Supplementary Material for Our Paper

Multi-Class (Anisotropic) Electrostatic Halftoning

Multi-Class (Anisotropic) Electrostatic Halftoning
Tradeoffs in Multi-Size Halftoning

A general requirement of halftoning algorithms is that the resulting dots represent the underlying image well. When halftoning with dots of different sizes, however, it is often also necessary that certain subsets represent the image as good as possible, e.g. all dots up to a certain size. However, these requirements contradict each other such that a good tradeoff between the different requirements must be found in practise. Since the importance of each requirement depends on the application, we included freely adjustable tradeoff parameters in our halftoning algorithm which can be used to weight the different requirements. On this page, we illustrate the effect of these parameters using only two particle sizes to halftone a grey ramp. However, as explained in our paper, these concepts immediately carry over to an arbitrary number of sizes, even if each particle has a unique size.

In the following images, each part of three images show the halftoning result for a different parameter setting given below the images. Shown are, from left to right, the complete image and its approximation only by small and large particles, respectively.

	C = 1				C = 2

C = 4

C = 2 for small instead of for large particles

As expected, only the overall image is approximated well for C=1 while the small and large particles alone do not represent the image well. Increasing C forces the large particles to approximate the image also without the smaller particles, which also yields an appropriate distribution of only the small particle. If C is chosen too large, however, the large particles nearly ignore the positions of the small particles, which yields an good approximation with only the large particles, but an inappropriate approximation when considering all particles.

Instead of forcing the large particles to distribute the image well without the small particles, one might also require the same for the small particles. The resulting halftone is illustrated in the last image triplet. One can notice at second glance that the small particles cluster around the larger ones in dark image regions. Apart from this issue, halftoning works well, though.

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