Automatic surface extraction by discrete, topologically controlled, region growing

Flat-mapping approaches [1,2,3] to anatomic visualization and functional modeling require polygonal surfaces that are topologitally correct and topologically equivalent to a sphere (a single, closed, non-intersecting manifold with no exposed edges or handles) or a plane (like a sphere with a connected, non-looping set of polygons removed). The surfaces produced by the widely used Marching Cubes algorithm exhibit local topological defects, including surface holes, fins, and unconnected polygons. Discrete algorithms for iso-surface extraction which do not produce topological defects have been proposed (cf. [4]). However, these algorithms do not provide any mechanism for controlling topological genus. Deformable geometric models [5] can control topological genus and produce a correct surface, however their computational cost is much higher than the the discrete methods for any given level of spatial resolution, and the algorithms can very be sensitive to initialization conditions, choices of parameter values, and the appropriateness of their implicit anatomical models to their subject matter (e.g. the cerebellum may require different assumptions than the cortex). To avoid these issues, we have developed a discrete algorithm for producing topologically correct surfaces, at an arbitrary sampling resolution, which is fast and robust.