Skip to main content
SpringerLink
Log in

Recognition of dependent objects based on acyclic Markov models

  • Plenary Papers
  • Published:
Pattern Recognition and Image Analysis Aims and scope Submit manuscript

Abstract

The problem to recognize objects that form an array of interrelated data is investigated. In the problem of machine learning, the array components belong to some class of a finite set. In this paper the interrelationship of array elements is presented by its adjacency graph. An efficient noniterative recognition algorithm for restoring an a posteriori marginal distributions of hidden classes for array elements is developed for a treelike adjacency graph. This algorithm modifies for each array element the hidden class distribution obtained as a result of learning for independent objects. Usually arbitrary graphs for real data contain cycles, for example, the rectangular adjacency lattice of points for 2D raster images or 3D seismic data. The treelike approximation of such graphs inevitably strongly distorts the interrelations between array elements. In the present paper, the reduced set of interrelations between array elements is balanced by an extended set of acyclic graphs themselves. By the example of the segmentation problem for texture raster images, we investigate a set of acyclic graphs and present the experimental results.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. R. Rabiner, “A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition,” Proc. IEEE 77(2), 257–286 (1977).

    Article  Google Scholar 

  2. S. Geman and D. Geman, “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,” IEEE Trans. PAMI 6 721–741 (1984).

    Article  MATH  Google Scholar 

  3. M. I. Schlesinger and B. Flach, “Some Solvable Subclasses of Structural Recognition Problems,” in Proc. Czech Pattern Recognition Workshop (Prague, 2000), pp. 55–62.

  4. S. Z. Li, Markov Random Field Modeling in Image Analysis (Springer-Verlag, London, 2009).

    MATH  Google Scholar 

  5. V. V. Mottl, S. D. Dvoenko, V. B. Levyant, and I. B. Muchnik, “Pattern Recognition in Spatial Data: A New Method of Seismic Explorations for Oil and Gas in Crystalline Basement Rocks,” in Proc. 15th ICPR’2000 (Barcelona, 2000), Vol. 3, pp. 210–213.

    Google Scholar 

  6. V. V. Mottl, S. D. Dvoenko, and A. V. Kopylov, “Pattern Recognition in Interrelated Data: The Problem, Fundamental Assumptions, Recognition Algorithms,” in Proc. 17th ICPR (Cambridge, 2004), Vol. 1, pp. 188–191.

    Google Scholar 

  7. S. D. Dvoenko, A. V. Kopylov, and V. V. Mottl, “The Problem of Pattern Recognition in Arrays of Interconnected Objects. Statement of the Recognition Problem and Basic Assumptions,” Automat. Remote Control 65(1), 127–141 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  8. S. D. Dvoenko, A. V. Kopylov, and V. V. Mottl, “A Problem of Pattern Recognition in Arrays of Interrelated Objects. Recognition Algorithm,” Automat. Remote Control 66(12), 2019–2032 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  9. V. Kolmogorov, “Convergent Tree-Reweighed Message Passing for Energy Minimization,” IEEE Trans. PAMI 10, 1568–1583 (2006).

    Article  Google Scholar 

  10. R. Szeliski, R. Zabih, D. Scharstein, O. Veksler, V. Kol- mogorov, A. Agarwala, M. Tappen, and C. Rother, “A Comparative Study of Energy Minimization Methods for Markov Random Fields with Smoothness-Based Priors,” IEEE Trans. PAMI 6, 1068–1080 (2007).

    Google Scholar 

  11. M. J. Wainwright and M. I. Jordan, “Graphical Models, Exponential Families, and Variational Inference,” Foundations Trends Mach. Learn. 1, 1–305 (2008).

    Article  MATH  Google Scholar 

  12. J. G. Kemeny and J. L. Snell, Finite Markov Chains (Springer-Verlag, New York, 1983).

    MATH  Google Scholar 

  13. W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1970), Vol. 1.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tula State University, Tula, Russia

    S. D. Dvoenko

Authors
  1. S. D. Dvoenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. D. Dvoenko.

Additional information

Sergey Danilovich Dvoenko. Graduated from the postgraduate courses of the Institute of Control Science, Russian Academy of Sciences. Received candidate’s degree in 1992. He received the associated professor designation in 1998. Graduated from the doctoral courses of Tula State University and received doctor’s degree in 2002 at the Dorodnitsyn Computing Centre, Russian Academy of Sciences. Professor at Tula State University (Automation and Remote Control Department). Member of the Russian organization “Association for Pattern Recognition and Image Analysis.” His scientific interests include the following fields: machine learning and pattern recognition, cluster-analysis and data mining, image processing, hidden Markov models and fields in applied problems.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dvoenko, S.D. Recognition of dependent objects based on acyclic Markov models. Pattern Recognit. Image Anal. 22, 28–38 (2012). https://doi.org/10.1134/S1054661812010130

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1054661812010130

Keywords

Search

Navigation