Dithering by Differences of Convex Functions
Department of Applied Mathematics
We analyze a halftoning framework where one minimizes a functional consisting of the difference of two convex functions. One of them describes attracting forces caused by the image gray values, the other one enforces repulsion between points. In one dimension, the minimizers of our functional can be computed analytically and have desirable properties. In the two-dimensional setting, we prove some useful properties of our functional like its coercivity and suggest to compute a minimizer by a forward-backward splitting algorithm. We show that the sequence produced by such an algorithm converges to a critical point of our functional. Furthermore, we suggest to compute the special sums occurring in each iteration step by a fast summation technique based on the fast Fourier transform at non-equispaced knots and present numerical results.
This is joint work with T. Teuber (University of Mannheim, Germany), P. Gwosdek, Ch. Schmaltz and J. Weickert (Saarland University, Germany).