Image-as-Matrix
Representation and Feature Extraction via Tensor Decomposition
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Hongcheng Wang and
Narendra Ahuja
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1.
Hongcheng Wang and
Narendra Ahuja,
Efficient Rank-R Approximation of Tensors: A New Approach to Compact
Representation of Image Ensembles and Recognition, IEEE
International Conference on Computer Vision and Pattern Recognition
(CVPR),
2005
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.
Full Text: Available
soon!
Also see:
Facial Expression Decomposition Using HOSVD
2.
Hongcheng Wang and
Narendra Ahuja,
Compact Representation of Multidimensional Data Using Tensor
Rank-One Decomposition, IEEE, International Conference on Pattern
Recognition, ICPR, 2004
Abstract:
This paper presents a new approach for representing multidimensional
data by a compact number of bases. We consider the multidimensional
data as tensors instead of matrices or vectors, and propose a Tensor
Rank-One Decomposition ( TROD) algorithm by decomposing
Nth-order data into a
collection of rank-1 tensors based on multilinear algebra. By
applying this algorithm to image sequence compression, we obtain
much higher quality images with the same compression ratio as
Principle Component Analysis (PCA). Experiments with gray-level and
color video sequencesare used to illustrate the validity of this
approach.
Full Text:
PDF (525K),
PS (6,190K)
Also see:
Facial Expression Decomposition Using
HOSVD
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Jan., 2005
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