Multilinear Projection for Appearance-Based Recognition in the Tensor Framework

Vasilescu, M. Alex O.; Terzopoulos, Demetri

doi:10.1109/iccv.2007.4409067

Cited by 35 publications

(31 citation statements)

References 10 publications

(19 reference statements)

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“…Multifactor Isomap can be defined by replacing the dot products in (10) with the kernel function k Isomap . Using this kernel function, the three matrices in (10) can be replaced with Again, the id, pose, and lighting parameters of Multifactor Isomap can be calculated by SVD of the three matrices in (17).…”

Section: Multifactor Isomapmentioning

confidence: 99%

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An extension of multifactor analysis for face recognition based on submanifold learning

Park

Savvides

2010

2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition

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Lately, Multilinear Principal Component Analysis (MPCA) has been successfully applied to face recognition since MPCA provides analysis of multiple factors of face images such as people's identities, viewpoints, and lighting conditions. MPCA employees multiple linear subspaces constructed by varying factors. In this paper, we propose nonlinear submanifold analysis, which can represent the variation of each factor more accurately than the conventional multilinear subspace analysis. Based on submanifold learning, we propose an extension of the multiple factor analysis. This paper proposes the kernel-based extension of MPCA whose definition of a kernel function and neighbors of each sample is robust for submanifold learning. The experimental results in this paper demonstrate that the proposed methods produce a synergetic advantage for face recognition. This is because our method offers the combined virtues of both multifactor analysis and manifold learning.

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Section: Multifactor Isomapmentioning

confidence: 99%

“…. , 1) approximation using the alternating least squares method [17] was applied. This method enables us to decompose the Kronecker product of multiple parameters into individual ones.…”

Section: Multilinear Pcamentioning

confidence: 99%

An extension of multifactor analysis for face recognition based on submanifold learning

Park

Savvides

2010

2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition

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“…We can see that the shadows have been removed. As a consequence, we achieve a competitive 94.3% accuracy by the recognition method in [19]. …”

Section: Face Representation and Recognitionmentioning

confidence: 99%

“…Vasilescu and Terzopoulos [1] introduce a multilinear tensor framework to the analysis of face ensembles that explicitly accounts for each of the multiple factors implicit in image formation. Possible applications of the multilinear approach cover face recognition [18][19][20], facial expression decomposition [21,20] and face super-resolution [22]. These methods are based on the higher order singular value decomposition [23], i.e.…”

Section: Related Workmentioning

confidence: 99%

Optimum Subspace Learning and Error Correction for Tensors

Yin

Yan

Zhou

et al. 2010

Computer Vision – ECCV 2010

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Abstract. Confronted with the high-dimensional tensor-like visual data, we derive a method for the decomposition of an observed tensor into a low-dimensional structure plus unbounded but sparse irregular patterns. The optimal rank-(R1, R2, ...Rn) tensor decomposition model that we propose in this paper, could automatically explore the low-dimensional structure of the tensor data, seeking optimal dimension and basis for each mode and separating the irregular patterns. Consequently, our method accounts for the implicit multi-factor structure of tensor-like visual data in an explicit and concise manner. In addition, the optimal tensor decomposition is formulated as a convex optimization through relaxation technique. We then develop a block coordinate descent (BCD) based algorithm to efficiently solve the problem. In experiments, we show several applications of our method in computer vision and the results are promising.

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“…Thus, for successful image analysis, it is often necessary to model multiple factor frameworks found in image sets. One leading method for multifactor analysis is Multilinear Principal Component Analysis (MPCA), also called Tensorfaces [12] [13], based on multilinear algebra.…”

Section: Introductionmentioning

confidence: 99%

Multifactor analysis based on factor-dependent geometry

Park

Savvides

2011

CVPR 2011

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This paper proposes a novel method that preserves the geometrical structure created by variation of multiple factors in analysis of multiple factor models, i.e., multifactor analysis. We use factor-dependent submanifolds as constituent elements of the factor-dependent geometry in a multiple factor framework. In this paper, a submanifold is defined as some subset of a manifold in the data space, and factor-dependent submanifolds are defined as the submanifolds created for each factor by varying only this factor. In this paper, we show that MPCA is formulated using factordependent submanifolds, as is our proposed method. We show, however, that MPCA loses the original shapes of these submanifolds because MPCA's parameterization is based on averaging the shapes of factor-dependent submanifolds for each factor. On the other hand, our proposed multifactor analysis preserves the shapes of individual factordependent submanifolds in low-dimensional spaces. Because the parameters obtained by our method do not lose their structures, our method, unlike MPCA, sufficiently covers original factor-dependent submanifolds. As a result of sufficient coverage, our method is appropriate for accurate classification of each sample.

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Multilinear Projection for Appearance-Based Recognition in the Tensor Framework

Cited by 35 publications

References 10 publications

An extension of multifactor analysis for face recognition based on submanifold learning

An extension of multifactor analysis for face recognition based on submanifold learning

Optimum Subspace Learning and Error Correction for Tensors

Multifactor analysis based on factor-dependent geometry

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