Quantitative analysis of grouping processes

  • Arnon Amir
  • Michael Lindenbaum
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1064)


This paper presents a quantitative approach to grouping. A generic grouping method, which may be applied to many domains, is given, and an analysis of its expected grouping quality is done. The grouping method is divided into two parts: Constructing a graph representation of the geometric relations in the data set, and then finding the “best” partition of the graph into groups. Both stages are implemented using known statistical tools such as Wald's SPRT algorithm and the Maximum Likelihood criterion. The accompanying quantitative analysis shows some relations between the data quality, the reliability of the grouping cues and the computational efforts, to the expected grouping quality. To our best knowledge, such an analysis of a grouping process is given here for the first time. The synthesis of specific grouping algorithms is demonstrated for three different grouping tasks and domains. Experimental results show the ability of this generic approach to provide successful algorithm in specific domains.


Grouping Analysis Perceptual Grouping Performance Prediction Generic Grouping Algorithm Graph Clustering Maximum Likelihood Wald's SPRT 


  1. 1.
    Adelson, E. H., and Wang, J. Y. A. Representing moving images with layers. Tech. Rep. 279, M.I.T, May 1994.Google Scholar
  2. 2.
    Amir, A., and Lindenbaum, M. The construction and analysis of a generic grouping algorithm. Tech. Rep. CIS-9418, Technion, Israel, Nov. 1994.Google Scholar
  3. 3.
    Guy, G., and Medioni, G., Perceptual grouping using global saliency-enhancing operators. In ICPR-92 (1992), vol. I, pp. 99–103.Google Scholar
  4. 4.
    Herault, L., and Horaud, R., Figure-ground discrimination: A combinatorial optimization approach. PAMI 15, 9 (Sep 1993), 899–914.Google Scholar
  5. 5.
    Jacobs, D. W., and Chennubhotla, C. Finding structurally consistent motion correspondences. In ICPR-94, Jerusalem (1994), pp. 650–653.Google Scholar
  6. 6.
    Lowe, D. G. Perceptual Organization and Visual Recognition. Kluwer Academic Pub., 1985.Google Scholar
  7. 7.
    Sha'ashua, A., and Ullman, S. Grouping contours by iterated pairing network. Neural Information Processing Systems (NIPS) 3 (1990).Google Scholar
  8. 8.
    Shapiro, L. G., and Haralick, R. M., Decomposition of two-dimentional shapes by graph-theoretic clustering. PAMI 1, 1 (Jan. 1979), 10–20.Google Scholar
  9. 9.
    Vosselman, G. Relational Matching, third ed. Lect. Notes in CS. Springer, 1992.Google Scholar
  10. 10.
    Wald, A. Sequencial Analysis, third ed. Wiley Publications in Statistics. 1947(1952).Google Scholar
  11. 11.
    Wu, Z., and Leahy, R., An optimal graph theoretic approach to data clustering: Theory and its application to image segmentation. PAMI 15, 11 (Nov 1993), 1001–1113.Google Scholar
  12. 12.
    Zisserman, A., Mundy, J., Forsyth, D., and Liu, J. Class-based grouping in perspective images. In ICCV-95, MIT (1995), pp. 183–188.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Arnon Amir
    • 1
  • Michael Lindenbaum
    • 1
  1. 1.Computer Science DepartmentTechnionHaifaIsrael

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