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Lecture 12 1 Introduction to Computer Vision Image Texture Analysis

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A few examples Morphological processing for background illumination estimation Optical character recognition Roger S. Gaborski2

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Image with nonlinear illumination 3 Original Image Thresholded with graythresh

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Obtain Estimate of Background Roger S. Gaborski4 background = imopen(I,strel('disk',15)); %GRAYSCALE figure, imshow(background, []) figure, surf(double(background(1:8:end,1:8:end))),zlim([0 1]);

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Roger S. Gaborski5 %subtract background estimate from original image I2 = I - background; figure, imshow(I2), title('Image with background removed') level = graythresh(I2); bw = im2bw(I2,level); figure, imshow(bw),title('threshold')

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Comparison Roger S. Gaborski6 Original Threshold Background Removal - Threshold

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Optical Character Recognition After segmenting a character we still need to recognize the character. How do we determine if a matrix of pixels represents an ‘A’, ‘B’, etc? Roger S. Gaborski7

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Approach Select line of text Segment each letter Recognize each letter as ‘A’, ‘B’, ‘C’, etc. Roger S. Gaborski10

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Roger S. Gaborski11 Select line 3 : Samples of segment of individual letters in line 3:

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We need labeled samples of each potential letter to compare to unknown Take the product of the unknown character and each labeled character and determine with labeled character is the closest match Roger S. Gaborski12

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Roger S. Gaborski13 %Load Database of characters (samples of known characters) load charDB mat whos char Name Size Bytes Class Attributes char x double EACH ROW IS VECTORIZED CHARACTER BITMAP

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Roger S. Gaborski14 BasicOCR.m CODE SOMETHING LIKE THIS: cc = ['A' 'B' 'C' 'D' 'E' 'F' 'G' 'H' 'I' 'J' 'K' 'L' 'M' 'N' 'O'... 'P' 'Q' 'R' 'S' 'T' 'U' 'V' 'W' 'X' 'Y' 'Z']; First, convert matrix of text character to a row vector for j=1:26 score(j)= sum(t.* char R(j,:)); end ind(i)=find(score= =max(score)); fprintf('Recognized Text %s, \n', cc(ind)) OUTPUT: Recognized Text HANSPETERBISCHOF,

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How can I segment this image? 15 University of Bonn Roger S. Gaborski Assumption: uniformity of intensities in local image region

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What is Texture? 16 University of Bonn Roger S. Gaborski

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Edge Detection Histogram Threshold - graythresh Roger S. Gaborski18

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Roger S. Gaborski22 lev = graythresh(I) lev = >> figure, imshow(I

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What is Texture No formal definition – There is significant variation in intensity levels between nearby pixels – Variations of intensities form certain repetitive patterns (homogeneous at some spatial scale) – The local image statistics are constant, slowly varying human visual system: textures are perceived as homogeneous regions, even though textures do not have uniform intensity 23 Roger S. Gaborski

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Texture Apparent homogeneous regions: – In both cases the HVS will interpret areas of sand or bricks as a ‘region’ in an image – But, close inspection will reveal strong variations in pixel intensity 24 A brick wallSand on a beach Roger S. Gaborski

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Texture Is the property of a ‘group of pixels’/area; a single pixel does not have texture Is scale dependent – at different scales texture will take on different properties Large number of (if not countless) primitive objects – If the objects are few, then a group of countable objects are perceived instead of texture Involves the spatial distribution of intensities – 2D histograms – Co-occurrence matrixes 25 Roger S. Gaborski

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Scale Dependency Scale is important – consider sand Close up – “small rocks, sharp edges” – “rough looking surface” – “smoother” Far Away – “one object – brown/tan color” 26 Roger S. Gaborski

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Terms (Properties) Used to Describe Texture Coarseness Roughness Direction Frequency Uniformity Density How would describe dog fur, cat fur, grass, wood grain, pebbles, cloth, steel?? 27 Roger S. Gaborski

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“The object has a fine grain and a smooth surface” Can we define these terms precisely in order to develop a computer vision recognition algorithm? 28 Roger S. Gaborski

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Features Tone – based on pixel intensity in the texture primitive Structure – spatial relationships between primitives A pixel can be characterized by its Tonal/Structural properties of the group of pixels it belongs to 29 Roger S. Gaborski

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30 Tonal: – Average intensity – Maximum intensity – Minimum intensity – Size, shape Spatial Relationship of Primitives: – Random – Pair-wise dependent Roger S. Gaborski

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Artificial Texture 31 Roger S. Gaborski

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Artificial Texture 32 Segmenting into regions based on texture Roger S. Gaborski

