Segmentation on surfaces by the closest point method

This thesis proposes a method to detect objects and patterns in textures on general surfaces. The 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 recent technique for solving partial differential equations (PDEs) on surfaces. To the segmentation on surface problem, a PDE defining a flow on the surface in terms of intrinsic in-surface differential operators [13] must be solved. There are various ways to solve this PDE, such as parameterization, and embedding methods using level set surface representation, etc; however, these methods have their own limitations. To avoid these limitations, we use the Closest Point Method [21] for solving this surface PDE. Various numerical experiments are presented.