Total curvature of noncompact piecewise Riemannian 2-polyhedra

Riemannian Mean Curvature Flow

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...

Mean Curvature of Riemannian Immersions

1. Let M and M' denote complete riemannian manifolds of dimension n and m respectively, and suppose that M is compact and oriented. For simplicity we assume that both manifolds and their metrics are smooth (i.e. of class C). In terms of local co-ordinates (x, x, ...,x") on M and local co-ordinates (y,y, •••,/") on M', the riemannian metrics are written ds = gtJ dx l dx, ds' = g'aP dy* dy * wher...

Curvature of sub-Riemannian spaces

Intrinsic Coupling on Riemannian Manifolds and Polyhedra

Starting from a central limit theorem for geometric random walks we give an elementary construction of couplings between Brownian motions on Riemannian manifolds. This approach shows that cut locus phenomena are indeed inessential for Kendall’s and Cranston’s stochastic proof of gradient estimates for harmonic functions on Riemannian manifolds with lower curvature bounds. Moreover, since the me...

Differentiable piecewise-Bézier interpolation on Riemannian manifolds

We propose a generalization of classical Euclidean piecewiseBézier surfaces to manifolds, and we use this generalization to compute a C1-surface interpolating a given set of manifold-valued data points associated to a regular 2D grid. We then propose an efficient algorithm to compute the control points defining the surface based on the Euclidean concept of natural C2-splines and show examples o...