Efficient Parallel Data Optimization for Homogeneous Diffusion Inpainting of 4K Images

TL;DR

This work tackles the challenge of data optimization for homogeneous diffusion inpainting used in inpainting-based image compression, focusing on 4K images. It introduces a fast, GPU-friendly workflow with two key pillars: spatial densification via Delaunay triangulation (augmented by a Voronoi-based initialization) and tonal optimization through a matrix-free, domain-decomposed solver (RAS) integrated with a fast multigrid ORAS inpainting backend. The proposed methods achieve sub-second runtimes for full data optimization and sub-half-second tonal optimization on modern GPUs, significantly outperforming prior state-of-the-art in both speed and quality, with near-linear scaling in image size. These advances enable practical, high-quality inpainting-based compression and can be extended to other inpainting operators and non-neural optimization scenarios while maintaining transparency and memory efficiency.

Abstract

Homogeneous diffusion inpainting can reconstruct missing image areas with high quality from a sparse subset of known pixels, provided that their location as well as their gray or color values are well optimized. This property is exploited in inpainting-based image compression, which is a promising alternative to classical transform-based codecs such as JPEG and JPEG2000. However, optimizing the inpainting data is a challenging task. Current approaches are either fairly slow or do not produce high quality results. As a remedy we propose fast spatial and tonal optimization algorithms for homogeneous diffusion inpainting that efficiently utilize GPU parallelism, with a careful adaptation of some of the most successful numerical concepts. We propose a densification strategy using ideas from error-map dithering combined with a Delaunay triangulation for the spatial optimization. For the tonal optimization we design a domain decomposition solver that solves the corresponding normal equations in a matrix-free fashion and supplement it with a Voronoi-based initialization strategy. With our proposed methods we are able to generate high quality inpainting masks for homogeneous diffusion and optimized tonal values in a runtime that outperforms prior state-of-the-art by a wide margin.

Figures (15)

• Figure 1: Domain Decomposition Example. The domain is divided into four overlapping subdomains. The subdomain $\Omega_1$ is highlighted in blue.
• Figure 1: Voronoi and Delaunay Example on trui with a 2% Mask Density.
• Figure 1: Tonal Optimization Example on trui with an Optimized Mask of 2% Density. The tonal optimization enhances the contrast and significantly improves the MSE.
• Figure 1: Our twelve test images of $4K$ resolution. Photos by J. Weickert.
• Figure 2: Reduced Full Multigrid Scheme. The initial guess is constructed in a coarse-to-fine manner, also known as one-way or cascadic multigrid BD96. Then we continue with additional V-cycle correction steps (a single V-cycle is visualized above).