The DOI matches its Crossref record; 12 of the 12 references it cites were found in a registry or an index.
Multilinear subspace analysis of image ensembles
Abstract
Multilinear algebra, the algebra of higher-order tensors, offers a potent mathematical framework for analyzing ensembles of images resulting from the interaction of any number of underlying factors. We present a dimensionality reduction algorithm that enables subspace analysis within the multilinear framework. This N-mode orthogonal iteration algorithm is based on a tensor decomposition known as the N-mode SVD, the natural extension to tensors of the conventional matrix singular value decomposition (SVD). We demonstrate the power of multilinear subspace analysis in the context of facial image ensembles, where the relevant factors include different faces, expressions, viewpoints, and illuminations. In prior work we showed that our multilinear representation, called TensorFaces, yields superior facial recognition rates relative to standard, linear (PCA/eigenfaces) approaches. We demonstrate factor-specific dimensionality reduction of facial image ensembles. For example, we can suppress illumination effects (shadows, highlights) while preserving detailed facial features, yielding a low perceptual error.
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Cites
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Some Mathematical Notes on Three-Mode Factor Analysis
Tucker, L. R. (1966) · Psychometrika · doi:10.1007/bf02289464 · Cited by 3,492
Human and machine recognition of faces: a survey
Chellappa, R., Wilson, C. L., & Sirohey, S. (1995) · Proceedings of the IEEE · doi:10.1109/5.381842 · Cited by 2,494
Low-dimensional procedure for the characterization of human faces
Sirovich, L., & Kirby, M. (1987) · Journal of the Optical Society of America A · doi:10.1364/josaa.4.000519 · Cited by 2,311
Visual learning and recognition of 3-d objects from appearance
Murase, H., & Nayar, S. K. (1995) · International Journal of Computer Vision · doi:10.1007/bf01421486 · Cited by 1,881
On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors
De Lathauwer, L., De Moor, B., & Vandewalle, J. (2000) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479898346995 · Cited by 1,567
Separating Style and Content with Bilinear Models
Tenenbaum, J. B., & Freeman, W. T. (2000) · Neural Computation · doi:10.1162/089976600300015349 · Cited by 840 · cited 1×
“It subsumes as special cases the simple linear (1-factor) analysis known as principal components analysis (PCA), as well as bilinear (2-factor) analysis [7].”
MethodMultilinear Analysis of Image Ensembles: TensorFaces
Vasilescu, M. A. O., & Terzopoulos, D. (2002) · Lecture Notes in Computer Science · doi:10.1007/3-540-47969-4_30 · Cited by 836
Self-citationPrincipal Component Analysis of Three-Mode Data by Means of Alternating Least Squares Algorithms
Kroonenberg, P. M., & de Leeuw, J. (1980) · Psychometrika · doi:10.1007/bf02293599 · Cited by 724
Teo, P. C., & Heeger, D. J. (2002) · Proceedings of 1st International Conference on Image Processing · doi:10.1109/icip.1994.413502 · Cited by 471
Cited by
Tensor Decompositions and Applications
Kolda, T. G., & Bader, B. W. (2009) · SIAM Review · doi:10.1137/07070111x · Cited by 10,301
A Survey of Face Recognition Techniques
Jafri, R., & Arabnia, H. R. (2009) · Journal of Information Processing Systems · doi:10.3745/jips.2009.5.2.041 · Cited by 677
Unsupervised Multiway Data Analysis: A Literature Survey
Acar, E., & Yener, B. (2009) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2008.112 · Cited by 434
Audio-driven facial animation by joint end-to-end learning of pose and emotion
Karras, T., Aila, T., Laine, S., Herva, A., & Lehtinen, J. (2017) · ACM Transactions on Graphics · doi:10.1145/3072959.3073658 · Cited by 434
Robust Low-Rank Tensor Recovery: Models and Algorithms
Goldfarb, D., & Qin, Z. (. (2014) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/130905010 · Cited by 408
Metadata
- Authors
- Vasilescu, M. A. O., & Terzopoulos, D.
- Venue
- 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings.
- Publisher
- IEEE Comput. Soc
- Published
- 2003-12-22
- Volume
- 2
- Pages
- II-93-9
- ISSN
- 1063-6919 (ISSN-L)
- OpenAlex
- W2160551639
- Cited by
- 375
- References
- 12
- FWCI
- 7.83
- Type
- conference paper
- Language
- en
- Open access
- closed
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