Stationary subdivision snakes for contour detection

In this paper we propose a method for computing the contour of an object in an image using a snake represented as a subdivision curve. The evolution of the snake is driven by its control points which are computed minimizing an energy that pushes the snake towards the boundary of the interest region. Our method profits from the hierarchical nature of subdivision curves, since the unknowns of the optimization process are the few control points of the subdivision curve in the coarse representation and, at the same time, good approximations of the energies and their derivatives are obtained from the fine representation. We develop the theory assuming that the subdivision scheme generating the snake is linear stationary and uniform. To illustrate the performance of our method we develop a computational tool called SubdivisionSnake, which computes the snakes associated with two classical subdivision schemes: the four point scheme and the cubic B-spline. Our experiments using synthetic and real images with SubdivisionSnake confirm that the proposed method is fast and successful.