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Color Can Play an Important role in Texture 33 Roger S. Gaborski

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Color Can Play an Important Role in Texture 34 Roger S. Gaborski

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Statistical and Structural Texture 35 Consider a brick wall: Statistical Pattern – close up pattern in bricks Structural (Syntactic) Pattern – brick pattern on previous slides can be represented by a grammar, such as, ababab ) Roger S. Gaborski

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36 Most current research focuses on statistical texture Edge density is a simple texture measure - edges per unit distance Segment object based on edge density HOW DO WE ESTIMATE EDGE DENSITY?? Roger S. Gaborski

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37 Move a window across the image and count the number of edges in the window ISSUE – window size? How large should the window be? What are the tradeoffs? How does window size affect accuracy of segmentation? Segment object based on edge density Roger S. Gaborski

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38 Move a window across the image and count the number of edges in the window ISSUE – window size? How large should the window be? Large enough to get a good estimate Of edge density What are the tradeoffs? Larger windows result in larger overlap between textures How does window size affect Accuracy of segmentation? Smaller windows result in better region segmentation accuracy, but poorer Estimate of edge density Segment object based on edge density Roger S. Gaborski

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Average Edge Density Algorithm Smooth image to remove noise Detect edges by thresholding image Count edges in n x n window Assign count to edge window Feature Vector [gray level value, edge density] Segment image using feature vector 39 Roger S. Gaborski

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Run Length Coding Statistics Runs of ‘similar’ gray level pixels Measure runs in the directions 0,45,90, Image Y( L, LEV, d) Where L is the number of runs of length L LEV is for gray level value and d is for direction d Roger S. Gaborski

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degrees Gray Level, LEV Run Length, L Gray Level, LEV Run Length, L Image 45 degrees Roger S. Gaborski

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degrees Gray Level, LEV Run Length, L Gray Level, LEV Run Length, L Image 45 degrees Roger S. Gaborski

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Run Length Coding For gray level images with 8 bits 256 shades of gray 256 rows 1024x1024 1024 columns Reduce size of matrix by quantizing: – Instead of 256 shades of gray, quantize each 8 levels into one resulting in 256/8 = 32 rows – Quantize runs into ranges; run 1-8 first column, 9-16 the second…. Results in 128 columns 43 Roger S. Gaborski

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Gray Level Co-occurrence Matrix, P[i,j] Specify displacement vector d = (d x, d y ) Count all pairs of pixels separated by d having gray level values i and j. Formally: P(i, j) = | {(x 1, y 1 ), (x 2, y 2 ): I(x 1, y 1 ) = i, I(x 2, 2 1 ) = j} | 44 Roger S. Gaborski

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Gray Level Co-occurrence Matrix Consider simple image with gray level values 0,1,2 Roger S. Gaborski x y One pixel right One pixel down x y Let d = (1,1)

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Count all pairs of pixels in which the first pixel has value i and the second value j displaced by d. P(1,0) 1 0 P(2,1) 2 1 Etc. Roger S. Gaborski

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Co-occurrence Matrix, P[i,j] i j P(i, j) There are 16 pairs, so normalize by 16 Roger S. Gaborski

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Uniform Texture 48 d=(1,1) Let Black = 1, White = 0 P[i,j] P(0,0)= P(0,1)= P(1,0)= P(1,1) = x y Roger S. Gaborski

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Uniform Texture 49 d=(1,1) Let Black = 1, White = 0 P[i,j] P(0,0)= 24 P(0,1)= 0 P(1,0)= 0 P(1,1) = 25 x y Roger S. Gaborski

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Uniform Texture 50 d=(1,0) Let Black = 1, White = 0 P[i,j] P(0,0)= ? P(0,1)= ? P(1,0)= ? P(1,1) = ? x y Roger S. Gaborski

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Uniform Texture 51 d=(1,0) x y Let Black = 1, White = 0 P[i,j] P(0,0)= 0 P(0,1)= 28 P(1,0)= 28 P(1,1) = 0 Roger S. Gaborski

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Randomly Distributed Texture 52 What if the Black and white pixels where randomly distributed? What will matrix P look like?? No preferred set of gray level pairs, matrix P will have approximately a uniform population Roger S. Gaborski

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Co-occurrence Features Gray Level Co-occurrence Matrices(GLCM) – Typically GLCM are calculated at four different angles: 0, 45,90 and 135 degrees – For each angles different distances can be used, d=1,2,3, etc. – Size of GLCM of a 8-bit image: 256x256 (2 8 ). Quantizing the image will result in smaller matrices. A 6-bit image will result in 64x64 matrices – 14 features can be calculated from each GLCM. The features are used for texture calculations 53 Roger S. Gaborski

