Download - TEXTURE ANALYSIS USING GABOR FILTERS
![Page 1: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/1.jpg)
TEXTURE ANALYSIS
USING
GABOR FILTERS
![Page 2: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/2.jpg)
![Page 3: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/3.jpg)
• Definition of Texture
• Texture types
Texture Types
Next >< Prev
Synthetic Natural Stochastic
![Page 4: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/4.jpg)
Texture Definition
• Purpose of texture analysis:– To identify different textured and non-
textured 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
Texture: the regular repetition of an element or pattern on a surface.
Ref: [Forsyth2003, Raghu95]
![Page 5: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/5.jpg)
Texture Regions & Edges
Next >< Prev
![Page 6: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/6.jpg)
IIT Madras
VP LAB
Image histograms
R1 R2
R3
R1 R2
R3R4 R4
Textured image
![Page 7: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/7.jpg)
Input Image
FILTERING
SMOOTHING
CLASSIFIER
Segmented Image
Flow-chart of a typical method of texture classification
![Page 8: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/8.jpg)
Synthetic TextureImage
Horizontal intensity profile
Filtered output
Nonlinear transform Smoothing
Segmented image
![Page 9: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/9.jpg)
Processing of Texture-like Images2-D Gabor Filter
A typical Gaussian filter with σ=30
A typical Gabor filter with
σ=30, ω=3.14 and θ=45°
⎥⎦⎤
⎢⎣⎡ +++
−= )sincos(
21exp
21),,,,,( ))()(( 22 θθω
σσσπσσσθω yxjyxyxf
yxyxyx
Next >< Prev
![Page 10: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/10.jpg)
Gabor filters with different combinations of spatial width σ, frequency ω and orientation θ.
![Page 11: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/11.jpg)
)2
exp(21),,(
2
2 xjxxf ωσσπ
σω +−
=
⎥⎦⎤
⎢⎣⎡ +++
−= )sincos())()((
21exp
21),,,,,( 22 θθω
σσσπσσσθω yxjyxyxf
yxyxyx
⎟⎟⎠
⎞⎜⎜⎝
⎛ −= 2
2
1 2exp
21)(
σσπxxg
2-D Gabor filter:
1-D Gabor filter:
1-D Gaussian function:
whereσ is the spatial spreadω is the frequencyθ is the orientation
![Page 12: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/12.jpg)
)2
exp(21),,(
2
2 xjxxf ωσσπ
σω +−
=⎟⎟⎠
⎞⎜⎜⎝
⎛ −= 2
2
1 2exp
21)(
σσπxxg
Processing of Texture-like Images1-D Gabor Filter
1-D Gaussian Filter
Odd Component
Even Component
Next >< Prev
![Page 13: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/13.jpg)
• 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.• (x0, y0) : Location of the peak of the Gaussian envelop.• (u0, v0) : Spatial frequencies of the sinusoidal carrier in Cartesiancoordinates. It can also be expressed in polar coordinates as (F0, ω0).• P : Phase of the sinusoidal carrier.
))sincos(2(exp( )))()((exp(),(
000
20
220
2
PyxFjyybxxaKyxg
++−+−−=ωωπ
π θθ
))(2())()((exp(),(
002
022
02 PyvxujyybxxaK
yxg+++−+−−
=
ππ θθ
![Page 14: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/14.jpg)
Asymmetric 2-D Gaussian function
![Page 15: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/15.jpg)
Asymmetrical Gaussian of 128×128 pixels. The parameters are as follows:
x0 = y0 = 0; a = 1/50 pixels; b = 1/40 pixels; θ = −45 deg.
The real and imaginary parts of a complex Gabor function in space domain, with
F0 = sqrt(2)/80 cycles/pixel, ω0 = 45 deg, P = 0 deg.
![Page 16: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/16.jpg)
at
exf2
)( −=
42
)(
)(ω
π
ωa
ea
F−
=
Gaussian and its integral
Fourier transform of the Gaussian
Fourier transform of the GABOR ??
![Page 17: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/17.jpg)
The frequency response of a typical dyadic bank of Gabor filters. One center-symmetric pair of lobes in the illustration
represents each filter.
![Page 18: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/18.jpg)
Some properties of Gabor filters:
• 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.
• Computational cost often high, due to the necessity of using alarge bank of filters in most applications
![Page 19: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/19.jpg)
TextureImage
Magnitude of theGabor Responses
SmoothedFeatures
![Page 20: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/20.jpg)
TextureImage
Magnitude of theGabor Responses
SmoothedFeatures
![Page 21: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/21.jpg)
Natural Textures Initial Classification Final Classification
< Back
![Page 22: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/22.jpg)
Segmentation using Gabor based features of a texture image containing five regions.
