Multiscale Covariance Fields, Local Scales, and Shape Transforms

  • Diego H. Diaz Martinez
  • Facundo Mémoli
  • Washington Mio
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8085)

Abstract

We introduce the notion of multiscale covariance tensor fields associated with a probability measure on Euclidean space and use these fields to define local scales at a point and to construct shape transforms. Local scales at x may be interpreted as scales at which key geometric features of the data organization around x are revealed. Shape transforms are employed to identify points that are most salient in terms of the local-global shape of a probability distribution, yielding a compact summary of the geometry of the distribution.

Keywords

covariance fields local scales shape features shape transforms 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Diego H. Diaz Martinez
    • 1
  • Facundo Mémoli
    • 2
  • Washington Mio
    • 1
  1. 1.Department of MathematicsFlorida State UniversityTallahasseeUSA
  2. 2.School of Computer ScienceThe University of AdelaideAdelaideAustralia

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