On the discrete maximum principle for the beltrami color flow

Lorina Dascal, Adi Ditkowski, Nir A. Sochen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We analyze the discrete maximum principle for the Beltrami color flow. The Beltrami flow can display linear as well as nonlinear behavior according to the values of a parameter β, which represents the ratio between spatial and color distances. In general, the standard schemes fail to satisfy the discrete maximum principle. In this work we show that a nonnegative second order difference scheme can be built for this flow only for small β, i.e. linear-like diffusion. Since this limitation is too severe, we construct a novel finite difference scheme, which is not nonnegative and satisfies the discrete maximum principle for all values of β. Numerical results support the analysis.

Original languageEnglish
Pages (from-to)63-77
Number of pages15
JournalJournal of Mathematical Imaging and Vision
Issue number1
StatePublished - Sep 2007


  • Color image analysis
  • Discrete maximum principle
  • Nonlinear parabolic differential equations
  • Nonnegative finite difference scheme


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