distribution of intensities along the axis appears to vary primarily according to geometric factors like surface orientation and viewer position. Lodwick (1981) argued that the first principle component of images relates almost totally to brightness differences due to factors such as sun position, slope and aspect. Since the intensity distributions for different views of the normal trees can be con-tained within a characteristic "envelope" in ITS, the orientations of distributions for individual views should be similar. However, the orientation of the central axis calcu-lated using a single view of a tree can be quite variable (Figure 4.14). Pooling the data for all views of a tree permits calculation of a central axis representative of the overall envelope for a tree. In Figure 4.15, the axes calculated from the intensity data pooled from all views for each normal tree are shown. 34 Figure 4.13: Stereogram of intensity triplet space for a "red" tree. The image intensities were sampled from the " T L " view of tree 119. The first principal component of the distribution has been superimposed. The first component explained 98.64% of the variation. Statistics relating to the calculation of the principal components are given in Table 4.1. 35 Table 4.1: Computation of the central axis for the "TL" view of tree 119. VARIANCE-COVARIANCE MATRIX blu grn red blu 2925.8 grn 2786.2 2699.3 red 2464.0 2385.1 2213.6 PRINCIPAL COMPONENTS (using variance-covariance matrix) pel pc2 pc3 eigenvalue 7.73206e+03 8.48588e+01 2.18448e+01 % variance 98.64 1.08 0.28 cumulative 98.64 99.72 100.00 COEFFICIENTS ( pel blu 0.6120 grn 0.5890 red 0.5278 igenvectors) pc2 pc3 -0.5051 -0.6086 -0.2225 0.7769 0.8339 -0.1613 PARAMETRIC EQUATIONS OF CENTRAL AXIS blu = 106.1712 + t( 0.6120) grn = 112.6055 + t( 0.5890) red = 139.8150 + t( 0.5278) 36 Figure 4.14: Central axes for each view of tree 50. The central axes for all nine views have been plotted. However, some of axes are obscured by others and are not visible in this figure. 37 Figure 4.15: Central axes for all five normal trees using pooled views for each tree. 38 4.2 Red, green and blue trees In Section 4.1, the effects of imaging geometry on intensity distributions in intensity triplet space were demonstrated for trees which appeared red in the photographs. In this section, intensity distributions will be shown which correspond to trees which appear different colours-red, green and blue. As in the previous section, the correspondence between colour appearance in the photographs and the tree's condition in the real world is not germane to the discussion. For clarity of presentation, the trees will be identified according to their general colour appearance in the photograph. Stereograms showing the distribution of image intensities in intensity triplet space for a green tree and a blue tree are given in Figures 4.16 and 4.17.2 Photographs of the trees are shown in Figures 4.18 and 4.19. The orientation of the central axes are different for trees which appear different colours. The axis for the red tree (Figure 4.13) pointed to a location along the red axis. The axis for the green tree points to a position on the green axis. The axis for the blue tree points to a spot on the blue/green plane of the cube. As in the case of single views of the red trees seen in Section 4.1, a central axis calculated using only a single view can be variable (Figure 4.20). However, axes which have been calculated using data pooled from multiple views have similar orientations for 2 G r o u n d data was collected only for trees w i t h foliage. Therefore, the "green" and "blue" trees were not given ground t r u t h numbers in the field. 39 Figure 4.16: Intensity triplet space for a green tree. Image intensities were sampled from the "TR" view of the green tree shown in Figure 4.18. The first principal component, superimposed over the data, explained 97.19% of the variation. 40 Figure 4.17: Intensity triplet space for a blue tree. Image intensities were sampled from the " M C " view of the blue tree shown in Figure 4.19. The first principal component, superimposed over the data, explained 98.66% of the variation. 41 42 43 Figure 4.20: Central axes for each view of a blue tree. The image sampled to produce the axes is shown in Figure 4.19. The orien-tations of axes based upon single views can be quite variable. 44 trees which appear the same colour (Figures 4.21 and 4.22). In Figure 4.23, the intensity distributions and axes from Figures 4.13, 4.16 and 4.17 have been shown together. When the axes are extrapolated, it appears that they converge toward a point outside of the intensity triplet space cube. 4 . 3 ITS and Ratioing Ratioing has been used to reduce the variability of densitometric measurements (Sec-tion 2.3). Using the intensity distributions seen in Section 4.2, the effectiveness of the technique for these data can be evaluated. In Figure 4.24, the mean intensities for each view of the red (119), green and blue trees have been plotted with the central axis which was computed for each tree. An ideal technique to reduce the variability of the mean intensities associated with the different views of the same tree would use the tendency of the means to be adjacent to the respective axes. Ratioing of the intensity values does not do this. The associated axes would have to pass through the origin of ITS for ratioing to be an ideal approach. Consider a two-dimensional rather than three-dimensional space. Two points and [x2,y2] lie on the line Y — mX + b t/i = mxi + b t /2 = mx2 + b 45 Figure 4.21: Central axes for five green trees using pooled views for each tree. Intensity data were sampled from five green trees as in Figure 4.18. The data from all views for each tree were pooled together to compute the axis for each tree. 46 Figure 4.22: Central axes for five blue trees using pooled views for each tree. Intensity data were sampled from five blue trees as in Figure 4.19. The data from all views for each tree were pooled together to compute the axis for each tree. 47 Figure 4.23: Convergence of central axes. The central axes for the red, green and blue trees converge when extrapolated outside intensity triplet space. The axes were computed using data from multiple views of tree 119, the green tree shown in Figure 4.18 and the blue tree in Figure 4.19. 48 Figure 4.24: Mean intensities and central axes for red, green and blue trees. The mean intensities for each view of the red (119), green and blue trees are shown with the computed axis for each tree. The positions of the means in ITS are very close to the respective axes. 49 Constructing the ratios, — = m H Xi Xi yi , b — = m H Xi x2 Therefore, if y±=m Xi x2 then b__b_ Xi x2 Ignoring the case where xi — x2 (and the two points are the same), b must equal 0 or, in other words, the line must pass through the origin. While ratioing of the intensities may reduce the variability in the data, it is not an ideal technique to use since the central axes for these data do not typically pass through the origin of ITS. A technique is required which is more suitable for data which has a central axis that does not pass through the origin. 4 . 4 Hue, saturation and lightness Figure 4.25 shows the geometric relationships between an orthogonal coordinate system, such as for intensity triplet space, and a cylindrical coordinate system which more closely approximates the visual sensations of hue, saturation and lightness (Judd and Wyszecki 1975). It depicts an idealized case in which the film and scanner have been calibrated. The lightness axis joins the triplet composed of the minimum intensity in each of the 50 B Figure 4.25: Comparison of hue, saturation and lightness with intensity triplet This figure represents an idealized comparison of the two coordinate sys-tems. The lightness axis joins the origin ([0,0,0]) and the triplet composed of the maxima in each of the blue, green and red dimensions ([255,255,255]). Saturation is the perpendicular distance of a point from the lightness axis. Hue is the azimuth of the saturation vector. 51 blue, green and red images ([0,0,0]) and the triplet composed of the maximum intensities ([255,255,255]). Saturation is measured perpendicular to the lightness axis. Hue is the azimuth of the saturation vector. The dimensions of hue, saturation and lightness are very close to capturing the char-acteristics required to differentiate between intensity distributions of the red, green and blue trees. The lightness axis is similar to the central axes shown in Figures 4.13, 4.16 and 4.17. The latter axes, however, do not have fixed orientations in relation to the space. The central axes observed for the sampled trees vary in orientation according to the visual colour of the tree on the film. It was noted in Section 4.2 that the axes appear to converge toward a common point. This will produce undesirable variation between frontlit and backlit views of trees for a classification scheme which uses saturation as a feature. Consider points A, B and C in Figure 4.26. While points A and B have the same calculated hue and saturation, it is points A and C which should be classed in the same category. 52 Figure 4.26: Three points in a hypothetical calibrated intensity triplet space. Points A, B and C lie in a plane with the lightness axis (shown as a dashed line). Points A and B have the same calculated hue (since they lie in the same plane with the lightness axis) and saturation (since they are the same perpendicular distance from the lightness axis). However, according to the relationships seen in Section 4.2, points A and C should be grouped together. 