We classify biharmonic submanifolds with certain geometric properties in Euclidean spheres. For codimension 1, we determine the biharmonic hypersurfaces with at most two distinct principal curvatures and the conformally flat biharmonic hypersurfaces. We obtain some rigidity results for pseudo-umbilical biharmonic submanifolds of codimension 2 and for biharmonic surfaces with parallel mean curva...

Given a smooth surface, a blue (red) ridge is a curve such that at each of its points, the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and therefore encode important informations used in segmentation, registration, matching and surface analysis. State of the art methods for ridge extraction either report red and blue ri...

We propose a method for the deformable registration of organic surfaces. Meaningful correspondences between a source surface and a target surface are established by means of a rich surface descriptor that incorporates three categories of features: (1) local and regional geometry; (2) surface anatomy; and (3) global shape information. First, surface intrinsic, geodesic distance integrals, are ex...

This paper describes a robust method for crease detection and curvature estimation on large, noisy triangle meshes. We assume that these meshes are approximations of piecewise-smooth surfaces derived from range or medical imaging systems and thus may exhibit measurement or even registration noise. The proposed algorithm, which we call normal vector voting, uses an ensemble of triangles in the g...

We describe an effective and novel approach to infer sign and direction of principal curvatures at each input site from noisy 3D data. Unlike most previous approaches, no local surface fitting, partial derivative computation of any kind, nor oriented normal vector recovery is performed in our method. These approaches are noise-sensitive since accurate, local, partial derivative information is o...

Existing curvature estimators of planar curves are applied to a binary representation of the object. The parametric curve description is 1D-smoothed to overcome quantization errors. In this paper we estimate object curvature directly from a properly sampled grayscale image using 2D isotropic derivative-of-Gaussian filters. Three times oversampling or a Gaussain σκ of 2.7 yields sampling-error f...