SMAPIP


Grant-in-Aid for Scientific Research on Priority Areas
``Statistical Mechanical Approach to Probabilistic Information Processing''

Research Project C02:
Design of Adaptive Filters for Image Processing
by means of Markov Random Field Models

[Japanese Version]

Project Leader:
Kazuyuki Takana

Graduate School of Information Sciences, Tohoku University (Japan)

Address, Phone, E-mail address:

  • Address: Graduate School of Information Sciences, Tohoku University,
    Aramaki-Aza-Aoba 6-3-09, Aoba-ku, Sendai 980-8579, Japan
  • Phone: +81-22-795-5885 E-mail: kazu [at mark] smapip.is.tohoku.ac.jp
  • Office: Room No.403 in Research Building No.3 - Electrical, Information and Physics Engineering, Aobayama Campus, Tohoku University


    1. Summary of Research Project:

        We design probabilistic image processing systems by using Markov random field models and statistical-mechanical approximations, for example, the advanced mean field methods, the cluster variation method and so on. Particularly, we propose some novel adaptive image processing filters by introducing prior probabilities with locally non-uniform correlations along pixels. Practical algorithms are contructed by using belief propagations, for example, sum-product algorithm, cluster variation method and so on. (Detail)

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      Recent Publications and Presentations:

      1. Kazuyuki Tanaka: Statistical Learning Procedure in Loopy Belief Propagation for Probabilistic Image Processing, Proceedings of International Conference on Computational Intelligence for Modelling, Control and Automation (November 28-30, 2005, Vienna, Austria), to appear (Paper: PDF, Postscript).
      2. Kazuyuki Tanaka: Linear Response Formula in Generalized Belief Propagation for Probabilistic Inference, Proceedings of International Conference on Computational Intelligence for Modelling, Control and Automation (November 28-30, 2005, Vienna, Austria), to appear (Paper: PDF, Postscript).
      3. Muneki Yasuda, Jun Ohkubo and Kazuyuki Tanaka: Digital Images Inpainting based on Markov Random Field, Proceedings of International Conference on Computational Intelligence for Modelling, Control and Automation (November 28-30, 2005, Vienna, Austria), to appear.
      4. Jun Ohkubo and Kazuyuki Tanaka: Preferential Urn Model on a Random Network, Proceedings of International Conference on Computational Intelligence for Modelling, Control and Automation (November 28-30, 2005, Vienna, Austria), to appear.
      5. Kazuyuki Tanaka: Bayesian Network and Probabilistic Image Processing ---Statistical Aspect of Belief Propagation Method---, Mathematical Aspects of Image Processing and Computer Vision 2005 (MAIPCV2005), (18 November, 2005, Hokkaidou University, Japan) (Extended Abstract: PDF, Postscript, Presentation Slide: PDF, Power Point).
      6. Kazuyuki Tanaka: Probabilistic Image Processing and Bayesian Network, Computational Intelligence Seminar in Japan (CISJ2005), (8 November, 2005, Waseda University, Japan) (Extended Abstract: PDF, Postscript, Presentation Slide: PDF, Power Point).
      7. Jun Ohkubo, Muneki Yasuda and Kazuyuki Tanaka: Statistical-mechanical Iterative Algorithms on Complex Networks, Physical Review E, Vol.72, No.4 (October 2005), Article No.046135, pp1-8. (PDF).
      8. Jun Ohkubo, Kazuyuki Tanaka and Tsuyoshi Horiguchi: Generation of Complex Bipartite Graphs by Using a Preferential Rewiring Process, Physical Review E, Vol.72, No.3 (September 2005), Article No.036120, pp.1-10. (PDF)
      9. Kazuyuki Tanaka: Graphical model and generalized belief propagation in probabilistic image processing, Statistical Physics of Disordered Systems and Its Applications (SPDSA2005), (6 September, 2005, Accademia dei Lincei, Roma, Italy) (Presentation Slide: Power Point, PDF).
      10. Kazuyuki Tanaka: Probabilistic image processing and Bayesian network, Randomness and Computation, Joint Workshop ``New Horizons in Computing'' and ``Statistical Mechanical Approach to Probabilistic Information Processing'', (18-21 July, 2005, Sendai International Center, Sendai, Japan). (Extended Abstract: PDF, Postscript, Tutorial Lecture Note: PDF, Postscript, Presentation Slide: Power Point)


      Related Reviews (in English)

      1. Kazuyuki Tanaka: Statistical-mechanical approach to image processing (Topical Review), Journal of Physics A: Mathematical and General, vol.35, no.37 (September 2002) pp.R81-R150.

