Skip to main content

Visual Pattern Recognition Framework Based on the Best Rank Tensor Decomposition

  • Chapter
  • First Online:
Developments in Medical Image Processing and Computational Vision

Part of the book series: Lecture Notes in Computational Vision and Biomechanics ((LNCVB,volume 19))

Abstract

In this paper a framework for visual patterns recognition of higher dimensionality is discussed. In the training stage, the input prototype patterns are used to construct a multidimensional array—a tensor—whose each dimension corresponds to a different dimension of the input data. This tensor is then decomposed into a lower-dimensional subspace based on the best rank tensor decomposition. Such decomposition allows extraction of the lower-dimensional features which well represent a given training class and exhibit high discriminative properties among different pattern classes. In the testing stage, a pattern is projected onto the computed tensor subspaces and a best fitted class is provided. The method presented in this paper, as well as the software platform, is an extension of our previous work. The conducted experiments on groups of visual patterns show high accuracy and fast response time.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Chen J, Saad Y (2009) On the tensor svd and the optimal low rank orthogonal approximation of tensors. SIAM J Matrix Anal Appl 30(4):1709–1734

    Article  MATH  MathSciNet  Google Scholar 

  2. Cichocki A, Zdunek R, Amari S (2008) Nonnegative matrix and tensor factorization. IEEE Signal Process Mag 25(1):142–145

    Article  Google Scholar 

  3. Cichocki A, Zdunek R, Phan AH, Amari S-I (2009) Nonnegative matrix and tensor factorizations. Applications to exploratory multi-way data analysis and blind source separation. Wiley, Chichester

    Google Scholar 

  4. Cyganek B (2013) Pattern recognition framework based on the best rank-( R 1, R 2,…, R K ) tensor approximation. In: Computational vision and medical image processing IV: proceedings of VipIMAGE 2013—IV ECCOMAS thematic conference on Computational vision and medical image processing, pp 301–306

    Google Scholar 

  5. Cyganek B (2013) Object detection and recognition in digital images: theory and practice. Wiley

    Google Scholar 

  6. Cyganek B, Malisz P (2010) Dental implant examination based on the log-polar matching of the maxillary radiograph images in the anisotropic scale space. IEEE Engineering in Medicine and Biology Conference, EMBC 2010, Buenos Aires, Argentina, pp 3093–3096

    Google Scholar 

  7. DeRecLib (2013) http://www.wiley.com/go/cyganekobject

  8. Duda RO, Hart PE, Stork DG (2001) Pattern classification.Wiley, NewYork

    MATH  Google Scholar 

  9. https://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html

  10. Tamara GK, Brett WB (2009) Tensor decompositions and applications. SIAM Rev 51(3):455–500

    Google Scholar 

  11. Lathauwer de L (1997) Signal processing based on multilinear algebra. PhD dissertation, Katholieke Universiteit Leuven

    Google Scholar 

  12. Lathauwer de L, Moor de B, Vandewalle J (2000) On the best rank-1 and rank-( R 1, R 2, …, R N) approximation of higher-order tensors. SIAM J Matrix Anal Appl 21(4):1324–1342

    Article  MATH  MathSciNet  Google Scholar 

  13. Muti D, Bourennane S (2007) Survey on tensor signal algebraic filtering. Signal Process 87:237–249

    Article  MATH  Google Scholar 

  14. Savas B, Eldén L (2007) Handwritten digit classification using higher order singular value decomposition. Pattern Recognit 40(3):993–1003

    Article  MATH  Google Scholar 

  15. Wang H, Ahuja N (2004) Compact representation of multidimensional data using tensro rankone decomposition. In: Proceedings of the 17th international conference on pattern recognition, Vol 1, 4pp 4–47

    Google Scholar 

  16. Wang H, Ahuja N (2008) A tensor approximation approach to dimensionality reduction. Int J Comput Vision 76(3):217–229

    Article  Google Scholar 

Download references

Acknowledgements

The financial support from the Polish National Science Centre NCN in the year 2014, contract no. DEC-2011/01/B/ST6/01994, is greatly acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B. Cyganek .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Cyganek, B. (2015). Visual Pattern Recognition Framework Based on the Best Rank Tensor Decomposition. In: Tavares, J., Natal Jorge, R. (eds) Developments in Medical Image Processing and Computational Vision. Lecture Notes in Computational Vision and Biomechanics, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-13407-9_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-13407-9_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13406-2

  • Online ISBN: 978-3-319-13407-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics