GPCA with denoising: A moments-based convex approach

Necmiye Ozay, Mario Sznaier, Constantino Manuel Lagoa, Octavia Camps

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    8 Scopus citations

    Abstract

    This paper addresses the problem of segmenting a combination of linear subspaces and quadratic surfaces from sample data points corrupted by (not necessarily small) noise. Our main result shows that this problem can be reduced to minimizing the rank of a matrix whose entries are affine in the optimization variables, subject to a convex constraint imposing that these variables are the moments of an (unknown) probability distribution function with finite support. Exploiting the linear matrix inequality based characterization of the moments problem and appealing to well known convex relaxations of rank leads to an overall semi-definite optimization problem. We apply our method to problems such as simultaneous 2D motion segmentation and motion segmentation from two perspective views and illustrate that our formulation substantially reduces the noise sensitivity of existing approaches.

    Original languageEnglish (US)
    Title of host publication2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010
    Pages3209-3216
    Number of pages8
    DOIs
    StatePublished - Aug 31 2010
    Event2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010 - San Francisco, CA, United States
    Duration: Jun 13 2010Jun 18 2010

    Publication series

    NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
    ISSN (Print)1063-6919

    Other

    Other2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010
    CountryUnited States
    CitySan Francisco, CA
    Period6/13/106/18/10

    All Science Journal Classification (ASJC) codes

    • Software
    • Computer Vision and Pattern Recognition

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