53 Chapter 5 "Projected intensity triplet space55 5.1 The transformation So far it has been claimed: • the distribution in intensity triplet space of image intensities sampled using multiple views of a tree can be characterized by a sausage-shaped "envelope" • the orientation and position of the envelope in ITS is related to a tree's colour in the image • the central axis, or first principal component, computed using the pooled intensity triplets from multiple views of a tree can provide an estimate of the orientation and position of the envelope • the frequency distribution in the direction of the central axis is strongly influenced by geometric factors such as surface orientation and viewer position 54 • the intensity triplet "envelopes" for trees of different colour point toward a common point outside the bounds of intensity triplet space A technique is needed which makes the "colour" of a sampled tree explicit and suppresses other information. It appears that the first principle component computed from the pooled intensities of multiple views of a tree could be used. However, the requirement to sample multiple images of a tree is not desirable. In Section 4.2, it was demonstrated that the orientation of central axes computed from single views could be quite variable. This section introduces "projected intensity triplet space" (PITS) as a transformation that will permit the assessment of the "colour" using a single view of a tree. Details regarding the implementation of the procedure will be given in Chapter 6. If the observations listed above are true, a perspective projection of intensity triplet space as shown in Figure 5.1 can be used to retain the orientation information related to the "colour" but remove the variation in the direction of the central axes. The point towards which the central axes converge (as shown in Section 4.2) is used as the viewpoint of the projection. A perspective projection from this "convergence point" will project down the central axes of a sampled tree regardless of its visual colour. Each pixel in an image associated with a tree is sampled and the intensity triplet is projected using the convergence point as the viewpoint. The sampled intensities are projected onto a plane at the origin of intensity triplet space. The plane is positioned perpendicularly to the line from the origin to the convergence point. Selection of the origin of intensity triplet space as the center of the plane is not crucial to the technique. 55 Figure 5.1: Projected intensity triplet space. Sampled image intensities are projected using a perspective projection from the convergence point onto a plane centred at the origin of intensity triplet space. However, the plane should be roughly perpendicular to the orientations of the central axes for the range of data to be sampled and projected. The plane is tesselated with a square grid. "Projected intensity triplet space" is the accumulated frequencies of intensity triplets projected onto each square of the grid. The resulting transformation is stored as an image in which the pixel intensities represent relative frequency. 56 In Figure 5.2, projected intensity triplet space images are shown for frontlit and backlit red, green and blue trees. The distributions for frontlit and backlit trees are similar indicating that variations due to changes in camera viewangle are not large. The projected intensity triplet spaces of the red, green and blue trees, however, are distinctly different in terms of the overall position and shape of the frequency distributions. 5.1.1 Identifying the "colour" Projected intensity triplet space is a form of histogram. Peaks of histograms are com-monly used to identify classes. We may be able to label the "colour" of a sampled tree using the location of peaks in projected intensity triplet space. Histograms may be noisy leading to confusion of small local peaks with major ones during selection. Glicksman (1982) used Gaussian smoothing to eliminate minor peaks in histograms prior to using a local operator to locate the major ones. The value of a in the 1-D Gaussian function determines the degree of smoothing performed on the histogram. In Figure 5.3, a his-togram has been smoothed using a values of 1 (b) and 5 (c). In Figure 5.3c, only the major peak is evident while in Figure 5.3b several minor peaks as well as the overall peak are evident. Once smoothed using the appropriate Gaussian filter, a local operator may be used to locate the peaks. Similarly, the projected intensity triplet space images may be smoothed using Gaus-57 Red frontl it Red backl i t C 0 Blue frontl it Blue backl i t Figure 5.2: Projected intensity triplet space images. Projected intensity triplet space images for frontlit and backlit red, green and blue trees. The data for the frontlit and backlit red tree are from the " M L " and "BR" views of tree 119 shown in Figure 4.1. The " T C and "BL" views of the green tree shown in Figure 4.18 and the " T C " and "BR" views of the blue tree in Figure 4.19 were used as the frontlit and backlit green and blue trees. The axes for ITS have also been projected to facilitate interpretation. 53 Figure 5.3: Gaussian smoothing of histograms. Histogram before Gaussian smoothing (a) and after smoothing using cr values of 1 (b) and 5 (c). Minor peaks are enminated by smoothing using an appropriate a value. After smoothing, a local operator may be used to locate the peaks. 59 sian smoothing to eliminate minor peaks. In Figure 5.4, a PITS image has been smoothed using a values of 1, 3 and 9. The corresponding peaks are shown in Figure 5.5. The location, or row and column coordinates, of the major peak in projected intensity triplet space may be used as an indicator of the overall colour of a sampled image of a tree. The locations of minor peaks in PITS may be relatable to features of interest in the image such as cones. 60 N o s m o o t h i n g S i g m a — 1 . 0 S i g m a = 3 . 0 S i g m a = 9 . 0 Figure 5.4: A PITS image smoothed at a values of 1, 3 and 9. 61 No s m o o t h i n g S i g m a = 1.0 S i g m a = 3 . 0 S i g m a = 9 . 0 gure 5.5: Peaks associated with smoothed PITS images in Figure 5. 62 Chapter 6 Implementation This chapter outlines the implementation of the projected intensity triplet space trans-formation to distinguish bark-beetle attacked spruce on colour infrared film. Section 6.1 discusses the procedure used to select the "convergence point" as a viewpoint for the projection. Section 6.2 outlines the choice of data for the "training set". The software and procedures used to sample and interpret trees in a photograph are described in Section 6.3. 6.1 Locating the convergence point It was observed in Section 4.2 that the central axes of distributions in intensity triplet space for trees which appeared red, green and blue converged toward a point outside the intensity triplet space cube. This point was labelled the "convergence point" in Chapter 5 and was used in the development of PITS as the viewpoint of the perspective projection. Trees were selected which visually appeared to be a uniform colour in the pho-63 tographs. Fifteen trees were chosen to calculate the convergence point; five each of trees which appeared blue, green and red in the photographs. Depending upon overlap-ping coverage in the photographs, six to nine views of each tree were made into composite images for sampling. Graphic masks were constructed interactively using the Raster Technologies Model One/25 image display. Pixels which visually appeared to be an inconsistent colour were excluded. Pixels lying on a boundary with another surface in the image were also avoided. Finally, only pixels with non-zero values (with a density less than 2D) in all three (blue, green and red) images were used. The parametric equations for the central axis of the distribution for each tree were calculated. The convergence point was the point which minimized the squares of the distances to each of the axes. The image intensities for all views of the tree were used together for the calculation. In Section 4.1, it was demonstrated that combining data from multiple views of a tree facilitated calculation of the central axis. Convergence points were calculated for each replication (one blue, one green and one red tree) individually and then calculated for all fifteen trees together. The calculated points are listed in Table 6.1 and shown in Figure 6.1. The point calculated using all fifteen trees ([383,366,353]) will be used as the view-point for the transformations to PITS. 64 Figure 6.1: Positions of calculated convergence points in relation to intensity triplet space. 