Two Radius of Convexity Problems

Convexity and Log Convexity for the Spectral Radius

The starting point of this paper is a theorem by J. F. C. Kingman which asserts that if the entries of a nonnegative matrix are log convex functions of a variable then so is the spectral radius of the matrix. A related result of J. Cohen asserts that the spectral radius of a nonnegative matrix is a convex function of the diagonal elements. The first section of this paper gives a new, unified pr...

Applications of convexity in some identification problems

Convexity Analysis of Active Contour Problems

A general active contour formulation is considered and a convexity analysis of its energy function is presented. Conditions under which this formulation has a unique solution are derived; these conditions involve both the active contour energy potential and the regularization parameters. This analysis is then applied to four particular active contour formulations, revealing important characteri...

Constant-Time Convexity Problems on Reconfigurable Meshes

The purpose of this paper is to demonstrate that the versatility of the reconngurable mesh can be exploited to devise constant-time algorithms for a number of important computational tasks relevant to robotics, computer graphics, image processing, and computer vision. In all our algorithms, we assume that one or two n-vertex (convex) polygons are pretiled, one vertex per processor, onto a recon...

Convexity Problems on Meshes with Multiple Broadcasting

The purpose of this work is to present simple time-optimal algorithms for a number of convexity-related problems on meshes with multiple broadcasting. More speciically, we show that with an n-vertex convex polygon P as input, the tasks of computing the perimeter , the area, the diameter, the width, the modality, the smallest-area enclosing rectangle, and the largest-area inscribed triangle shar...