      Related Reviews (in Japanese)

      1. Kazuyuki Tanaka: Statistical-Mechancal Method in Image Restoration, Butsuri, Vol.54, No.1 (January 1999) pp.25-33 (Published by The Physical Society of Japan, in Japanese).
      2. Kazuyuki Tanaka: Image Restiration and Statistical Physics, Special Issue ``Statistical-mechanical Approach to Intelligent Information Processing'', Mathematical Sciences, No.438 (December 1999) pp.20-27 (in Japanese).
      3. Kazuyuki Tanaka and Yoshiyuki Kabashima: Large-Scale Statistical Model and Information Processing ---Science of Material and Art of Information Processing,Journal of the Society of Instrument and Control Engineerings, Vol.42, No.8 (August 2003), pp.622-625 (in Japanese).
      4. Kazuyuki Tanaka: Probabilistic Image Processing Algorithm by means of Statistical Mechanical Method ---Belief Propagation and Statistical Mechanics,Journal of the Society of Instrument and Control Engineerings, Vol.42, No.8 (August 2003), pp.631-636 (in Japanese).
      5. Kazuyuki Tanaka: Probabilistic Models and Image Analysis ---Novel Computational Paradigm based on Fluctuation, Mathematical Sciences No.489 (March 2004), pp.15-21 (in Japanese).
      6. Kazuyuki Tanaka, Yoshiyuki Kabashima and Toshiyuki Tanaka: Probabilistic Information Processing ---New Developments in Information Processing by Probabilistic Models and Statistical Mechanics---, Mathematical Sciences No.507 (September 2005), pp.77-83 (in Japanese).
      7. Kazuyuki Tanaka: Mathematics of Bayesian Network and Probabilistic Inference, Mathematical Sciences No.507 (September 2005), pp.77-83 (in Japanese).
      8. Kazuyuki Tanaka, Yoshiyuki Kabashima and Toshiyuki Tanaka: Introduction: New Research Paradigm of Probabilistic Inference and Statistical Learning, The Journal of the Institute of Electronics, Information and Communication Engineerings, Vol.88, No.9 (September 2005), pp.696-697.
      9. Kazuyuki Tanaka: Probabilistic Inference and Estimation in Large-scale Random Fields, The Journal of the Institute of Electronics, Information and Communication Engineerings, Vol.88, No.9 (September 2005), pp.698-702.

