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Subspace Methods

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Computer Vision

Synonyms

Multiple similarity method

Related Concepts

Dimensionality Reduction; Principal Component Analysis (PCA)

Definition

Subspace analysis in computer vision is a generic name to describe a general framework for comparison and classification of subspaces. A typical approach in subspace analysis is the subspace method (SM) that classifies an input pattern vector into several classes based on the minimum distance or angle between the input pattern vector and each class subspace, where a class subspace corresponds to the distribution of pattern vectors of the class in high-dimensional vector space.

Background

Comparison and classification of subspaces has been one of the central problems in computer vision, where an image set of an object to be classified is compactly represented by a subspace in high-dimensional vector space.

The subspace method is one of the most effective classification method in subspace analysis, which was developed by two Japanese researchers, Watanabe and...

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References

  1. Oja E (1983) Subspace methods of pattern recognition. Research Studies Press, Letchworth

    Google Scholar 

  2. . Kurosawa Y (2007) The engineer's guide to the subspace method. In: ACCV 2007 workshop Subspace 2007, Tokyo, pp 1–8

    Google Scholar 

  3. Watanabe S, Lambert PF, Kulikowski CA, Buxton JL, Walker R (1967) Evaluation and selection of variables in pattern recognition. In: Tou J (ed) Computer and information sciences. Academic, New York

    Google Scholar 

  4. . Iijima T, Genchi H, Mori K (1973) A theory of character recognition by pattern matching method. In: Proceedings of 1st international conference on pattern recognition (ICPR), pp 50–56

    Google Scholar 

  5. Turk M, Pentland A (1991) Eigenfaces for recognition. J Cogn Neurosci 3:71–86

    Article  Google Scholar 

  6. Kittler J (1978) The subspace approach to pattern recognition. Prog Cybern Syst Res 3:92

    Google Scholar 

  7. Fukunaga K, Koontz W (1970) Application of the Karhunen-Loève expansion to feature selection and ordering. IEEE Trans Comp 19(4):311–318

    Article  MATH  Google Scholar 

  8. . Kohonen T, Nemeth G, Jalanko M, Riittinen H (1979) Spectral classification of phonemes by learning subspace methods. In: Proceedings of IEEE international conference on acoustics, speech, and signal processing (ICASSP1979), Washington, DC, vol 4, pp 97–100

    Google Scholar 

  9. Oja E, Kuusela M (1983) The ALSM algorithm – an improved subspace method of classification. Pattern recognition 16:421–427

    Article  Google Scholar 

  10. . Maeda E, Murase H (1999) Multi-category classification by kernel based nonlinear subspace method. In: Proceedings of IEEE international conference on acoustics, speech, and signal processing (ICASSP1999), Phoenix, vol 2, pp 1025–1028

    Google Scholar 

  11. Tsuda K (1999) Subspace classifier in the hilbert space. Pattern Recogn Lett 20:513–519

    Article  Google Scholar 

  12. . Maeda K, Watanabe S (1985) A pattern matching method with local structure. Trans IEICE J68-D:345–352 (in Japanese)

    Google Scholar 

  13. Hotelling H (1936) Relations between two sets of variates. Biometrika 28:321–377

    Article  MATH  Google Scholar 

  14. Chatelin F (1993) Eigenvalues of matrices (enlarged translation of the French publication with masson). Wiley, Chichester

    Google Scholar 

  15. . Fukui K, Yamaguchi O (2003) Face recognition using multi-viewpoint patterns for robot vision. In: 11th international symposium of robotics research (ISRR2003), Siena, pp 192–201

    Google Scholar 

  16. . Kawahara T, Nishiyama M, Kozakaya T, Yamaguchi O (2007) Face recognition based on whitening transformation of distribution of subspaces. ACCV 2007 workshops Subspace2007, Tokyo, pp 97–103

    Google Scholar 

  17. . Sakano H, Mukawa N (2000) Kernel mutual subspace method for robust facial image recognition. In: Fourth international conference on knowledge-based intelligent engineering systems & allied technologies (KES2000), Brighton, vol 1, pp 245–248

    Google Scholar 

  18. Wolf L, Shashua A (2003) Learning over sets using kernel principal angles. J Mach Learn Res 4: 913–931

    MathSciNet  Google Scholar 

  19. . Fukui K, Stenger B, Yamaguchi O (2006) A framework for 3D object recognition using the kernel constrained mutual subspace method. In: Proceedings of Asian conference on computer vision (ACCV2006), Hyderabad, pp 315–324

    Google Scholar 

  20. . Fukui K, Stenger B, Yamaguchi O (2007) The kernel orthogonal mutual subspace method and its application to 3D object recognition. In: Proceedings of Asian conference on computer vision (ACCV2007), Tokyo, pp 467–476

    Google Scholar 

  21. . Yamaguchi O, Fukui K, Maeda K (1998) Face recognition using temporal image sequence. In: Proceedings of IEEE international conference on automatic face and gesture recognition (FG), Nara, pp 318–323

    Google Scholar 

  22. Georghiades AS, Belhumeur PN, Kriegman DJ (2001) From few to many: illumination cone models for face recognition under variable lighting and pose. IEEE Trans Pattern Anal Mach Intell 23:643–660

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Japan

    Kazuhiro Fukui

Authors
  1. Kazuhiro Fukui
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Editor information

Editors and Affiliations

  1. Institute of Industrial Science, The University of Tokyo, Tokyo, Japan

    Katsushi Ikeuchi

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Fukui, K. (2014). Subspace Methods. In: Ikeuchi, K. (eds) Computer Vision. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-31439-6_708

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