Strobl22

Applied Harmonic Analysis and Friends

June 19th - 25th 2022

Strobl, AUSTRIA

"Enhanced Digital Halftoning via Weighted Sigma-Delta Modulation"

Veselovska, Anna

In this talk, we consider error diffusion techniques for digital halftoning from the perspective of $1$-bit $\Sigma \Delta$ quantization. We introduce a method to generate $\Sigma \Delta$ schemes for two-dimensional signals as a weighted combination of its one-dimensional counterparts and show that various error diffusion schemes proposed in the literature can be represented in this framework via $\Sigma \Delta$ schemes of first order. Under the model of two-dimensional bandlimited signals, which is motivated by a mathematical model of human visual perception, we derive quantitative error bounds for such weighted $\Sigma \Delta$ schemes. Motivated by the correspondence between existing error diffusion algorithms and first-order $\Sigma \Delta$ schemes, we study the performance of the analogous weighted combinations of second-order $\Sigma \Delta$ schemes and show that they exhibit a superior performance in terms of guaranteed error decay for two-dimensional bandlimited signals. In numerical simulations for real world images, we demonstrate that with some modifications to enhance stability this high-quality performance also translates to the problem of digital halftoning.
http://univie.ac.at/projektservice-mathematik/e/talks/Veselovska_2022-02_Strobl22(3).pdf

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