Advertisement

Fast Edge Preserving Picture Recovery by Finite Markov Random Fields

  • Michele Ceccarelli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3617)

Abstract

We investigate the properties of edge preserving smoothing in the context of Finite Markov Random Fields (FMRF). Our main result follows from the definition of discontinuity adaptive potential for FMRF which imposes to penalize linearly image gradients. This is in agreement with the Total Variation based regularization approach to image recovery and analysis. We also report a fast computational algorithm exploiting the finiteness of the field, it uses integer arithmetic and a gradient descent updating procedure. Numerical results on real images and comparisons with anisotropic diffusion and half-quadratic regularization are reported.

Keywords

IEEE Transaction Conjugate Gradient Algorithm Recovery Algorithm Smoothing Process Total Variation Norm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Alvarez, L., Lions, P.L., Guichard, F., Morel, J.M.: Axioms and Fundamental equations of Image Processing. Archives for Rational Mechanics and Analysis 16(9), 200–257 (1993)MathSciNetGoogle Scholar
  2. 2.
    Blake, A., Zisserman, A.: Visual Reconstruction. MIT Press, Cambridge (1987)Google Scholar
  3. 3.
    Ceccarelli, M., De Simone, V.: Well Posed Anisotropic Diffusion for Image Denoising. In: IEE Proceedings Proceedings-Vision, Image and Signal Processing, vol. 149(4), pp. 244–252 (2002)Google Scholar
  4. 4.
    Charbonnier, P., Blanc-Feraud, L., Aubert, G., Barlaud, M.: Deterministic Edge-Preserving Regularization in Computed Imaging. IEEE Transactions on Image Processing 5, 298–311 (1997)CrossRefGoogle Scholar
  5. 5.
    Geman, S., Geman, D.: Stochastic Relaxation, Gibbs Distribution and the Bayesian Restoration of Images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 721–741 (1984)zbMATHCrossRefGoogle Scholar
  6. 6.
    Geman, S., Reynolds, G.: Constrained Restoration and the Recovery of Discontinuities. IEEE Transactions on Pattern Analysis and Machine Intelligence 14, 367–383 (1992)CrossRefGoogle Scholar
  7. 7.
    Geman, S., McClure, D.E.: Bayesian image analysis: an application to single photon emission tomography. In: Proc. Statistical Computational Section, Amer. Statistical Assoc., Washington, DC, pp. 12–18 (1995)Google Scholar
  8. 8.
    Green, P.J.: Bayesian reconstruction for emission tomography using a modified EM algorithm. IEEE Transactions on Medical Imaging 9, 84–93 (1990)CrossRefGoogle Scholar
  9. 9.
    Hebert, T., Leahy, R.: A Generalized EM Algorithm for 3-D Bayesian Reconstruction form Poisson Data using Gibbs Priors. IEEE Transactions on Medical Imaging 8, 194–202 (1990)CrossRefGoogle Scholar
  10. 10.
    Immerkaer, J.: Fast Noise Variance Estimation. CVGIP: Image Understanding 64, 300–302 (1996)Google Scholar
  11. 11.
    Li, S.Z.: On Discontinuity-Adaptive Smoothness Priors in Computer Vision. IEEE Transactions on Pattern Analysis and machine Intelligence 17, 576–586 (1995)CrossRefGoogle Scholar
  12. 12.
    Li, S.Z.: Markov Random Field Modeling in Computer Vision. Springer, Berlin (1995)Google Scholar
  13. 13.
    Mumford, D., Shah, J.: Optimal approximation by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics 42, 577–685 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffution. IEEE Transaction on Pattern Analysis and Machine Intelligence 12, 345–362 (1990)CrossRefGoogle Scholar
  15. 15.
    Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation noise removal algorithms. Physica D 60, 259–268 (1992)zbMATHCrossRefGoogle Scholar
  16. 16.
    Poggio, T., Torre, V., Koch, C.: Computational Vision and Regularization Theory. Nature 317, 314–319 (1985)CrossRefGoogle Scholar
  17. 17.
    You, Y.L., Xu, W., Tannebaum, A., Kaveh, M.: Behavioral Analysis of Anisotropic Diffution in Image Processing. IEEE Transactions of Image Processing 5, 1539–1553 (1996)CrossRefGoogle Scholar
  18. 18.
    Terzopoulos, D.T.: Regularization of inverse visual problems involving discontinuities. IEEE Transactions on PAMI 8(4), 413–442 (1986)Google Scholar
  19. 19.
    Vogel, C.R., Oman, E.: Iterative Methods for Total Variation Denoising. SIAM Journ. on Scientific Computing 17, 227–238 (1996)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Michele Ceccarelli
    • 1
  1. 1.Research Centre on Software Technologies-RCOSTUniversity of SannioBeneventoItaly

Personalised recommendations