Introduction to Computer Vision Image Texture Analysis. Lecture 12. How can I segment this image?. Assumption: uniformity of intensities in local image region. University of Bonn. What is Texture?. University of Bonn. What is Texture. No formal definition

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Introduction to Computer Vision Image Texture Analysis

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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 Roger S. Gaborski

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 • Sand on a beach • A brick wall Roger S. Gaborski

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 Roger S. Gaborski

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

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?? Roger S. Gaborski

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 Roger S. Gaborski

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

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

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

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

Statistical and Structural Texture 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

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

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

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

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 Roger S. Gaborski

Run Length Coding Statistics • Runs of ‘similar’ gray level pixels • Measure runs in the directions 0,45,90,135 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 Image Roger S. Gaborski

Image 45 degrees 0 degrees Run Length, L Run Length, L Gray Level, LEV Gray Level, LEV Roger S. Gaborski

Image 45 degrees 0 degrees Run Length, L Run Length, L Gray Level, LEV Gray Level, LEV Roger S. Gaborski

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 Roger S. Gaborski

Gray Level Co-occurrence Matrix, P[i,j] • Specify displacement vector d = (dx, dy) • Count all pairs of pixels separated by d having gray level values i and j. Formally: P(i, j) = |{(x1, y1), (x2, y2): I(x1, y1) = i, I(x1, y1) = j}| Roger S. Gaborski

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

Uniform Texture 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

Uniform Texture 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

Uniform Texture 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

Uniform Texture x d=(1,0) 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

Randomly Distributed Texture What if the Black and white pixels where randomly distributed? What will matrix P look like?? 1 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 No preferred set of gray level pairs, matrix P will have approximately a uniform population Roger S. Gaborski

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 (28). 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 Roger S. Gaborski

Co-occurrence Features • P(ga,gb,d,t): • ga gray level pixel ‘a’ • gb gray level pixel ‘b’ • d distance d • t angle t (0, 45,90,135) In many applications the transition ga to gb and gb to ga 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

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? Roger S. Gaborski

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. Roger S. Gaborski

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

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

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 Roger S. Gaborski