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8/13/2019 Lect Gabor Filt
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TEXTURE ANALYSIS
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• Texture types
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yn e c a ura Stochastic
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Texture: the regular repetition ofan element or pattern on a surface.
• urpose o ex ure ana ys s: – To identif different textured and non-
textured regions in an image.
–
an image.
– To extract boundaries between major texturere ions.
– To describe the texel unit.
– 3-D shape from texture
Ref: [Forsyth2003, Raghu95]
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Texture Regions & Edges
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IIT Madras
R1 R2
R3 R4
ex ure mage
VP LAB
Image histograms
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Input Image
FILTERING
SMOOTHING
Segmented Image
Flow-chart of a typical method of texture classification
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Synthetic Texture
Image
intensity
rofile
Filteredoutput
Nonlinear
transformSmoothing
image
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Processing of Texture-like Images
2-D Gabor Filter−
+++= )sincos(
2exp
2),,,,,( 22
θ θ ω σ σ σ πσ
σ σ θ ω y x j y x y x y x
y x
A t ical Gaussian A t ical Gabor filter withfilter with σ=30
σ=30, ω=3.14 and =45°
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Gabor filters with different combinations of
spatial width σ, frequency ω and orientation .
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-
+++−= sincos1ex1 22θ θ σ σ θ x y x x y x
22 σ σ σ πσ y x y x
where
σ is the spatial spreadω is the frequency
θ is the orientation
)exp(1
),,(
2
2 x j
x x f ω σ ω +
−=
1-D Gabor filter:
−=
2
ex
1 x
x
1-D Gaussian function:
1 σ σ π
i f lik
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Processing of Texture-like Images
1 2 x−
1-D Gabor Filter
1-D Gaussian Filter22
,,2
σ σ π
−=
2
12
exp2
1)(
σ σ π
x x g
Even Component
Odd Component
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symmetr c - auss an unct on
)))()((()( 2222 bKb +
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)))()((exp(),( 2
0
22
0
2 y yb x xa K y x gab −+−−= π θ θ
• K : Scales the magnitude of the
000
Gaussian envelop.
• (a, b) : Scale the two axis of the
Gaussian envelop.• : (Rotation) angle of the Gaussian
envelop.
• (x0, y0) : Location of the peak of theGaussian 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.),( y x gab =
))(2())()((exp( 00
2
0
22
0
2 P yv xu j y yb x xa K +++−+−− π π θ θ
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Asymmetrical Gaussian of 128×128 pixels. The parameters
x0 = y0 = 0; a = 1/50 pixels; b = 1/40 pixels; = −45 deg.
The real and imaginary parts of a complex Gabor
function in s ace domain withF 0 = sqrt (2)/80 cyc les /p ixel, = 45 deg, P = 0 deg.
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Gaussian and
Fourier transformof the Gaussian
at
e x g
2
)(
−
=
)(uG =
42au−
Fourier transformof the GABOR ??
Green – Gaussian; Yellow - FT of Gaussian
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The frequency response of a typical d y a d i c bank of Gabor filters.One center-symmetric pair of lobes in the illustration
.
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Octave bands,due to Dyadic
decompositioner an
[3/32]
Read more about – in wavelets, QMFB
and Q-factor
etc.
Center frequencies: …. 0.0938 (3/32); 0.1875 (3/16); 0.375 (3/8); 0.75 (3/4).
Some properties of Gabor filters:
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Some properties of Gabor filters:
• Similar to a STFT or windowed Fourier transform
• Satisfies the lower-most bound of the time-spectrum resolution
• It’s a multi-scale, multi-resolution filter
• Has selectivity for orientation, spectral bandwidth and spatial
.
• Has res onse similar to that of the Human visual cortex first
few layers of brain cells) – ,
fingerprint recognition.
• Computational cost often high, due to the necessity of using a
large bank of filters (or Gabor jet) in most applications
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Texture
Image
Magnitude of the
Gabor Res onses
Smoothed
Features
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Texture
Image
Magnitude of the
Gabor Res onses
Smoothed
Features
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Natural Textures Initial Classification Final Classification
< Back
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Segmentation using Gabor based featuresof a texture image containing five regions.
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SIR-C/X-SAR image
of Lost City of Ubar
Classification using
multispectral information
Classification using
multispectral and texturalinformation
< Back
• Filtering methods:
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• Filtering methods:
– screte ave et rans orm au ec es - aps
– 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:
– .
