Problem statement

• Problem statement :
  
  given a satellite image, we want to make a classification, i.e. to assign a label to each pixel. The classification we expect has to lead to a partition compound of homogeneous regions (the classes) with regular boundaries (with minimal length).
  This work takes place in the general framework concerning automatic feature extraction.
  
  
  
• Proposed approach :
  
  within a variational framework, the idea is to obtain an optimal partition of the observed data through the minimization of a functional. We use a level set formulation to model the set of interfaces and to define the set of regions (a region is a set of pixels with same label).
  
  
  
• Hypothesis :
  
  herein, we are interested in the local distribution of intensity (grey level), but other discrimant features as the texture one for instance can be considered. The number K of classes and their parameters are supposed to be given from a prior estimation : it is a supervised classification. Herein, we suppose that the classes have a Gaussian distribution of intensity, therefore a class is characterized by its mean $\mu_i$ and its standard deviation $\sigma_i$. The label designing the i^th class is set to the value $\mu_i$.