The human cerebral cortex is topologically equivalent to a sheet and can be considered topologically spherical if it is closed at the brain stem. Low-level segmentation of magnetic resonance (MR) imagery typically produces cerebral volumes whose tessellations are not topologically spherical. We present a novel algorithm that analyzes and constrains the topology of a volumetric object. Graphs are formed that represent the connectivity of voxel segments in the foreground and background of the image. These graphs are analyzed and minimal corrections to the volume are made prior to tessellation. We apply the algorithm to a simple test object and to cerebral white matter masks generated by a low-level tissue identification sequence. We tessellate the resulting objects using the marching cubes algorithm and verify their topology by computing their Euler characteristics. A key benefit of the algorithm is that it localizes the change to a volume to the specific areas of its topological defects.