Growing Least Squares for the Analysis of Manifolds in Scale-Space

Nicolas Mellado 1, 2 Gaël Guennebaud 1, 2, 3 Pascal Barla 1, 2, 3 Patrick Reuter 1, 2 Christophe Schlick 1, 2
2 MANAO - Melting the frontiers between Light, Shape and Matter
LaBRI - Laboratoire Bordelais de Recherche en Informatique, Inria Bordeaux - Sud-Ouest, LP2N - Laboratoire Photonique, Numérique et Nanosciences
Abstract : We present a novel approach to the multi-scale analysis of point-sampled manifolds of co-dimension 1. It is based on a variant of Moving Least Squares, whereby the evolution of a geometric descriptor at increasing scales is used to locate pertinent locations in scale-space, hence the name "Growing Least Squares". Compared to existing scale-space analysis methods, our approach is the first to provide a continuous solution in space and scale dimensions, without requiring any parametrization, connectivity or uniform sampling. An important implication is that we identify multiple pertinent scales for any point on a manifold, a property that had not yet been demonstrated in the literature. In practice, our approach exhibits an improved robustness to change of input, and is easily implemented in a parallel fashion on the GPU. We compare our method to state-of-the-art scale-space analysis techniques and illustrate its practical relevance in a few application scenarios.
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Nicolas Mellado, Gaël Guennebaud, Pascal Barla, Patrick Reuter, Christophe Schlick. Growing Least Squares for the Analysis of Manifolds in Scale-Space. Computer Graphics Forum, Wiley, 2012, Proceedings of Symposium on Geometry Processing 2012, 31 (5), pp.1691-1701. ⟨10.1111/j.1467-8659.2012.03174.x⟩. ⟨hal-00713678v2⟩

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