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

TL;DR

This paper introduces a fast, graph-based local algorithm for denoising 3D point clouds by approximating k-nearest-neighbor graphs with bipartite graphs and applying total variation regularization, achieving superior results.

Contribution

The paper presents a novel bipartite graph approximation method combined with total variation regularization for efficient 3D point cloud denoising, outperforming existing techniques.

Findings

Achieves the best denoising performance compared to state-of-the-art methods.

Provides a fast and scalable algorithm with similar complexity to existing schemes.

Demonstrates superior subjective and objective denoising quality.

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 fast graph-based local 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 ||p-q||_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 l2-l1-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.