![Page 23: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/23.jpg)
SIR-C/X-SAR image of Lost City of Ubar
Classification using multispectral information
Classification using multispectral and
textural information
< Back
![Page 24: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/24.jpg)
Texture Image Output ofCanny’s
algorithm
Desired output
![Page 25: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/25.jpg)
Texture Boundary Detection
• Edge extraction using 2-D Gabor filters smears the edge information
• The magnitude of the 1-D Gabor filter output is used as a feature to detect boundaries for texture-like images
• Advantage of 1-D processing: Feature extraction and edge extraction are applied along orthogonal directions. The Gaussianfunction (1-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
![Page 26: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/26.jpg)
Bank of 1-D Gabor Filters
Input Image
Filtered Image
Edge evidence
Combining the Edge evidence using ConstraintSatisfaction Neural Network Mode
Edge map
Texture Edge Extraction using a set of 1-D Gabor Filters
Post-processing using 1-D Differential operator and Thresholding
![Page 27: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/27.jpg)
2-D Gabor Filter Bank 1-D Gabor Filter bankGray level Image
Results of Edge Extraction using Gabor Magnitude (contd.)
Next >< Prev
![Page 28: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/28.jpg)
2-D Gabor Filter Bank 1-D Gabor Filter bankGray level Image
Results of Edge Extraction using Gabor Magnitude (contd.)
Next >< Prev
![Page 29: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/29.jpg)
• Filtering methods:– Discrete Wavelet Transform (DWT) (Daubechies 8-Taps) – Gabor Filter (Bank of 8 Gabor filters) – Discrete Cosine Transform (DCT) (9 filters) Ref: [Ng 92]– Gaussian Markov random field models Ref: [Cesmeli 2001]– Combination of DWT and Gabor filter Ref: [Rao 2004]– Combination of DWT and MRF Ref: [Wang 99]
• Non-linearity:– Magnitude (| . |)
• Smoothing:– Gaussian filter
• Feature vectors:– Mean (computed in a local window around a pixel)
• Classification:– Fuzzy-C Means (FCM) (unsupervised classifier)
• Combine Edge and region mapusing a CSNN
![Page 30: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/30.jpg)
IIT Madras
VP LAB
Input Image
Segmented map before integration
Edge map before integration
Segmented map and Edge map after integration
Results
![Page 31: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/31.jpg)
IIT Madras
VP LAB
ResultsInput Image
Segmented map before integration
Edge map before integration
Segmented map and Edge map after integration
![Page 32: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/32.jpg)
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) occurin 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.
![Page 33: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/33.jpg)
Spatial relationship between two pixels:
GLCM texture considers the relation between two pixels at a time, called the reference and the neighbourpixel. 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 (1,0) relation: (i, j) -> (i+1, j).
Each pixel within the window becomes the reference pixel in turn, starting in the upper left corner and proceeding to the lower right.
3322222011001100
10003130020020101220
3210NPV>RPV
A small imageneighborhood
Neighbor/Reference Pixel Value
![Page 34: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/34.jpg)
3322222011001100
10003130020020101220
3210NPV>RPV
A small imageneighborhood
EAST GLCM
11003030120022100020
3210NPV>RPV
WEST GLCM (why transpose ?)
21003160120042101240
3210NPV>RPV
Symmetrical (1,0) GLCM
(-1,0) relation: (i, j) -> (i-1, j).
![Page 35: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/35.jpg)
21003160120042101240
3210NPV>RPV
Symmetrical (1,0) GLCM 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.
.083.04200
.042.250.042
00.166.083
0 (0/24)
.042 (1/24)
.083 (2/24)
.166 (4/24)
![Page 36: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/36.jpg)
020002000000
222201222100
024000200220
020600030203
3322222011001100
A small imageneighborhood
0.08300.083.083.083.083
0.083.16600.0830.250Normalized symmetrical
vertical GLCM
Find,(1,0), South GLCM (solve it):
Any reason forDiagonal dominance ?
![Page 37: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/37.jpg)
References1. Haralick, R.M. 1979. Statistical and Structural Approaches to Texture. Proceedings
of the IEEE, 67:786-804; (also 1973, IEEE-T-SMC)
2. Simona E. Grigorescu, Nicolai Petkov, and Peter Kruizinga; Comparison of Texture Features Based on Gabor Filters; IEEE Transactions on Image Processing, Vol. 11, No. 10, OCT. 2002; pp 1160-1167.
3. J. Randen and J. S. Husoy, Texture Segmentation using filters with Optimized Energy Separation, IEEE Transactions on Image Processing, Vol. 8, No. 4, April 1999, pp 571-582.
4. 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 1999, pp 408-420.
5. 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. 30, No. 4, August 2000, pp 610-615.
6. 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 215-218.
7. "Integrating Region and Edge Information for Texture Segmentation using a modified Constraint Satisfaction Neural Network", Lalit Gupta, Utthara GosaMangai and Sukhendu Das, Accepted for Publication in the Journal of Image and Vision Computing, December 2007 (Article in Press - available ONLINE).
![Page 38: TEXTURE ANALYSIS USING GABOR FILTERS](https://reader031.vdocuments.us/reader031/viewer/2022020706/61fd401331bf0705fb38452d/html5/thumbnails/38.jpg)