The problem of image segmentation through the minimization of an energy criterion involving both region and boundary functionals is considered. We study the derivation of these functionals using the notion of shape derivative. From the derivative, we deduce the evolution equation of an active contour that will make it evolve towards a minimum of the criterion introduced. We focus on geometric and statistical features globally attached to the boundary or to the region, and we take explicitly into account their evolution in the derivation. First, statistical region-based descriptors using the variance of a region or the distance to a reference region histogram are introduced. Then a geometric prior term is combined with statistical features for homogeneous region segmentation. This geometric prior is introduced to provide a free form deformation from a reference shape. Some experimental results on real images and video sequences show the benefit of combining geometrical and statistical features for segmentation.