Lots of works have been recently carried out in the field of non-rigid registration to ensure the estimation of one-to-one mappings. However, warping a binary image with such transformations may alter its discrete topological properties if common resampling strategies are considered. This paper proposes an original method for warping a binary image according to some continuous and bijective mapping, while preserving its discrete topological properties. Results obtained in the context of atlas-based segmentation highlight the interest of the approach. Indeed, the method has been successfully applied to the segmentation of skull structures from a database of 15 CT-scans, providing both geometrically and topologically satisfactory results.