Matching Structures by Computing Minimal Paths on a Manifold

Shape Matching by Variational Computation of Geodesics on a Manifold

Klassen et al. [9] recently developed a theoretical formulation to model shape dissimilarities by means of geodesics on appropriate spaces. They used the local geometry of an infinite dimensional manifold to measure the distance dist(A,B) between two given shapes A and B. A key limitation of their approach is that the computation of distances developed in the above work is inherently unstable, ...

Computing Geodesics on a Riemannian Manifold

SurfCut: Surfaces of Minimal Paths From Topological Structures

We present SurfCut, an algorithm for extracting a smooth, simple surface with an unknown 3D curve boundary from a noisy 3D image and a seed point. Our method is built on the novel observation that certain ridge curves of a function defined on a front propagated using the Fast Marching algorithm lie on the surface. Our method extracts and cuts these ridges to form the surface boundary. Our surfa...

Tracking Meteorological Structures through Curves Matching Using Geodesic Paths

This paper is concerned with the problem of tracking clouds structures like vortices in meteorological images. For this purpose we characterize the deformation between two successive occurrences, by matching their two boundary curves. Our approach is based on the computation of the set of paths connecting the two curves to be matched. It minimizes a cost function which measures the local simila...

Shortest paths on a polyhedron, Part I: Computing shortest paths

We present an algorithm for determining the shortest path between any two points along the surface of a polyhedron which need not be convex. This algorithm also computes for any source point on the surface of a polyhedron the inward layout and the subdivision of the polyhedron which can be used for processing queries of shortest paths between the source point and any destination point. Our algo...