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Texture. Texture is a description of the spatial arrangement of color or intensities in an image or a selected region of an image. Structural approach: a set of texels in some regular or repeated pattern. Problem with Structural Approach. How do you decide what is a texel?. Ideas?.

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TextureTexture is a description of the spatial arrangement of color orintensities in an image or a selected region of an image.Structural approach: a set of texels in some regular or repeated patternProblem with Structural ApproachHow do you decide what is a texel?Ideas?Natural Textures from VisTexgrassleavesWhat/Where are the texels?The Case for Statistical Texture Segmenting out texels is difficult or impossible in real images. Numeric quantities or statistics that describe a texture can be computed from the gray tones (or colors) alone. This approach is less intuitive, but is computationally efficient. It can be used for both classification and segmentation. Some Simple Statistical Texture Measures1. Edge Density and Direction Use an edge detector as the first step in texture analysis. The number of edge pixels in a fixed-size region tells us how busy that region is. The directions of the edges also help characterize the texture Two Edge-based Texture Measures1. edgeness per unit area2. edge magnitude and direction histogramsFedgeness = |{ p | gradient_magnitude(p) threshold}| / Nwhere N is the size of the unit areaFmagdir = ( Hmagnitude, Hdirection )where these are the normalized histograms of gradientmagnitudes and gradient directions, respectively.Example Original Image Frei-Chen Thresholded Edge Image Edge ImageLocal Binary Pattern Measure For each pixel p, create an 8-bit number b1 b2 b3 b4 b5 b6 b7 b8, where bi = 0 if neighbor i has value less than or equal to p’s value and 1 otherwise. Represent the texture in the image (or a region) by the histogram of these numbers. 1 2 3100 101 103 40 50 80 50 60 90451 1 1 1 1 1 0 08 7 6ExampleFids (Flexible Image DatabaseSystem) is retrieving imagessimilar to the query imageusing LBP texture as thetexture measure and comparingtheir LBP histogramsExampleLow-levelmeasures don’talways findsemanticallysimilar images.Co-occurrence Matrix FeaturesA co-occurrence matrix is a 2D array C in which Both the rows and columns represent a set of possible image values. C (i,j)indicates how many times valueico-occurs with valuejin a particular spatial relationshipd. The spatial relationship is specified by a vectord = (dr,dc). dCo-occurrence Example10 1 21 1 0 01 1 0 00 0 2 20 0 2 20 0 2 20 0 2 2ij0121 0 32 0 20 0 13Cdco-occurrence matrixd = (3,1)gray-tone imageFrom Cd we can compute Nd, the normalized co-occurrence matrix,where each value is divided by the sum of all the values.Co-occurrence FeaturesWhat do these measure?sums.Energy measures uniformity of the normalized matrix.But how do you choose d? This is actually a critical question with all the statistical texture methods. Are the “texels” tiny, medium, large, all three …? Not really a solved problem. Zucker and Terzopoulos suggested using a 2 statisticaltest to select the value(s) of d that have the most structurefor a given class of images. ExampleLaws’ Texture Energy Features Signal-processing-based algorithms use texture filters applied to the image to create filtered images from which texture features are computed. The Laws Algorithm Filter the input image using texture filters. Compute texture energy by summing the absolute value of filtering results in local neighborhoods around each pixel. Combine features to achieve rotational invariance. Law’s texture masks (1)Law’s texture masks (2)Creation of 2D MasksE5L5E5L59D feature vector for pixelSubtract mean neighborhood intensity from (center) pixel Apply 16 5x5 masks to get 16 filtered images Fk , k=1 to 16 Produce 16 texture energy maps using 15x15 windows Ek[r,c] = ∑ |Fk[i,j]|9 features defined as follows: Laws FiltersLaws ProcessExample: Using Laws Features to ClusterwatertigerfenceflaggrassIs there aneighborhoodsize problemwith Laws?small flowersbig flowersFeatures from sample imagesGabor FiltersSimilar approach to Laws Wavelets at different frequencies and different orientations Gabor FiltersGabor FiltersSegmentation with Color and Gabor-Filter Texture (Smeulders)A classical texture measure:Autocorrelation functionAutocorrelation function can detect repetitive patterns of texels Also defines