65 Table 6.1: Convergence points repl blue green red 1 368 355 338 2 400 382 367 3 370 356 344 4 390 372 365 5 393 373 357 all 383 366 353 6.2 Interpreting attack status Trees were selected as training sets for three classes: unattacked trees, current attack and old attack. Multiple photographic views of each were'sampled and the major peaks in PITS were determined. By definition, the normal trees (the training set for the unattacked class) all have a similar colour appearance in the photographs (Section 2.2). These trees have been referred to as the "red trees" in previous sections. Five trees were selected which had been identified in the field as "potential normal" trees and had the visual characteristics of a normal tree in the photographs. Twelve attacked trees were selected to represent the range of appearances in the 66 photographs expected for attacked trees. These trees appeared from "tan-coloured" (Figure 6.2) to "tan-coloured with green spots" (Figure 6.3). These trees would have mostly green foliage when seen on the ground. The "yellow flagging" seen in Figures 2.1 and 2.2 contribute to the tan colour. The green spots result from bare spots in the tree's crown created by foliage loss. All of the chosen trees were fully current attacked according to the field data. The green and blue trees used in locating the convergence point were used again as the training set for the "old attack" class. Multiple views of five green and five blue trees were sampled. Trees which appear green in the photos are dead and mostly defoliated. They still have their fine branches. Trees which appear blue in the photos have been dead longer than the green trees and have also lost their fine branches. The major peaks in PITS for all of the trees used for the training set are shown in Figure 6.4. Straight-line decision boundaries are shown that separate the unattacked, current attack and old attack categories of the training set with only minor overlap. 6 . 3 Putting it together Four programs are used in the process of "interpreting" a tree: 1. tform samples the image and transforms the data to PITS 2. direct does the Gaussian smoothing 3. getpeak identifies the location of the major peak 67 Figure 6.2: Multiple views of a "tan-coloured" current attacked tree. There is a small tree next to the sampled tree which appears as an area of "red" or vigorous foliage. The sampled portion of the photo included only the area which is tan-coloured in appearance. 68 69 G • u n a t t a c k e d • c u r r e n t a t t a c k • o l d a t t a c k Figure 6.4: Decision boundaries and the training set Decision boundaries may be drawn to separate the peaks for the unattacked, current attack and old attack classes with a minimum of confusion. 70 4. classify produces a decision on the interpreted attack status of the sampled tree A 3-colour image and graphic masks identifying the locations of each of the trees to be interpreted are required as input. A text file containing a decision of "unattacked", "current attack" or "old attack" for each tree is the output. Pixels in the 3-colour image are sampled by tform if non-zero values are found in the corresponding row and column of the graphic mask. The intensity triplet is transformed to a location in PITS as outlined in Section 5.1 using the perspective transformation given in Newman and Sproull (1979). The frequency of projected intensity triplets is accumulated for each location in the transformed space and then written out as an image in which the frequencies are represented by pixel intensities. A a of 9.0 is used for the Gaussian smoothing requiring a mask size of 45 pixels. There is a tradeoff in the choice of a. A larger value of a ensures that the smoothed PITS image will have only one peak. However, the convolution operation varies according to n2 x 2m where n and m are the pixel dimensions of the image and mask files.1 Increases in the mask size result in larger computation times. Getpeak looks throughout the smoothed PITS image for pixels which have the largest intensity within a 25 x 25 window. The row and column coordinates and associated intensity value are output. In most cases, only one peak will be found. However, outlying pixels in the projected intensity triplet space may produce minor peaks such as those in 1 Direct performs two one-dimensional convolutions over the image to produce the effect of one two-dimensional convolution at a smaller computational cost. A two-dimensional convolution would vary according to n 2 X m 2 . 71 Figure 5.4 in the image smoothed using a = 3.0. The intensities for the peaks are used by classify to select the appropriate peak. Classify uses the row and column coordinates of the major peak in PITS and the equations of the two boundaries shown in Figure 6.4 to produce a decision on the attack status of a sampled tree. A n equation of a straight line in PITS may be expressed as A(row) + B(column) + C = 0 Substitution of the coordinates of the major peak into the equation of one of the bound-aries produces a zero result if the peak lies on the boundary, a positive result if it lies on one side of the boundary, and a negative result if it lies on the other side. Substituting coordinates into the equations of both boundaries gives two results which could each be zero, positive or negative. The two results are then used to access a look-up table which provides the appropriate interpretation. 72 Chapter 7 Methodology Evaluation 7.1 The convergence point Accurate location of the convergence point is crucial to the use of projected intensity triplet space. If the convergence point is actually located at the intersection of the central axes of the sampled trees, then according to the relationships summarized in Chapter 5.1, the locations of major peaks for frontlit and backlit views of trees should not be significantly different. If, however, it has not been accurately located, the locations of peaks in projected intensity triplet space will differ according to the viewangle as well as the "colour" of the trees. The peaks in projected intensity triplet space are the basis for interpreting the attack status of trees. Therefore, the adequacy of the convergence point should be assessed in terms of the peaks in projected intensity triplet space rather than on the numbers of trees sampled or coordinates of the convergence point. If the selected convergence point has been located well, the positions of peaks for different views of the same tree should 73 Figure 7.1: Points displaced around the convergence point. Points were computed with distances of 25 and 50 intensity units from the convergence point in six directions. The directions of displacement have been labelled with the numbers 1 to 6. The same labels are used to identify the directions in Figure 7.2. be less variable than if another viewpoint were used for the projection. In Figure 7.1, points have been located which are 25 and 50 intensity units from the convergence point [383,366,353]. The displaced points were used as the viewpoint to compute projected intensity triplet space images to assess the positioning of the convergence point. Gaussian smoothing was performed and the major peak for each view was located. 74 Nine views each of two trees were used. Tree 166 is a normal tree which was not used for the determination of the convergence point. Tree 396 is a current attacked tree. The distances between the locations of peaks for each view and the mean position of the major peaks for the tree were calculated. In Figure 7.2, the mean distance and stan-dard deviation of the calculated distances are plotted for each point shown in Figure 7.1. Points in the first four directions are displaced in directions perpendicular to the line joining the convergence point and the origin of intensity triplet space. For both trees, the mean distances and standard deviations of the distances are greater using the displaced points than when the projection was done using the convergence point. The locations of the major peaks for different views of the same tree are more variable when the displaced points are used as the projection viewpoint. This supports the view that the convergence point was well placed with respect to the direction from the origin of intensity triplet space. The points in directions 5 and 6 are displaced along the line joining the convergence point and the origin of intensity triplet space. Displacement of the projection viewpoint in these cases does not have the pronounced effect seen before. Displacement toward the origin marginally increases the variability of the locations of peaks while movement away from the origin marginally decreases the variability. However, the average distances between the locations of peaks for each view and the location for the overall peak for the trees is less than two intensity units apart whether the convergence point or a point displaced toward or away from the origin is used as 75 'iL using convergence point • using point 25 units out I | using point SO units out 25 -\ T I I I I _ f : i ; i . i : i T I I T • : i : i TREE 166 T : i — L : i 6 T I t! TREE 396 T T 3 4 Direction 6 Figure 7.2: Effect of displacement of the projection viewpoint. Means and standard deviations of distances between peaks for each view and the mean of those peaks using points located 25 and 50 intensity units from the convergence point as the projection viewpoint. Numbers on the ordinate axis refer to the directions given in Figure 7.1. The means are indicated by points. One standard deviation is indicated by the dashed lines. The mean distance and standard deviation for when the convergence point was used as the projection viewpoint are shown by the horizontal line and shaded area. 76 the projection viewpoint. The standard deviations are also not appreciably different. Movement of the projection viewpoint toward or away from the origin will not affect the results as significantly as displacement in a perpendicular direction. 