Active contour segmentation with affine coordinate-based parametrization

In this paper, we present a new framework for image segmentation based on parametrized active contours. The contour and the points of the image space are parametrized using a set of reduced control points that have to form a closed polygon in two dimensional problems and a closed surface in three dimensional problems. By moving the control points, the active contour evolves. We use mean value coordinates as the parametrization tool for the interface, which allows to parametrize any point of the space, inside or outside the closed polygon or surface. Region-based energies such as the one proposed by Chan and Vese can be easily implemented in both two and three dimensional segmentation problems. We show the usefulness of our approach with several experiments.