We introduce a new global approach for image dithering, stippling, screening and sampling. It is inspired by the physical principles of electrostatics. Repelling forces between equally charged particles create a homogeneous distribution in flat areas, while attracting forces from the image brightness values ensure a high approximation quality. Our model is transparent and uses only two intuitive parameters: One steers the granularity of our halftoning approach, and the other its regularity. We evaluate two versions of our algorithm: A discrete version for dithering that ties points to grid positions, as well as a continuous one which does not have this restriction, and can thus be used for stippling or sampling density functions. Our methods create very few visual artefacts, reveal favourable blue-noise behaviour in the frequency domain, and have a lower approximation error under Gaussian convolution than state-of-the-art methods.

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 (DC). 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 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 like its coercivity and propose to compute a minimizer by a forwardbackward splitting algorithm. 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 which requires only O(m log m) arithmetic operations for m points. Finally, we present numerical results showing the excellent performance of our dithering method.

Abstract. Gaussian convolution is of fundamental importance in linear scale-space theory and in numerous applications. We introduce iterated extended box filtering as an efficient and highly accurate way to compute Gaussian convolution. Extended box filtering approximates a continuous box filter of arbitrary non-integer standard deviation. It provides a much better approximation to Gaussian convolution than conventional iterated box filtering. Moreover, it retains the efficiency benefits of iterated box filtering where the runtime is a linear function of the image size and does not depend on the standard deviation of the Gaussian. In a detailed mathematical analysis, we establish the fundamental properties of our approach and deduce its error bounds. An experimental evaluation shows the advantages of our method over classical implementations of Gaussian convolution in the spatial and the Fourier domain.

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The Euler-Lagrange (EL) framework is the most widely-used strategy for solving variational optic flow methods. We present the first approach that solves the EL equations of state-of-the-art methods on sequences with 640 × 480 pixels in near-realtime on GPUs. This performance is achieved by combining two ideas: (i) We extend the recently proposed Fast Explicit Diffusion (FED) scheme to optic flow, and additionally embed it into a coarse-to-fine strategy. (ii) We parallelise our complete algorithm on a GPU, where a careful optimisation of global memory operations and an efficient use of on-chip memory guarantee a good performance. Applying our approach to the variational 'Complementary Optic Flow' method (Zimmer et al. (2009)), we obtain highly accurate flow fields in less than a second. This currently constitutes the fastest method in the top 10 of the widely used Middlebury benchmark.