A variational model for image classification and restoration

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