We address the problem of moving object segmentation using active contours. As far as segmentation of moving objects is concerned, region-based terms must be incorporated in the evolution equation of the active contour, in addition to classical boundary-based terms. In this paper, we propose a general framework for region-based active contours. Novel aspects of the segmentation method include a new Eulerian proof to compute the evolution equation of the active contour from the minimization of a criterion, and the introduction of functions named "descriptors" of the regions. In this proof, the dynamical scheme is directly introduced in the criterion before differentiation. With such a method, the case of descriptors depending on the evolution of the curve, i.e. depending upon features globally attached to the region, can readily be taken into account. The variation of these descriptors upon the evolution of the curve induces additional terms in the evolution equation of the active contour. The proof ensures the fastest decrease of the active contour towards a minimum of the criterion. Inside this theoretical framework, a set of descriptors is evaluated on real sequences for the detection of moving objects.