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Co-occurrence Features P(g a,g b,d,t) : – g a gray level pixel ‘ a ’ – g b gray level pixel ‘ b ’ – d distance d – t angle t (0, 45,90,135) 54 In many applications the transition g a to g b and g b to g a are both counted. This results in symmetric GLCMs: For P(0,0,1,0) 0 0 results in an entry of 2 for the ‘0 0’ entry Roger S. Gaborski

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Co-occurrence Features The data in the GLCM are used to derive the features, not the original image data How do we interpret the contrast equation? 55 Roger S. Gaborski

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Co-occurrence Features The data in the GLCM are used to derive the features, not the original image data: Measures the local variations in the gray-level co-occurrence matrix. How do we interpret the contrast equation? The term (i-j) 2 : weighing factor (a squared term ) – values along the diagonal (i=j) are multiplied by zero. These values represent adjacent image pixels that do not have a gray level difference. – entries further away from the diagonal represent pixels that have a greater gray level difference, that is more contrast, and are multiplied by a larger weighing factor. 56 Roger S. Gaborski

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Co-occurrence Features Dissimilarity: – Dissimilarity is similar to contrast, except the weights increase linearly 57 Roger S. Gaborski

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Co-occurrence Features Inverse Difference Moment – IDM has smaller numbers for images with high contrast, larger numbers for images low contrast 58 Roger S. Gaborski

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Co-occurrence Features Angular Second Moment(ASM) measures orderliness: how regular or orderly the pixel values are in the window Energy is the square root of ASM Entropy: where ln(0)=0 59 Roger S. Gaborski

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Matlab Texture Filter Functions FunctionDescription rangefiltCalculates the local range of an image. stdfiltCalculates the local standard deviation of an image. entropyfilt Calculates the local entropy of a grayscale image. Entropy is a statistical measure of randomness 60 Roger S. Gaborski

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rangefilt Roger S. Gaborski61 A = Symmetrical Padding max = 4, min = 1, range =

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rangefilt Results (3x3) Roger S. Gaborski62 A = >> R = rangefilt(A) R =

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rangefilt Results (5x5) Roger S. Gaborski63 A = >> R = rangefilt(A, ones(5)) R =

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Original image 64 Roger S. Gaborski

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65 Imfilt = rangefilt(Im); figure, imshow(Imfilt, []), title('Image by rangefilt') Roger S. Gaborski

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66 Imfilt = stdfilt(Im); figure, imshow(Imfilt, []), title('Image by stdfilt') Roger S. Gaborski

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67 Imfilt = entropyfilt(Im); figure, imshow(Imfilt, []), title('Image by entropyfilt') Roger S. Gaborski

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Matlab function: graycomatrix Computes GLCM of an image – glcm = graycomatrix(I) analyzes pairs of horizontally adjacent pixels in a scaled version of I. If I is a binary image, it is scaled to 2 levels. If I is an intensity image, it is scaled to 8 levels. – [glcm, SI] = graycomatrix(...) returns the scaled image used to calculate GLCM. The values in SI are between 1 and 'NumLevels'. 68 Roger S. Gaborski

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Parameters ‘Offset’ determines number of co-occurrences matrices generated offsets is a q x 2matrix – Each row in matrix has form [row_offset, col_offset] – row_off specifies number of rows between pixel of interest and its neighbors – col_off specifies number of columns between pixel of interest and its neighbors Roger S. Gaborski69

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Offset [0,1] specifies neighbor one column to the left Angle Offset 0 [0 D] 45 [-D D] 90 [-D 0] 135 [-D –D] Roger S. Gaborski70

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Orientation of offset The figure illustrates the array: offset = [0 1; -1 1; -1 0; -1 -1] Roger S. Gaborski71 90, [-1,0] 135, [-1,-1]45, [ -1,1] 0, [ 0,1]0, [ 0,1]

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Intensity Image – mat2gray Convert matrix to intensity image. I = mat2gray(A,[AMIN AMAX]) converts the matrix A to the intensity image I. The returned matrix I contains values in the range 0.0 (black) to 1.0 Roger S. Gaborski72

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graycomatrix Example Roger S. Gaborski73 From textbook, p 649 >> f = [ ; ; ; ; ; ] f = Need to convert to an Intensity image [0,1]

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Roger S. Gaborski74 >> fm = mat2gray(f) fm =

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Quantize to 8 Levels Roger S. Gaborski75 IS =

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Roger S. Gaborski76 >> offsets = [0 1]; >> [GS, IS] = graycomatrix(fm,'NumLevels', 8, 'Offset', offsets) GS = See NEXT PAGE

