Digital halftoning
Digital halftones by dot diffusion
ACM Transactions on Graphics (TOG)
A fast algorithm for particle simulations
Journal of Computational Physics
A Markovian framework for digital halftoning
ACM Transactions on Graphics (TOG)
Fast Fourier transforms for nonequispaced data
SIAM Journal on Scientific Computing
A simple and efficient error-diffusion algorithm
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
NPAR '02 Proceedings of the 2nd international symposium on Non-photorealistic animation and rendering
Improving mid-tone quality of variable-coefficient error diffusion using threshold modulation
ACM SIGGRAPH 2003 Papers
Efficient illumination by high dynamic range images
EGRW '03 Proceedings of the 14th Eurographics workshop on Rendering
Fast convolution with radial kernels at nonequispaced knots
Numerische Mathematik
Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations
SIAM Journal on Numerical Analysis
ACM SIGGRAPH 2008 papers
Image Processing for Computer Graphics and Vision
Image Processing for Computer Graphics and Vision
Capacity-constrained point distributions: a variant of Lloyd's method
ACM SIGGRAPH 2009 papers
Structure-aware error diffusion
ACM SIGGRAPH Asia 2009 papers
Halftoning via direct binary search using analytical and stochastic printer models
IEEE Transactions on Image Processing
On vector and matrix median computation
Journal of Computational and Applied Mathematics
Quadrature nodes meet stippling dots
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Multi-Class Anisotropic Electrostatic Halftoning
Computer Graphics Forum
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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 $\mathcal{O}(m\log m)$ arithmetic operations for $m$ points. Finally, we present numerical results showing the excellent performance of our dithering method.