CAREER: Reconstructing Geometrically and Topologically Correct Models

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Abstract:PI: Ju, Tao (0846072)CAREER: Reconstructing Geometrically and Topologically Correct ModelsBio-medical imaging and 3D scanning are widely used for acquiring realistic digital models of real-world objects, from those that are around us, like coffee mugs and statues, to those within us, like proteins and organs. In many applications, polygonal surfaces need to be reconstructed from the data captured by scanning or imaging. Besides visualization, these polygonal models have wide uses in computation and manufacturing, where geometrically and topologically correct models are required. However, as the input data is often noisy or incomplete, it is still difficult in practice to obtain correct polygonal surfaces using existing reconstruction algorithms. The reconstructed surface may exhibit geometric inconsistencies including gaps, holes and intersections, and more often, topological artifacts such as handles and disconnections. Furthermore, most reconstruction algorithms that promise geometrically correct outputs are designed for closed surfaces with well-defined inside and outside, and hence not applicable to surfaces that contain intended open boundaries or interior membranes. These more general surfaces are commonly used in CAD as well as bio-medical modeling.This research is developing robust polygonal surface reconstruction algorithms that offer guarantees for geometric and topological correctness. To achieve this goal, an integrated framework is developed that combines and extends existing surface reconstruction and model repair algorithms to produce correct polygonal models that best represent the input data, in the form of either 3D point clouds or grayscale volumes. The research is also exploring new reconstruction and repair algorithms for open and non-manifold surfaces, thereby extending the correctness guarantees to a much larger class of models than those can be handled by existing methods.