A Lennard-Jones Layer for Distribution Normalization

Mulun Na, Jonathan Klein, Dmitry Lyakhov, Biao Zhang, Wojciech Pałubicki, Soren Pirk, Dominik Michels

Keywords: Lennard-Jones Potential, Network Architecture, Point Cloud Generation, Point Cloud Denoising, Blue Noise

TL;DR: Lennard-Jones layers can be added to existing network architectures to normalize point cloud distributions to improve overall results.

Abstract: We introduce a Lennard-Jones layer (LJL) to equalize the density across the distribution of 2D and 3D point clouds by systematically rearranging points without destroying their overall structure (distribution normalization). LJL simulates a dissipative process of repulsive and weakly attractive interactions between individual points by solely considering the nearest neighbor of each point at a given moment in time. This pushes the particles into a potential valley, reaching a well-defined stable configuration that approximates an equidistant sampling after the stabilization process. We apply LJLs to redistribute randomly generated point clouds into a randomized uniform distribution. Moreover, LJLs are embedded in point cloud generative network architectures by adding them at later stages of the inference process. The improvements coming with LJLs for generating 3D point clouds are evaluated qualitatively and quantitatively. Finally, we apply LJLs to improve the point distribution of a score-based 3D point cloud denoising network. In general, we demonstrate that LJLs are effective for distribution normalization which can be applied at negligible cost without retraining the given neural networks.

Primary Area: general machine learning (i.e., none of the above)

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Submission Number: 5825