Equilateral polygon approximation of closed contours

Abstract

Numerous algorithms have been suggested for computing polygonal approximations of closed contours. We present an algorithm which as a unique feature creates polygons which are equilateral, that is, whose edges are all of the same length. This allows one-dimensional shape descriptions to be derived using the interior polygon angles. Conceptually, the algorithm is an optimization framework for finding the minimum energy configuration of a mechanical system of particles and springs that represent the contour points, the polygon vertices and their interaction. In practice, the dominant points are detected on the Gaussian smoothed contour and used to seed an initial polygon. Nonlinear programming is then used to minimize the system energy subject to the constraint that adjacent vertices must be equidistant. The objective function is the sum of a curvature weighted distance between each vertex and a set of contour points associated therewith. Experimental results are given for closed contours obtained from grey-scale images.