      Related Papers in Journals

      1. Kazuyuki Tanaka and Tohru Morita: Cluster Variation Method and Image Restoration Problem. Physics Letters A, Vol.203, No.2-3 (July 1995) pp.122-128.
      2. Tohru Morita and Kazuyuki Tanaka: Determination of Parameters in an Image Recovery by Statistical-mechanical Means. Physica A, Vol.223, No.1-2 (1996) pp.244-262.
      3. Kazuyuki Tanaka, Mikako Ichioka, Tohru Morita: Statistical-Mechanical Iterative Method in Image Restoration, IEICE Transactions (A), Vol.J80-A, No.1 (January 1997) pp.260-268 ( PDF, in Japanese).
      4. Kazuyuki Tanaka and Tohru Morita: Statistical-Mechanical Iterative Algorithm for Image Restoration of a Gray Level Image, IEICE Transactions (A), Vol.J80-A, No.6 (June 1997) pp.1033-1037 ( PDF, in Japanese).
      5. Kazuyuki Tanaka and Tsuyoshi Horiguchi: Quantum Statistical-Mechanical Iterative Method in Image Restoration, IEICE Transactions (A), Vol.J80-A, No.12 (December 1997) pp.2117-2126 ( PDF (in Japanese)); translated in Electronics and Communications in Japan, Part 3: Fundamental Electronic Science, Vol.83, No.3 (March 2000) pp.84-94 ( PDF in English).
      6. Tohru Morita and Kazuyuki Tanaka: Cluster ZTP in the Recovery of an Image. Pattern Recognition Letters, Vol.18, No.14 (1997), pp.1479-1493.
      7. Kazuyuki Tanaka: Maximum Posterior Marginal Estimate in Statistical Method for Image Restoration, IEICE Transactions (A), Vol.J82-A, No.10 (October 1999), pp.1679-1684. ( PDF, in Japanese),
      8. Kazuyuki Tanaka: Theoretical Study of Hyperparameter Estimation by Maximization of Marginal Likelihood in Image Restoration by means of Cluster Variation Method, IEICE Transactions (A), Vol.J83-A, No.10 (October 2000), pp.1148-1160 ( PDF, in Japanese); translated in Electronics and Communications in Japan, Part 3: Fundamental Electronic Science, Vol.85, No.7 (July 2002) pp.50-62 ( PDF in English).
      9. Kazuyuki Tanaka: Maximum Marginal Likelihood Estimation and Constrained Optimization in Image Restoration, Transactions of Japanese Society for Artificial Intelligence, Vol.16, No.2 (March 2001), pp.246-258.
      10. Kazuyuki Tanaka: Staistical-mechanical Iterative Algorithm by means of Cluster Variation Method in Compound Gauss-Markov Random Field Model, Transactions of Japanese Society for Artificial Intelligence, Vol.16, No. 2 (March 2001), pp.259-267.
      11. Kazuyuki Tanaka: Image Restorations by using Compound Gauss-Markov Random Field Model with Quantumized Line Fields, IEICE Transactions (D-II), Vol.J84-D-II, No.4 (April 2001), pp.737-743 ( PDF (in Japanese)).
      12. Jun-ichi Inoue and Kazuyuki Tanaka: Dynamics of the maximum likelihood hyper-parameter estimation in image restoration: Gradient descent versus expectation and maximization algorithm, Physical Review E, Vol. 65, No.1 (January 2002), Article No. 016125, pp.1-11 ( PDF File, PS File (in English)).
      13. Kazuyuki Tanaka and Jun-ichi Inoue: Maximum Likelihood Hyperparameter Estimation for Solvable Markov Random Field Model in Image Restoration, IEICE Transactions on Information and Systems, Vol.E85-D, No.3 (March 2002), pp.546-557. ( PDF file).
