An Accurate Operator Splitting Scheme for Nonlinear Difusion Filtering

  • Danny Barash
  • Moshe Israeli
  • Ron Kimmel
Conference paper
Part of the Lecture Notes in Computer Science 2106 book series (LNCS, volume 2106)


Effcient numerical schemes for nonlinear difusion filtering based on additive operator splitting (AOS) were introduced in [10]. AOS schemes are efficient and unconditionally stable, yet their accuracy is low. Future applications of nonlinear difusion filtering may require additional accuracy at the expense of a relatively modest cost in computations and complexity.

To investigate the effect of higher accuracy schemes, we first examine the Crank-Nicolson and DuFort-Frankel second-order schemes in one dimension. We then extend the AOS schemes to take advantage of the higher accuracy that is achieved in one dimension, by using symmetric multiplicative splittings. Quantitative comparisons are performed for small and large time steps, as well as visual examination of images to find out whether the improvement in accuracy is noticeable.


Large Time Step Accurate Operator Relative Error Percentage Norm Error Estimation Additive Operator Splitting 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Danny Barash
    • 1
  • Moshe Israeli
    • 2
  • Ron Kimmel
    • 2
  1. 1.Hewlett-Packard Laboratories IsraelHaifaIsrael
  2. 2.Computer Science DepartmentTechnion-Israel Institute of TechnologyHaifaIsrael

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