For an image analysis application I am writing using the PDL, I needed to compute some texture measures. After some research, I decided to go with the measures proposed by Rober Haralick based on the Gray Level Co-occurrence Matrix (GLCM). To make a long story short, I found a nice tutorial on the GLCM and started implementing the code for computing the GLCM and the texture measures following the equations presented in the tutorial. Here is my first take to computing the GLCM and some of the texture measures:

`#!/usr/bin/perl`

use warnings;

use strict;

use PDL;

use PDL::NiceSlice;

# ================================

# cooccurrence:

#

# $glcm = cooccurrence( $pdl, $dir, $dist, $symmetric )

#

# computes the grey level coocurrence coocurrence

# matrix of piddle $pdl for a given direction and

# distance

#

# Inputs:

# $pdl

# $dir: direction of evaluation

# $dir angle

# 0 +90

# 1 +45

# 2 0

# 3 -45

# 4 -90

# $dist: distance between pixels

# $symmetric: 0 => non-symmetric $glcm

#

# ================================

sub cooccurrence {

my ( $pdl, $dir, $dist, $symmetric ) = @_;

```
```my $min_quantization_level = int( min( $pdl ) );

my $max_quantization_level = int( max( $pdl ) );

my $glcm = zeroes( $max_quantization_level

- $min_quantization_level + 1

, $max_quantization_level

- $min_quantization_level + 1 );

my ($dir_x, $dir_y);

if ( $dir == 0 ){

$dir_x = 0;

$dir_y = 1;

} elsif ( $dir == 1 ){

$dir_x = 1;

$dir_y = 1;

} elsif ( $dir == 2 ){

$dir_x = 1;

$dir_y = 0;

} elsif ( $dir == 3 ){

$dir_x = 1;

$dir_y = -1;

} elsif ( $dir == 4 ){

$dir_x = 0;

$dir_y = -1;

} else {

$dir_x = 0;

$dir_y = 0;

}

$dir_x *= $dist;

$dir_y *= $dist;

my $glcm_ind_x = 0;

my $glcm_ind_y = 0;

foreach my $grey_level_1 ( $min_quantization_level .. $max_quantization_level ){

my ( $ind_x_1, $ind_y_1 )

= whichND( $pdl == $grey_level_1 );

$ind_x_1 += $dir_x;

$ind_y_1 += $dir_y;

foreach my $grey_level_2 ( $min_quantization_level .. $max_quantization_level ){

my ( $ind_x_2, $ind_y_2 )

= whichND( $pdl == $grey_level_2 );

my $count = 0;

foreach my $i (0..$ind_x_1->getdim(0) - 1) {

foreach my $j (0..$ind_x_2->getdim(0) - 1) {

if ( ($ind_x_1($i) == $ind_x_2($j))

and ($ind_y_1($i) == $ind_y_2($j)) ) {

$count++;

}

}

}

$glcm( $glcm_ind_x, $glcm_ind_y ) .= $count;

$glcm_ind_y++;

}

$glcm_ind_y = 0;

$glcm_ind_x++;

}

if ( $symmetric ) {

$glcm += transpose( $glcm );

}

$glcm /= sum( $glcm );

return $glcm;

}

# ================================

# texture_descriptors:

#

# ( $contrast, $dissimilarity, $homogeneity

# , $inverse_difference, $asm, $energy )

# = texture_descriptors( $glcm );

#

# computes a set of texture descriptors

# associated with the GLCM $glcm

#

# $contrast:

# Range = [0 .. ($glcm->getdim(0)-1)^2]

# $contrast = 0 for a constant image.

# $homogeneity:

# Measures the closeness of the distribution

# of elements in the GLCM to the GLCM diagonal.

# Range = [0 1]

# $homogeneity is 1 for a diagonal GLCM.

# ================================

sub texture_descriptors{

my $glcm = pdl( @_ );

my $n = $glcm->getdim(0);

my $i = sequence( $n );

my $j = sequence( $n );

my $diff = $i->dummy(0, $n) - $j->dummy(1, $n);

my $contrast = sum( $glcm * ($diff ** 2) );

my $dissimilarity = sum( $glcm * abs( $diff ) );

my $homogeneity = sum( $glcm / ( 1 + $diff ** 2) );

my $inverse_difference = sum( $glcm / ( 1 + abs( $diff ) ) );

my $asm = sum( $glcm ** 2 );

my $energy = sqrt( $asm );

return ( $contrast, $dissimilarity, $homogeneity

, $inverse_difference, $asm, $energy );

}

my $pdl = pdl([0,0,1,1],[0,0,1,1],[0,2,2,2],[2,2,3,3]);

my $glcm = cooccurrence( $pdl, 2, 1, 1 );

print "glcm: $glcm\n";

my ( $contrast, $dissimilarity, $homogeneity

, $inverse_difference, $asm, $energy )

= texture_descriptors( $glcm );

`print "contrast: $contrast\tdissimilarity: $dissimilarity\n";`

print "homogeneity: $homogeneity\t";

print "inverse difference: $inverse_difference\n";

print "ASM: $asm\tenergy: $energy\n";

All suggestions are welcome 🙂

Cheers

Lino

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