In this work we introduce a curvature based shape feature extraction technique. To construct the proposed descriptor, first an input color channel is subject to edge detection and gradient computations. Then, based on the gradient map and edge map, the local curvature of the contour is computed for each pixel as the angular difference between the maximum and minimum gradient angle within a cert...

We derive the entropy formula for the linear heat equation on general Riemannian manifolds and prove that it is monotone non-increasing on manifolds with nonnegative Ricci curvature. As applications, we study the relation between the value of entropy and the volume of balls of various scales. The results are simpler version, without Ricci flow, of Perelman’s recent results on volume non-collaps...

A geometric model for segmentation of images with missing boundaries is presented. Some classical problems of boundary completion in cognitive images, like the pop up of subjective contours in the famous triangle of Kanizsa, are faced from a surface evolution point of view. The method is based on the mean curvature evolution of a graph with respect to the Riemannian metric induced by the image....

STUDY DESIGN A prospective study; 2-group design. OBJECTIVE This study aims to assess the time response of scoliotic spines to orthotic intervention using clinical ultrasound. SUMMARY OF BACKGROUND DATA Patients with moderate adolescent idiopathic scoliosis are generally advised orthotic treatment. However, the time to reach maximum correction after donning spinal orthosis or the time to re...

This paper presents a rank rigidity result for negatively curved spaces. Let M be a compact manifold with negative sectional curvature and suppose that along every geodesic in M there is a parallel vector field making curvature −a with the geodesic direction. We prove that M has constant curvature equal to −a if M is odd dimensional, or if M is even dimensional and has sectional curvature pinch...

The shape-frequency and shape-amplitude after-effects, or SFAE and SAAE, refer respectively to the shifts observed in the perceived shape-frequency and shape-amplitude of a sinusoidal test contour following adaptation to a similar-shaped contour. As with other shape after-effects the shifts are in a direction away from that of the adapting stimulus. Using a variety of procedures we tested wheth...

PURPOSE Anterior corneal curvature shows significant heritability. Scheimpflug imaging also permits assessment of posterior tomography. We estimated heritability of posterior and anterior tomographic parameters. METHODS Oculus Pentacam images were obtained in twins from the TwinsUK cohort. Mean anterior and posterior radii of curvature (right cornea) were compared within twin pairs, and herit...

We describe a novel approach to curve inference based on curvature information. The inference procedure is divided into two stages: a trace inference stage, to which this paper is devoted, and a curve synthesis stage, which will be treated in a separate paper. It is shown that recovery of the trace of a curve requires estimating local models for the curve at the same time, and that tangent and ...

We obtain a local uniqueness result for bubbling solutions of the prescribed scalar curvature problem in R . Such result implies that some bubbling solutions preserve the symmetry from the scalar curvature K(y). In particular, we prove in this paper that if K(y) is periodic in y1 with period 1 and has a local maximum point at 0, then a bubbling solution whose blow-up set is {(jL, 0, · · · , 0) ...

We propose a fully automatic and view-independent computational procedure for detecting salient curvature extrema in range data. Our method consists of two major steps: (1) smoothing given range data by applying a nonlinear diffusion of normals with automatic thresholding; (2) using a Canny-like non-maximum suppression and hysteresis thresholding operations for detecting crease pixels. A delica...