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Some Recent Advances in Multiscale Geometric Analysis of Point Clouds

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Wavelets and Multiscale Analysis

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

We discuss recent work based on multiscale geometric analyis for the study of large data sets that lie in high-dimensional spaces but have low-dimensional structure. We present three applications: the first one to the estimation of intrinsic dimension of sampled manifolds, the second one to the construction of multiscale dictionaries, called Geometric Wavelets, for the analysis of point clouds, and the third one to the inference of point clouds modeled as unions of multiple planes of varying dimensions.

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Authors and Affiliations

  1. Duke University, Durham, NC, USA

    Mauro Maggioni

Authors
  1. Guangliang Chen
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  2. Anna V. Little
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  3. Mauro Maggioni
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  4. Lorenzo Rosasco
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Correspondence to Mauro Maggioni .

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Editors and Affiliations

  1. , Department of Mathematical Sciences, DePaul University, North Kenmore Avenue 2320, Chicago, 60614-3250, Illinois, USA

    Jonathan Cohen

  2. , Department of Mathematical Sciences, DePaul University, North Kenmore Avenue 2320, Chicago, 60614-3250, Illinois, USA

    Ahmed I. Zayed

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Chen, G., Little, A.V., Maggioni, M., Rosasco, L. (2011). Some Recent Advances in Multiscale Geometric Analysis of Point Clouds. In: Cohen, J., Zayed, A. (eds) Wavelets and Multiscale Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8095-4_10

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