Segmentation as a Riemannian Drum Problem

In this paper, the segmentation problem is formulated as a problem of segmenting a Riemannian manifold. The image domain is endowed with an anisotropic metric and its segmentation is obtained by thresholding the second eigenvector of the Laplace-Beltrami operator on the Riemannian manifold so defined. The formulation is an analytic analog of a recently proposed approach to segmentation based on graph theory. However, the analytic formulation has built-in invariance properties and permits more general metrics. The formulation may also be viewed as a generalization of the method of curve evolution which is based on isotropic metrics.