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 schemeand the neighborhood size .
 In this paper, we define and evaluate a weighting scheme for neighborhoods in point sets. Our weighting takes the shape of the geometry , i.e. the normal information, into account. This causes the obtained neighborhoods to be more reliable in the sense that connectivity also depends on the orientation of the point set. We utilize a sigmoid to define the weights based on the normal variation. For an evaluation of the weighting scheme , we turn to a Shannon entropy model for feature separation and rigorously prove its non-degeneracy for our family of weights . Based on this model, we evaluate our weighting terms on a large scale of both clean and real-world models. This evaluation provides results regarding the choice of optimal parameters within our weighting scheme. Furthermore, the large-scale evaluation also reveals that neighborhood sizes should not be fixed globally when processing models. This is in contrast to current general practice in the field of geometry processing .
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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.
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optimal parameters within our weighting scheme. Furthermore, the large-scale evaluation also reveals that neighborhood sizes should not be fixed globally when processing models. This is in contrast to current general practice in the field of geometry processing