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. 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.

Herein, we present a variational model devoted to image classification coupled with an edge-preserving regularization process. 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 compound of homogeneous regions with regularized boundaries. The soundness of this 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.

The dynamics of Raibert's planar one legged hopper have been studied quite extensively in the particular case of vertical hopping and no translational velocity. These studies have pointed out the possibility of complicated behaviors. The forward motion of the one legged hopper has also been investigated in recent literature, with the restriction of low velocities. It appears from these references that the control of the energy of the hopper is a difficult problem due to the necessity of integrating the hopper's dynamical equations during the stance phases. In this paper, the authors consider the problem of controlling the leg's forward motion under the assumption that the energy of the hopper is constant. The authors unveil results that do not depend on the spring of the leg and analyse a few simple control schemes.>