Pascal Gwosdek

Fast electrostatic halftoning

Electrostatic halftoning is a high-quality method for stippling, dithering, and sampling, but it suffers from a high runtime. This made the technique difficult to use for most real-world applications. A recently proposed minimisation scheme based on the non-equispaced fast Fourier transform (NFFT) lowers the complexity in the particle number M from

An adaptive domain-decomposition technique for parallelization of the fast marching method

\mathcal{O}(M^2)

Fast PDE-Based image analysis in your pocket

to

Variational optic flow on the Sony PlayStation 3 – accurate dense flow fields for real-time applications

\mathcal{O}(M \log M).

Variational optic flow on the Sony PlayStation 3

However, the NFFT is hard to parallelise, and the runtime on modern CPUs lies still in the orders of an hour for about 50,000 particles, to a day for 1 million particles. Our contributions to remedy this problem are threefold: we design the first GPU-based NFFT algorithm without special structural assumptions on the positions of nodes, we introduce a novel nearest-neighbour identification scheme for continuous point distributions, and we optimise the whole algorithm for n-body problems such as electrostatic halftoning. For 1 million particles, this new algorithm runs 50 times faster than the most efficient technique on the CPU, and even yields a speedup of 7,000 over the original algorithm.

High Performance Parallel Optical Flow Algorithms on the Sony Playstation 3.

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 images 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