  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.
