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The paper deals with video and image segmentation using region based active contours. We consider the problem of segmentation through the minimization of a new criterion based on information theory. We first propose to derive a general criterion based on the probability density function using the notion of shape gradient. This general derivation is then applied to criteria based on information theory, such as the entropy or the conditional entropy for the segmentation of sequences of images. We present experimental results on grayscale images and color videos showing the accuracy of the proposed method.