Consistency of variational continuous-domain quantization via kinetic theory

Massimo Fornasier, Jan Haškovec*, Gabriele Steidl

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We study the kinetic mean-field limits of the discrete systems of interacting particles used for halftoning of images in the sense of continuous-domain quantization. Under mild assumptions on the regularity of the interacting kernels, we provide a rigorous derivation of the mean-field kinetic equation. Moreover, we study the energy of the system, show that it is a Lyapunov functional and prove that in the long time limit the solution tends to an equilibrium given by a local minimum of the energy. In a special case we prove that the equilibrium is unique and is identical to the prescribed image profile. This proves the consistency of the particle halftoning method when the number of particles tends to infinity.

Original languageEnglish (US)
Pages (from-to)1283-1298
Number of pages16
JournalApplicable Analysis
Issue number6
StatePublished - Jun 2013


  • dithering
  • halftoning
  • image processing
  • interacting particles
  • mean-field limit

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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