7.2 Geometry independence Is projected intensity triplet space independent of viewangle and other geometric effects? The major peaks for each of the nine views of tree 119 are shown in Figure 7.3. Some variation is to be expected since in each view, different portions of the tree are in view. However, is the variation seen in Figure 7.3 greater than what should be considered natural variation? For each normal tree, the distances, measured in PITS units, from the positions of the peaks for each view to the mean position or centre of the cluster of peaks were computed. The distances from the mean positions for each normal tree to the mean position for all normal trees were also calculated. A Kruskal and Wallis test (Steel and Torrie 1960) was performed to investigate whether the distances associated with different views were significantly larger than those between different trees. To perform the test, all of the measured distances were ranked from smallest to largest. The test criterion compares the accumulated ranks of the distances. The normal trees, by definition, visually appear to be the same colour. If the variation in locations of peaks among different views of the same tree is not greater than among 77 Figure 7.3: Major peaks in PITS for the nine views of tree 119. Some variation in the locations of peaks in PITS for different views of a tree must be expected. However, is this variation greater than what can be considered "natural variation"? 78 the various normal trees, then for purposes of interpretation, the variation between views may be considered insignificant. The results of the test are given in Table 7.1. The H of 8.548 with 8 degrees of freedom is not significant. The variation associated with locations of peaks for different views of the same tree is not greater than the variation from one normal tree to another. The accumulated rank of 438 is the second largest case. Generally, the variation found among normal trees tends to be larger than among different views of the same tree. By the reasoning given above, therefore, the variation attributable to differences in camera viewangle at the time of photo acquisition is not significant. 7.3 Gaussian smoothing In this thesis, each intensity triplet has been transformed to projected intensity triplet space. Gaussian smoothing has been used to reduce the projected data to a single representative point or "major peak". This same end result could be accomplished by computing the mean intensity triplet initially from the sampled image intensities and then projecting only the one point to PITS. The latter approach would be much less expensive to compute. Calculating the mean involves only accumulating the image intensities as they are sampled and dividing by the number of pixels. Only one perspective projection would have to be performed. The former approach requires performing hundreds of matrix multiplications for the perspective projections. Gaussian smoothing is also an expensive operation (Section 6.3). 79 Table 7.1: Kruskal and Wallis test of distances from peaks to means. tree E n 50 9 328 81 9 316.5 119 9 309 166 9 379.5 262 8 349 482 9 450 945 9 322 1063 9 ; 268 all normals 8 438 ; 79 3160 H = ^ i y E ^ - 3 ( n + l) i where: nt- is the number of samples in the »th sample and Zi is the sum of the ranks for the tth sample = T W ( 1 3 0 9 0 1 - 7 9 ) " 3 ( 8 0 ) = 8.548 with 8 df (not significant) 80 The more expensive approach was used for this thesis for two reasons: 1. Transforming every intensity triplet rather than just the mean facilitates a more complete visual inspection of the characteristics of the data. Immediate reduction of the data to a mean could "conceal" sources of variation which may have been evident otherwise. 2. It was initially thought that minor peaks might be useful for dealing with po-tentially misleading crown characteristics such as cones. Preliminary sampling demonstrated, however, that the major peaks were not affected by the presence of cones sufficiently to warrant the added complexity of considering minor peaks in PITS as well as the major peaks. Given that computational economy was not a major consideration for this thesis, it was considered that the benefit of being able to visually inspect the distribution of the transformed intensity triplets in PITS outweighed the added computational expense. 81 Chapter 8 The test frame A full 70-mm photo frame, which had a mixture of spruce beetle attack classes according to the ground data, was used to test the application of the projected intensity triplet space technique for detecting bark beetle-attacked spruce. A stereogram of the test frame is presented in Figure 8.1. Results of the computer-based interpretation are given in Table 8.1. The number of classes for the computer-based interpretation are less than the number of ground data classes. It was noted from the literature in Section 2.2 that there was some indication that whether a tree was attacked or unattacked could be interpreted by its overall colour appearance in CIR photographs. Trees which have been strip attacked or which have pitched out the beetle attack have been attacked, albeit with limited success. It is not likely the case that the tree's condition has deteriorated to the same extent that it would have for a successfully attacked tree. From the perspective of evaluating the interpretation technique, therefore, it is important to separate the computer-based interpretation results for these trees from those which were successfully attacked. 82 • m W*w Figure 8.1: Stereogram of the test frame. 83 Table 8.1: Interpretation results of test frame. Ground Truth Class Computer-based Classification E unattacked current attack old attack unattacked 21 (84%) 4 (16%) 25 full current attack 18 (32%) 39 (68%) 57 old attack 7 (11%) 56 (89%) 63 1983 strip attack 21 (78%) 6 (22%) 27 , 1983 pitch-out 46 (94%) 3 ( 6%) 49 old/mixed strip attack 10(40%) 15 (60%) • 25 E 116 74 56 246 84 Incorrect interpretations might be attributable to two primary causes: the system: a failure of the computational approach used to distinguish between trees which visually appear red-coloured, tan-coloured and green- or blue-coloured on colour infrared film, or the data: variation in the appearance of trees on the film and therefore a failure of the assumption that attacked trees may be interpreted by their overall colour in a GIR photograph. The following discussion will examine the computer-based interpretation to assess the relative importance of each factor. Briefly, the interpretation accuracy for trees which were unattacked, current attacked and old attacked was high (84, 68 and 89 percent respectively). These represent the "full" ground data classes: fully unattacked, fully current attacked or fully old attacked. In contrast, the percentage of trees from the 1983 strip attacked and 1983 pitched-out ground data classes which were interpreted by the computer to be attacked was very low (22 and 6 percent). A colour print of the test frame and results of the interpretation are presented at the end of the chapter. The figures are categorized according to attack class as given by the ground data. Trees referred to in the discussion are labelled in the appropriate figures. The figures to be found starting on page 91 include: Figure 8.2: Photograph of test frame. Figure 8.3: Key to locations of unattacked trees and their interpretation. Figure 8.4: Peaks in PITS for unattacked trees. 85 Figure 8.5: Key to locations of 1983 current attacked trees and their interpretation. Figure 8.6: Peaks in PITS for 1983 current attacked trees. Figure 8.7: Key to locations of old (1982) attacked trees and their interpretation. Figure 8.8: Peaks in PITS for old (1982) attacked trees. Figure 8.9: Key to locations of 1983 pitched-out trees and their interpretation. Figure 8.10 Figure 8.11 Figure 8.12 Figure 8.13 Peaks in PITS for 1983 pitched-out trees. Key to locations of 1983 strip attacked trees and their interpretation. Peaks in PITS for 1983 strip attacked trees. Key to locations of old (1982) and mixed (1982/1983) strip attacked trees and their interpretation. Figure 8.14: Peaks in PITS for old (1982) and mixed (1982/1983) strip attacked trees. Four unattacked trees were misinterpreted by the computer as current attack. Trees 1099 and 1017 visually appear distinctly tan-coloured. Tree 1030 is difficult to visually interpret due to its position at the edge of the frame. However, it does not appear particularly red-coloured. According to the ground data, all three of these trees had heavy cone crops. This may have also influenced the interpretation since cones tend to appear tan-coloured or yellowish in the test frame. The peak for 1023 lies next to the unattacked/current attack boundary in projected intensity triplet space. It appears red but also has shades of tan and green. The unattacked trees which were correctly interpreted mostly appear red. Trees such as 1103, 1105, 1024 and 945 appear less red than some of the others and lie closest to the unattacked/current attack boundary. Tree 1104 appears to be more red than 1103 or 1105 and it is the furthest of the three peaks from the boundary. 