Survey on sparsity in geometric modeling and processing

Abstract

Techniques from sparse representation have been successfully applied in many areas like digital image processing, computer vision and pattern recognition in the past ten years. However, sparsity based methods in geometric processing is far from popular than its applications in these areas. The main reason is that geometric signal is a two-dimensional manifold and its discrete representations are always irregular, which is different from signals like audio and image. Therefore, existing techniques cannot be directly extended to handle geometric models. Fortunately, sparse models are beginning to see significant success in many classical geometric processing problems like mesh denoising, point cloud compression, etc. This review paper highlights a few representative examples of how the interaction between sparsity based methods and geometric processing can enrich both fields, and raises a number of open questions for future study.