SEGMENTATION ON SURFACES WITH THE CLOSEST POINT METHOD

We propose a method to detect objects and patterns in textures on general surfaces. Our approach applies the Chan–Vese variational model for active contours without edges to the problem of segmen-tation of scalar surface data. This leads to gradient descent equa-tions which are level set equations on surfaces. These equations are evolved using the Closest Point Method, which is a recent technique for solving partial differential equations (PDEs) on surfaces. The fi-nal algorithm has a particularly simple form: it merely alternates a time step of the usual Chan–Vese model in a small 3D neighborhood of the surface with an interpolation step. We remark that the method can treat very general surfaces since it uses a closest point function to represent the underlying surface. Various experimental results are presented, including segmentation on smooth surfaces, non-smooth surfaces, open surfaces, and general triangulated surfaces