1. Computer VisionChapter 9 Texture Presented by 王夏果 and 傅楸善教授 Cell phone: 0937384214 E-mail: r94922103@ntu.edu.tw Digital Camera and Computer Vision Laboratory Department of Computer Science and Information Engineering National Taiwan University, Taipei, Taiwan, R.O.C.

2. Introduction • What does texture mean? Formal approach or precise definition of texture does not exist! • Texture discrimination techniques are for the part ad hoc. DC & CV Lab. CSIE NTU

3. Definition of Texture • Non-local property, characteristic of region larger than its size • Repeating patterns of local variations in image intensity which are too fine to be distinguished as separated objects at the observed resolution DC & CV Lab. CSIE NTU

4. Definition of Texture (cont.) • For humans, texture is the abstraction of certain statistical homogeneities from a portion of the visual field that contains a quantity of information grossly in excess of the observer’s perceptual capacity DC & CV Lab. CSIE NTU

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11. Texture Analysis Issues • Pattern recognition: given texture region, determine the class the region belongs to • Generative model: given textured region, determine a description or model for it • Texture segmentation: given image with many textured areas, determine boundaries DC & CV Lab. CSIE NTU

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13. Statistical Texture-Feature Approaches • Autocorrelation function • Spectral power density function • Edgeness per unit area • Spatial gray level co-occurrence probabilities • Graylevel run-length distributions • Relative extrema distributions • Mathematical morphology DC & CV Lab. CSIE NTU

14. Image Texture Analysis • Give a generative model and the values of its parameters, one can synthesize homogeneous image texture samples associated with the model and the given value of its parameters. DC & CV Lab. CSIE NTU

15. Image Texture Analysis (cont.) • Verification: verify given image textures sample consistent with model • Estimation: estimate values of model parameters based on observed sample examples of model-based techniques DC & CV Lab. CSIE NTU

16. Some Model-Based Techniques • Autoregressive, moving-average, time-series models (extended to 2D) • Markov random fields • Mosaic models DC & CV Lab. CSIE NTU

17. Texel • Texture element, basic textural unit of some textural primitives qualitatively evaluated image texture properties DC & CV Lab. CSIE NTU

18. Some Texture Features • Fineness • Coarseness • Contrast • Directionality • Roughness • Regularity • Smoothness • Granulation DC & CV Lab. CSIE NTU

19. Some Texture Features (cont.) • Randomness • Lineation • Mottled • Irregular • Hummocky DC & CV Lab. CSIE NTU

20. Take a Break DC & CV Lab. CSIE NTU

21. Texture and Scale • For any textural surface, there exists a scale at which, when the surface is examined, it appears smooth and textureless. (see from infinite distance) • As resolution increases, the surfaces appears as a fine texture and then a coarse one, and for multiple-scale textural surface the cycle of smooth, fine, and coarse may repeat. DC & CV Lab. CSIE NTU

22. Texture and Scale (cont.) • Thus, texture cannot be analyzed without frame of reference on scale or resolution. • Texture is a scale-dependent phenomenon. DC & CV Lab. CSIE NTU

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24. Characterizing Texture • Characterize gray level primitive properties • Characterize spatial relationships between them DC & CV Lab. CSIE NTU

25. First-Order Gray-Level Statistics • Statistics of single pixels • E.g. Histogram, mean, median, variance DC & CV Lab. CSIE NTU

26. Second-Order Gray-Level Statistics • The combined statistics of gray levels of pairs of pixels in which each two pixels in a pair have a fixed relative position • E.g. co-occurrence • Gray level spatial dependence: characterize texture by co-occurrence DC & CV Lab. CSIE NTU

27. Co-Occurrence Matrix • The gray level co-occurrence can be specified in a matrix of relative frequencies Pij with which two neighboring pixels separated by distance d occur on the image, one with gray level i and the other with gray level j • Symmetric matrix • Function of angle and distance between pixels DC & CV Lab. CSIE NTU

