TEXTURE ANALYSIS USING GABOR FILTERS
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1 TEXTURE ANALYSIS USING GABOR FILTERS
2
3 Texture Types Definition of Texture Texture types Synthetic Natural Stochastic < Prev Next >
4 Texture Definition Texture: the regular repetition of an element or pattern on a surface. Purpose of texture analysis: To identify different textured and nontextured regions in an image. To classify/segment different texture regions in an image. To extract boundaries between major texture regions. To describe the texel unit. 3-D shape from texture Ref: [Forsyth3, Raghu95]
5 Texture Regions & Edges < Prev Next >
6 IIT Madras R R R R R3 R4 R3 R4 Textured image Image histograms VP LAB
7 Input Image FILTERING SMOOTHING CLASSIFIER Segmented Image Flow-chart of a typical method of texture classification
8 Synthetic Texture Image Horizontal intensity profile Filtered output Nonlinear transform Smoothing Segmented image
9 Processing of Texture-like Images f -D Gabor Filter x y ( x, y, ω, θ, σx, σy) = exp (( ) + ( ) ) πσxσy σx σy + jω( x cosθ + y sinθ ) A typical Gaussian filter with σ=3 < Prev A typical Gabor filter with σ=3, ω=3.4 and θ=45 Next >
10 Gabor filters with different combinations of spatial width σ, frequency ω and orientation θ.
11 -D Gabor filter: f ( x, y, ω, θ, σx, σy) = x exp (( ) πσxσy σx + y ( ) σy ) + jω( x cosθ + y sinθ ) where σ ω θ is the spatial spread is the frequency is the orientation -D Gabor filter: f x ( x, ω, σ ) = exp( + πσ σ jω ) x -D Gaussian function: g( x) exp x = πσ σ
12 Processing of Texture-like Images -D Gaussian Filter g( x) x exp σ = πσ -D Gabor Filter x f ( x, ω, σ ) = exp( + πσ σ Even Component jω ) x Odd Component < Prev Next >
13 K : Scales the magnitude of the Gaussian envelop. (a, b) : Scale the two axis of the Gaussian envelop. θ : (Rotation) angle of the Gaussian envelop. (x, y ) : Location of the peak of the Gaussian envelop. (u, v ) : Spatial frequencies of the sinusoidal carrier in Cartesian coordinates. It can also be expressed in polar coordinates as (F, ω ). P : Phase of the sinusoidal carrier. ) ) sin cos ( ( exp( )) ) ( ) ( ( exp( ), ( P y x F j y y b x x a K y x g = ω ω π π θ θ ) ) ( ( ) ) ( ) ( ( exp( ), ( P y v x u j y y b x x a K y x g = π π θ θ
14 Asymmetric -D Gaussian function
15 Asymmetrical Gaussian of 8 8 pixels. The parameters are as follows: x = y = ; a = /5 pixels; b = /4 pixels; θ = 45 deg. The real and imaginary parts of a complex Gabor function in space domain, with F = sqrt()/8 cycles/pixel, ω = 45 deg, P = deg.
16 Gaussian and its integral Fourier transform of the Gaussian f ( x) = e t a F ( ω ) = ( a π ) e aω 4 Fourier transform of the GABOR??
17 The frequency response of a typical dyadic bank of Gabor filters. One center-symmetric pair of lobes in the illustration represents each filter.
18 Some properties of Gabor filters: Computational cost often high, due to the necessity of using a large bank of filters in most applications A tunable bandpass filter Similar to a STFT or windowed Fourier transform Satisfies the lower-most bound of the time-spectrum resolution (uncertainty principle) It s a multi-scale, multi-resolution filter Has selectivity for orientation, spectral bandwidth and spatial extent. Has response similar to that of the Human visual cortex (first few layers of brain cells) Used in many applications texture segmentation; iris, face and fingerprint recognition.
