Abstract : This synthetic paper deals with image and sequence segmentation when looking at the segmentation task from a criterion optimization point of view. Such a segmentation criterion involves so-called (boundary and region) descriptors which, in the general case, may depend on their respective boundary or region. This dependency must be taken into account when computing the criterion derivative with respect to the unknown object domain (defined by its boundary). If not, some correctional terms may be omitted. This article focuses computing the derivative of the segmentation criterion using a dynamic scheme. The presented scheme is general enough to provide a framework for a wide variety of applications in segmentation. It also provides a theoretical meaning to the active contour philosophy.