Image segmentation is the partitioning of an image into regions of interest and a background. Image segmentation can be performed using an active contour algorithm in a variational framework. In the case of a single region of interest, the active contour evolves from an initial contour towards the region of interest according to an evolution equation. In the variational framework, the evolution equation is deduced from the derivative of a criterion. The criterion should characterize the region of interest in terms of, for example, its motion, its color homogeneity or its texture. We differentiate the criterion using shape gradients, a theory originally developed for shape optimisation.We propose two criteria and we provide for each criterion the development leading to the associated evolution equation.The first criterion defines a free form a priori constraint on the contour by minimizing the distance between the active contour and a reference contour. We applied this criterion to shape warping, image segmentation, and video tracking. The second criterion assumes that the object motion can be described by a motion model on a group of pictures. The evolution of theactive contour allowing to minimize this criterion provides a joint motion segmentation and motion estimation. We applied this criterion to sequence segmentation and to video tracking.
