This paper describes a new method for determining correspondence between points on pairs of surfaces based on shape using a combination of geodesic distance and surface curvature. An initial sparse set of corresponding points are generated using a shapebased matching procedure. Geodesic interpolation is employed in order to capture the complex surface. In addition, surface correspondence and tr...

This paper presents a new method for 2-D and 3-D shape retrieval based on geodesic signatures. These signatures are high dimensional statistical distributions computed by extracting several features from the set of geodesic distance maps to each point. The resulting high dimensional distributions are matched to perform retrieval using a fast approximate Wasserstein metric. This allows to propos...

There are dierent ways to code the geodesic flows on surfaces with negative curvature. Such code spaces give a useful tool to verify the dynamical properties of geodesic flows. Here we consider special subspaces of geodesic flows on Hecke surface whose arithmetic codings varies on a set with innite alphabet. Then we will compare the topological complexity of them by computing their topological ...

We prove existence and uniqueness of the minimizer for the average geodesic distance to the points of a geodesically convex set on the sphere. This implies a corresponding existence and uniqueness result for an optimal algorithm for halfspace learning, when data and target functions are drawn from the uniform distribution.

We consider how to test for group differences of shapes given longitudinal data. In particular, we are interested in differences of longitudinal models of each group's subjects. We introduce a generalization of principal geodesic analysis to the tangent bundle of a shape space. This allows the estimation of the variance and principal directions of the distribution of trajectories that summarize...

Recently, Chan et al. have proposed a new cycle embedding property called balanced pancyclicity [Discrete Applied Mathematics 155(15) (2007) 1971-1978]. For a graph G(V, E) and any two nodes x and y of V, a cycle R contains x and y can be divided into two paths, Pt1 and Pt2, joining x and y such that len(Pt1)len(Pt2), where len() denote the length of the path . A balanced cycle of an even (r...

An obstacle representation of a graph is a mapping of the vertices onto points in the plane and a set of connected regions of the plane (called obstacles) such that the straight-line segment connecting the points corresponding to two vertices does not intersect any obstacles if and only if the vertices are adjacent in the graph. The obstacle representation and its plane variant (in which the re...

We describe an elastic matching procedure between plane curves based on computing a minimal deformation cost between the curves. The design of the deformation cost is based on a geodesic distance defined on an infinite dimensional group acting on the curves. The geodesic paths also provide an optimal deformation process, which allows interpolation between any plane curves. q 1999 Elsevier Scien...