Reiner Lenz, Pedro Latorre Carmona



In this paper we introduce the representation theory of the symmetric group~$ SPG$ as a tool to investigate the structure of the space of $RGB$-histograms. We show that the theory reveals that typical histogram spaces are highly structured and that these structures originate partly in group theoretically defined symmetries. The algorithms exploit this structure and constructs a PCA like decomposition without the need to construct correlation or covariance matrices and their eigenvectors. We implemented these algorithms and investigate their properties with the help of two real-world databases (one from an image provider and one from a image search engine company) containing over one million images.


  1. Chirikjian, G. S. and Kyatkin, A. B. (2000). Engineering Applications of noncommutative Harmonic Analysis: with emphasis on rotation and Motion Groups. CRC Press, Boca Raton, FL.
  2. Comaniciu, D., Ramesh, V., and Meer, P. (2003). Kernelbased object tracking. IEEE-TPAMI, 25:564-577.
  3. Cooley, J. W. and Tukey, J. W. (1965). An algorithm for machine calculation of complex fourier series. Mathematical Computations, 19:297-301.
  4. Diaconis, P. (1988). Group representation in probability and statistics. Inst. Math. Stat., Hayward, Calif.
  5. Fässler, A. and Stiefel, E. (1992). Group theoretical methods and their applications. Birkhäuser Boston.
  6. Fulton, W. and Harris, J. (1991). Representation Theory. Springer, New York.
  7. Geusebroek, J. M. (2006). Compact object descriptors from local colour invariant histograms. In Proc. British Machine Vision Conf..
  8. Hafner, J., Sawhney, H. S., Equitz, W., Flickner, M., and Niblack, W. (1995). Efficient Color Histogram indexing for quadratic form distance functions. IEEETPAMI, 17(7):729-736.
  9. . R. (1994). Group Theoretical Transforms in Image Processing. LNCS, Springer˜reile/LNCS413.
  10. Lenz, R. (1995). Investigation of receptive fields using representations of dihedral groups. J. Vis. Comm. Im. Rep.,6(3):209-227.
  11. Lenz, R. (2007). Crystal vision-applications of point groups in computer vision. Proc. ACCV 2007, volume 4844, of LNCS, page 744-753, Springer.
  12. Rockmore, D. (2004). Recent progress and applications in group ffts. In Byrnes, J. and Ostheimer, G., editors, Computational Noncommutative Algebra and applications. Kluwer.
  13. Serre, J. P. (1977). Linear representations of finite groups, Springer.
  14. Smeulders, A. W. M., Worring, M., Santini, S., Gupta, A., and R., J. (2000). Content based image retrieval at the end of the early years. IEEE TPAMI, 22:1349-1380.
  15. Sridhar, V., Nascimento, M. A., and Li, X. (2002). Regionbased image retrieval using multiple-features. In LNCS, 2314. Springer.
  16. Srivastava, A., Jermyn, I., and Joshi, S. (2007). Riemannian analysis of probability density functions with applications in vision. In 2007 IEEE CVPR'07, Minneapolis, MN.
  17. Swain, M. and Ballard, D. (1991). Color indexing. Int J Comput Vision, 7(1):11-32.
  18. Tran, L. V. and Lenz, R. (2005). Compact colour descriptors for colour-based image retrieval. Signal Processing, 85(2):233-246.
  19. Yoo, H. W., Jang, D. S., Jung, S. H., and Park, J. H. (2002). Visual information retrieval system via content-based approach. Pattern Recognition, 35:749-769.

Paper Citation

in Harvard Style

Lenz R. and Latorre Carmona P. (2009). TRANSFORM CODING OF RGB-HISTOGRAMS . In Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2009) ISBN 978-989-8111-69-2, pages 117-124. DOI: 10.5220/0001653501170124

in Bibtex Style

author={Reiner Lenz and Pedro Latorre Carmona},
booktitle={Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2009)},

in EndNote Style

JO - Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2009)
SN - 978-989-8111-69-2
AU - Lenz R.
AU - Latorre Carmona P.
PY - 2009
SP - 117
EP - 124
DO - 10.5220/0001653501170124