Bayesian Texture Segmentation Using Multi-layer Perceptron and Markov Random Field Model

다층 퍼셉트론과 마코프 랜덤 필드 모델을 이용한 베이지안 결 분할

  • 김태형 (부산대학교 전자공학과) ;
  • 엄일규 (부산대학교 전자공학과) ;
  • 김유신 (부산대학교 컴퓨터및정보통신연구소)
  • Published : 2007.01.25

Abstract

This paper presents a novel texture segmentation method using multilayer perceptron (MLP) networks and Markov random fields in multiscale Bayesian framework. Multiscale wavelet coefficients are used as input for the neural networks. The output of the neural network is modeled as a posterior probability. Texture classification at each scale is performed by the posterior probabilities from MLP networks and MAP (maximum a posterior) classification. Then, in order to obtain the more improved segmentation result at the finest scale, our proposed method fuses the multiscale MAP classifications sequentially from coarse to fine scales. This process is done by computing the MAP classification given the classification at one scale and a priori knowledge regarding contextual information which is extracted from the adjacent coarser scale classification. In this fusion process, the MRF (Markov random field) prior distribution and Gibbs sampler are used, where the MRF model serves as the smoothness constraint and the Gibbs sampler acts as the MAP classifier. The proposed segmentation method shows better performance than texture segmentation using the HMT (Hidden Markov trees) model and HMTseg.

이 논문은 다중 스케일 베이지안 관점에서 다층 퍼셉트론과 마코프 랜덤 필드를 사용한 새로운 결 분할 방법을 제안한다. 다층 퍼셉트론의 출력은 사후 확률을 모델링하므로 본 논문에서는 다중 스케일 웨이블릿 계수들을 다층 퍼셉트론의 입력으로 사용한다. 다층 퍼셉트론으로부터 구한 사후 확률과 MAP (maximum a posterior) 분류를 이용하여 각 스케일에서 결 분류를 수행한다. 또한 가장 섬세한 스케일에서 더 개선된 분할 결과를 얻기 위하여 모든 스케일에서 MAP 분류 결과들을 거친 스케일에서 섬세한 스케일까지 차례로 융합한다. 이런 과정은 한 스케일에서의 분류 정보와 그 인접한 보다 거친 스케일에서 얻어지는 문맥과 관련한 연역적 정보를 이용하여 MAP 분류를 행함으로써 이루어진다. 이 융합 과정에서, MRF (Markov random fields) 사전 모델이 평탄화 제한자로서 동작하고, 깁스 샘플러 (Gibbs sampler)는 MAP 분류기로서 동작한다. 제안한 분할 방법은 HMT (Hidden Markov Trees) 모델과 HMTseg 알고리즘을 이용한 결 분할 방법보다 더 좋은 성능을 보인다.

