Large-Scale Evaluation of Shape-Aware Neighborhood Weights Neighborhood Sizes
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Point sets arise naturally in many 3D acquisition processes and have diverse applications in several areas of geometry processing. Besides their advantages—for instance low storage cost—they do not provide connectivity information. Thus, for each point, the notion of its neighborhood has to be defined and computed. Common approaches include combinatorial or geometric neighborhoods. However, neither of these incorporates curvature information of the point set. In this paper, we present an approach to take the shape of the geometry into account when weighting its neighborhoods. This makes the obtained neighborhoods more reliable in the sense that connectivity also depends on the orientation of the point set. For example, these neighborhoods grow on a comparably flat part of the geometry and do not include points on a nearby surface patch with differently oriented normals. We utilize a sigmoid to define a neighborhood weighting scheme based on the normal variation. For its evaluation, we turn to a Shannon entropy model for feature separation. Based on this model, we apply our weight terms to a large scale of clean and to several real world models. This evaluation provides results regarding the choice of a weighting scheme and the neighborhood size.
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