Distributed algorithms for polygonal approximation of convex contours

Abstract

We propose algorithms that compute polygon approximations for convex contours. This geometric problem is relevant in interpolation theory, data compression, and has potential applications in robotic sensor networks. The algorithms are based on simple feedback ideas, on limited nearest-neighbor information, and amount to gradient descent laws for appropriate cost functions. The approximations are based on intuitive performance metrics, such as the area of the inner, outer, and "outer minus inner" approximating polygons