On the Design of Energy Kernels and Uniformity Improvement in Blue Noise Mask Generation

Abstract

In the potential-theoretic energy minimization approach for generating blue noise masks, we demonstrate that using a logarithmic kernel or its approximated variants as the energy kernel improves the uniformity of the masks. We also implement a high-speed mask generation method that allows setting the kernel radius to an arbitrary size. Furthermore, we confirm that the energy exhibits equivalence to a ball-discrepancy and a type of graininess evaluation measure, providing an effective mathematical framework for evaluating the uniformity of images.