Rank-R approximation of tensors using image-as-matrix representation

Hongcheng Wang, Narendra Ahuja

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

Abstract

We present a novel multilinear algebra based approach for reduced dimensionality representation of image ensembles. We treat an image as a matrix, instead of a vector as in traditional dimensionality reduction techniques like PCA, and higher-dimensional data, as a tensor. This helps exploit spatio-temporal redundancies with less information loss than image-as-vector methods. The challenges lie in the computational and memory requirements for large ensembles. Currently, there exists a rank-R approximation algorithm which, although applicable to any number of dimensions, is efficient for only low-rank approximations. For larger dimensionality reductions, the memory and time costs of this algorithm become prohibitive. We propose a novel algorithm for rank-R approximations of third-order tensors, which is efficient for arbitrary R but for the important special case of 2D image. ensembles, e.g. video. Both of these algorithms reduce redundancies present in all dimensions. Rank-R tensor approximation yields the most compact data representation among all known image-as-matrix methods. We evaluated the performance of our algorithm vs. other approaches on a number of datasets with the following two main results. First, for a fixed compression ratio, the proposed algorithm yields the best representation of image ensembles visually as well as in the least squares sense. Second, proposed representation gives the best performance, for object classification.

Original languageEnglish (US)
Title of host publicationProceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005
PublisherIEEE Computer Society
Pages346-353
Number of pages8
ISBN (Print)0769523722, 9780769523729
DOIs
StatePublished - Jan 1 2005
Event2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005 - San Diego, CA, United States
Duration: Jun 20 2005Jun 25 2005

Publication series

NameProceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005
VolumeII

Other

Other2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005
CountryUnited States
CitySan Diego, CA
Period6/20/056/25/05

ASJC Scopus subject areas

  • Engineering(all)

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  • Cite this

    Wang, H., & Ahuja, N. (2005). Rank-R approximation of tensors using image-as-matrix representation. In Proceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005 (pp. 346-353). [1467463] (Proceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005; Vol. II). IEEE Computer Society. https://doi.org/10.1109/CVPR.2005.290