ul 2004 
of the 
ziven in 
mputed 
ed. size. 
oduce a 
studied 
nts are 
'ely, the 
nearest 
1clidean 
t all the 
ne same 
unt the 
creasing 
portant, 
ach one 
ther rare 
ally, the 
different 
bhieve a 
ount of 
of the 
that it is 
' image. 
itions of 
d on the 
d in the 
am and 
ased on 
' results 
d on the 
mber of 
wavelet 
'an hat" 
t lead to 
wavelet 
' fits the 
racy and 
1 present 
ite more 
y of the 
jon were 
Hólder 
yy linear 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
  
regression on a neighbourhood of 16 by 16 pixels. The large 
deviation spectrum was computed for each point of the image 
by the box method over a 32 by 32 pixels window. The number 
of quantization values of the fractal components was fixed to a 
reasonable value to avoid a too long computing time. The 
singularity spectrum values in each point are the input to a k- 
means algorithm. 
All the parameters of the LMS algorithm were fixed in an 
empirical way. The choice of the sizes of the neighbourhood 
and of the studying windows results from a compromise 
between the processing time and the quality of the results. 
However, the size of the neighbourhoods is strongly related to 
the characteristic dimension of the objects that have to be 
detected in the image. The automatic estimation of all these 
parameters will be the subject of future work, so that the 
segmentation algorithm will be completely automatic. 
e 
4. RESULTS AND COMMENTS 
In order to appreciate the contribution of the LMS method, we 
compare the results with those obtained by the grey-level co- 
occurrence method (Haralick et al, 1973) and by the Laws 
filters method (Laws, 1980). We use only six of Haralick 
texture parameters: energy, entropy, dissimilarity, contrast, 
homogeneity and the correlation. The Laws filters of size 5 are 
used, then the energy measures used for the segmentation are 
computed by averaging the output of the filters on a square 
window of size 15. Then, for each method, the computed 
parameters are used as input to the k-means algorithm. 
We initially carried out tests on images of the brodatz set of 
textural images, then on a very high spatial resolution image of 
a forestry scene. The results obtained for each image are then 
compared with those resulting from the analysis based on the 
grey-level co-occurrence matrices. The results are compared by 
means of percentage of good classification in the case of the 
brodatz image, and qualitatively in the case of the satellite 
image. A ground truth map of this region will be done in a 
future work. This will enable the computation of classification 
rates for the IKONOS image. This map will be realized by 
image-interpretation. 
4.1 The brodatz image 
    
f 
Figure 1. Image create 
The brodatz set of textural images provides many images of 
natural textures. Some of them are rather close to what can be 
seen in our IKONOS image. That is why we chose them to try 
out our algorithm. They are usually used in the field of the 
textural analysis, and thus it is easy to compare the results 
provided with those presented in other articles. We have created 
an image of 500x500 pixels with 5 different textures from the 
brodatz set of natural textures (D29, D93, D100, D9 and D4), 
see Figure 1. 
The results given by the three methods are presented in Figure 
2, Figure 3 and Figure 4. 
  
    
Le 55 
Figure 4. The LMS method 
We noticed that the LMS method gives more homogeneous and 
compact segments and that the rate of classification is much 
better. The Laws filters method is not efficient for thé central 
texture because it is a very chaotic texture which can be easily 
confused with the others. The grey level co-occurrence method 
can not differentiate some of the classes and gives the worst 
results. 
  
  
  
  
Method used Classification 
results (in 96) 
LMS algorithm 81 
Grey level co-occurrence 57 
Laws filters 67 
  
  
  
  
Table 1. Classification results on the brodatz image