Differentiable Search Based Halftoning

Halftoning is fundamental to image reproduction on devices with a limited set of output levels, such as printers. Halftoning algorithms reproduce continuous-tone images by distributing dots with a fixed tone but variable size or spacing. Search-based approaches optimize for a dot distribution that minimizes a given visual loss function w.r.t. an input image. This class of methods is not only the most intuitive and versatile but can also yield the highest quality results depending on the merit of the employed loss function. However, their combinatorial nature makes them computationally inefficient. We introduce the first differentiable search-based halftoning algorithm. Our proposed method can be natively used to perform multi-color, multi-level halftoning. Our main insight lies in introducing a relaxation in the discrete choice of dot assignment during the backward pass of the optimization. We achieve this by associating a fictitious distance from the image plane to each dot, embedding the problem in three dimensions. We also introduce a novel loss component that operates in the frequency domain and provides a better visual loss when combined with existing image similarity metrics. We validate our approach by demonstrating that it outperforms stochastic optimization methods in both speed and objective value, while also scaling significantly better to large images. The code is available at https:gitlab.mpi-klsb.mpg.de/aidam-public/differentiable-halftoning