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.

翻译：均匀扩散修复能够从已知像素的稀疏子集中高质量地重建缺失图像区域，前提是这些像素的位置及其灰度或颜色值均得到良好优化。这一特性被应用于基于修复的图像压缩技术中，该技术是JPEG和JPEG2000等经典变换编解码器的有前景的替代方案。然而，优化修复数据是一项具有挑战性的任务。现有方法要么速度较慢，要么无法产生高质量结果。为此，我们提出了用于均匀扩散修复的快速空间与色调优化算法，该算法高效利用GPU并行计算能力，并对若干最成功的数值概念进行了细致适配。在空间优化方面，我们提出了一种结合误差扩散抖动思想与Delaunay三角剖分的密集化策略。对于色调优化，我们设计了一种区域分解求解器，以无矩阵方式求解相应的正规方程，并辅以基于Voronoi图的初始化策略。采用我们提出的方法，我们能够以远超现有先进技术的运行时间，为均匀扩散修复生成高质量的修复掩码及优化后的色调值。