Delaunay Averages method compresses images to under 1% data storage

In a new arXiv paper, researchers Vassillen Chizhov and Joachim Weickert present Delaunay Averages, a novel method for inpainting-based image compression. Traditional approaches store an optimized subset of pixel locations and color values, but this work introduces a new feature type: the vertex locations of a Delaunay triangulation along with the average color values inside each triangle. By combining this feature with homogeneous diffusion inpainting, the method yields an elegant mathematical formulation with a positive definite linear system of equations, allowing even simple solvers like the conjugate gradient method to handle large images efficiently.

The researchers developed a data optimization strategy specifically tailored to these Delaunay averages, incorporating ideas from stippling literature to maximize adaptability to the image. Experimental results show the approach outperforms popular inpainting methods with optimized color values by a large margin. Notably, the method exhibits favorable scaling behavior: doubling the image resolution allows halving the percentage of stored data while maintaining quality. For modern high-resolution images, data densities below 1% yield appealing reconstructions, making this technique particularly attractive for efficient compression and storage of large visual datasets.