GMAT: The Groupwise Medial Axis Transform for Fuzzy Skeletonization and Intelligent Pruning

There is a frequent need to compute medial shape representations of each of a group of structures, e.g. for use in a medical study of anatomical shapes. We present a novel approach to skeletonization that leverages information provided from such a group. We augment the traditional medial axis transform with an additional coordinate stored at each medial locus, indicating the confidence that the branch on which that locus lies represents signal and not noise. This confidence is calculated based on the support given to that branch by corresponding branches in other skeletons in the group. We establish the aforementioned correspondence by a set of bipartite graph matchings using the Hungarian algorithm, and compute branch support based on similarity of computed geometric and topological features at each branch. This groupwise skeletonization approach supports an intelligent pruning algorithm, which we show to operate quickly and provide pruning in an intuitive manner. We show that the method is amenable to automatic detection of skeletal configurations with one, or more than one, topological class of skeletons. This is useful to medical studies which often involve patient groups whose structures may differ topologically.