Abstract: 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.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: Following the advise of the AE, we have addressed Request 1 (theorem outlining the convergence properties of the LJL and proof on page 17 of the updated manuscript) and Request 2 (multiple changes throughout the paper addressing the promised revisions).
Video: https://www.youtube.com/watch?v=XlLpASZ2QE4
Assigned Action Editor: ~David_Fouhey2
Submission Number: 2141
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