- 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
and its standard deviation .
The label designing
the i^{th} class is set to the value .