Advertisement

Computationally efficient eigenspace decomposition of correlated images characterized by three parameters

  • K. Saitwal
  • A. A. MaciejewskiEmail author
  • R. G. Roberts
Theoretical Advances

Abstract

Eigendecomposition is a common technique that is performed on sets of correlated images in a number of pattern recognition applications including object detection and pose estimation. However, many fast eigendecomposition algorithms rely on correlated images that are, at least implicitly, characterized by only one parameter, frequently time, for their computational efficacy. In some applications, e.g., three-dimensional pose estimation, images are correlated along multiple parameters and no natural one-dimensional ordering exists. In this work, a fast eigendecomposition algorithm that exploits the “temporal” correlation within image data sets characterized by one parameter is extended to improve the computational efficiency of computing the eigendecomposition for image data sets characterized by three parameters. The algorithm is implemented and evaluated using three-dimensional pose estimation as an example application. Its accuracy and computational efficiency are compared to that of the original algorithm applied to one-dimensional pose estimation.

Keywords

Eigenspace Singular value decomposition Computational complexity Image sequences Three-dimensional correlations Computer vision 

Notes

Acknowledgments

This work was supported in part by the National Imagery and Mapping Agency under contract no. NMA201-00-1-1003, through collaborative participation in the Robotics Consortium sponsored by the US Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0012, and the Missile Defense Agency under the contract no. HQ0006-05-C-0035. Approved for Public Release 07-MDA-2783 (26 SEPT 07). The US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the US Government. A preliminary version of portions of this work was presented at the IEEE Southwest Symposium on Image Analysis and Interpretation held at Denver, CO, USA, March 26–28, 2006.

