Beta-connection: Generating a family of models from planar cross sections

Despite the significant evolution of techniques for 3D-reconstruction from planar cross sections, establishing the correspondence of regions in adjacent slices remains an important issue. In this article, we propose a novel approach for solving the correspondence problem in a flexible manner. We show that from the 3D Delaunay triangulation, it is possible to derive a distance measure among regions lying in adjacent slices. Such distance is used to define a positive integer parameter, called β, responsible for establishing the connections. Varying β thus allows the construction of different models from a given set of cross-sectional regions: small values of β causes closer regions to be connected into a single component, and as β increases, more distant regions are connected together. The algorithm, named β-connection, is described, and examples are provided that illustrate its applicability in solid modeling and model reconstruction from real data. The underlying reconstruction method is effective, which jointly with the β-connection correspondence strategy, improve the usability of volumetric reconstruction techniques considerably.