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In this paper we study various chain codes, which are representations of binary image contours, in terms of their ability to compress in the best way the contour information using memory models. We consider five chain codes, including the widely used AF8 and 30T codes, and note that they correspond to memory models of first and second order for contour representation. In order to provide predictive distributions for the arithmetic coding, memory distribution models such as Markov models and context trees utilized in adaptive configurations are used on top of the chain codes. By additionally accounting for all side costs we obtain losslessly decodable files and find the best performer to be the context tree modeling applied to the sequence of 30T chain codes, surpassing all results recently reported in the literature for the same data set of bilevel images.