E.G.M. PetrakisTexture1 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

E.G.M. PetrakisTexture2 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

E.G.M. PetrakisTexture3 examples of texture from Ballard and Brown ‘84

E.G.M. PetrakisTexture4 examples of texels (a)circles (b)circles and (c)ellipses line segments

E.G.M. PetrakisTexture5 examples of aerial image textures

E.G.M. PetrakisTexture6 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

E.G.M. PetrakisTexture7 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

E.G.M. PetrakisTexture8 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)

E.G.M. PetrakisTexture9 semi-regular tessellations

E.G.M. PetrakisTexture10 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

E.G.M. PetrakisTexture11 Shape Grammar Hexagonal texture: the grammar is a 4-tuple –G = –V t ={ }: finite set of “terminal” shapes –V m : finite set of shapes such that V t /V m = 0 (non-terminal shape elements or markers) –R: set of rules for producing patterns of V t S –V t S: elements of V t used a multiple number of times in any location, orientation and scale

E.G.M. PetrakisTexture12 Example of Texture Grammar Apply the rules in reverse order until a symbol in S is produced A failure means that the texture cannot be recognized from G textures to be recognized

E.G.M. PetrakisTexture13 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 = (v 1,v 2, …, v n ) –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

E.G.M. PetrakisTexture14 effective features ineffective features texture classification as as pattern recognition problem

E.G.M. PetrakisTexture15 Co-Coherence Matrix P[i,j] : counts pairs of pixels separated by distance d = (dx,dy) having gray levels i, j in [0,2] i j P[i,j] d = (1,1)

E.G.M. PetrakisTexture16 Co-Coherence Matrix (cont.) There are 16 pairs of pixels which satisfy the spatial separation d in direction 45 o 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 –P is not symmetric –normalize P by the total number of pairs –P: probability mass function

E.G.M. PetrakisTexture17 Co-Coherence Matrix (cont.) P captures 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 high values for uniform P (no preferred gray- level, no texture)

E.G.M. PetrakisTexture18 More Texture Feaures Measure P for several d,θ Existence of texture: –maximization of one of these measures or –minimization of entropy

E.G.M. PetrakisTexture19 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

E.G.M. PetrakisTexture20 Fourier Method When texture exhibits periodicity or orientation –detect peaks in the power spectrum –partition the Fourier space into bins of r or θ –texture features are defined on the spectrum |F| 2 v uu v r θ angual bins radial bins

Partitioning the Fourier Spectrum E.G.M. PetrakisTexture21

E.G.M. PetrakisTexture22 Radial Features Radial feature vector: –V = (Vr 0 r 0,Vr 0 r 1,…, Vr k r l ), 0<= k,l <= m –Vr k r l is the spectral content of a ring [r k,r l ] Exploit the sensitivity of the power spectrum to the size of the texture [r 1,r 2 ] define one of the radial bins

E.G.M. PetrakisTexture23 Angular Features Angular feature vector: –V = (Vθ 0 θ 0,Vθ 0 θ 1,…, Vθ k θ l ), 0<= k,l <= m –Vθ k θ l is the spectral content in a piece [θ k,θ l ] Exploit the sensitivity of the power spectrum to the directionality of the texture [θ k,θ l ] define one of the sectors

E.G.M. PetrakisTexture24 Comments on Fourier Method Radial features are correlated with texture coarseness –smooth texture has high Vr 1 r 2 for small radii –coarse texture has higher Vr 1 r 2 for larger radii Angular features are correlated with the directionality of the texture –if the texture has many lines or edges in a given direction θ then |F| 2 tends to give high values between θ and θ + π/2