Tensor sparse coding for region covariances

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

47 Scopus citations

Abstract

Sparse representation of signals has been the focus of much research in the recent years. A vast majority of existing algorithms deal with vectors, and higher-order data like images are usually vectorized before processing. However, the structure of the data may be lost in the process, leading to poor representation and overall performance degradation. In this paper we propose a novel approach for sparse representation of positive definite matrices, where vectorization would have destroyed the inherent structure of the data. The sparse decomposition of a positive definite matrix is formulated as a convex optimization problem, which falls under the category of determinant maximization (MAXDET) problems [1], for which efficient interior point algorithms exist. Experimental results are shown with simulated examples as well as in real-world computer vision applications, demonstrating the suitability of the new model. This forms the first step toward extending the cornucopia of sparsity-based algorithms to positive definite matrices.

Original languageEnglish (US)
Title of host publicationComputer Vision, ECCV 2010 - 11th European Conference on Computer Vision, Proceedings
PublisherSpringer- Verlag
Pages722-735
Number of pages14
EditionPART 4
ISBN (Print)364215560X, 9783642155604
DOIs
StatePublished - Jan 1 2010
Event11th European Conference on Computer Vision, ECCV 2010 - Heraklion, Crete, Greece
Duration: Sep 10 2010Sep 11 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 4
Volume6314 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th European Conference on Computer Vision, ECCV 2010
Country/TerritoryGreece
CityHeraklion, Crete
Period9/10/109/11/10

Keywords

  • MAXDET optimization
  • Positive definite matrices
  • region covariances
  • sparse coding

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