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A new lossless compression scheme for bilevel images targeted at binary shapes of image and video objects is presented. The scheme is based on a local analysis of the digital straightness of the causal part of the object boundary, which is used in the context definition for arithmetic encoding. Tested on individual images of binary shapes and binary layers of digital maps the algorithm outperforms PWC, JBIG and MPEG-4 CAE. On the binary shapes the code lengths are reduced by 21%, 25%, and 42%, respectively. On the maps the reductions are 34%, 32%, and 59%, respectively. The algorithm is also more efficient than the state-of-the-art and more complex free tree coder for most of the binary shape and map test images.