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

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    Date
    2012
    Author
    Mellado, Nicolas ORCID
    Guennebaud, Gaël
    Barla, Pascal
    Reuter, Patrick
    Schlick, Christophe
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    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.
    BibTeX
    @article {10.1111:j.1467-8659.2012.03174.x,
    journal = {Computer Graphics Forum},
    title = {{Growing Least Squares for the Analysis of Manifolds in Scale-Space}},
    author = {Mellado, Nicolas and Guennebaud, Gaël and Barla, Pascal and Reuter, Patrick and Schlick, Christophe},
    year = {2012},
    publisher = {The Eurographics Association and Blackwell Publishing Ltd.},
    ISSN = {1467-8659},
    DOI = {10.1111/j.1467-8659.2012.03174.x}
    }
    URI
    http://dx.doi.org/10.1111/j.1467-8659.2012.03174.x
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    • 31-Issue 5
    • SGP12: Eurographics Symposium on Geometry Processing

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