Shape gradients for histogram segmentation using active contours

We consider the problem of image segmentation using active contours through the minimization of an energy criterion involving both region and boundary functionals. These functionals are derived through a shape derivative approach instead of classical calculus of variation. The equations can be elegantly derived without converting the region integrals into boundary integrals. From the derivative, we deduce the evolution equation of an active contour that makes it evolve towards a minimum of the criterion. We focus more particularly on statistical features globally attached to the region and especially to the probability density functions of image features such as the color histogram of a region. A theoretical framework is set for the minimization of the distance between two histograms for matching or tracking purposes. An application of this framework to the segmentation of color histograms in video sequences is then proposed. We briefly describe our numerical scheme and show some experimental results.