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Point-Based Multi-Scale Surface Representation

In this paper we present a new multi-scale surface representation based on point samples. Given an unstructured point cloud as input, our method first computes a series of point-based surface approximations at successively higher levels of smoothness, i.e., coarser scales of detail, using geometric low-pass filtering. These point clouds are then encoded relative to each other by expressing each level as a scalar displacement of its predecessor. Low-pass filtering and encoding are combined in an efficient multi-level projection operator using local weighted least squares fitting. Our representation is motivated by the need for higher level editing semantics, which allow surface modifications at different scales. The user is enabled to edit the surface at different approximation levels to perform coarse-scale edits on the whole model as well as very localized modifications on the surface detail. Additionally, the multi-scale representation provides a separation in geometric scale, which can be understood as a spectral decomposition of the surface geometry. Based on this observation, advanced geometric filtering methods can be implemented, that mimic the effects of Fourier filters to achieve effects such as smoothing, enhancement or band-bass filtering.