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The estimation of one-to-one mappings is one of the most intensively studied topics in the research field of nonrigid registration. Although the computation of such mappings can be now accurately and efficiently performed, the solutions for using them in the context of binary image deformation is much less satisfactory. In particular, warping a binary image with such transformations may alter its discrete topological properties if common resampling strategies are considered. In order to deal with this issue, this paper proposes a method for warping such images according to continuous and bijective mappings while preserving their discrete topological properties (i.e., their homotopy type). Results obtained in the context of the atlas-based segmentation of complex anatomical structures highlight the advantages of the proposed approach.