Riemannian drums, anisotropic curve evolution and segmentation

Abstract

The method of curve evolution is a popular method for recovering shape boundaries. However isotropic metrics have always been used to induce the flow of the curve and potential steady states tend to be difficult to determine numerically, especially in noisy or low-contrast situations. Initial curves shrink past the steady state and soon vanish. In this paper, anisotropic metrics are considered which remedy the situation by taking the orientation of the feature gradient into account. The problem of shape recovery or segmentation is formulated as the problem of finding minimum cuts of a Riemannian manifold. Approximate methods, namely anisotropic geodesic flows and solution of an eigenvalue problem are discussed.