Two variational models for multispectral image classification

We propose two variational models for supervised classification of multispectral data. Both models take into account contour and region information by minimizing a functional compound of a data term (2D surface integral) taking into account the observation data and knowledge on the classes, and a regularization term (1D length integral) minimizing the length of the interfaces between regions. This is a free discontinuity problem and we have proposed two different ways to reach such a minimum, one using a Gamma-convergence approach and the other using a level set approach to model contours and regions. Both methods have been previously developed in the case of monospectral observations. Multispectral techniques allow to take into account information of several spectral bands of satellite or aerial sensors. The goal of this paper is to present the extension of both variational classification methods to multispectral data. We show an application on real data from SPOT (XS mode) satellite for which we have a ground truth. Our results are also compared to results obtained by using a hierarchical stochastic model.