International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
  
have thought of a local criterion convergence which can be 
regarded as a zero number of pixels which change state on each 
class, other classes being masked. This procedure can be seen as 
the decomposition of ICM process on a number of under- 
processes. Each under-process relates to one class and is slow or 
fast according to the heterogeneity of this class (Khedam et al., 
2002). 
BEGIN 
| Initial Configuration | 
» | 
FIN 
| Modification i of site s | 
  
  
  
  
| 
| Energie Ui ( x,/ y,) | 
  
  
  
Accepted Modification 
arg min iU: (x s/ys ) } 
A 
  
  
  
  
  
  
   
All sites are visited 
  
Figure 2. ICM flow chart 
ICM algorithm is looked as a regularisation process of an initial 
labelled configuration. The regularisation is operated through Potts 
model which is a function of regularisation parameter ß and a 
neighbourhood topology adopted in the image (4-connexivity or 8- 
connexivity). ICM Development consists to sweep the whole of 
sites image (initial configuration) and to choose for each site the 
class which minimises the energy function given by expression 
(9). This operation must be repeated a number of times to reach a 
stationary state flowing the selected convergence criterion. This 
relaxation technique is fast, but strongly depends on the initial 
configuration and regularisation parameters. A stochastic 
algorithm like a simulated annealing or genetic algorithm (Khedam 
et al., 2003) can be operated in the same way but using a random 
initial configuration and allowing local energy increasing. Optimal 
convergence is obtained after a great number of iterations. 
5. EXPERIMENTAL RESULTS 
We have tested the presented classification process on SPOT 
image acquired on February 23, 1986. It contains three spectral 
bands covering Blida region located at 50km in the south-west of 
capital Algiers ( north of Algeria) as shown on figure 3. Our data 
set of size 256x256 is presented on figure 4. A composite color 
have be done on this set. The aim of this pre-processing is to have 
a better visual interpretation of the scene and to be able to identify 
representative areas which will constitute a training base for the 
supervised process. Recall that prior to supervised classifications 
an unsupervised cluster classification can be applied to uncover 
the major land cover classes that exist in the image, without prior 
knowledge of what they might be. Seven discriminating classes 
have been defined and presented on table 1. According to these 
classes, we define a training samples image (figure 5.(a)) which 
will be used for classification and ground truth image (figure 
5.(b)) which will be used for assessing classification accuracy. 
The training stage is important since its characteristics determine 
the outcome of the classification. In theory, a statistically based 
algorithm requires a minimum of n+1 pixels for training in each 
class (Brogaard et al, 1998), where n is the number of 
wavelength bands. However, in practice, the use of a minimum of 
10n to 100n is advised by Lillesand and Kiefer (1994). Numbers 
of pixels used for classification and those used for assessing 
classification are given on table 2. To applied ICM algorithm, a 
good initial configuration is required. For our study, we first 
execute the gaussian maximum likelihood algorithm to product a 
punctual classification (figure 6. (a)) which may be non-optimal 
and need so to be improved. Secondly, we execute a 
regularisation process with taking a punctual classification result 
as the initial configuration. Generally, regularisation parameter [3 is 
selected in an empirical way. In the present study, B is taken 0,8 
and a 8-connexivity is adopted. ICM classification result is 
presented on figure 6.(b). A statistical classification assessing is 
carried out by means of confusion matrix established between 
truth ground and obtained classifications. From this matrix, is 
calculated the statistical parameter "kappa" (Congalton, 1991) 
which is a global indicator of classification accuracy. Let be Xij 
the confusion matrix elements, Xi+ the total sum of elements in 
lines, X+i the total sum of elements in columns, Xii the diagonal 
elements, N the total number of the pixels of the matrix and M the 
number of considered classes "Kappa" is given by the following 
expression: 
  
M M 
: NS xr XUL xA) 10 
E i=] i i=] n 
N? Moon) 
Note that if a confusion matrix is established between the 
classified image and a truth ground representing only some 
homogeneous pieces of the scene, then expression (10) 
represents statistical parameter called "Khat". There is another 
more significant criterion introduced recently by Shabah (Shabah 
et al., 2001). It is a local kappa calculated for each class i and 
given by the following expression: 
NX ; -(X, xx) 
Kı= (11) 
NX 2) 
The next section deals on the discussion of the experimental 
results. 
Internc 
Figure 
  
  
Figu