Image and sequence segmentation of a the segmentation task are discussed from the point of view of optimizing the segmentation criterion. Such a segmentation criterion involves so-called (boundary and region) descriptors, which, in general, may depend on their respective boundaries or regions. This dependency must be taken into account when one is computing the criterion derivative with respect to the unknown object domain (defined by its boundary). If this dependency not considered, some correctional terms may be omitted. Computing the derivative of the segmentation criterion with a dynamic scheme is described. The scheme is general enough to provide a framework for a wide variety of applications in segmentation. It also provides a theoretical meaning to the philosophy of active contours.
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