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Roger S. Gaborski77 GS = IS =

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Roger S. Gaborski78 'GrayLimits' Two-element vector, [low high], that specifies how the grayscale values in I are linearly scaled into gray levels. Grayscale values less than or equal to low are scaled to 1. Grayscale values greater than or equal to high are scaled to NumLevels. If graylimits is set to [], graycomatrix uses the minimum and maximum grayscale values in the image as limits, [min(I(:)) max(I(:))]. >> [GS, IS] = graycomatrix(f,'NumLevels', 8, 'Offset', offsets, 'G',[])

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Roger S. Gaborski79 >> [GS, IS] = graycomatrix(f,'NumLevels', 8, 'Offset', offsets, 'G',[]) >> I = rand(5) I =

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Roger S. Gaborski80 >> [GS, IS] = graycomatrix(f,'NumLevels', 8, 'Offset', offsets, 'G',[]) GS = IS =

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Roger S. Gaborski81 >> [GS, IS] = graycomatrix(f,'NumLevels', 4, 'Offset', offsets, 'G',[]) GS = IS = ORIGINAL IMAGE QUANTIZED TO 4 LEVELS

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Texture featureformula Energy Provides the sum of squared elements in the GLCM. (square root of ASM) Entropy Measure uncertainty of the image(variations) Contrast Measures the local variations in the gray-level co-occurrence matrix. Homogeneity Measures the closeness of the distribution of elements in the GLCM to the GLCM diagonal. 82 Roger S. Gaborski

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glcms = graycomatrix(Im, 'NumLevels', 256, 'G',[])) stats = graycoprops(glcms, 'Contrast Correlation Homogeneity’); figure, plot([stats.Correlation]); title('Texture Correlation as a function of offset'); xlabel('Horizontal Offset'); ylabel('Correlation') 83 Roger S. Gaborski

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Texture Measurement 84 Quantize 256 Gray Levels to 32 Data Window 31x31 or 15x15 GLCM0 GLCM45 GLCM90 GLCM135 Feature for Each Matrix ENERGY ENTROPY CONTRAST etc Generate Feature Matrix For Each Feature Roger S. Gaborski

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85 image Ideal map Roger S. Gaborski

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86 Classmaps generated using the 3 best CO feature images Roger S. Gaborski

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87 31x31 produces the Best results, but large errors at borders Classmaps generated using the 7 best CO feature images Roger S. Gaborski

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Law’s Texture Energy Features Use texture energy for segmentation General idea: energy measured within textured regions of an image will produce different values for each texture providing a means for segmentation Two part process: – Generate 2D kernels from 5 basis vectors – Convolve images with kernels 88 Roger S. Gaborski

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Law’s Kernel Generation Level L5 = [ ] Ripple R5 = [ 1 –4 6 –4 1 ] Edge E5 = [ -1 – ] To generate kernels, multiply one vector by the transpose of itself or another vector: L5E5 = [ ]’ * [ -1 – ] possible 2D kernels are possible, but only 24 are used L5L5 is sensitive to mean brightness values and is not used Spot S5 = [ –1 ] Wave W5 = [ ] Roger S. Gaborski

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textureExample.m Reads in image Converts to double and grayscale Create energy kernels Convolve with image Create data ‘cube’ 93 Roger S. Gaborski

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stone_building.jpg 94 Roger S. Gaborski

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Test 2 98 Roger S. Gaborski

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Scale How will scale affect energy measurements? Reduce image to one quarter size imGraySm = imresize(imGray, 0.25, bicubic'); 101 Roger S. Gaborski

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Data ‘cube’ 102 >> data = cat(3, im(:,:,1), im(:,:,2), im(:,:,3), imL5R5, imR5E5); >> figure, imshow(data(:,:,1:3)) >> data_value=data(7,12,:) data_value(:,:,1) = 142 data_value(:,:,2) = 166 data_value(:,:,3) = 194 data_value(:,:,4) = 22 data_value(:,:,5) = 10 Roger S. Gaborski

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Fractal Dimension Hurst coefficient can be used to calculate the fractal dimension of a surface The fractal dimension can be interpreted as a measure of texture Consider the 5 pixel wide neighborhood (13 pixels) 103 d cbc dbabd cbc d Pixel Class Number Distance from center a10 b41 c d42 Roger S. Gaborski

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Fractal Dimension Algorithm Lay mask over original image Examine pixels in each of the classes Record the brightest and darkest for each class The pixel brightness difference (range) for each pixel class is used to generate the Hurst plot Use least squares fit to construct a ln distance vs ln range plot The slope of this line is the Hurst coefficient for the specific pixel 104 Roger S. Gaborski

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