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Hierarchical S(3)-Coding of RGB Histograms

  • Conference paper
Computer Vision, Imaging and Computer Graphics. Theory and Applications (VISIGRAPP 2009)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 68))

Abstract

In this paper we introduce the representation theory of the symmetric group S (3) as a tool to investigate the structure of the space of RGB-histograms and to construct fast transforms suitable for search in huge image databases. We show that the theory reveals that typical histogram spaces are highly structured. The algorithms exploit this structure and construct a PCA like decomposition without the need to construct correlation or covariance matrices and their eigenvectors. A hierarchical transform is applied to analyze the internal structure of these histogram spaces. We apply the algorithms to two real-world databases (one from an image provider and one from a image search engine company) containing over one million images.

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References

  1. Chirikjian, G.S., Kyatkin, A.B.: Engineering applications of noncommutative harmonic analysis: with emphasis on rotation and motion groups. CRC Press, Boca Raton (2000)

    Book  Google Scholar 

  2. Comaniciu, D., Ramesh, V., Meer, P.: Kernel-based object tracking. IEEE Trans. Pattern Analysis and Machine Intelligence 25, 564–577 (2003)

    Article  Google Scholar 

  3. Cooley, J.W., Tukey, J.W.: An algorithm for machine calculation of complex Fourier series. Mathematical Computations 19, 297–301 (1965)

    MATH  MathSciNet  Google Scholar 

  4. Diaconis, P.: Group representation in probability and statistics. Institute of Mathematical Statistics, Hayward, Calif. (1988)

    Google Scholar 

  5. Fässler, A., Stiefel, E.: Group theoretical methods and their applications. Birkhäuser, Basel (1992)

    MATH  Google Scholar 

  6. Fulton, W., Harris, J.: Representation Theory. Springer, Heidelberg (1991)

    MATH  Google Scholar 

  7. Geusebroek, J.M.: Compact object descriptors from local colour invariant histograms. In: Proc. British Machine Vision Conference, BMVC (2006)

    Google Scholar 

  8. Hafner, J., Sawhney, H.S., Equitz, W., Flickner, M., Niblack, W.: Efficient color histogram indexing for quadratic form distance functions. IEEE Trans. Pattern Analysis and Machine Intelligence 17(7), 729–736 (1995)

    Article  Google Scholar 

  9. Holmes, R.B.: Mathematical foundations of signal processing. SIAM Review 21(3), 361–388 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  10. Lenz, R.: Group Theoretical Transforms in Image Processing. Springer, Heidelberg (1994)

    Google Scholar 

  11. Lenz, R.: Investigation of receptive fields using representations of dihedral groups. J. Visual Communication and Image Representation 6(3), 209–227 (1995)

    Article  Google Scholar 

  12. Lenz, R.: Crystal vision-applications of point groups in computer vision. In: Yagi, Y., Kang, S.B., Kweon, I.S., Zha, H. (eds.) ACCV 2007, Part II. LNCS, vol. 4844, pp. 744–753. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. Rockmore, D.: Recent progress and applications in group FFT’s. In: Computational noncommutative algebra and applications. Kluwer, Dordrecht (2004)

    Google Scholar 

  14. Serre, J.P.: Linear representations of finite groups. Springer, Heidelberg (1977)

    MATH  Google Scholar 

  15. Smeulders, A.W.M., Worring, M., Santini, S., Gupta, A., Jain, R.: Content based image retrieval at the end of the early years. IEEE Trans. Pattern Analysis and Machine Intelligence 22, 1349–1380 (2000)

    Article  Google Scholar 

  16. Sridhar, V., Nascimento, M.A., Li, X.: Region-based image retrieval using multiple-features. In: Chang, S.-K., Chen, Z., Lee, S.-Y. (eds.) VISUAL 2002. LNCS, vol. 2314, pp. 61–75. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  17. Srivastava, A., Jermyn, I., Joshi, S.: Riemannian analysis of probability density functions with applications in vision. In: IEEE Conf. Comp. Vision and Pattern Recognition, Minneapolis, MN, pp. 1–8 (2007)

    Google Scholar 

  18. Swain, M.J., Ballard, D.H.: Color indexing. Int. J. Comp. Vision 7(1), 11–32 (1991)

    Article  Google Scholar 

  19. Yoo, H.W., Jang, D.S., Jung, S.H., Park, J.H.: Visual information retrieval system via content-based approach. Pattern Recognition 35, 749–769 (2002)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. Science and Engineering, Linköping University, SE-60174, Norrköping, Sweden

    Reiner Lenz

  2. Dept. Lenguajes y Sistemas Informáticos, Jaume I University, Campus Riu Sec s/n, 12071, Castellón, Spain

    Pedro Latorre Carmona

Authors
  1. Reiner Lenz
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  2. Pedro Latorre Carmona
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Editor information

Editors and Affiliations

  1. INSTICC, Avenida D. Manuel I, 2910, Setúbal, Portugal

    AlpeshKumar Ranchordas

  2. Departamento de Engenharia Informática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001, Lisboa, Portugal,

    João Madeiras Pereira

  3. Institute for Systems and Robotics, Department of Electrical and Computer Engineering Polo II, University of Coimbra, 3030-290, Coimbra, Portugal

    Hélder J. Araújo

  4. Departamento de Engenharia Mecânica e Gestão Industrial, Rua Dr. Roberto Frias, s/n, 4200-465, Porto, Portugal

    João Manuel R. S. Tavares

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Lenz, R., Latorre Carmona, P. (2010). Hierarchical S(3)-Coding of RGB Histograms. In: Ranchordas, A., Pereira, J.M., Araújo, H.J., Tavares, J.M.R.S. (eds) Computer Vision, Imaging and Computer Graphics. Theory and Applications. VISIGRAPP 2009. Communications in Computer and Information Science, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11840-1_14

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  • DOI: https://doi.org/10.1007/978-3-642-11840-1_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11839-5

  • Online ISBN: 978-3-642-11840-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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