A Lennard-Jones Layer for Distribution Normalization

Embargo End Date
2024-05-14

Type
Thesis

Authors
Na, Mulun

Advisors
Michels, Dominik L.

Committee Members
Wonka, Peter
Pottmann, Helmut

Program
Computer Science

KAUST Department
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

Date
2023-05-11

Access Restrictions
At the time of archiving, the student author of this thesis opted to temporarily restrict access to it. The full text of this thesis will become available to the public after the expiration of the embargo on 2024-05-14.

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 over the 2D Euclidean plane and 3D mesh surfaces. 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.

Citation
Na, M. (2023). A Lennard-Jones Layer for Distribution Normalization [KAUST Research Repository]. https://doi.org/10.25781/KAUST-960B5

DOI
10.25781/KAUST-960B5

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