Texture

1. Texture • Repeative patterns of local variations of intensity on a surface • texture pattern: texel • Texels: similar shape, intensity distribution and probably orientation or size • geometric shapes, lines, dots, points • Different applications, different texture Texture

2. Texture Resolution • The resolution at which the image is observed determines the scale at which the texture is perceived • The texture changes or vanishes depending on the distance from which an image is observed • e.g., when a tiled floor is observed from a large distance the texture is formed by the placement of tiles • when the same image is observed from a closer distance only a few tiles are within the field of view and the texture is formed by the placement of dots, lines etc. composing each tile Texture

3. examples of texture from Ballard and Brown ‘84 Texture

4. examples of texels • circles • circles and • ellipses line segments Texture

5. examples of aerial image textures Texture

6. Texture Analysis • Segmentation: determine the boundaries of textured regions • region and boundary-based methods • Classification: identify a textured region • find the most similar from multiple classes of texture • extract and classify texels • Shape recovery from texture: use variations in size and orientation of texels to estimate surface shape and orientation Texture

7. Texture Classification • Structural: the texels are large enough (can be distinguished from the background) to be individually segmented and described • e.g., grammars, tessellation models etc. • Statistical: describe the gray level distribution of textured areas • apply when the texels exhibit variations which can be described statistically Texture

8. Tessellation Methods • The texels tessellate the place in an ordered way • in a regular tessellation the polygons surrounding a vertex have the same number of sides • semi-regular tessellations have two or more kinds of polygons • these tessellations are described by listing in order the number of sides of the polygons surrounding each vertex • e.g., hexagonal tessellations: (6,6,6) Texture

9. semi-regular tessellations Texture

10. Grammatical Methods • A grammar describes how to generate patterns by applying rewriting rules to a small number of symbols • a grammar can generate complex textural patterns • stochastic grammars: real world variations can be incorporated into a grammar by attaching probabilities to different rules • no unique grammar for a given texture • variants: shape, tree and array grammars Texture

11. Shape Grammar • Hexagonal texture: the grammar is a 4-tuple • G = <Vt, Vm, R, S> • Vt ={ }: finite set of “terminal” shapes • Vm: finite set of shapes such that Vt/Vm = 0 (non-terminal shape elements or markers) • R: set of rules for producing patterns of VtS • VtS: elements of Vt used a multiple number of times in any location, orientation and scale Texture

12. Example of Texture Grammar textures to be recognized • Apply the rules in reverse order until a symbol in S is produced • A failure means that the texture cannot be recognized from G Texture

13. Statistical Methods • The texture is described by the spatial distribution of intensities • the texels cannot be recognized individually • Texture recognition as a pattern classification: • compute a vector V = (v1,v2, …, vn) • classify the vector into one of M classes • select the features of V • classify a vector according to its minimum distance from a class vector Texture

14. effective features ineffective features texture classification as as pattern recognition problem Texture

15. Co-Coherence Matrix P[i,j] d = (1,1) 0 i 1 1 j 16 2 0 1 2 • P[i,j]: counts pairs of pixels separated by distance d = (dx,dy) having gray levels i, j in [0,2] Texture

16. Co-Coherence Matrix (cont.) • There are 16 pairs of pixels which satisfy the spatial separation din direction 45o • Count all pairs of pixels in which the first pixel has value i and its matching pair displaced by d, θ has value j • Enter this count in the (i,j) position of P • e.g., if there are 3 pairs [2,1]then P[2,1] = 3 • Pis not symmetric • normalize P by the total number of pairs • P: probability mass function Texture

17. Co-Coherence Matrix (cont.) • Pcaptures the spatial distribution of gray levels for the specified d,θ • repeat the same for all i, j • Textured regions exhibit a non-random distribution of values in P • Entropy: feature which measures randomness • takes highvalues for uniform P(no preferred gray-level, no texture) Texture

18. More Texture Feaures • Measure P for several d,θ • Existence of texture: • maximization of one of these measures or • minimization of entropy Texture

19. Auto-Correlation • Compute A of image f of size N x N for various k,l • A measures the periodicity of texture • Textured images: A exhibits periodic behavior with a period equal to the spacing between pixels • coarse texture: A drops slowly • fine texture: A drops rapidly Texture

20. v v radial bins angual bins r θ u u Fourier Method • When texture exhibits periodicity or orientation • detect peaks in the power spectrum • partition the Fourier space into bins of rorθ • texture features are defined on the spectrum |F|2 Texture

21. Partitioning the Fourier Spectrum Texture

22. Radial Features [r1,r2] define one of the radial bins • Radial feature vector: • V = (Vr0r0,Vr0r1,…, Vrkrl), 0<= k,l <= m • Vrkrl is the spectral content of a ring [rk,rl] • Exploit the sensitivity of the power spectrum to the size of the texture Texture

23. Angular Features [θk,θl] define one of the sectors • Angular feature vector: • V = (Vθ0θ0,Vθ0θ1,…, Vθkθl), 0<= k,l <= m • Vθkθlis the spectral content in a piece[θk,θl] • Exploit the sensitivity of the power spectrum to the directionality of the texture Texture

24. Comments on Fourier Method • Radial features are correlated with texture coarseness • smooth texture has high Vr1r2for small radii • coarse texture has higher Vr1r2for larger radii • Angular features are correlated with the directionality of the texture • if the texture has many lines or edges in a given direction θthen|F|2 tends to give high values between θandθ + π/2 Texture