86 This suggests that variability in the visual colour of the trees in the photographs is more of a problem with regards to interpretation accuracy than failings of the computa-tional approach. However, some variation is attributable to the analysis technique. For example, trees 1023 and 1024 have been interpreted differently primarily because of the proximity of the peaks to a decision boundary rather than some visually apparent difference in the overall colour of the two trees. The variability in location of peaks seen in Section 7.2 among different views of the same tree is sufficient to produce changes in the classification decision in these borderline cases. While human interpreters must also deal with borderline cases, they can make use of other cues to help resolve ambiguities. The current attacked trees which were misinterpreted as being unattacked generally appear red-coloured. The trees which were correctly interpreted as attacked mostly look tan-coloured. Once again, there are trees such as 1101 and 1102 or 1054 and 1110 whose peaks lie close to the unattacked/current attacked boundary for which there is no visually apparent reason for different interpretations. The lower percentage of correct interpretations for current attacked trees versus unattacked trees is to be expected. The rate of degradation, once attacked success-fully, seems to be variable from tree to tree. Some trees do not show foliar symptoms of the attack as soon as others and, therefore, appear unattacked. Variability in the rate of degradation might be expected based upon the variable life cycles (Schmid, 1976; Churcher, 1984) and rates of needle-drop (Massey and Wygant, 1954; Schmid, 1976) 87 noted in Section 2.1. The reduced percentage of correct interpretations for current at-tacked versus unattacked trees is probably attributable more to variation in the condition of the attacked trees than to a problem in the computational technique. Seven of the old attacked trees were misinterpreted as current attack. All seven of these are substantially tan-coloured and visually appear to be current attacked with very advanced symptoms. Figures 8.8 and 8.6 show that the peaks in projected intensity triplet space of these old attacked trees overlap with those of some of the advanced currently attacked trees. The significant factor affecting interpretation accuracy of the old attacked trees is population variation. Only six percent of the 1983 pitched-out trees were "correctly" interpreted as current attack. The other way of expressing this, however, is more to the point. Ninety-four percent of the 1983 pitched-out trees were interpreted as unattacked. The general distri-bution of peaks for the 1983 pitched-out and unattacked trees in Figures 8.10 and 8.4 is essentially the same. Visual inspection of the trees in Figure 8.2 shows that they mostly appear red-coloured, similar to unattacked trees. Of the three which have been classified by the computer as attacked, two (1067 and 924) are clearly tan-coloured. The third (988) is severely backlit but appears somewhat tan-coloured. The 1983 strip attacked trees show similar trends. Seventy-eight percent of the trees were interpreted by the computer to be unattacked. Once again, the overall distribution of peaks in projected intensity triplet space (Figure 8.12) closely resembles that of the unattacked trees (Figure 8.4). Some variations in classification are due to borderline trees 88 again. Trees 1045 and 1068 appear visually to be very similar, but the proximity of the peaks to the unattacked/current attack boundary has resulted in different interpretations for each of them. The old (1982) and mixed (1982/1983) strip attacked trees were more successfully interpreted by the computer with 60 percent identified as attacked. Visual assessment of the trees in Figure 8.2 affirms again that the computational approach has generally worked as prescribed. There is a progression of successful detection from the 1983 pitched-out trees (6 percent), 1983 strip attacked trees (22 percent), old and mixed strip attacked trees (60 percent) to the full current attacked trees (68 percent). This is an indication of the level of stress required for a bark beetle-attacked spruce to display the overall shift in colour on film which the analysis used for this thesis requires. The least stress was probably experienced by the pitched-out trees. This is reflected by the effective equivalence of the number of detected pitched-out trees and the number of "detected" trees in the unattacked population. The three pitched-out trees classified as attacked could be part of a natural "error rate" typical of unattacked trees. Consequently, it is questionable that any of the pitched-out trees were truly "detected". Conversely, the trees subjected to the greatest stress would be those in the full current attack class. Although the overflight was not conducted until September 10, about three months after the beetle attack, over thirty percent of the fully attacked trees were not detected. This points to a requirement for sufficient time to elapse between the time of beetle attack and photo acquisition for the foliage of the attacked trees to degrade to a 89 point where an overall colour shift from "red" to "tan" will show on the film. In summary, it appears that using the major peaks of the distributions in projected intensity triplet space has produced results that resemble what a human interpreter might interpret when using overall visual colour as the primary cue. There are "border-line cases" for which different computer-based interpretation will occur for no visually apparent reason. However, such cases should be expected to occur when a system of discrete classes are imposed upon a population which shows continuous variation in the feature to be classified. The results of the test frame suggest that there is a requirement for a substantial shift in the overall visual colour of trees on the film from "red" to "tan" to achieve separability of unattacked and attacked trees. This apparently requires both a complete attack and a time period of several months between the beetle attack and photo acquisition for the effects of the attack to manifest themselves in terms of a high rate of current attack detection. 90 Figure 8.2: Photograph of test frame. 91 , 1 0 3 0 « / ' 1 0 : 5 1 0 2 3 — % ft ^ - 1 0 M 9 o o <> Figure 8.3: Key to the unattacked trees. Locations of the unattacked trees in test frame and the computer-based interpretation for each. • unattacked | current attack • old at tack 92 Figure 8.4: Peaks in PITS for the unattacked trees. The interpretation classes associated with the boundaries shown in this figure are identified in Figure 6.4. 93 iica I 0 IP * 1 y Figure 8.5: Key to the current attacked trees. Locations of current attacked trees in test frame and the computer-based interpretation for each. • unattacked [§ current at tack • old attack 94 Figure 8.6: Peaks in PITS for the current attacked trees. The interpretation classes associated with the boundaries shown in this are identified in Figure 6.4. 95 Figure 8.7: Key to the old attacked trees. Locations of old attacked trees in test frame and the computer-based inter-pretation for each. • unattacked IJI current attack • old at tack 96 Figure 8 . 8 : Peaks in PITS for the old attacked trees. The interpretation classes associated with the boundaries shown in this figure are identified in Figure 6.4. 97 ^7 0 Q <5 Ci 0 0 o 1067 St I 988 Figure 8.9: Key to the 1983 pitched-out trees. Locations of the 1983 pitched-out trees in test frame and the computer-based interpretation for each. • unattacked 9 current at tack • old attack 98 Figure 8.10: Peaks in PITS for the 1983 pitched-out trees. T h e interpretat ion classes associated w i t h the boundaries shown i n this figure are identif ied i n Figure 6.4. 99 0 Figure 8.11: Key to the 1983 strip attacked trees. Locat ions o f the 1983 str ip attacked trees in test frame and the computer-based interpretat ion for each. • unattacked fl current at tack • old attack 100 Figure 8.12: Peaks in PITS for the 1983 strip attacked trees. The interpretation classes associated with the boundaries shown in this figure are identified in Figure 6.4. 101 l i Figure 8.13: Key to the old and mixed strip attacked trees. Locations of the old and mixed strip attacked trees in test frame and the computer-based interpretation for each. • unattacked B current at tack • old attack 102 Figure 8.14: Peaks in PITS for the old and mixed strip attacked trees. The interpretation classes associated with the boundaries shown in this figure are identified in Figure 6.4. 103 Chapter 9 Conclusions Multiple views of trees were sampled and the intensity distributions in-intensity triplet space were studied. Some characteristic features of those distributions were noted in-cluding: • the orientation of the intensity distribution or "envelope" of frequencies in intensity triplet space for a particular tree is related to its perceived colour • the specific frequency distribution within the "envelope" is primarily related to geometric factors such as surface orientation and viewer position • the intensity distributions of all trees appear to converge outside the bounds of intensity triplet space toward a common point labelled the convergence point These observations were used to define projected intensity triplet space. Transforma-tion of raw images to projected intensity triplet space, as the initial stage of analysis for a particular tree, permitted consideration of the attack status of the tree without regard for the effects of geometric factors such as the tree's relative position in the photo 104 frame or changes in the orientation of the tree's foliage. Projected intensity triplet space facilitated computer-based interpretations of attack status on an individual tree basis. Results of the test frame demonstrated that the major peaks of trees transformed to projected intensity triplet space could be used to distinguish between "red" trees, "tan" trees and "green/blue" trees. This translated to correct interpretations of 84 percent, 68 percent and 89 percent for the unattacked, full current attack and old attacked trees. The interpretation accuracy for the old strip and mixed strip attack class was slightly less at 60 percent. The 1983 strip attacked and 1983 pitched-out classes had interpretation accuracies of only 22 and 6 percent respectively. The reduced detection in these latter classes was ascribed to the absence of an overall change in the trees' colour on the film. Presumably, these trees had not been stressed sufficiently to cause a major degradation in foliage condition. The projected intensity triplet space approach is useful as a demonstration of the use of a feature rather than raw image data as the basis for analysis. However, as the basis of a practical tool which could be applied to the problem of detecting bark beetle-attacked spruce in the real world, the approach suffers from a number of limitations. In Section 7.1 it was noted that accurate location of the convergence point is crucial. However, once the convergence point has been decided upon and the interpretation pro-ceeds, there is no internal check to validate the position of the point. Such an internal check would be desirable in a "real" system since things such as variations in film sensi-tivity or development and changing illumination during the acquisition of photography would influence the correct position of the convergence point. 