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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 pixel
  • Subtract 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 Filters
  • Similar 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 function
  • Autocorrelation 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 autocorrelation
  • Coarse 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 spectrum
  • High frequency power  fine texture
  • Concentrated power  regularity
  • Directionality  directional texture
  • Blobworld Texture Features
  • Choose the best scale instead of using fixed scale(s)
  • Used successfully in color/texture segmentation in Berkeley’s Blobworld project
  • Feature Extraction
  • Input: 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 Scale
  • Texture 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 Terminology
  • Gradient 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 Extraction
  • Extract 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 Images
  • K-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 Images
  • K-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 ) formatReferences
  • Chad 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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