An optimal segmentation encoding scheme in the rate distortion sense

In this paper, we present two fast and efficient methods for the lossy encoding of object boundaries which are given as 8-connect chain codes. We approximate the boundary by a polygon and consider the problem of finding the polygon which leads to the smallest distortion for a given number of bits. We introduce two different approaches to find the best polygonal approximation when an additive distortion measure is employed. The first approach is based on Lagrangian relaxation and a shortest path algorithm. This scheme results in solutions which belong to the convex hull of the operational rate-distortion curve. The second algorithm is based on a tree pruning scheme and finds all optimal solutions. We present results of the proposed algorithms using an object from the "Miss America" sequence.