We present here a new method for correcting the topology of objects segmented from medical images. Whereas previous techniques alter a surface obtained from the hard segmentation of the object, our technique works directly in the image domain, propagating the topology for all isosurfaces of the object. From an analysis of topological changes and critical points in implicit surfaces, we introduce a topology progagation algorithm that enforces any desired topology using a fast marching technique. Compared to previous topology correction techniques, the method successfully corrects topology while effecting fewer changes to the original volume.