Lect Gabor Filt

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TEXTURE ANALYSIS





• Texture types

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yn e c a ura Stochastic



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]



Texture Regions & Edges

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IIT Madras

R1 R2

R3 R4

ex ure mage

VP LAB

Image histograms



Input Image

FILTERING

SMOOTHING

Segmented Image

Flow-chart of a typical method of texture classification



Synthetic Texture

Image

intensity

rofile

Filteredoutput

Nonlinear

transformSmoothing

image



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 .



-

+++−= 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



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 +



)))()((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



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.



Gaussian and

Fourier transformof the Gaussian

at

e x g

2

)(

−

=

)(uG =

42au−

Fourier transformof the GABOR ??

Green – Gaussian; Yellow - FT of Gaussian



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

.



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:



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



Texture

Image

Magnitude of the

Gabor Res onses

Smoothed

Features



Texture

Image

Magnitude of the

Gabor Res onses

Smoothed

Features



Natural Textures Initial Classification Final Classification

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Segmentation using Gabor based featuresof a texture image containing five regions.



SIR-C/X-SAR image

of Lost City of Ubar

Classification using

multispectral information

Classification using

multispectral and texturalinformation

< Back

• Filtering methods:



• 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



Segmented mapbefore integration

Edge map before

inte ration

Segmented map

and Edge map

VP LAB

IIT Madras



Input Image

Segmented mapbefore integration

Edge map before

integration

Segmented map

and Edge map

VP LAB

GLCM based texture feature (statistical)



- ,

(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



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



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



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



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



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.

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Lect Gabor Filt