This paper describes the Subgradient Marching algorithm to compute the derivative of the geodesic distance with respect to the metric. The geodesic distance being a concave function of the metric, this algorithm computes an element of the subgradient in O(N log(N)) operations on a discrete grid ofN points. It performs a front propagation that computes the subgradient of a discrete geodesic dist...

The d-convex sets in a metric space are those subsets which include the metric interval between any two of its elements. Weak modularity is a certain interval property for triples of points. The d-convexity of a discrete weakly modular space X coincides with the geodesic convexity of the graph formed by the two-point intervals in X. The Helly number of such a space X turns out to be the same as...

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dN is a geodesic Borel distance which makes (X, dN ) a possibly branching geodesic space. We show that under some assumptions on the transference plan we can reduce the transport problem to transport problems along family of geodesics. We introduce three assumptions on a given dN -monotone trans...

we prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of aliouche, et al. [2], rao et al. [14] and [15].

We study the geodesic flow on the normal line congruence of a minimal surface in R induced by the neutral Kähler metric on the space of oriented lines. The metric is lorentz with isolated degenerate points and the flow is shown to be completely integrable. In addition, we give a new holomorphic description of minimal surfaces in R and relate it to the classical Weierstrass representation.

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dN is a geodesic Borel distance which makes (X, dN ) a possibly branching geodesic space. We show that under some assumptions on the transference plan we can reduce the transport problem to transport problems along family of geodesics. We introduce two assumptions on the transference plan π whic...

This paper presents a fast geodesic shooting algorithm for diffeomorphic image registration. We first introduce a novel finite-dimensional Lie algebra structure on the space of bandlimited velocity fields. We then show that this space can effectively represent initial velocities for diffeomorphic image registration at much lower dimensions than typically used, with little to no loss in registra...

We show that, in the region where monopoles are well separated, the L-metric on the moduli space of n-monopoles is exponentially close to the Tn-invariant hyperkähler metric proposed by Gibbons and Manton. The proof is based on a description of the Gibbons-Manton metric as a metric on a certain moduli space of solutions to Nahm’s equations, and on twistor methods. In particular, we show how the...

In this paper we explicitly derive a level set formulation for mean curvature flow in a Riemannian metric space. This extends the traditional geodesic active contour framework which is based on conformal flows. Curve evolution for image segmentation can be posed as a Riemannian evolution process where the induced metric is related to the local structure tensor. Examples on both synthetic and re...

We obtain sharp inequalities between the large scale asymptotic of J functional with respect to $$d_1$$ metric on space Kähler metrics. Applications regarding initial value problem for geodesic rays are presented.