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29. Co-Occurrence Matrix (cont.) • Probability of horizontal, d pixels apart pixels P(i, j, d, 0°) = #{[(k, l), (m, n)] | k-m = 0, |l-n| = d, I(k, l) = i, I(m,n) = j} • Probability of 45°, d pixels apart pixels P(i, j, d, 45°) = #{[(k, l), (m, n)] | (k-m = d, l-n = -d) or (k-m = -d, l-n = d), I(k, l) = i, I(m,n) = j} DC & CV Lab. CSIE NTU

30. Co-Occurrence Matrix (cont.) • Probability of 90°, d pixels apart pixels P(i, j, d, 90°) = #{[(k, l), (m, n)] | |k-m| = d, l-n = 0, I(k, l) = i, I(m,n) = j} • Probability of 135°, d pixels apart pixels P(i, j, d, 135°) = #{[(k, l), (m, n)] | (k-m = d, l-n = d) or (k-m = -d, l-n = -d), I(k, l) = i, I(m,n) = j} DC & CV Lab. CSIE NTU

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32. Co-Occurrence Matrix (cont.) • Matrix symmetric: P(i, j, d, a) = P(j, i, d, a) DC & CV Lab. CSIE NTU

33. Take a Break DC & CV Lab. CSIE NTU

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35. Matrix with Highest Entropy • When all entries in Pij are equal • Image where no preferred gray-level pairs exist features calculated from the co-occurrence matrix DC & CV Lab. CSIE NTU

36. Generalized Gray Level Spatial Dependence Models for Texture • Simple generalization: consider more than two pixels at a time DC & CV Lab. CSIE NTU

37. Generalized Co-Occurrence • Strong texture measures take into account the co-occurrence between texture primitives. DC & CV Lab. CSIE NTU

38. Texture Primitive • Connected set of pixels characterized by attribute set • Simplest primitive: pixel with gray level attribute • More complicated primitive: connected set of pixels homogeneous in level, characterized by size, elongation, orientation, and average gray level DC & CV Lab. CSIE NTU

39. Spatial Relationship • We have a list of primitives, their center coordinate, and their attributes after the primitives have been constructed. DC & CV Lab. CSIE NTU

40. Spatial Relationship (cont.) DC & CV Lab. CSIE NTU

41. Autocorrelation Function • Texture relates to the spatial size of the gray level primitives on an image • Gray level primitives of larger size are indicative of coarser texture • Gray level primitives of smaller size are indicative of finer texture DC & CV Lab. CSIE NTU

42. Autocorrelation Function (cont.) • Autocorrelation function describes the size of gray level primitives DC & CV Lab. CSIE NTU

43. Autocorrelation Function (cont.) DC & CV Lab. CSIE NTU

44. Autocorrelation Function (cont.) DC & CV Lab. CSIE NTU

45. Autocorrelation Function (cont.) • If the gray level on image is relatively large: texture is coarse, autocorrelation drops off slowly with distance • If the gray level on image is relatively small: texture is fine, autocorrelation drops off quickly with distance • Periodic DC & CV Lab. CSIE NTU

46. Take a Break DC & CV Lab. CSIE NTU

47. Digital Transform Methods and Texture • In the digital transform method of texture analysis, the digital image is typically divided into a set of non-overlapping small square subimages • The vectors is reexpressed in a new coordinate system • Fourier transform uses the complex sinusoid basic set, Handamard transfer uses the Walsh function basic set, ….. DC & CV Lab. CSIE NTU

48. Texture Energy • The image is first convolved with a variety of kernels • Then each convolved image is processed with a nonlinear operator to determine the total textural energy in each pixel’s neighborhood DC & CV Lab. CSIE NTU

49. Texture Edgeness • Autocorrelation function and digital transform both reference texture to spatial frequency • Texture Edgeness: conceive texture in terms of edgeness per unit area DC & CV Lab. CSIE NTU

50. Texture Edgeness (cont.) • Use small neighborhood to detect microedge • Use large neighborhood to detect macroedge DC & CV Lab. CSIE NTU