105 Furthermore, the procedure used to locate the convergence point used backlit and frontlit views of the trees to provide a stable computation of the central axis. The stability was essential to permit extrapolation of the axes in the location of the convergence point. Providing the photographic overlap required to obtain multiple views of single trees would be impractical in an operational system. Projected intensity triplet space, as developed in this thesis, is a procedure which requires a human interpreter to define trees in the image and determine their species. As it is, the method could most easily be further developed as part of a human interpreter's workstation to act as an aid. One has to wonder, however, about the economy of investing money in an interpreter's aid whose major feature is that it can distinguish an object which appears red in a photograph from one which appears tan-coloured . . . something that is not difficult for a human interpreter to do without the aid. Current generation airborne multispectral sensors such as the MEIS II (Zwick 1979; Neville et al. 1983) raise the possibility of directly acquiring digital data with spatial resolution which is comparable to that of the images used in this thesis. The digital nature of the data naturally lends itself to machine-based interpretation. Analysis tech-niques capable of extracting key features such as "colour" might be important to future developments in automated interpretation systems using these kinds of data. A n interesting aspect of the thesis is the open question that it raises about reasons for the possible existence of a "convergence point". The convergence of the distributions in intensity triplet space was observed empirically and this trend was utilized in the analysis techniques which were developed. However, it was beyond the scope of the 106 thesis to investigate the cause of the convergence in the data. Is the convergence of the intensity distributions due to some underlying physical phenomena which would apply to all sensors or is it simply a product of using a mul-tiple emulsion film? This could be the subject of future research. As the trend toward use of sensors having finer spatial resolution continues in the future, a more detailed understanding of the characteristics of high resolution data will become crucial to the development of analysis techniques for many applications. 107 Literature Cited Anon. 1975. Operator's manual for transmission reflection densitometer TR-524- MacBeth Division of Kollmorgen Corp. Newburgh, N.Y. 18 pp. Anon. 1982. The real enemy. British Columbia Ministry of Forests. Publ. No. G30-81082. 20 pp. Banner, A . V . 1984. Defining the standard normal tree - revisited! Unpubl. Forestry 542 paper submitted to Dr. R.J . Woodham, Faculty of Forestry, University of British Columbia. Vancouver, B . C . 92 pp. Churcher, J.J. 1984. Detection of spruce beetle (Dendroctonus rufipennis) infestations us-ing aerial photographs. MSc. Thesis. Faculty of Forestry, University of British Columbia. Vancouver, B . C . 71 pp. Churcher, J.J. and J .A. McLean. 1984. Visual detection of beetle-attacked white spruce trees using aerial photography. Proc. RNRF Symposium on the Application of Remote Sensing to Resource Management. American Society of Photogrammetry. Falls Church, Virginia, pp. 445-450. Deigan, J. 1981. The mechanics of colour microdensitometry for digital image processing. Proceedings 8th Biennial Workshop on Colour Aerial Photography. American So-ciety of Photogrammetry. Falls Church, Virginia, pp. 137-143. Dyer, E . D . A . and R.S. Hodgkinson (eds.) 1981. Spruce beetle management seminar and workshop. Proceedings in abstract. Oct. 7-8, 1980. Prince George, B .C. British Columbia Ministry of Forests. Pub. No. R15-81005. 16 pp. Fox, D.J . 1976 Elementary statistics using MIDAS, 2nd edition. Statistical Research Labo-ratory, University of Michigan. Ann Arbor, Mich. 300 pp. Fox, D.J . and K . E . Guire. 1976. Documentation for MIDAS, 3rd edition. Statistical Research Laboratory, University of Michigan. Ann Arbor, Mich. 203 pp. 108 Glicksman, J. 1982. A cooperative scheme for image understanding using multiple sources of information. PhD. Thesis. Department of Computer Science, University of British Columbia. Vancouver, B .C . 286 pp. Hall, P . M . 1981. Remote sensing of Douglas fir trees newly infested by bark beetles. MSc. Thesis. Faculty of Forestry, University of British Columbia. Vancouver, B .C. 68 pp. Hall, P .M. , P.A. Murtha and J .A. McLean. 1981. Remote sensing of Douglas fir trees newly infested by bark beetles. Proceedings Eighth Biennial Workshop on Color Aerial Photography. American Society of Photogrammetry. Falls Church, Virginia, pp. 91-98. Hall, P . M . , J .A. McLean and P.A. Murtha. 1983. Dye-layer density analysis identifies new Douglas fir beetle attacks. Canadian Journal of Forest Research 13(2):279-282. Heiss, D . G . 1985. Calibrating the photographic reproduction of colour digital images. MSc. Thesis. Dept. of Computer Science, University of British Columbia. Vancouver, B . C . 78 pp. Heller, R .C . and J .L. Bean. 1951. Aerial surveying methods for detecting forest insect out-breaks. U.S. Dept. Agr. B E P Q Prog. Rpt. CITED IN: Heller et al. (1959). Heller, R . C , R . C . Aldrich and W.F . Bailey. 1959. An evaluation of aerial photography for detecting southern pine beetle damage. Photogrammetric Engineering 25(4):595-606. Heller, R .C . and J.J. Ulliman (eds.) 1983. Forest resource assessments, pp. 2274-2277 in Manual of Remote Sensing, 2nd edition. Colwell, R.N. , D.S. Simonett, F . T . Ulaby, J .E. Estes and G . A . Thorley (eds.), American Society of Photogrammetry. Falls Church, Virginia. Hobbs, A . J . 1983. Effects of air photo scale on early detection of Mountain Pine Beetle infestation. MSc. Thesis. Faculty of Forestry, University of British Columbia. Vancouver, B . C . 136 pp. Hobbs, A . J . and P.A. Murtha. 1984. Visual interpretation of four scales of aerial photography for early detection of mountain pine beetle infestation. Proc. RNRF Symposium on the Application of Remote Sensing to Resource Management. American Society of Photogrammetry. Falls Church, Virginia, pp. 433-444. Horn, B .K.P . 1977. Understanding image intensities. Artificial Intelligence 8(2):201-231. Judd, D . B . and G . Wyszecki. 1975. Color in Science, Business and Industry. John Wiley & Sons, New York. 553 pp. 109 Lodwick, G . D . 1981. Topographic mapping using Landsat data. Proc. Fifteenth International Symposium on Remote Sensing of Environment. Ann Arbor, Michigan, pp. 527-534. Massey, C . L . and N.D. Wygant. 1954. Biology and control of the Engelmann spruce beetle in Colorado. U.S. Dept. Agric. Circ. 944. 35pp. Murtha, P.A. 1972. A guide to air photo interpretation of forest damage in Canada. Can. For. Serv. Pub. No. 1292. 63 pp. Murtha, P.A. 1985. Photo interpretation of spruce beetle-attacked spruce. Canadian Journal of Remote Sensing ll(l):93-102. Murtha, P.A. and R. Cozens. 1985. Color infra-red photo interpretation and ground surveys evaluate spruce beetle attack. Canadian Journal of Remote Sensing 11(2):177-187. Murtha, P.A. and J .A. McLean. 1981. Extravisual damage detection? Defining the standard normal tree. Photogramm. Eng. and Remote Sensing 47(4):515-522. Neville, R .A. , W . D . McColl and S .M. Til l . 1983. Development and Evaluation of the MEIS II Multi-Detector Electro-optical Imaging Scanner. Proceedings of the Soci-ety of Photo-optical Instrumentation Engineers International Technical Conference, Geneva, Switzerland, 8 pp. Newman, W . M . and R.F . Sproull. 1979. Principles of interactive computer graphics. McGraw-Hill Book Company, New York. 541 pp. Scarpace, F . L . 1978. Densitometry on multiemulsion imagery. Photogramm. Eng. and Remote Sensing 44(10) .1279-92. Schmid, J . M . 1976. Temperatures, growth,and fall of needles on Engelmann spruce infested by spruce beetles. USDA For. Serv. Res. Note RM-331, Rocky Mt. For. and Range Exp. Stn., Fort Collins, Colo. 4 pp. Schmid, J . M . and R . H . Frye. 1977. Spruce beetle in the Rockies. USDA For. Serv. Gen. Tech. Rep. RM-49, Rocky Mt. For. and Range Exp. Stn., Fort Collins, Colo. 38 pp. Steel, R . G . D . and J .H. Torrie. 1960. Principles and Procedures of Statistics. McGraw-Hill Book Company, New York. 481 pp. Williams, P . G . 