Keywords

References

  1. M. D. Richard, R. P. Lippmann, 'Neural Network Classifiers Estimate Bayesian a posteriori Probabilities,' Neural Computation, vol. 3, pp. 461-483, 1991 https://doi.org/10.1162/neco.1991.3.4.461
  2. H. Gish, 'A probabilitic approach to the understanding and training of neural network classifiers,' in Proc. IEEE Intl. Conf. on Acoustics, Speech and Signal Processing (Albuquerque, NM), pp. 1361-1364, 1990 https://doi.org/10.1109/ICASSP.1990.115636
  3. R. Rojas, 'Short proof of the posterior probability property of classifier neuralnetworks,' Neural Computation 8, pp. 41-43, 1996 https://doi.org/10.1162/neco.1996.8.1.41
  4. Kwang In Kim, Keechul Jung, Se Hyun Park, and Hang Joon Kim, 'Support Vector Machine for Texture Classification,' IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 11, pp. 1542-1550, November 2002 https://doi.org/10.1109/TPAMI.2002.1046177
  5. Hyeokho Choi and Richard G. Baraniuk, 'Multiscale Image Segmentation UsingWavelet-Domain Hidden Markov Models,' IEEE Transaction on image processong, vol. 10, no. 9, pp. 1309-1321, September 2001 https://doi.org/10.1109/83.941855
  6. Kim Tae Hyung, Eom Il Kyu, and Kim Yoo Shin, 'Texture segmentation Using Neural Networks and Multi-scale Wavelet Feature,' Lecture Note in Computer Science 3611, pp. 395-404, Springer-Verlag Berlin Heidelberg, 2001 https://doi.org/10.1007/11539117_59
  7. S. Z. Li, Markov Random Field Modeling in Computer Vision, Springer-Verlag, New York, 1995
  8. S. Z. Li, Markov Random Field Modeling in Image Analysis, 2nd ed., Computer Science Workbench, T. L. Kunii eds. Springer-Verlag, 2001
  9. H. Derin and H. Elliot, 'Modeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields,' IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 9, no. 1, pp. 39-55, January 1987 https://doi.org/10.1109/TPAMI.1987.4767871
  10. Guoliang Fan and Xiang-Gen Xia, 'A Joint Multicontext and Multiscale Approach to Bayesian Image Segmentation,' IEEE Transaction on Geoscience and Remote Sensing, vol. 39, no. 12, pp. 2680-2688, December 2001 https://doi.org/10.1109/36.975002
  11. Y. Meyer, Wavelets Algorithm and Application, SIAM, Philadelphia, PA, 1993
  12. Jia Li, R.M. Gray, and R.A. Olshen, 'Multiresolution Image Classification by Hierarchical Modeling with Two-Dimensional Hidden Markov Models,' IEEE Transaction on Information Theory, vol. 46, no. 5, pp. 1826-1841, August 2000 https://doi.org/10.1109/18.857794
  13. Guoliang Fan and Xiang-Gen Xia, 'Wavelet-Based Texture Analysis and Synthesis Using Hidden Markov Models,' IEEE Transaction on Circuits and Systems I: Fundamental Theory and Applications, vol. 50, no. 1, pp. 106-120, January 2003 https://doi.org/10.1109/TCSI.2002.807520
  14. Guoliang Fan and Xiang-Gen Xia, 'Image Denosing Using a Local Contextual Hidden Markov Model in the Wavelet Domain,' IEEE Signal Processing Letters, vol. 8, no. 5, pp. 125-128, May 2001 https://doi.org/10.1109/97.917691
  15. E. P. Simoncelli, 'Statistical Models for Images: Compression, Restoration and Synthesis,' in Proc. 31st Asilomar Conf. Signals, Systems and Computers, pp. 673-678, Pacific Grove, CA, November 1997 https://doi.org/10.1109/ACSSC.1997.680530
  16. J.M. Shapiro, 'Embedded Image Coding Using Zerotrees of Wavelet Coefficients,' IEEE Transaction on Signal Processing, vol. 41, no. 12, pp. 3445-3462, December 1993 https://doi.org/10.1109/78.258085
  17. Z. Chen, T.J. Houkes, and Z. Houkes, 'Texture Segmentation Based on Wavelet and Kohonen Network for Remotely Sensed Images,' IEEE International Conf. on Systems, Man, and Cybernetics, pp. 816-821, Tokyo, Japan, 1999 https://doi.org/10.1109/ICSMC.1999.816656
  18. Xiaoyue Jiang and Rongchun Zhao, 'A New Method of Texture Segmentation,' IEEE International Conf. on Neural Networks and Signal Processing, pp. 1083-1086, Nanjing, China, December 14-17, 2003 https://doi.org/10.1109/ICNNSP.2003.1281057
  19. Martin Reidmiller and Heinrich Braun, 'A direct adaptive method for faster backpropagation learning: the Rprop algorithm', Proceedings of the ICNN, San Francisco, 1993 https://doi.org/10.1109/ICNN.1993.298623
  20. Howard Demuth and Mark Beale, 'Neural Network Toolbox For Use with MATLAB,' The MathWorks, Inc., User's Guide Version 4, pp.164-182
  21. Richard O. Duda, Peter E. Hart, and David G. Stork, Pattern Classification, 2nd Edition, revised chapter section 2.11, A Wiley Interscience publication, 2002
  22. Guoliang Fan and Xiang-Gen Xia, 'Improved Hidden Markov Models in the Wavelet-Domain', IEEE Transaction on signal processong, vol. 49, NO. 1, January 2001 https://doi.org/10.1109/78.890351