      14. Kazuyuki Tanaka and Tsuyoshi Horiguchi: Probabilistic, Iterated and Quantum-Iterated Computational Methods in Gray-Level Image Restration, Interdisciplinary Information Sciences, Vol.8, No.1 (March 2002), pp.33-50. (Postscript File).
      15. Kazuyuki Tanaka and Tsuyoshi Horiguchi: Solvable Markov Random Field Model in Color Image Restoration, Physical Review E, Vol.65, No.4 (April 2002), Article No.046142, pp.1-18 (PDF file, Postscript file).
      16. Kazuyuki Tanaka, Daiki Furusato, Tsuyoshi Horiguchi: Coupled Markov Random Field Models with Phases as Line Field and Region Field, IEICE Transactions (D-II), Vol.J85-D-II, No.5 (May 2002), pp.805-814. ( PDF, in Japanese); translated in Systems and Computers in Japan, Vol.34, No.30 (June 2003) pp.24-33 (PDF in English).
      17. Kazuyuki Tanaka: Automatic Hyperparameter Estimation in Probabilistic Image Restoration Algorithm based on Gibbs Microcanonical Distribution. IEICE Transactions (D-II), Vol.J85-D-II, No.5 (May 2002), pp.815-824. ( PDF); to be translated in Systems and Computers in Japan.
      18. Kazuyuki Tanaka: Probabilistic Inference by means of Cluster Variation Method and Linear Response Theory, IEICE Transactions on Information and Systems, Vol.E86-D, No.7 (July 2003) pp.1228-1242 (PDF).
      19. Kazuyuki Tanaka, Norihiro Hoshi and Tsuyoshi Horiguchi: Color Image Compression Algorithm Using Self-Organizing Feature Map, Interdisciplinary Information Sciences, Vol.9, 2003, to appear (Postscript, Compressed Postscript).
      20. Jun-ichi Inoue and Kazuyuki Tanaka: Mean Field Theory of EM Algorithm for Bayesian Gray Scale Image Restoration, Journal of Physics A: Mathematical and General, Vol. 36, No. 43 (October 2003), pp.10997-11010 (PDF).
      21. Kazuyuki Tanaka, Jun-ichi Inoue and D. M. Titterington: Probabilistic image processing by means of Bethe approximation for Q-Ising model, Journal of Physics A: Mathematical and General, Vol. 36, No. 43 (October 2003), pp.11023-11036 (PDF).
      22. Kazuyuki Tanaka, Hayaru Shouno, Masato Okada and D. M. Titterington: Accuracy of the Bethe Approximation for Hyperparameter Estimation in Probabilistic Image Processing, Journal of Physics A: Mathematical and General, Vol.37, No.36 (September 2004), pp.8675-8696 (PDF).
      23. Jun Ohkubo, Kazuyuki Tanaka and Tsuyoshi Horiguchi: Generation of Complex Bipartite Graphs by Using a Preferential Rewiring Process, Physical Review E, Vol.72, No.3 (September 2005), Article No.036120, pp.1-10. (PDF)
      24. Jun Ohkubo, Muneki Yasuda and Kazuyuki Tanaka: Statistical-mechanical Iterative Algorithms on Complex Networks, Physical Review E, Vol.72, No.4 (October 2005), Article No.046135, pp1-8. (PDF).
      25. Kazuyuki Tanaka: Generalized Belief Propagation Formula in Probabilistic Information Processing based on Gaussian Graphical Model, IEICE Transactions (D-II), Vol.J88-D-II, No.12 (December 2005), pp.2368-2379 (PDF, in Japanese).
      26. Jun Ohkubo, Muneki Yasuda, and Kazuyuki Tanaka: Preferential Urn Model and Nongrowing Complex Networks, Physical Review E, Vol.72, No.6 (December 2005), Article No.065104(R), pp.1-4 (PDF).

