In a square raster digital image, each pixel is surrounded by 
eight neighbouring pixels. The local texture information for a 
pixel can be extracted from a neighbourhood of 3 x 3 pixels, 
which represents the smallest complete unit (in the sense of 
having eight directions surrounding the pixel). 
Given a neighbourhood of 3x3 pixels, which will be denoted 
by a set containing nine elements: V= {Vo, Vi, ..., V8), 
where Vo represents the intensity value of the central pixel 
and Vi, {i=l, 2, ..., 8}, is the intensity value of the 
neighbouring pixel i, we define the corresponding texture unit 
by a set containing eight elements, TU={Ei, E2, ..., Es}, 
where Ei, (i=l, 2,..., 8) is determined by the formula: 
{ 0 if Vi<Vo 
1 if V i= V 0 for: i=l,2,..., 8 
2 if Vi>Vo 
and the element Ei occupies the same position as the pixel i. 
As each element of TU has one of three possible values, the 
combination of all the eight elements results in 3 8 =6561 
possible texture units in total. 
There is no unique way to label and order the 6561 texture 
units. In our study, the 6561 texture units are labeled by 
using the following formula: 
8 
NTU = ^ Ei* 3 1 - 1 
i=l 
where Ntu represents the Texture Unit Number and Ei is the 
ith element of texture unit set TU={Ei, E2,..., Es}. 
The previously defined set of 6561 texture units describes the 
local texture aspect of a given pixel, that is, the relative grey 
level relationships between the central pixel and its 
neighbours. Thus, the statistics on frequency of occurrence of 
all the texture units over a large region of an image should 
reveal texture information. We termed texture spectrum the 
frequency distribution of all the texture units, with the 
abscissa indicating the texture unit number Ntu and the 
ordinate representing its occurrence frequency. 
It should be noted that the labeling method chosen may affect 
the relative positions of texture units in the texture spectrum, 
but will not change their frequency values in the texture 
spectrum. II 
II should be also noted that the local texture for a given pixel 
is characterized by the corresponding texture unit, while the 
texture aspect for an uniform texture image is revealed by its 
texture spectrum calculated within an appropriate window. 
The size of the window depends on the nature of the texture 
image. 
3 TEXTURAL EDGE DETECTION 
The principal idea of textural edge detection is to use texture 
spectrum as the texture feature and to combine it with 
traditional operators. That is, when applying a traditional edge 
detection operator over an image, the grey level of each 
element of the operator will be replaced by the texture 
spectrum calculated from the corresponding neighbourhood. 
Some texture images have been choosen to evaluate the 
method. They are illustrated in Figures 1 and 2. These images 
are represented by 512x512 pixels with 64 normalized grey 
levels and are composed of six different textured areas. These 
six texture images are extracted from Brodatz' album 
(Brodatz, 1968). They are respectively the images D4: 
pressed cork; D24: pressed calf leather; D29: beach sand; 
D38: water; D57: handmade paper and D93: fur hide of 
unborn calf. These natural texture images have been chosen 
because they are broadly similar to one another, and are 
similar to parts of digital images usually encountered in 
practice, for example, landscape scenes provided by earth 
observation satellites. 
The six textures of Figure 1 constitute one vertical boundary 
and four diagonal ones, while Figure 2 presents four circles 
with two straight lines (horizontal and vertical). This may 
represent most of the complex situations encountered in 
natural images. 
In our study, the Roberts operator was used as the edge 
detection operator. Texture spectra were calculated using a 
moving window of 30 x 30 pixels. The integrated absolute 
difference between two texture spectra has been taken as the 
difference between two elements of the edge detection 
operator: 
R(oberts) = V d] + d 2 2 
6561 
Dl= I Si J(k) “Si+l,j+l(k)l 
k=l 
D2 = 6 ^ISij + i(k)-Si + i,j(k)l 
k=l 
where: Sij(k) denotes the kth element of the texture spectrum 
calculated from the window located at the position (i, j). 
Thus, Di and D2 give the absolute difference between two 
texture spectra located in diagonal positions. 
The convolution using the above operator was carried out 
over the whole images of Figures 1 and 2 with a step of 1 in 
line and column. The results are illustrated respectively in 
Figures 3 and 4, where the grey levels of the images are 
linearly stretched from 0 to 250.