Equivalence Results for TV Diffusion and TV Regularisation

  • Thomas Brox
  • Martin Welk
  • Gabriele Steidl
  • Joachim Weickert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2695)


It has been stressed that regularisation methods and diffusion processes approximate each other. In this paper we identify a situation where both processes are even identical: the space-discrete 1-D case of total variation (TV) denoising. This equivalence is proved by deriving identical analytical solutions for both processes. The temporal evolution confirms that space-discrete TV methods implement a region merging strategy with finite extinction time. Between two merging events, only extremal segments move. Their speed is inversely proportional to their size. Our results stress the distinguished nature of TV denoising. Furthermore, they enable a mutual transfer of all theoretical and algorithmic achievements between both techniques.


Equivalence Result Homogeneous Neumann Boundary Condition Total Variation Minimization Mathematical Image Merging Event 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Thomas Brox
    • 1
  • Martin Welk
    • 1
  • Gabriele Steidl
    • 2
  • Joachim Weickert
    • 1
  1. 1.Mathematical Image Analysis Group Faculty of Mathematics and Computer ScienceSaarland UniversitySaarbrückenGermany
  2. 2.Faculty of Mathematics and Computer Science, D7, 27University of MannheimMannheimGermany

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