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Center for Intelligent Machines. His current research interests include computer vision, mathematical morphology, and biomedical image analysis.

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We introduce the notion of the medial scaffold, a hierarchical organization of the medial axis of a 3D shape in the form of a graph constructed from special medial curves connecting special medial points. A key advantage of the scaffold is that it captures the qualitative aspects of shape in a hierarchical and tightly condensed representation. We propose an efficient and exact method for computing the medial scaffold based on a notion of propagation along the scaffold itself, starting from initial sources of the flow and constructing the scaffold during the propagation. We examine this method specifically in the context of an unorganized cloud of points in 3D, e.g., as obtained from laser range finders, which typically involve hundreds of thousands of points, but the ideas are generalizable to data arising from geometrically described surface patches. The computational bottleneck in the propagation-based scheme is in finding the initial sources of the flow. We thus present several ideas to avoid the unnecessary consideration of pairs of points which cannot possibly form a medial point source, such as the "visibility" of a point from another given a third point and the interaction of clusters of points. An application of using the medial scaffold for the representation of point samplings of real-life objects is also illustrated.

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We propose an algorithm for surface reconstruction from unorganized points based on a view of the sampling process as a deformation from the original surface. In the course of this deformation the Medial Scaffold (MS)-a graph representation of the 3D Medial Axis (MA)-of the original surface undergoes abrupt topological changes (transitions) such that the MS of the unorganized point set is significantly different from that of the original surface. The algorithm seeks a sequence of transformations of the MS to invert this process. Specifically, some MS curves (junctions of 3 MA sheets) correspond to triplets of points on the surface and represent candidates for generating a (Delaunay) triangle to mesh that portion of the surface. We devise a greedy algorithm that iteratively transforms the MS by "removing" suitable candidate MS curves (gap transform) from a rank-ordered list sorted by a combination of properties of the MS curve and its neighborhood context. This approach is general and applicable to surfaces which are: non-closed (with boundaries), non-orientable, non-uniformly sampled, non-manifold (with self-intersections), nonsmooth (with sharp features: seams, ridges). In addition, the method is comparable in speed and complexity to current popular Voronoi/Delaunay-based algorithms, and is applicable to very large datasets.

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