Structure-Aware Joint Sparse Optimization for Point Cloud Denoising.

Point clouds are widely used to represent real-world objects in the fields of augmented/virtual reality, robotics, etc. However, they are often corrupted with noise, hindering downstream tasks such as mesh surface reconstruction, rendering, etc. In this paper, we revisit sparse point cloud representation for denoising. We observe that existing works generally assume global sparsity of noise across point cloud surfaces, leading to over-smoothing, and typically adopt multiple stages to recover features, inevitably introducing biases and structural inconsistencies. To address these challenges, we propose a structure-aware joint sparse optimization approach for point cloud denoising. Specifically, considering that sparsity primarily lies in feature areas, we propose a novel group-level sparsity-based approximate deviation to characterize surface distortion for different structures. Based on that, we develop an optimization model that can protect structural integrity. We further derive a linear approximate solution and provide a parallel denoising algorithm. Experimental results on different types of datasets demonstrate that the proposed approach outperforms the state-of-the-art works.