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Selection of Optimal Stopping Time for Nonlinear Difusion Filtering

  • Pavel Mrázek⋆
Conference paper
Part of the Lecture Notes in Computer Science 2106 book series (LNCS, volume 2106)

Abstract

We develop a novel time-selection strategy for iterative image restoration techniques: the stopping time is chosen so that the correlation of signal and noise in the filtered image is minimised. The new method is applicable to any images where the noise to be removed is uncorrelated with the signal; no other knowledge (e.g. the noise variance, training data etc.) is needed. We test the performance of our time estimation procedure experimentally, and demonstrate that it yields near-optimal results for a wide range of noise levels and for various filtering methods.

Keywords

Input Image Noise Variance Noisy Image Ideal Signal Coherence Direction 
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.

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References

  1. 1.
    F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll. Image selective smoothing and edge-detection by nonlinear difusion. SIAM Journal on Numerical Analysis, 29(1):182–193, 1992.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    I. CapuzzoDolcetta and R. Ferretti.Optimal stopping time formulation of adaptive image filtering. Applied Mathematics and Optimization, 2000. To appear.Google Scholar
  3. 3.
    Tony Lindeberg. Scale-Space Theory in Computer Vision. Kluwer Academic Publishers, 1994.Google Scholar
  4. 4.
    Pavel Mrázek. Nonlinear Difusion for Image Filtering and Monotonicity Enhancement. PhD thesis, Czech Technical University, 2001. To appear.Google Scholar
  5. 5.
    Athanasios Papoulis. Probability and Statistics. Prentice-Hall, 1990.Google Scholar
  6. 6.
    P. Perona and J. Malik. Scale-space and edge-detection using anisotropic difusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7):629–639, 1990.CrossRefGoogle Scholar
  7. 7.
    Jon Sporring and Joachim Weickert. Information measures in scale-spaces. IEEE Transactions on Information Theory, 45:1051–1058, 1999.MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    J. Weickert, B.M. ter Haar Romeny, and M.A. Viergever. Efficient and reliable schemes for nonlinear difusion filtering. IEEE Transactions on Image Processing, 7:398–410, 1998.CrossRefGoogle Scholar
  9. 9.
    Joachim Weickert. Anisotropic Difusion in Image Processing. European Consortium for Mathematics in Industry. B.G.Teubner, Stuttgart, 1998.Google Scholar
  10. 10.
    Joachim Weickert. Coherence-enhancing difusion of colour images. Image and Vision Computing, 17:201–212, 1999.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Pavel Mrázek⋆
    • 1
  1. 1.Center for Machine PerceptionCzech Technical UniversityCzech Republic

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