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Growing Least Squares for the Analysis of Manifolds in Scale‐Space
Author(s) -
Mellado Nicolas,
Guennebaud Gaël,
Barla Pascal,
Reuter Patrick,
Schlick Christophe
Publication year - 2012
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2012.03174.x
Subject(s) - scale (ratio) , computer science , scale space , robustness (evolution) , manifold (fluid mechanics) , parametrization (atmospheric modeling) , dimension (graph theory) , space (punctuation) , algorithm , point (geometry) , moving least squares , property (philosophy) , mathematics , artificial intelligence , geometry , pure mathematics , image processing , image (mathematics) , chemistry , engineering , operating system , biochemistry , quantum mechanics , mechanical engineering , physics , gene , radiative transfer , philosophy , epistemology
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.