We present here a new method for correcting the topology of objects segmented from medical images. Whereas previous techniques alter a surface obtained from a binary segmentation of the object, our technique can be applied directly to the image intensities of a probabilistic or fuzzy segmentation, thereby propagating the topology for all isosurfaces of the object. From an analysis of topological changes and critical points in implicit surfaces, we derive a topology propagation algorithm that enforces any desired topology using a fast marching technique. The method has been applied successfully to the correction of the cortical gray matter / white matter interface in segmented brain images and is publicly released as a software plug-in or the MIPAV package.