CiteULike is a free online bibliography manager. Register and you can start organising your references online.
Tags

# Dithering by Differences of Convex Functions

SIAM Journal on Imaging Sciences, Vol. 4, No. 1. (January 2011), pp. 79-108, doi:10.1137/100790197  Key: citeulike:11897438

## Likes (beta)

This copy of the article hasn't been liked by anyone yet.

### Abstract

Motivated by a recent halftoning method which is based on electrostatic principles, we analyze a halftoning framework where one minimizes a functional consisting of the difference of two convex functions. One describes attracting forces caused by the image's gray values; the other one enforces repulsion between points. In one dimension, the minimizers of our functional can be computed analytically and have the following desired properties: The points are pairwise distinct, lie within the image frame, and can be placed at grid points. In the two-dimensional setting, we prove some useful properties of our functional, such as its coercivity, and propose computing a minimizer by a forward-backward splitting algorithm. We suggest computing the special sums occurring in each iteration step of our dithering algorithm by a fast summation technique based on the fast Fourier transform at nonequispaced knots, which requires only $\mathcalO(m\log m)$ arithmetic operations for m points. Finally, we present numerical results showing the excellent performance of our dithering method.

### Citations (CiTO)

No CiTO relationships defined