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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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    1. Introduction to Computer VisionImage Texture Analysis Lecture 12

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

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

    4. 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

    5. 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

    6. 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

    7. 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

    8. 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

    9. “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? Roger S. Gaborski

    10. 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

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

    12. Artificial Texture                         Roger S. Gaborski

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

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

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

    16. 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

    17. 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

    18. 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

    19. 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

    20. 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

    21. 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

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

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

    24. 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

    25. 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

    26. 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

    27. 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

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

    29. 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

    30. 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

    31. 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

    32. 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

    33. 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

    34. 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

    35. 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

    36. 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

    37. 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

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

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

    40. 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

    41. Roger S. Gaborski

    42. Matlab Texture Filter Functions Roger S. Gaborski

    43. rangefilt max (4) –min(1) = 3 Roger S. Gaborski

    44. rangefilt max (5) –min(1) = 4 Roger S. Gaborski

    45. rangefilt max (6) –min(2) = 4 Roger S. Gaborski

    46. rangefilt max (8) –min(1) = 7 Roger S. Gaborski

    47. rangefilt max (8) –min(1) = 7 Roger S. Gaborski

    48. rangefilt max (7) –min(2) = 5 Roger S. Gaborski

    49. rangefilt max (7) –min(2) = 5 Roger S. Gaborski

    50. Original image Roger S. Gaborski