• Smoothing: • Combine Edge and region map
usin a CSNN – auss an er
• Feature vectors:
– Mean (computed in a local window around a pixel)
• Classification: – Fuzzy-C Means (FCM) (unsupervised classifier)
IIT Madras
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Segmented mapbefore integration
Edge map before
inte ration
Segmented map
and Edge map
VP LAB
IIT Madras
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Input Image
Segmented mapbefore integration
Edge map before
integration
Segmented map
and Edge map
VP LAB
GLCM based texture feature (statistical)
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- ,
(also called the Grey Tone Spatial Dependency Matrix)
The GLCM is a tabulation of how often different
in an image.
e s usua y e ne or a ser es o secon
order" texture calculations.
Second order means they consider the relationshipbetween groups of two pixels in the original image.
First order texture measures are statistics calculated
consider pixel relationships. Third and higher order textures(considering the relationships among three or more pixels)
are eore ca y poss e u no mp emen e ue ocalculation time and interpretation difficulty.
0 0 1 1 NPV>0 1 2 3
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0 1 2 3
0 2 2 2 0 2 2 1 02 2 3 3
1 0 2 0 0A small image
2 0 0 3 10 0 0 1
neighborhood
pat a re at ons pbetween two pixels: Neighbor/Reference Pixel Value
GLCM texture considers the relation between twopixels at a time, called the reference and the neighbourp xe . et, t e ne g our p xe s c osen to e t e one to t e
east (right) of each reference pixel. This can also be- > + , , .
Each pixel within the window becomes the reference
p xe n turn, start ng n t e upper e t corner an procee ngto the lower right.
0 0 1 1 NPV>0 1 2 3
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0 1 2 3
0 2 2 2 0 2 2 1 0EAST2 2 3 3
1 0 2 0 0A small image
3 0 0 0 1neighborhood
-1 0 relation: i -> i-1 .
WEST GLCM (why transpose ?)
Symmetrical (1,0) GLCMNPV>
RPV0 1 2 3
NPV>
RPV0 1 2 3
0 2 0 0 0 0 4 2 1 0
1 2 2 0 0 1 2 4 0 0
3 0 0 1 1 3 0 0 1 2
Symmetrical (1,0) GLCMExpressing the GLCM
b bili
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NPV>as a probability:
RPV0 1 2 3
This is the number of times
1 2 4 0 0
this outcome occurs, divided by the
total number of possible outcomes.
2 1 0 6 1This process is called
normalizin the matrix.3 0 0 1 2
Normalization involves dividing
b the sum of values.
(4/24)
(2/24)
(1/24)
(0/24).083 .166 0 0
.042 0 .25 .042
. .
0 0 1 1
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0 0 1 1
0 0 1 1
0 2 2 2
neighborhood
2 2 3 3(1,0), South GLCM (solve it):
3 0 2 0 3 0 0 0 6 0 2 00 2 2 0 0 2 0 0 0 4 2 0
0 0 1 2 2 2 1 0 2 2 2 2
0 0 0 0 0 0 2 0 0 0 2 0
.250 0 .083 0Normalized symmetrical. .
.083 .083 .083 .083
vertical GLCM
Any reason for
0 0 .083 0Diagonal dominance ?
References
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1. Haralick R.M. 1979. Statistical and Structural A roaches to Texture. Proceedin s
of the IEEE, 67:786-804; (also 1973, IEEE-T-SMC)
2. Simona E. Grigorescu, Nicolai Petkov, and Peter Kruizinga; Comparison of Textureea ures ase on a or ers; ransac ons on mage rocess ng, o . ,
No. 10, OCT. 2002; pp 1160-1167.
. . . . ,
Energy Separation, IEEE Transactions on Image Processing, Vol. 8, No. 4, April1999, 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:
, . , . , , - .
6. J. Randen and J. S. Husoy, "Optimal Filter-bank Design for Multiple textureDiscrimination", Proceedin s of the International Conference on Ima e
Processing (ICIP '97), pp 215-218.
7. "Integrating Region and Edge Information for Texture Segmentation using a
mo e ons ra n a s ac on eura e wor , a up a, ara osaMangai and Sukhendu Das, Image and Vision Computing, Vol. 26, No. 8, pp. 1106-
1117, August 2008.