An Optimal Polygonal Boundary Encoding Scheme
In this chapter, we present fast and efficient methods for the lossy encoding of object boundaries which are given as 8-connect chain codes [180, 182, 177, 179]. 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 also address the dual problem of finding the polygon which leads to the smallest bit rate for a given distortion. We consider two different classes of distortion measures. The first class is based on the maximum operator and the second class is based on the summation operator. For the first class, we derive a fast and optimal scheme which is based on a shortest path algorithm for a weighted directed acyclic graph. For the second class we propose a solution approach which is based on the Lagrangian multiplier method, which uses the above mentioned shortest path algorithm. Since the Lagrangian multiplier method can only find solutions on the convex hull of the operational rate distortion function, we also propose a tree pruning algorithm which can find all optimal solutions. Finally we present results of the proposed schemes using objects from the “Miss America” sequence.
KeywordsBoundary Point Short Path Algorithm Lagrangian Multiplier Method Pruning Scheme Distortion Measure
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