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We propose a new approach to front propagation algorithms based on a topological variant of well-composedness which contrasts with previous methods based on simple point detection. This provides for a theoretical justification, based on the digital Jordan separation theorem, for digitally “gluing” evolved well-composed objects separated by well-composed curves or surfaces. Additionally, our framework can be extended to more relaxed topologically constrained algorithms based on multisimple points. For both methods this framework has the additional benefit of obviating the requirement for both a user-specified connectivity and a topologically-consistent marching cubes/squares algorithm in meshing the resulting segmentation.