1978. A wing-tip camera system for large scale photography. Proc. Symposium on Remote Sensing for Vegetation Damage Assessment. Falls Church, Virginia, pp. 127-134. Woodham, R.J . 1984. Photometric method for determining shape from shading, in Im-age Understanding. S. Ullman and W. Richards (eds.), Ablex Publishing Corp., Norwood, N.J. pp. 97-125. 110 Zwick, H . H . 1979. Evaluation results from a push-broom imager for remote sensing. Canadian Journal of Remote Sensing 5(2):101-117. I l l Appendix A Summary of Banner (1984) A . l Methodology The data used in Banner (1984) were the five "normal tree" images used in this thesis (trees 50, 81, 119, 262 and 945). Multiple views of each tree were used as shown for tree 119 in Figure 4.1. Eight separate views of tree 262 and nine views of the other trees were used. Graphic masks of nonzero image values were constructed to sample the pixel inten-sities associated with each view of the trees and to produce text files of their values. The data were analysed using the MIDAS statistical package (Fox 1976; Fox and Guire 1976). The hypothesis that "viewing geometry does not alter the distribution of image in-tensities" was tested separately for each tree. A particular view, such as " T L " , did not correspond to physically identical viewing geometries for each tree but only served as a label to identify one of the nine subimages of each composite image. 112 Histograms of the image intensities showed that the data were skewed and did not meet the normality assumption required by parametric tests. Therefore, the MIDAS "ksample" command was used to perform a median test (Fox 1976; Fox and Guire 1976). This tests the null hypothesis that the distribution of a variable is the same in all of the specified populations against the alternative hypothesis that at least one of the populations differs from the others. The test is based upon finding, for each sample, the number of cases that are less than the median of the entire set of observations if all the samples were combined. A.2 Results and Discussion The results of median tests for the blue, green and red images of each of the five trees are given in Tables A . l to A.15. The attained significance levels for all of the tests are " 0 . " which is the highest significance that MIDAS displays. The null hypothesis is rejected in all cases. In each of the blue, green and red images of the five trees, the distribution of intensities associated with at least one of the views was different from the others. Variations in viewer position causing changes in the distribution of image intensities corresponding to a particular tree should not be a surprise. In Figure 4.1, the severely backlit B R view is visibly darker than the frontlit views. The significant results, however, are not only a function of comparisons between the extremes of frontlit and backlit sides of trees. Considering the "TC"and " M L " views of tree 119 in Figure 4.1, neither appears to be severely backlit and therefore both should 113 be suitable for densitometric measurements. Comparison of the relative proportion of cases above and below the median for each view indicates that these particular views are contributing to the significance of the median test. Furthermore, changes in surface orientation have effects similar to those of changes in view angle. The variations in image irradiance resulting from changes in surface orientation are the basis of the "shape from shading" methods used to compute the shape of objects from images. The use of image intensity to determine object shape is discussed in Horn (1977) and Woodham (1984). The average intensity is a function of the specific geometry of individual trees as well as view angle. Geometry plays a major role in determining the intensities found in an image-particularly in large scale photographs. Such an important factor should not simply be dismissed as a random source of error as implied by the use of standard statistical tests of intensity or film response values. 114 Table A . l : Median test of blue image intensities sampled from nine views of tree 50. Test statistic 553.11 Degrees of freedom 8 Significance 0. view n avg. rank mec ian = 87 n< n> n= B C 396 1826.506 256 139 1 B L 185 1084.862 168 15 2 BR 271 1113.779 231 37 3 M C 365 1908.299 219 143 3 M L 650 2221.289 325 321 • 4 M R 276 1648.464 195 79 2 T C 775 2718.397 266 506 3 T L 930 2586.770 345 578 7 T R 653 2753.636 226 422 5 115 Table A.2: Median test of green image intensities sampled from nine views of tree 50. Test statistic 521.18 Degrees of freedom 8 Significance 0. view n avg. rank mec ian 97 n< n> n= B C 396 1801.206 256 137 3 B L 185 1127.224 162 22 1 BR 271 1102.173 230 39 2 M C 365 1966.640 212 : 151 2 M L 650 2251.705 326 317 7 M R 276 1644.803 194 78 4 T C 775 2693.197 267 497 11 T L 930 2622.399 332 587 11 T R 653 2679.621 240 410 3 116 Table A.3: Median test of red image intensities sampled from nine views of tree 50. Test statistic 405.35 Degrees of freedom 8 Significance 0. view n avg. rank med ian 139 n< n> n= B C 396 1923.576 240 154 ; 2 BL 185 1231.005 159 23 3 BR 271 1203.491 234 3 7 0 i M C 365 2104.673' 200 159 6 M L • 650 : 2251.353 ! 312 330 » M R 276 1828.759 175 100 1 T C 775 2660.843 279 491 5 T L 930 2388.999 419 505 6 T R 653 2750.212 232 416 5 117 Table A.4: Median test of blue image intensities sampled from nine views of tree 81. Test statistic 609.76 Degrees of freedom 8 Significance 0. view n avg. rank med l a n = 118. n< n> n= B C 255 1084.643 221 32 2 BL 438 1934.872 252 184 2 BR 397 942.262 364 31 2 M C ! 378 ! 2272.347 ; 174 197 7 M L ; 647 2361.862 •262 380 1 5 M R 293 1902.454 169 122 2 T C 449 2578.852 155 292 2 T L 605 2578.822 206 395 4 T R 789 2378.843 295 483 11 118 Table A.5: Median test of green image intensities sampled from nine views of tree 81. Test statistic 607.70 Degrees of freedom 8 Significance 0. view n avg. rank med ian = 126 n< n> n= B C 255 1164.243 219 35 1 B L 438 1918.395 254 182 2 BR 397 947.707 363 32 2 M C 378 2265.533 179 195 4 M L 647 2376.388 256 382 9 M R 293 1899.416 173 117 3 T C 449 2560.624 157 289 3 T L 605 2550.327 206 392 7 T R 789 2384.228 293 488 8 119 Table A.6: Median test of red image intensities sampled from nine views of tree 81. Test statistic 475.05 Degrees of freedom 8 Significance 0. view n avg. rank med ian 151 n< n> n= BG 255 1258.088 213 40 2 B L 438 2041.789 236 198 4 BR 397 1054.237 346 44 7 M C 378 2305.069 170 207 1 M L 647 2418.331 241 400 6 M R 293 1958.920 161 130 2 T C 449 2529.911 164 279 6 T L 605 2459.649 228 370 7 T R 789 2243.373 329 449 11 120 Table A.7: Median test of blue image intensities sampled from nine views of tree 119. Test statistic 1348.6 Degrees of freedom 8 Significance 0. view n avg. rank mec lian = 125 n< n> n= B C 704 5150.156 416 282 6 B L 930 4626.148 634 284 12 BR 417 2809.644 383 29 5 M C 1007 3679.017 ; 827 ! 172 : 8 M L 1970 : 6598.318 819 ! 1136 15 M R 1613 7641.288 538 1068 7 T C 1241 5262.782 737 494 10 T L 1646 6176.567 766 865 15 T R 2591 7184.444 928 1636 27 121 Table A.8: Median test of green image intensities sampled from nine views of tree 119. Test statistic 1367.0 Degrees of freedom 8 Significance 0. view n avg. rank mec ian = 130 n< n> n= B C 704 5228.729 415 284 5 B L 930 4428.532 651 269 10 BR 417 2781.324 380 35 2 M C ; 1007 3771.141 822 175 10 M L 1970 6673.822 801 1156 13 M R 1613 7565.323 548 1051 14 T C 1241 5258.636 727 499 15 T L 1646 6212.865 752 873 21 T R 2591 7171.591 911 1654 26 122 Table A.9: Median test of red image intensities sampled from nine views of tree 119. Test statistic 1075.0 Degrees of freedom 8 Significance 0. view n avg. rank mec Ian 158 n< n > n= B C 704 5562.810 378 310 16 BL 930 4597.772 630 282 18 BR 417 2970.631 373 40 4 M C 1007 4011.932 762 222 23 M L 1970 6440.304 849 : 1098 23 M R 1613 7777.247 528 1076 9 T C 1241 5243.973 737 489 15 T L 1646 6166.395 772 853 21 T R 2591 6978.183 984 1587 20 123 Table A.10: Median test of blue image intensities sampled from eight views of tree 262. Test statistic 378.41 Degrees of freedom 7 Significance 0. view n avg. rank med l a n = 104 n< n> n= B C 482 1433.356 371 109 2 BL 334 1336.837 268 66 0 M C 430 2106.558 228 199 3 M L 529 2577.436 209 316 4 M R 616 2234.239 317 297 2 T C 618 2549.628 249 363 6 T L 702 2432.113 294 404 4 T R 782 2595.655 293 486 3 124 Table A.11: Median test of green image intensities sampled from eight views of tree 262. Test statistic 431.78 Degrees of freedom 7 Significance 0. view n avg. rank med ian = 110 n< n> n= B C 482 1379.745 383 96 3 B L 334 1306.000 269 61 4 M C 430 2088.093 229 199 2 M L , 529 2568.792 202 323 4 M R 616 2172.038 325 285 6 T C 618 2615.375 244 370 4 T L 702 2458.087 287 412 3 T R r 782 2631.591 286 489 7 125 Table A.12: Median test of red image intensities sampled from eight views of tree 262. Test statistic 303.48 Degrees of freedom 7 Significance 0. view n avg. rank med l a n = 141 n< n> n= B C 482 1557.345 356 120 6 B L 334 1467.605 ! 