Adaptive active contours without edges

In this paper, we develop a novel active contour model in PDE (partial differential equation) formulation, which is based on the Chan–Vese “active contours without edges” model and the Sobolev gradient. Our evolution PDE consists of an adaptive force which is derived from the L2L2 gradient of the fidelity term of the Chan–Vese functional, and a regularized force which is the Sobolev gradient of the contour length. For a two-phase piecewise constant image, we prove that the adaptive force has exactly opposite sign in the interior and exterior of objects, and the zero-level set of the evolution function can match with the boundary between objects and background in a single iteration if the initial function is suitably chosen as a sign-changing and bounded function. The proposed model has the advantages of flexible initialization and very fast segmentation process (so re-initialization is not necessary). The proposed model has been applied to both synthetic and real images with promising results.