Consistency of Variational Continuous-Domain Quantization via Kinetic Theory

  title={Consistency of Variational Continuous-Domain Quantization via Kinetic Theory},
  author={M. Fornasier and J. Haskovec and Gabriele Steidl},
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… CONTINUE READING

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