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 quite 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稀疏的已知像素子集中高质量重建缺失图像区域，前提是这些像素的位置及其灰度或颜色值经过充分优化。这一特性被应用于基于修复的图像压缩中，成为经典变换编码器（如JPEG和JPEG2000）的一种有前景的替代方案。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并行性，并精心适配了一些最成功的数值概念。我们提出了一种基于误差图抖动与德劳内三角剖分相结合的致密化策略，用于空间优化。对于色调优化，我们设计了一种无矩阵形式的区域分解求解器，用于求解相应的正规方程，并辅以基于沃罗诺伊图初始化策略。利用我们提出的方法，能够生成用于均匀扩散的高质量修复掩膜及优化色调值，其运行时间大幅优于现有最佳技术。