This paper presents a novel approach for object segmentation in medical images that respects the topological relationships of multiple structures as given by a template. The algorithm combines advantages of tissue classification, digital topology, and level-set evolution into a topology-invariant multiple-object fast marching method. The technique can handle any given topology and enforces object-level relationships with little constraint over the geometry. Applied to brain segmentation, it sucessfully extracts gray matter and white matter structures with the correct spherical topology without topology correction or editing of the subcortical structures.