Texture

Raul Queiroz Feitosa

Gilson A. O. P. Costa

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Objective

To introduce basic techniques to describe

texture.

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Content

Introduction

Texture Filters

Gray Scale Co-occurrence Matrix

Gabor Filter Bank

Local Binary Patterns

What is texture?

“Texture is a phenomenon that is widespread, easy

to recognize, and hard to define.”

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1 Computer Vision a Modern Approach, 2nd Ed., Forsyth.D.A., Ponce,. J., 2011

What is texture?

“If the brightness is

interpreted as elevation

in a representation of

the image as a surface,

then the texture is a

measure of the surface

roughness1.”

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1 Image Processing Handbook, 3rd Ed. 1999,

Jhon Huss

Sentinel 1 image sample

Venice, Italy (2016)

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Content

Introduction

Texture Filters

Gray Scale Co-occurrence Matrix

Gabor Filter Bank

Local Binary Patterns

Texture filters

Compute some statistic on a neighborhood 𝑁 𝑝

around the pixel of interest 𝑝, whose value is assigned

to pixel 𝑝 in the output matrix.

Example of statistics:

Max-min

Standard deviation

Entropy

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mn = max𝑞∈𝑁 𝑝

𝐼 𝑞 − min𝑞∈𝑁 𝑝

𝐼 𝑞

𝜎 =1

# 𝑁 𝑝 − 1 𝐼 𝑞 − 𝐼 𝑞 2

𝑞∈𝑁 𝑝

1/2

𝐸 = − 𝑃 𝐼 𝑞

𝑞∈𝑁 𝑝

log 𝑃 𝐼 𝑞

mean value

in the

neighborhood

probability of

I(q) in the

neighborhood

Texture filters

Exercise 1:

Learn how to use the MATLAB functions that implement the texture filters

shown in previous slide:

rangefilt

stdfilt

entropyfilt

Show the results in a single figure using some of the Brodatz texture.

Look at the sensitivity to the neighborhood size.

Exercise 2:

Read the article Texture Segmentation using Texture Features from

MathWorks, and observe the sensitivity of the segmentation result to

neighborhood size.

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Content

Introduction

Texture Filters

Gray Scale Co-occurrence Matrix

Gabor Filter Bank

Local Binary Patterns

Gray Level Co-occurrence Matrix

The GLCM is a tabulation

of how often different

combinations of pixel

brightness values (grey

levels) occur in an image.

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Haralick, R.M., K. Shanmugan, and I. Dinstein, "Textural Features for Image Classification",

IEEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-3, 1973, pp. 610-621.

Robert. M. Haralick,

Distinguished Professor,

Universiy City of New York.

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Co-occurrence matrix

P(i,j,d,a) is the number of times two pixels at a

distance d forming an angle a occur, so that one

has gray level i and the other j. Example: d=1 (non symmetric)

)3,3(#)2,3(#)1,3(#)0,3(#3

)3,2(#)2,2(#)1,2(#)0,2(#2

)3,1(#)2,1(#)1,1(#)0,1(#1

)3,0(#)2,0(#)1,0(#)0,0(#0

3210

gray level

grey

level

image

1000

1300

0020

0122

HP

a=0º

0200

0122

0020

0003

VP

a=90º

0100

0220

0010

0012

LDP

a=45º

0200

0013

0011

0001

SDP

a=135º

0 0 1 1

0 0 1 1

0 2 2 2

2 2 3 3

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Co-occurrence matrix

A variant, called symmetric, does not consider the

order of pixel values. Thus P(i,j,d,a) = P(j,i,d,a)

and the co-occurrence matrix is symmetric.

)3,3(#)2,3(#)1,3(#)0,3(#3

)3,2(#)2,2(#)1,2(#)0,2(#2

)3,1(#)2,1(#)1,1(#)0,1(#1

)3,0(#)2,0(#)1,0(#)0,0(#0

3210

gray level

grey

level

2100

1601

0042

0124

HP

a=0º

0200

2222

0240

0206

VP

a=90º

0100

1420

0221

0014

LDP

a=45º

0200

0013

0121

0312

SDP

a=135º

Example: d=1 (symmetric)

image

0 0 1 1

0 0 1 1

0 2 2 2

2 2 3 3

Texture features from GLCM

In what follows the co-occurrence matrices are

normalized, so that their elements can be regarded

as probabilities, i.e., they must sum up to 1.