fineness/coarseness of the texture Compare the dot product (energy) of non shifted image with a shifted image Interpreting autocorrelationCoarse texture function drops off slowly Fine texture function drops off rapidly Can drop differently for r and c Regular textures function will have peaks and valleys; peaks can repeat far away from [0, 0] Random textures only peak at [0, 0]; breadth of peak gives the size of the texture Fourier power spectrumHigh frequency power fine texture Concentrated power regularity Directionality directional texture Blobworld Texture FeaturesChoose the best scale instead of using fixed scale(s) Used successfully in color/texture segmentation in Berkeley’s Blobworld project Feature ExtractionInput: image Output: pixel features Color features Texture features Position features Algorithm: Select an appropriate scale for each pixel and extract features for that pixel at the selected scale feature extractionPixel Features PolarityAnisotropyTexture contrastOriginal imageTexture ScaleTexture is a local neighborhood property. Texture features computed at a wrong scale can lead to confusion. Texture features should be computed at a scale which is appropriate to the local structure being described. The white rectangles show some sample texture scales from the image.Scale Selection TerminologyGradient of the L* component (assuming that the image is in the L*a*b* color space) :▼I Symmetric Gaussian : Gσ (x, y) = Gσ (x) * Gσ (y) Second moment matrix: Mσ (x, y)= Gσ (x, y) * (▼I)(▼I)T IxIyIx2 IxIyIxIy Iy2Notes: Gσ (x, y) is a separable approximation to a Gaussian.σ is the standard deviation of the Gaussian [0, .5, … 3.5].σ controls the size of the window around each pixel [1 2 5 10 17 26 37 50]. Mσ(x,y) is a 2X2 matrix and is computed at different scales defined by σ.Scale Selection (continued)Make use of polarity (a measure of the extent to which the gradient vectors in a certain neighborhood all point in the same direction) to select the scale at which Mσ is computed Edge: polarity is close to 1 for all scales σTexture: polarity varies with σUniform: polarity takes on arbitrary valuesScale Selection (continued)polarity p n is a unit vector perpendicular to the dominant orientation. The notation [x]+ means x if x > 0 else 0 The notation [x]- means x if x < 0 else 0 We can think of E+ and E- as measures of how many gradient vectors in the window are on the positive side and how many are on the negative side of the dominant orientation in the window. Example:n=[1 1]x = [1 .6]x’ = [-1 -.6]Scale Selection (continued)Texture scale selection is based on the derivative of the polarity with respect to scale σ. Algorithm: Compute polarity at every pixel in the image for σk = k/2, (k = 0,1…7). 2. Convolve each polarity image with a Gaussian with standard deviation 2k to obtain a smoothed polarity image. 3. For each pixel, the selected scale is the first value of σ for which the difference between values of polarity at successive scales is less than 2 percent. Texture Features ExtractionExtract the texture features at the selected scale Polarity (polarity at the selected scale) : p = pσ* Anisotropy: a = 1 – λ2 / λ1 λ1and λ2 denote the eigenvalues of Mσλ2 /λ1 measures the degree of orientation: when λ1 is large compared to λ2 the local neighborhood possesses a dominant orientation. When they are close, no dominant orientation. When they are small, the local neighborhood is constant.Local Contrast: C = 2(λ1+λ2)3/2 A pixel is considered homogeneous if λ1+λ2 < a local threshold Blobworld Segmentation Using Color and TextureApplication to Protein Crystal ImagesK-mean clustering result (number of clusters is equal to 10 and similarity measure is Euclidean distance) Different colors represent different textures Original image in PGM (Portable Gray Map ) formatApplication to Protein Crystal ImagesK-mean clustering result (number of clusters is equal to 10 and similarity measure is Euclidean distance) Different colors represent different textures Original image in PGM (Portable Gray Map ) formatReferencesChad Carson, Serge Belongie, Hayit Greenspan, and Jitendra Malik. "Blobworld: Image Segmentation Using Expectation-Maximization and Its Application to Image Querying." IEEE Transactions on Pattern Analysis and Machine Intelligence 2002; Vol 24. pp. 1026-38. W. Forstner, “A Framework for Low Level Feature Extraction,” Proc. European Conf. Computer Vision, pp. 383-394, 1994.

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