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(a) Matrix mapping for a threshold (b) Matrix mapping for 2 threshold 
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Figure 3: Gray level cooccurrence matrix mapping 
4 TEXTURE ANALYSIS 
4.1 Multiresolution cooccurrence matrix 
Our approach is based on the idea of representing transition information between background and objects. The gray level 
cooccurrence matrix gives an overall idea about the spatial variations of gray levels in the texture image. This method 
consists of the computation of a matrix by counting the number of gray level occurrences of 2 pixels under predefined 
distance d and orientation 0. The most important drawback to characterize texture in an image is the choice of the best set 
of couples (d,0), which will give the best texture description. 
Morphological pyramidal inter-level links, previously described, allow us to compute a new cooccurrence matrix by 
considering gray level occurrences between a son-pixel taken at level / and its father-pixel at upper level / + 1. This 
configuration presents two interesting properties. Indeed, such a construction doesn't concern only relation between 2 
pixels but it describes a relation between a pixel and one of its neighboring. Besides, the choice of an optimal couple (d) 
is then discarded. 
4.2 Data analysis 
Texture description step is based on information extracted from multidimensionnal cooccurrence matrices computed by 
considering two successive morphological pyramid levels, / and / -- 1. Let C be this one. C contains data types that can 
be divided into 2 categories. 
4.2.1 Diagonal information Classical cooccurrence matrices valued on intensity images contain many information 
about regions (Chubb and Yellot, 2000). Data analysis can be done by studying matrix diagonal (Rouquet et al., 1996, 
Rouquet et al., 1998), which is relevant to texture homogeneity variation along pyramidal representation (Paquis et al, 
1999), 
By construction, such a distribution contains histogram of the image which is represented in level / -- 1. Texture variation 
analysis is performed by extracting statistical parameters (skewness and kurtosis) from a residual distribution, which 
results from subtraction operation between matrix diagonal distribution and image histogram at level / + 1. In practice, 
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we consider only the first 5 pyramid levels. So, a features vector y c R is obtained. 
4.2.2 Matrix shape information Another way to extract features from cooccurrence matrix is to consider its shape 
(Haddon and Boyce, 1990, Houzelle and Giraudon, 1991, Tremeau et al., 1996). Let ¢ be a threshold, which maps the 
original texture into a set of distinct regions : region Ry, corresponding to the uniform background and a set of regions Ri, 
representing objects of different intensities. Because of REDUCE operation, used to compute the morphological pyramid, 
matrix C is divided into 3 non-empty blocks as shown in figure 3.(a) : 
B1(t) : coefficients which belong to the background of the input texture image 
B2(t) : coefficients linked to the objects 
B3(t) : coefficients linked to transition between background and objects 
  
688 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
  
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