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

    7 Citations (Scopus)

    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

    Fingerprint

    Linear matrix inequalities
    Probability distributions
    Distribution functions

    All Science Journal Classification (ASJC) codes

    • Software
    • Computer Vision and Pattern Recognition

    Cite this

    Ozay, N., Sznaier, M., Lagoa, C. M., & Camps, O. (2010). GPCA with denoising: A moments-based convex approach. In 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010 (pp. 3209-3216). [5540075] (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition). https://doi.org/10.1109/CVPR.2010.5540075
    Ozay, Necmiye ; Sznaier, Mario ; Lagoa, Constantino Manuel ; Camps, Octavia. / GPCA with denoising : A moments-based convex approach. 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010. 2010. pp. 3209-3216 (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition).
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    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.",
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    Ozay, N, Sznaier, M, Lagoa, CM & Camps, O 2010, GPCA with denoising: A moments-based convex approach. in 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010., 5540075, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 3209-3216, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010, San Francisco, CA, United States, 6/13/10. https://doi.org/10.1109/CVPR.2010.5540075

    GPCA with denoising : A moments-based convex approach. / Ozay, Necmiye; Sznaier, Mario; Lagoa, Constantino Manuel; Camps, Octavia.

    2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010. 2010. p. 3209-3216 5540075 (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition).

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

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    Ozay N, Sznaier M, Lagoa CM, Camps O. GPCA with denoising: A moments-based convex approach. In 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010. 2010. p. 3209-3216. 5540075. (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition). https://doi.org/10.1109/CVPR.2010.5540075