International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
2. TEXTURE ANALYSIS METHODS 
In this chapter we will briefly describe the four methods used 
for texture analysis and feature extraction: (1) Statistical 
methods based on the grey level coocurrence matrix, (2) energy 
filters and edgeness factor, (3) Gabor filters, and (4) wavelet 
transform based methods. 
2.1 Grey level coocurrence matrix (GLCM) 
The elements of this matrix, p(ij), represent the relative 
frequency by which two pixels with grey levels "i" and "j", that 
are at a distance *d" in a given direction, are in the image or 
neighbourhood. It is a symmetrical matrix, and its elements are 
expressed by 
3. P(i, (1) 
pli,j) = és i) 
S PG D 
i=0 j=0 
where Ng represents the total number of grey levels. Using this 
matrix, Haralick (1973) proposed several statistical features 
representing texture properties, like contrast, uniformity, mean, 
variance, inertia moments, etc. Some of those features were 
calculated, selected and used in this study. 
2.2 Energy filters and edgeness 
The energy filters (Laws, 1985) were designed to enhance some 
textural properties of the images. This method is based on the 
application of convolutions to the original image, /, using 
different filters gj, g5...,gw , therefore obtaining N new images 
J, 1 * g, (n 7 LN). Then, the energy in the neighbourhood 
of each pixel is calculated. In order to reduce the error due to 
the border effect between different textures, a post-processing 
method proposed by Hsiao y Sawchuk (1989) was used. This 
method is based on the calculation, for each pixel of the filtered 
image J, | of the mean and variance of the four square 
neighbourhoods in which each pixel is a corner, and assigning 
as the final value for that pixel the mean of the neighbourhood 
with the lowest variance, which is supposed to be more 
homogeneous and, consequently, should contain only one type 
of texture (no borders). 
The edgeness factor is a feature that represents the density of 
edges present in a neighbourhood. Thus, the gradient of an 
image / is computed as a function of the distance “d” between 
neighbour pixels, using the expression: 
gli, judy = SAG N= 1G +d. I+ 1G) 1G=d. D+ (2) 
(DEN 
e|, j) - 16, j * )| | IG) - 1G. j - d) 
where g(i,j,d) represents the edgeness per unit area surrounding 
a generic pixel (i,j) (Sutton and Hall, 1972). 
2.3 Gabor filters 
These filters are based on multichannel filtering, which 
emulates some characteristics of the human visual system. The 
human visual system decomposes an image formed in the retina 
into several filtered images, each of them having variations in 
intensity within a limited range of frequencies and orientations 
(Jain and Farrokhnia, 1991). A Gabor filters bank is composed 
of a set of Gaussian filters that cover the frequency domain with 
different radial frequencies and orientations. In the spatial 
domain, a Gabor filter A(x.y) is a Gaussian function modulated 
by a sinusoidal function: 
Ges | 
1 ; 
h(x, y) = -exp[- Ai -exp( j2zF(x cos 0 + ysen0)) 
  
2 
27167 20 
where o, determines the spatial coverage of the filter. In the 
frequency domain, the Gabor function is a Gaussian curve 
(Bodnarova et al., 2002). The Fourier transform of the Gabor 
function is: 
^ 
H(u,v) - expE2x^ o, ((u — Fcos0)? +(v-Fsen0})] (4) 
The parameters that define each of the filters are: 
|. The radial frequency (F) where the filter is centered 
in the frequency domain. 
2. The standard deviation (6) of the Gaussian curve. 
3. The orientation (9. 
For the purpose of simplicity, we assume that the Gaussian 
curve is symmetrical. The filter bank was created with 6 
orientations (0°, 30°, 60°, 90°, 120° and 150°) and 3 
combinations of frequency and standard deviation: F=0.3536 
and o =2.865, F=0.1768 and oc =5.73, F-0.0884 and c 
=11.444. This operation produced a total of 18 filters covering 
the map of frequencies. Once the filters were applied and their 
magnitude computed, the image was convolved by a Gaussian 
filter (c —5) to reduce the variance. 
2.4 Wavelet transform 
The use of wavelet transform was first proposed for texture 
analysis by Mallat (1989). This transform provides a robust 
methodology for texture analysis in different scales. The 
wavelet transform allows for the decomposition of a signal 
using a series of elemental functions called wavelets and 
scaling, which are created by scalings and translations of a base 
function, known as the mother wavelet: 
seW ue”N 
1 
Wu (X) = "| 
X—U 
S 
where *s" governs the scaling and "4" the translation. The 
wavelet decomposition of a function is obtained by applying 
each of the elemental functions or wavelets to the original 
function: 
(6) 
. A 1 wl: Xm 
Wf(s,u)= | fo) v D “Jas 
i is ig 
In practice, wavelets are applied as high-pass filters, while 
scalings are equal to low-pass filters. As a result of this, the 
wavelet transform decomposes the original image into à series 
of images with different scales, called trends and fluctuations. 
The former are averaged versions of the original image, and the 
latter contain the high frequencies at different scales or levels 
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