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𝑝 𝑖, 𝑗 =𝑃 𝑖, 𝑗

𝑃 𝑖, 𝑗𝑖,𝑗

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Texture features from GLCM

Descriptor Explanation Formula

Contrast A measure of the contrast between a pixel and its neighbor

over the whole image. Contrast is 0 for a constant image.

Correlation

A measure of how correlated a pixel is to its neighbor over

the whole image. Correlation is 1 or -1 for a perfectly

positively or negatively correlated image.

Energy

(Uniformity)

A measure of uniformity in range [0 1]. Energy is 1 for a

constant image.

Homogeneity

Measures the spatial closeness of the distribution of

elements to the diagonal. The range of values is [0 1].

Homogeneity is 1 for a diagonal GLCM.

𝑖 − 𝑗 2

𝑖,𝑗

𝑝 𝑖, 𝑗

𝑖 − 𝜇𝑖 𝑗 − 𝜇𝑗 𝑝 𝑖, 𝑗

𝜎𝑖𝜎𝑗𝑖,𝑗

for σi, σj ≠ 0

𝑝 𝑖, 𝑗 2

𝑖,𝑗

𝑝 𝑖, 𝑗

1 + 𝑖 − 𝑗𝑖,𝑗

𝜇𝑖 = 𝑖 𝑝 𝑖, 𝑗

𝑗𝑖

𝜇𝑗 = 𝑗 𝑝 𝑖, 𝑗

𝑖𝑗

𝜎𝑖2 = 𝑖 − 𝜇𝑖

2 𝑝 𝑖, 𝑗

𝑗𝑖

𝜎𝑗2 = 𝑗 − 𝜇𝑗

2 𝑝 𝑖, 𝑗

𝑖𝑗

where

MATLAB Example

% Read grayscale image and display it. The example converts the true color

% image to a grayscale image and then rotates it 90° for this example.

circuitBoard = rot90(rgb2gray(imread('board.tif')));

imshow(circuitBoard)

% Define offsets of varying direction and distance. The example specifies a set of

% horizontal offsets that only vary in distance.

offsets0 = [zeros(40,1) (1:40)'];

% Create the GLCMs.

glcms = graycomatrix(circuitBoard,'Offset',offsets0)

% Derive statistics from the GLCMs using the graycoprops function.

stats = graycoprops(glcms,'Contrast Correlation');

% Plot correlation as a function of offset.

figure, plot([stats.Correlation]);

title('Texture Correlation as a function of offset');

xlabel('Horizontal Offset')

ylabel('Correlation')

% The plot contains peaks at offsets 7, 15, 23, and 30. What does it mean?

% Taken from MATLAB help.

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MATLAB Example

% The plot contains peaks at offsets 7, 15, 23, and 30.

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GLCM

Exercise 3:

Write a MATLAB function that calculates the

GLCM features, having as input parameters

the input image in gray scale

the window size

the set of displacements and directions

Hint: try the MATLAB function blkproc.

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Content

Introduction

Texture Filters

Gray Scale Co-occurrence Matrix

Gabor Filter Bank

Local Binary Patterns

Texture Representation using Filters

Local feature representation may be obtained by

filtering the image by a set of filters at various

scales and then preparing a summary.

The summary at a pixel is a description of the

texture in the neighborhood around that pixel.

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Gabor Filter Bank

Gabor filter kernels look like sine/cosine multiplied

by a Gaussian.

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Gabor Filter Bank

Gabor filter kernels look like sine/cosine multiplied

by a Gaussian.

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Gabor Filter Bank

Gabor filters come in pairs, often referred to as

quadrature pairs: symmetric and antisymmetric

components.

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cos 𝑘𝑥𝑥 + 𝑘𝑦𝑦 exp −𝑥2 + 𝑦2

2𝜎2 sin 𝑘𝑥𝑥 + 𝑘𝑦𝑦 exp −

𝑥2 + 𝑦2

2𝜎2

Gabor Filter Bank

Gabor filter responds strongly at points in an image

where there are components that locally have a

particular spatial frequency and orientation.

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Gabor Filter Bank

Exercise 4:

Read the help of the MATLAB (2016) functions

gabor that creates a Gabor filter bank.

imgaborfilt that computes the Gabor features.