254 76 ' 4 M C 430 2195.422 216 211 3 M L 529 2623.019 | 197 ; 322 ; io M R 616 2232.755 313 300 3 T C 618 2535.586 250 361 7 T L 702 2225.670 347 353 2 T R 782 2581.269 296 479 7 126 Table A.13: Median test of blue image intensities sampled from nine views of tree 945. Test statistic 873.58 Degrees of freedom 8 Significance 0. view n avg. rank med l a n — 109 n< n> n= B C 349 1228.891 296 49 4 B L 351 1359.219 269 76 6 BR 217 649.325 217 0 0 M C 404 1942.571 225 176 3 ' M L 514 2239.537 226 283 5 M R 448 1860.061 262 179 7 T C 801 3037.923 165 632 4 T L 530 2146.310 243 281 6 T R 634 2583.367 203 429 2 127 Table A.14: Median test of green image intensities sampled from nine views of tree 945. Test statistic 875.90 Degrees of freedom 8 Significance 0. view n avg. rank med ian - 119 n< n> n= B C 349 1217.668 301 42 6 B L 351 1342.184 271 76 4 BR 217 671.940 217 0 0 M C 404 1943.817 215 183 6 M L 514 2258.467 ; 227 281 6 M R 448 1852.191 257 187 4 T C 801 3028.335 167 629 5 T L 530 2166.360 243 280 7 T R 634 2576.009 206 422 6 128 Table A. 15: Median test of red image intensities sampled from nine views of tree 945. Test statistic 680.62 Degrees of freedom 8 Significance 0. view n avg. rank med l a n = 140 n< n> n= B C 349 1305.695 275 66 8 B L 351 1525.735 252 95 4 BR 217 734.318 215 2 0 M C i 404 2054.976 212 189 3 M L 1 514 ' 2335.580 224 287 3 M R 448 1898.998 253 193 2 T C 801 2870.207 197 594 10 T L 530 2069.437 260 264 6 T R 634 2518.961 215 411 8 129 Appendix B Flight Line Marker Assembly The need for large overlap between flight lines prompted the development of a system to mark each flight line so that it was clearly visible from the air during photo acquisition. Each line was marked at each end using tarps measuring 3 metres by 3 metres in size. The tarps were suspended from the tops of four trees using ropes. Each pair of tarps was a distinct colour (red, orange, yellow, blue or white) for immediate recognition of the matching tarps at either end. They were made of a reinforced polyvinyl material selected for its strength and resistance to rot and mildew. The tarps marking the beginnings of several lines are visible in Figure 3.2. A diagrammatic sketch of the tarp setup is given in Figure B . l . . There are two ropes associated with each corner of a tarp. One rope has a ring on one end. The rope is wrapped around a tree as an anchor. The other rope is fitted with a clip to attach to the corner of a tarp. This rope is passed through the ring of the anchor rope and is used to hoist up the tarp in a pulley fashion. 130 A modified crossbow1 was used to fire fishing line over the trees. Ropes were pulled over the crowns of trees using the fishing line. The setup of a tarp involves the following steps: 1. Four trees of similar height along the proposed flight line are selected to act as anchor trees (Figure B.2). 2. Use the crossbow to pass fishing line over the crown of one of the anchor trees from outside of the tarp plot toward the centre (Figure B.3). 3. The arrow is retrieved in the centre of the plot. The arrow is cut from the line and the line is tied to the end of the anchor rope (without the ring). Duct tape is used to taper the joint between the fishing line and rope. 4. The anchor rope is pulled over the tree crown by reeling in the fishing line with the crossbow (Figure B.4). While one person reels in the line, another shakes the rope on the other end to ensure that the joint between the fishing line and rope does not get caught in the foliage. 5. As the ring leaves the ground, the pulley rope (with the snap) is passed through the ring (Figure B.5). The anchor rope is pulled over further until the ring on the end is at the top of the crown. Both ends of the pulley rope are kept on the ground (Figure B.6). S u p p l i e d b y D r . H . M o e c k , Pacif ic Forest Research Centre , C a n a d i a n Forestry Service, V i c t o r i a , B . C . 131 6. The two ends of the pulley rope are tied securely to a neighbouring tree to hold the ring in place while the anchor rope is secured. 7. The anchor rope is wrapped numerous times around the the tree. The first "wrap" at the top of the crown is passed over the highest possible branches. Subsequent wraps are weaved through the branches to get the rope close to the trunk of the tree (Figure B.7). The end of the anchor rope is tied securely to a second tree to prevent slippage. 8. The procedure is repeated for each corner of the tarp. 9. The pulley ropes are attached to the tarp using the snaps. The tarp is hoisted up using the four pulley ropes (Figure B.8). 10. The pulley ropes are pulled tight and secured to trees to suspend the tarp between the four anchor trees (Figure B.9). Using this procedure, tarps may be suspended high in the canopy to provide a clear indication of the intended flight lines (Figure B.10). Setting the tarps up, however, is a time consuming task. On average, a full day was required for two people to set up one tarp. The labour required makes the procedure practical only in cases where accuracy of flight line navigation is critical or where the lines will be flown repeatedly and the tarps can be left up for a long period. 132 Figure B . l : Sketch of tarp setup. 133 Figure B.2: Looking up at anchor trees prior to setup. 134 Figure B.3: Firing fishing line over crown. 135 Figure B.4: Pulling the anchor rope over a tree. 136 Figure B.5: Passing pulley rope through ring of the anchor rope. 137 Figure B.6: The anchor rope is pulled up with the pulley rope passed through it. 138 Figure B.7: The anchor rope is pulled close to the trunk of the tree. 139 Figure B.8: The tarp is hoisted using the pulley ropes. 140 Figure B.9: Looking up at anchor trees with tarp in place. 141 Figure B.10: Tarps can be suspended high in the canopy. 142 Appendix C Summary of Software Several programs were written or adapted to develop and implement the projected inten-sity triplet space transformation. All programs were written in C unless noted otherwise and are installed on the V A X 11/780 at the U B C Laboratory for Computational Vision. The major programs include: accumulate: Sample a 3-colour image and produce a table of intensity triplet space frequencies. The frequency values may be added to those of an existing table to produce ITS data for groups of trees. Written by A l Banner. aceuspace: Uses ITS tables created by accumulate to plot intensity triplet space images (for the frequency data) and an overlaying plotfile of the axes as in Figure 4.2. Written by A l Banner. axisview: Permits axes calculated using eigen to be viewed interactively on the Raster Technologies Model One/25 image display. Up to 4 differently coloured axes may be viewed at once. Written by A l Banner using 3-D graphics software written by Marc Majka. 143 classify: Make a decision on the attack status of a sampled tree based upon the position of the major peak in projected intensity triplet space. Written by A l Banner using suggestions by Dr. R. J . Woodham. clist: Produce a list of blue, green and red intensities by sampling a 3-colour image using an optional graphic mask. Written by A l Banner. cspace: Sample a 3-colour image and plot the intensity values in intensity triplet space. A colour output (for slides) or plotfile (no frequency information) may be produced. Adapted by A l Banner from a program written by Detlef Heiss. cview: Look at the distribution of up to three lists of intensity values (produced with clist) interactively on the Raster Technologies Model One/25 image display. Adapted by A l Banner from a program written by Marc Majka. direct: Smooth an image by doing two one-dimensional convolutions with a Gaussian mask. Written by Alan Carter. eigen: Use principal component analysis to compute the parametric equations of the central axis for an image intensity distribution in intensity triplet space. Adapted by A l Banner from a program written by Francois Dumoulin. getpeak: Locate high intensity peaks in a projected intensity triplet space image. Writ-ten by A l Banner. getview: Uses equations for the principal axes of intensity distributions (as computed by eigen) to locate the "convergence point". Written by A l Banner. 144 stereo: Produce stereograms of intensity data in intensity triplet space (as in Fig-ure 4.13). Written in Lisp by Jim Little. t form: Sample a 3-colour image and transform the data to projected intensity triplet space. Written by Al Banner using 3-D graphics software written by Marc Majka. Other general purpose programs on the L C V V A X (written by graduate student, staff or U B C Faculty in the Laboratory for Computational Vision) as well as several "single-use" programs were used during the course of the thesis. 145 P u b l i c a t i o n s 1. Lawrence, G. and A. Banner, 1980. The application of thermography for locating potential frost pockets in forest cutovers. Proceedings 6th Canadian Symposium on Remote Sensing, Halifax, Nova Scotia, pp 369-376. 2. Banner, A. and T. Lynham, 1981. Multitemporal analysis of Landsat data for forest cutover mapping: a trial of two procedures. Proceedings 7th Canadian Symposium on Remote Sensing, Winnipeg, Manitoba, pp 233-239. 3. Lawrence, G., A. Banner and H. MacKay, 1981. Interpretation of aerial thermographic data. SPIE Vol. 313 Thermosense IV. pp 12-17. 4. Ryerson, R.A., R. Yazdani, A. Banner and P.R. Stephens, 1981. De-tection of changes in the Grand Falls area using remote sensing. In-vited Presentation at Land Information Systems 1990 (II), Fredericton, N.B., February 18-19. 5. Bonn, F.J., S. Aronoff, H. Audirac, A. Banner, P.J. Howarth, T. Lyn-ham and G. Rochon, 1982. The use of Landsat in monitoring re-source development in Canada. IN: Thompson, M.D. (ed.) Landsat for monitoring the changing geography of Canada. A special report for COSPAR by the Geography Working Group, Canadian Advisory Committee on Remote Sensing, pp 65-75. 6. Banner, A.V. 1984. Poster Session Review - Vegetation Damage. Pro-ceedings of the RNRF Symposium on the Application of Remote Sens-ing to Resource Management, Seattle, Washington, pp 403-405. 

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