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Point Cloud Compression via Constrained Optimal Transport

Zezeng Li, Weimin Wang, Ziliang Wang, Na Lei

TL;DR

This paper presents a novel point cloud compression method COT-PCC, which takes the bitrate of compressed features as an extra constraint of optimal transport (OT) which learns the distribution transformation between original and reconstructed points.

Abstract

This paper presents a novel point cloud compression method COT-PCC by formulating the task as a constrained optimal transport (COT) problem. COT-PCC takes the bitrate of compressed features as an extra constraint of optimal transport (OT) which learns the distribution transformation between original and reconstructed points. Specifically, the formulated COT is implemented with a generative adversarial network (GAN) and a bitrate loss for training. The discriminator measures the Wasserstein distance between input and reconstructed points, and a generator calculates the optimal mapping between distributions of input and reconstructed point cloud. Moreover, we introduce a learnable sampling module for downsampling in the compression procedure. Extensive results on both sparse and dense point cloud datasets demonstrate that COT-PCC outperforms state-of-the-art methods in terms of both CD and PSNR metrics. Source codes are available at \url{https://github.com/cognaclee/PCC-COT}.

Point Cloud Compression via Constrained Optimal Transport

TL;DR

This paper presents a novel point cloud compression method COT-PCC, which takes the bitrate of compressed features as an extra constraint of optimal transport (OT) which learns the distribution transformation between original and reconstructed points.

Abstract

This paper presents a novel point cloud compression method COT-PCC by formulating the task as a constrained optimal transport (COT) problem. COT-PCC takes the bitrate of compressed features as an extra constraint of optimal transport (OT) which learns the distribution transformation between original and reconstructed points. Specifically, the formulated COT is implemented with a generative adversarial network (GAN) and a bitrate loss for training. The discriminator measures the Wasserstein distance between input and reconstructed points, and a generator calculates the optimal mapping between distributions of input and reconstructed point cloud. Moreover, we introduce a learnable sampling module for downsampling in the compression procedure. Extensive results on both sparse and dense point cloud datasets demonstrate that COT-PCC outperforms state-of-the-art methods in terms of both CD and PSNR metrics. Source codes are available at \url{https://github.com/cognaclee/PCC-COT}.
Paper Structure (11 sections, 9 equations, 6 figures, 1 table)

This paper contains 11 sections, 9 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Preliminaries
  4. Formulation of PCC with COT
  5. Implementation of COT
  6. Experiments
  7. Setup
  8. Quantitative results
  9. Qualitative results
  10. Ablation Study
  11. Conclusion

Figures (6)

  • Figure 1: The framework of the proposed COT-PCC. The Encoder consists of three stages of Sampler, which is a learnable sampling module. As the output of the last stage, coordinates $P_3$ and features $F_3$ are followed by Quantizer for bit compression. Decoder reconstructs the data from compressed $\hat{P}_3$ and $\hat{F}_3$. The COT objective quantifies the reconstruction performance via OT loss within the bitrate constraint. Dash lines indicate the process only in the training phase.
  • Figure 2: The Encoder. $\oplus$ and $\circleddash$ denote concatenation and subtraction of tensor, respectively. Indexing means sampling points and features according to the index.
  • Figure 3: Quantitative results on SemanticKITTI and ShapeNet.
  • Figure 4: Quantitative results on MPEG PCC dataset.
  • Figure 5: Decompression examples from SemanticKITTI and ShapeNet datasets. Cool colors indicate small errors.
  • ...and 1 more figures