A Lennard-Jones Layer for Distribution Normalization
This addresses distribution normalization for point cloud processing, offering a plug-in solution for tasks like generation and denoising, but it appears incremental as it adapts known physical interactions to neural networks.
The paper tackles the problem of normalizing the density of 2D and 3D point clouds by introducing the Lennard-Jones layer (LJL), which rearranges points to approximate an equidistant sampling without destroying overall structure, and demonstrates its effectiveness in improving point cloud generation and denoising at negligible cost.
We introduce the Lennard-Jones layer (LJL) for the equalization of the density of 2D and 3D point clouds through 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 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 the generation process of point cloud networks by adding them at later stages of the inference process. The improvements in 3D point cloud generation utilizing LJLs 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 network.