Look at the texture features produced by each filter

and compare with the input image. Hint: Test the

functions for the bands of an IKONOS image or

any other gray scale image you wish.

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Gabor Filter Bank

Exercise 5: for MATLAB 2015

Read the MathWorks example of working with

Gabor filter for image segmentation.

Test it with images containing more than two

textures, such as,

the IKONOS image

a Sentinel 1 image.

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Content

Introduction

Texture Filters

Gray Scale Co-occurrence Matrix

Gabor Filter Bank

Local Binary Patterns

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Local Binary Patterns – LBP

Each pixel is assigned to a pattern given by the sign of the

difference between the central pixel intensity and the intensity

of its m neighbors arranged over a circle of radius R.

interpolation is used whenever the sampling point does not fall

in the center of a pixel

m=8, R=1 m=16, R=2 m=8, R=2

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Local Binary Patterns – LBP

Illumination invariance is achieved by considering only the

signal of difference

Scale invariance is achieved by using multiple values for R

Rotation invariance is achieved by considering the pattern

circular and, for instance, by taking the rotation with the

minimum value. Example: all patterns below are considered

equivalent …

1 0 0 1 0 1 0 1

1 1 0 0 1 0 1 0

0 1 1 0 0 1 0 1

1 0 1 1 0 0 1 0

0 1 0 1 1 0 0 1

1 0 1 0 1 1 0 0

0 1 0 1 0 1 1 0

0 0 1 0 1 0 1 1 … to this one.

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Face Recognition with LBP

1. Compute LBP face representation (for example with

m=8, R=2)

x

y

X

Y

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Face Recognition with LBP

2. Compute the LBP histogram for each n×n non

overlapping block

. . .

0HX 1HX

kHX

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Face Recognition with LBP

3. Compute the χ2 distance between corresponding

blocks

. . .

. . .

c Y

b

X

b

Y

b

X

b

Y

b

X

b

cHcH

cHcHHH

2

2 ,

χ2( 0HX,0HY) χ2( 1HX,1HY) χ2( kHX, kHY) . . .

- - -

= = =

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Face Recognition with LBP

4. Compute the weighted sum of block distances

for instance,

with black squares indicate weight 0.0, dark gray 1.0,

light gray 2.0 and white 4.0.

b

Y

b

X

b

bYX HHwHH ,, 22

T. Ahonen, A. Hadid and M. Pietikäinen, Face description with local binary patterns: application to face recognition, IEEE

Transactions on Pattern Analysis and Machine Intelligence, vol. 28 no. 12, pp. 2037-2041, 2006

Face Recognition with LBP

5. In the so called uniform LBP only codes

containing up to 2 transitions 0 to 1 or 1 to 0

are considered. This reduces the number of

possible codes from 256 to 59.

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Face Recognition with LBP

Exercise 6: for MATLAB 2015 upwards

Download the file containing the LBP

implementation in MATLAB. Using the functions

Compute_Uniform_LBP and LBP_Discrepancy

determine the recognition rate for the face images in

file Images. mat.

Hint: for each image taken as a probe, determine the

most similar one. Compute the average percentage

of correct identification.

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LBP in Remote Sensing

Texture (Local Binary Patterns – LBP)

LBP×GLCM for classification of Remote Sensing imagery

M. Musci*, R. Q. Feitosa, M. L. F. Velloso, T. Novack, G. A. Costa, Assessment of binary coding techniques for texture

characterization in remote sensing imagery , IEEE Geoscience and Remote Sensing Ltters, vol10(6, pp. 1607-1611, 2013.

Reference

1. Computer Vision A Modern Approach, 2nd Ed., Forsyth & Ponce, 2011,

2. T. Ahonen, A. Hadid and M. Pietikäinen, Face description with local

binary patterns: application to face recognition, IEEE Transactions on

Pattern Analysis and Machine Intelligence, vol. 28 no. 12, pp. 2037-2041,

2006

3. M. Musci, R. Q. Feitosa, M. L. F. Velloso, T. Novack, G. A. Costa,

Assessment of binary coding techniques for texture characterization in

remote sensing imagery , IEEE Geoscience and Remote Sensing Ltters,

vol10(6, pp. 1607-1611, 2013.

4. Oxford Visual Geometry Group:

http://www.robots.ox.ac.uk/~vgg/research/texclass/index.html

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Texture

END