References

  1. 1.
    Fukunaga K (1990) Introduction to statistical pattern recognition. Academic Press, LondonzbMATHGoogle Scholar
  2. 2.
    Martinez AM, Kak AC (2001) PCA versus LDA. IEEE Trans PAMI 23(2):228–233Google Scholar
  3. 3.
    Sirovich L, Kirby M (1987) Low-dimensional procedure for the characterization of human faces. J Opt Soc Am 4(3):519–524CrossRefGoogle Scholar
  4. 4.
    Kirby M, Sirovich L (1990) Application of the Karhunen–Loeve procedure for the characterization of human faces. IEEE Trans PAMI 12(1):103–108Google Scholar
  5. 5.
    Turk M, Pentland A (1991) Eigenfaces for recognition. J Cogn Neurosci 3(1):71–86CrossRefGoogle Scholar
  6. 6.
    Belhumeur PN, Hespanha JP, Kriegman DJ (1997) Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans PAMI 19(7):711–720Google Scholar
  7. 7.
    Brunelli R, Poggio T (1993) Face recognition: features versus templates. IEEE Trans PAMI 15(10):1042–1052Google Scholar
  8. 8.
    Pentland A, Moghaddam B, Starner T (1994) View-based and modular eigenspaces for face recognition. In: Proc of the IEEE comp soc conf on computer vision and pattern recognition. Seattle, WA, USA, Jun 21–23, pp. 84–91Google Scholar
  9. 9.
    Yang MH, Kriegman DJ, Ahuja N (2002) Detecting faces in images: a survey. IEEE Trans PAMI 24(1):34–58Google Scholar
  10. 10.
    Murase H, Sakai R (1996) Moving object recognition in eigenspace representation: gait analysis and lip reading. Pattern Recognit Lett 17(2):155–162CrossRefGoogle Scholar
  11. 11.
    Chiou G, Hwang JN (1997) Lipreading from color video. IEEE Trans Image Process 6(8):1192–1195CrossRefGoogle Scholar
  12. 12.
    Murase H, Nayar SK (1994) Illumination planning for object recognition using parametric eigenspaces. IEEE Trans PAMI 16(12):1219–1227Google Scholar
  13. 13.
    Huang CY, Camps OI, Kanungo T (1997) Object recognition using appearance-based parts and relations. In: Proc of the IEEE comp soc conf on computer vision and pattern recognition. San Juan, PR, USA, 17–19 June 1997, pp 877–883Google Scholar
  14. 14.
    Campbell RJ, Flynn PJ (1999) Eigenshapes for 3D object recognition in range data. In: Proc of the IEEE comp soc conf on computer vision and pattern recognition. Fort Collins, CO, USA, 23–25 June 1999, pp 505–510Google Scholar
  15. 15.
    Jogan M, Leonardis A (2000) Robust localization using eigenspace of spinning-images. In: Proc of the IEEE workshop on omnidirectional vision. Hilton Head Island, South Carolina, USA, pp 37–44Google Scholar
  16. 16.
    Yoshimura S, Kanade T (1994) Fast template matching based on the normalized correlation by using multiresolution eigenimages. In: 1994 IEEE workshop on motion of non-rigid and articulated objects. Austin, Texas, 11–12 November 1994, pp 83–88Google Scholar
  17. 17.
    Winkeler J, Manjunath BS, Chandrasekaran S (1999) Subset selection for active object recognition. In: Proc of the IEEE comp soc conf on computer vision and pattern recognition. Fort Collins, Colorado, USA, 23–25, pp 511–516Google Scholar
  18. 18.
    Nayar SK, Murase H, Nene SA (1994) Learning, positioning, and tracking visual appearance. In: Proc of the IEEE int conf on robot automat. San Diego, CA, USA, 8–13 May 1994, pp 3237–3246Google Scholar
  19. 19.
    Black MJ, Jepson AD (1998) Eigentracking: robust matching and tracking of articulated objects using a view-based representation. Int J Comput Vis 26(1):63–84CrossRefGoogle Scholar
  20. 20.
    Murase H, Nayar SK (1995) Visual learning and recognition of 3-D objects from appearance. Int J Comput Vis 14(1):5–24CrossRefGoogle Scholar
  21. 21.
    Murase H, Nayar SK (1997) Detection of 3D objects in cluttered scenes using hierarchical eigenspace. Pattern Recognit Lett 18(4): 375–384CrossRefGoogle Scholar
  22. 22.
    Nayar SK, Nene SA, Murase H (1996) Subspace method for robot vision. IEEE Trans Robot Automat 12(5):750–758CrossRefGoogle Scholar
  23. 23.
    Moghaddam B, Pentland A (1997) Probabilistic visual learning for object representation. IEEE Trans PAMI 19(7):696–710Google Scholar
  24. 24.
    Stewart GW (1973) Introduction to matrix computation. Academic, New YorkGoogle Scholar
  25. 25.
    Shlien S (1982) A method for computing the partial singular value decomposition. IEEE Trans PAMI 4(6):671–676zbMATHGoogle Scholar
  26. 26.
    Haimi-Cohen R, Cohen A (1987) Gradient-type algorithms for partial singular value decomposition. IEEE Trans PAMI 9(1):137–142zbMATHGoogle Scholar
  27. 27.
    Yang X, Sarkar TK, Arvas E (1089) A survey of conjugate gradient algorithms for solution of extreme eigen-problems for a symmetric matrix. IEEE Trans ASSP 37(10):1550–1556CrossRefMathSciNetGoogle Scholar
  28. 28.
    Vogel CR, Wade JG (1994) Iterative SVD-based methods for ill-posed problems. SIAM J Sci Comput 15(3):736–754zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Murakami H, Kumar V (1982) Efficient calculation of primary images from a set of images. IEEE Trans PAMI 4(5):511–515Google Scholar
  30. 30.
    Chandrasekaran S, Manjunath B, Wang Y, Winkeler J, Zhang H (1997) An eigenspace update algorithm for image analysis. CVGIP: graphic models and image processing 59(5):321–332CrossRefGoogle Scholar
  31. 31.
    Murase H, Lindenbaum M (1995) Partial eigenvalue decomposition of large images using the spatial temporal adaptive method. IEEE Trans Image Process 4(5):620–629CrossRefGoogle Scholar
  32. 32.
    Chang CY, Maciejewski AA, Balakrishnan V (2000) Fast eigenspace decomposition of correlated images. IEEE Trans Image Process 9(11):1937–1949zbMATHCrossRefMathSciNetGoogle Scholar
  33. 33.
    Saitwal K, Maciejewski AA, Roberts RG, Draper BA (2006) Using the low-resolution properties of correlated images to improve the computational efficiency of eigenspace decomposition. IEEE Trans Image Process 15(8):2376–2387CrossRefGoogle Scholar
  34. 34.
    Davis PJ (1979) Circulant matrices. Wiley, New YorkzbMATHGoogle Scholar
  35. 35.
    Saitwal K (2006) Fast eigenspace decomposition of correlated images using their spatial and temporal properties. PhD Dissertation, Colorado State University, USAGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2008

Authors and Affiliations

  • K. Saitwal
    • 1
  • A. A. Maciejewski
    • 2
    Email author
  • R. G. Roberts
    • 3
  1. 1.Behavioral Recognition Systems, Inc.HoustonUSA
  2. 2.Department of Electrical and Computer EngineeringColorado State UniversityFort CollinsUSA
  3. 3.Department of Electrical and Computer EngineeringFlorida A & M—Florida State UniversityTallahasseeUSA

Personalised recommendations