3D Point Cloud Denoising Using Graph Laplacian Regularization of a Low Dimensional Manifold Model

• Published in: IEEE transactions on image processing Vol. 29; pp. 3474 - 3489
• Main Authors: Zeng, Jin, Cheung, Gene, Ng, Michael, Pang, Jiahao, Yang, Cheng
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.01.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Computer simulation; Data acquisition; Distance measurement; Graph signal processing; Image acquisition; Image denoising; Laplace equations; low-dimensional manifold; Manifolds; Manifolds (mathematics); Noise measurement; Noise reduction; Numerical stability; Patches (structures); point cloud denoising; Regularization; Robustness (mathematics); Salience; Self-similarity; Surface treatment; Three dimensional models; Three-dimensional displays; Visual perception
• ISSN: 1057-7149; 1941-0042; 1941-0042
• DOI: 10.1109/TIP.2019.2961429

3D point cloud-a new signal representation of volumetric objects-is a discrete collection of triples marking exterior object surface locations in 3D space. Conventional imperfect acquisition processes of 3D point cloud-e.g., stereo-matching from multiple viewpoint images or depth data acquired directly from active light sensors-imply non-negligible noise in the data. In this paper, we extend a previously proposed low-dimensional manifold model for the image patches to surface patches in the point cloud, and seek self-similar patches to denoise them simultaneously using the patch manifold prior. Due to discrete observations of the patches on the manifold, we approximate the manifold dimension computation defined in the continuous domain with a patch-based graph Laplacian regularizer, and propose a new discrete patch distance measure to quantify the similarity between two same-sized surface patches for graph construction that is robust to noise. We show that our graph Laplacian regularizer leads to speedy implementation and has desirable numerical stability properties given its natural graph spectral interpretation. Extensive simulation results show that our proposed denoising scheme outperforms state-of-the-art methods in objective metrics and better preserves visually salient structural features like edges.