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In this paper, we present fast and efficient methods for the lossy encoding of object boundaries that are given as eight-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 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 baseddoi:10.1109/83.650847 pmid:18267376 fatcat:mafqxobstngondhyxmbajxi2pa