      Related Paper in International Conferences

      1. Kazuyuki Tanaka and Tohru Morita: Application of cluster variation method to image restoration problem, Theory and Applications of the Cluster Variation and Path Probability Methods, ed. J.L. Mor\'an-L\'opez and J.M. Sanchez, Plenum Press, New York, (1996) pp.353-373. (Proceedings of the international workshop on the theory and applications of the cluster variation and path probability methods, June 18-22, 1995, Teotihuacan, Mexico)
      2. Kazuyuki Tanaka and Tohru Morita: Correlated Random Field Ising Model and Image Restoration Problem, edited by M. Suzuki and N. Kawashima, pp.150-153, World Scientific Publishing Coporation Press (Proceedings of International Symposium on Coferent Approaches to Fluctuations, July 17-20, 1995, Kyoto).
      3. Kazuyuki Tanaka and Tohru Morita: Statistical-mechanical Study of the Image Restoration based on the Markov Random Field Model, Proceedings of International Workshop on Soft Computing in Industory, pp.78-83, Muroran Institute of Technology Press (April 27-28, 1996, Muroran, Japan).
      4. Kazuyuki Tanaka, Mikako Ichioka and Tohru Morita: Statistical-Mechanical Algorithm in MRF Model based on Variational Principle, Proceedings of the 13th international conference on Pattern Recognition, Vol.II, Track B: Pattern Recognition and Signal Analysis, pp.381-388, IEEE Computer Society Press, Los Alamos, Carifornia, 1996 (August 25-29, 1996, Vienna, Austria).
      5. Kazuyuki Tanaka: Approximate Optimization Algorithms in Markov Random Field Model based on Statistical-mechanical techniques, Proceedings of International Workshop on Soft Computing in Industry'99, pp.165-170, Muroran Institute of Technology Press (June 16-18, 1999, Muroran, Japan).
      6. Kazuyuki Tanaka: Probabilistic Computational Method in Image Restoration based on Statistical-mechanical Texhniques, Y. Suzuki, S. Ovaska, T. Furuhashi, R. Roy and Y. Dote (Eds), Soft Computing in Industrial Applications, pp.401-414, Springer-Verlag Press, London, 2000 (Proceedings of 4th On-line World Conference on Soft Computing in Industrial Applications, September, 1999).
      7. Jun-ichi Inoue and Kazuyuki Tanaka: Dynamical properties of image restoration and hyper-parameter estimation, Neural Networks for Signal Processing XI ---Proceedings of the 2001 IEEE Signal Processing Society Workshop (September 10-14, 2001, Boston, USA), pp. 383-392, 2001.
      8. Kazuyuki Tanaka, Jun-ichi Inoue and D. M. Titterington: Loopy belief propagation and probabilistic image processing, Neural Networks for Signal Processing XIII ---Proceedings of the 2003 IEEE Signal Processing Society Workshop (September 17-19, 2003, Toulouse, France), pp.329-338 (Paper: PDF, Postscript, Presentation Slide: Powerpoint).
      9. Kazuyuki Tanaka and D. M. Titterington: Probabilistic image processing based on the Q-Ising model by means of the mean-field method and loopy belief propagation, Proceedings of 17th International Conference on Pattern Recognition (ICPR2004) Vol.2 (August 23-26, 2004, Combridge, UK), pp.40-43 (IEEE Computer Society Press) (Paper: PDF, Presentation Slide: Powerpoint).
      10. Kazuyuki Tanaka and D. M. Titterington: First-order phase transition and Bayesian image processing by loopy belief propagation, Satellite Meeting of STATPHYS 22 Statistical Physics of Disordered Systems and Its Applications, (July 12-15, 2004, Hayama, Japan)(Paper: PDF, Postscript, Presentation Slide: Powerpoint).
      11. Jun-ichi Inoue and Kazuyuki Tanaka: Dynamics and its stability of Boltzmann-machine learning algorithm for gray scale image restoration, Proceedings of 3rd International Symposium on Slow Dynamics in Complex Systems (edited by M. Tokuyama and I. Oppenheim, November 3-8, 2003, Sendai, Japan), pp.731-734 (American Institute of Physics Press).
      12. Kazuyuki Tanaka: Linear Response Formula in Generalized Belief Propagation for Probabilistic Inference, Proceedings of International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'05; November 28-30, 2005, Vienna, Austria), Vol.I (2006, IEEE Computer Society Press), pp.669-675 (Presentation Slide: Power Point, PDF).
      13. Jun Ohkubo and Kazuyuki Tanaka: Preferential Urn Model on a Random Network, Proceedings of International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'05; November 28-30, 2005, Vienna, Austria), Vol.I (2006, IEEE Computer Society Press), pp.1153-1159.
      14. Kazuyuki Tanaka: Statistical Learning Procedure in Loopy Belief Propagation for Probabilistic Image Processing, Proceedings of International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06; November 28-30, 2005, Vienna, Austria), Vol.II (2006, IEEE Computer Society Press), pp.741-746 (Presentation Slide: Power Point, PDF).
      15. Muneki Yasuda, Jun Ohkubo and Kazuyuki Tanaka: Digital Images Inpainting based on Markov Random Field, Proceedings of International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'05; November 28-30, 2005, Vienna, Austria), Vol.II (2006, IEEE Computer Society Press), pp.747-752.
      16. Jun Ohkubo and Kazuyuki Tanaka: Fat-Tailed Degree Distributions Generated by Quenched Disorder, Proceedings of International Conference on Complex Systems (ICCS2006; June 25-30, 2006, Marriott Boston Quincy, Boston, USA), to appear.

      Basic Programs for Probabilistic Image Processing



    Contant Address: Kazuyuki Tanaka
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