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 segmentation of scalar surface data. This leads to gradient descent equations which are level set equations on surfaces. These equations are evolved using the closest point method, which is a technique for solving partial differential equations (PDEs) on surfaces. The final 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.