A variational model for image classification and restoration

Herein, we present a variational model devoted to image classification coup led with an edge-preserving regularization process. The discrete nature of classification (i.e., to attribute a label to each pixel) has led to the de velopment of many probabilistic image classification models, but rarely to variational ones. In the last decade, the variational approach has proven i ts efficiency in the field of edge-preserving restoration. In this paper, w e add a classification capability which contributes to provide images compo sed of homogeneous regions with regularized boundaries, a region being defi ned as a set of pixels belonging to the same class. The soundness of our mo del is based on the works developed on the phase transition theory in mecha nics. The proposed algorithm is fast, easy to implement, and efficient. We compare our results on both synthetic and satellite images with the ones ob tained by a stochastic model using a Potts regularization.