Gradients versus Grey Values for Sparse Image Reconstruction and Inpainting-Based Compression

Interpolation methods that rely on partial differential equations can reconstruct images with high quality from a few prescribed pixels. A whole class of compression codecs exploits this concept to store images in terms of a sparse grey value representation. Recently, Brinkmann et al. (2015) have suggested an alternative approach: They propose to store gradient data instead of grey values. However, this idea has not been evaluated and its potential remains unknown. In our paper, we compare gradient and grey value data for homogeneous diffusion inpainting w.r.t. two different aspects: First, we evaluate the reconstruction quality, given a comparable amount of data of both kinds. Second, we assess how well these sparse representations can be stored in compression applications. To this end, we establish a framework for optimising and encoding the known data. It allows a fair comparison of both the grey value and the gradient approach. Our evaluation shows that gradientbased reconstructions avoid visually distracting singularities involved in the reconstructions from grey values, thus improving the visual fidelity. Surprisingly, this advantage does not carry over to compression due to the high sensitivity to quantisation.