Local 3D Point Cloud Denoising via Bipartite Graph Approximation & Total Variation

Abstract

Acquired 3D point cloud data, whether from active sensors directly or from stereo-matching algorithms indirectly, typically contain non-negligible noise. To address the point cloud denoising problem, we propose a local graph-based algorithm. Specifically, given a $k$ -nearest-neighbor graph of the 3D points, we first approximate it with a bipartite graph (independent sets of red and blue nodes) using a KL divergence criterion. For each partite of nodes (say red), we first define surface normal of each red node using 3D coordinates of neighboring blue nodes, so that red node normals n can be written as a linear function of red node coordinates p. We then formulate a convex optimization problem, with a quadratic fidelity term $\Vert \mathbf{p}-\mathbf{q}\Vert_{2}^{2}$ given noisy observed red coordinates q and a graph total variation (GTV) regularization term for surface normals of neighboring red nodes. We minimize the resulting $l_{2}-l_{1}$-norm using alternating direction method of multipliers (ADMM) and proximal gradient descent. The two partites of nodes are alternately optimized until convergence. Experimental results show that compared to state-of-the-art schemes with similar complexity, our proposed algorithm achieves the best overall denoising performance objectively and subjectively.