19 Texture Image Magnitude of the Gabor Responses Smoothed Features
20 Texture Image Magnitude of the Gabor Responses Smoothed Features
21 Natural Textures Initial Classification Final Classification < Back
22 Segmentation using Gabor based features of a texture image containing five regions.
23 SIR-C/X-SAR image of Lost City of Ubar Classification using multispectral information Classification using multispectral and textural information < Back
24 Texture Image Output of Canny s algorithm Desired output
25 Texture Boundary Detection Edge extraction using -D Gabor filters smears the edge information The magnitude of the -D Gabor filter output is used as a feature to detect boundaries for texture-like images Advantage of -D processing: Feature extraction and edge extraction are applied along orthogonal directions. The Gaussian function (-D) of the Gabor filter will not effect the edge information in the orthogonal direction The edge evidence obtained from a set of Gabor filters are combined using a constraint satisfaction neural network to obtain the final output
26 Texture Edge Extraction using a set of -D Gabor Filters Input Image Bank of -D Gabor Filters Filtered Image Post-processing using -D Differential operator and Thresholding Edge evidence Combining the Edge evidence using Constraint Satisfaction Neural Network Mode Edge map
27 Results of Edge Extraction using Gabor Magnitude (contd.) Gray level Image -D Gabor Filter Bank -D Gabor Filter bank < Prev Next >
28 Results of Edge Extraction using Gabor Magnitude (contd.) Gray level Image -D Gabor Filter Bank -D Gabor Filter bank < Prev Next >
29 Filtering methods: Discrete Wavelet Transform (DWT) (Daubechies 8-Taps) Gabor Filter (Bank of 8 Gabor filters) Discrete Cosine Transform (DCT) (9 filters) Ref: [Ng 9] Gaussian Markov random field models Ref: [Cesmeli ] Combination of DWT and Gabor filter Ref: [Rao 4] Combination of DWT and MRF Ref: [Wang 99] Non-linearity: Magnitude (. ) Smoothing: Gaussian filter Feature vectors: Combine Edge and region map using a CSNN Mean (computed in a local window around a pixel) Classification: Fuzzy-C Means (FCM) (unsupervised classifier)
30 IIT Madras Results Input Image Segmented map before integration Edge map before integration Segmented map and Edge map after integration VP LAB
31 IIT Madras Results Input Image Segmented map before integration Edge map before integration Segmented map and Edge map after integration VP LAB
32 GLCM based texture feature (statistical) The Grey Level Co-occurrence Matrix, GLCM (also called the Grey Tone Spatial Dependency Matrix) The GLCM is a tabulation of how often different combinations of pixel brightness values (grey levels) occur in an image. The GLCM is usually defined for a series of "second order" texture calculations. Second order means they consider the relationship between groups of two pixels in the original image. First order texture measures are statistics calculated from the original image values, like variance, and do not consider pixel relationships. Third and higher order textures (considering the relationships among three or more pixels) are theoretically possible but not implemented due to calculation time and interpretation difficulty.
33 3 3 A small image neighborhood Spatial relationship between two pixels: NPV> 3 RPV 3 3 Neighbor/Reference Pixel Value GLCM texture considers the relation between two pixels at a time, called the reference and the neighbour pixel. Let, the neighbour pixel is chosen to be the one to the east (right) of each reference pixel. This can also be expressed as a (,) relation: (i, j) -> (i+, j). Each pixel within the window becomes the reference pixel in turn, starting in the upper left corner and proceeding to the lower right.
34 NPV> RPV A small image neighborhood EAST GLCM NPV> RPV WEST GLCM (why transpose?) NPV> RPV Symmetrical (,) GLCM (-,) relation: (i, j) -> (i-, j).
35 Expressing the GLCM as a probability: This is the number of times this outcome occurs, divided by the total number of possible outcomes. This process is called normalizing the matrix. Normalization involves dividing by the sum of values. Symmetrical (,) GLCM NPV> RPV (4/4).83 (/4).4 (/4) (/4)
36 A small image neighborhood Normalized symmetrical vertical GLCM Find, (,), South GLCM (solve it): Any reason for Diagonal dominance?
37 References. Haralick, R.M Statistical and Structural Approaches to Texture. Proceedings of the IEEE, 67:786-84; (also 973, IEEE-T-SMC). Simona E. Grigorescu, Nicolai Petkov, and Peter Kruizinga; Comparison of Texture Features Based on Gabor Filters; IEEE Transactions on Image Processing, Vol., No., OCT. ; pp J. Randen and J. S. Husoy, Texture Segmentation using filters with Optimized Energy Separation, IEEE Transactions on Image Processing, Vol. 8, No. 4, April 999, pp M. L. Comer and E. J. Delp, Segmentation of Textured Images using a Multiresolution Gaussian Autoregressive Model, IEEE Transactions on Image Processing, Vol. 8, No. 3, March 999, pp B. Thai and G. Healey, Optimal Spatial Filter Selection for Illumination-Invariant Color Texture Discrimination, IEEE Trans. Systems, Man and Cybernetics, Part B: Cybernetics, Vol. 3, No. 4, August, pp J. Randen and J. S. Husoy, "Optimal Filter-bank Design for Multiple texture Discrimination", Proceedings of the International Conference on Image Processing (ICIP '97), pp "Integrating Region and Edge Information for Texture Segmentation using a modified Constraint Satisfaction Neural Network", Lalit Gupta, Utthara Gosa Mangai and Sukhendu Das, Accepted for Publication in the Journal of Image and Vision Computing, December 7 (Article in Press - available ONLINE).
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