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A Lennard-Jones Layer for Distribution Normalization

arXiv 2402.03287 ↗First posted 5 Feb 2024cs.LG physics.comp-phcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 27 of its 73 references that are in the map. First posted on arXiv 5 Feb 2024.

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References · 27

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
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  12. 2019PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flowscited by 487
15 more
  1. 2018PCN: Point Completion Networkcited by 382
  2. 2019Point-Voxel CNN for Efficient 3D Deep Learningcited by 343
  3. 2020Learning Gradient Fields for Shape Generationcited by 245
  4. 2019Differentiable Surface Splatting for Point-based Geometry Processingcited by 238
  5. 2020GRNet: Gridding Residual Network for Dense Point Cloud Completioncited by 174
  6. 2019PU-GAN: a Point Cloud Upsampling Adversarial Networkcited by 162
  7. 2020PF-Net: Point Fractal Network for 3D Point Cloud Completioncited by 146
  8. 2020Cascaded Refinement Network for Point Cloud Completioncited by 112
  9. 2019PointCleanNet: Learning to Denoise and Remove Outliers from Dense Point Cloudscited by 99
  10. 2021Score-Based Point Cloud Denoisingcited by 83
  11. 2019Total Denoising: Unsupervised Learning of 3D Point Cloud Cleaningcited by 58
  12. 2020Learning Graph-Convolutional Representations for Point Cloud Denoisingcited by 40
  13. 2020Weakly-supervised 3D Shape Completion in the Wildcited by 33
  14. 2019Feature Graph Learning for 3D Point Cloud Denoisingcited by 28
  15. 2022Gaussian Blue Noisecited by 6

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