# Learnable Chamfer Distance for Point Cloud Reconstruction

arXiv: https://arxiv.org/abs/2312.16582 · HTML: https://mlsanity.com/paper/2312.16582/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 27 Dec 2023.

## Builds on (most cited first, 12 of 12)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [PU-GAN: a Point Cloud Upsampling Adversarial Network](https://mlsanity.com/paper/1907.10844/) (2019)
- [PF-Net: Point Fractal Network for 3D Point Cloud Completion](https://mlsanity.com/paper/2003.00410/) (2020)
- [Morphing and Sampling Network for Dense Point Cloud Completion](https://mlsanity.com/paper/1912.00280/) (2019)
- [Cascaded Refinement Network for Point Cloud Completion](https://mlsanity.com/paper/2004.03327/) (2020)
- [Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completion](https://mlsanity.com/paper/2111.12702/) (2021)
- [Global-Local Bidirectional Reasoning for Unsupervised Representation Learning of 3D Point Clouds](https://mlsanity.com/paper/2003.12971/) (2020)
- [SampleNet: Differentiable Point Cloud Sampling](https://mlsanity.com/paper/1912.03663/) (2019)

## Built on by (most cited first, 4 of 4)

- [APML: Adaptive Probabilistic Matching Loss for Robust 3D Point Cloud Reconstruction](https://mlsanity.com/paper/2509.08104/) (2025)
- [Generating Adversarial Point Clouds Using Diffusion Model](https://mlsanity.com/paper/2507.21163/) (2025)
- [Textured Geometry Evaluation: Perceptual 3D Textured Shape Metric via 3D Latent-Geometry Network](https://mlsanity.com/paper/2512.01380/) (2025)
- [On the Structural Failure of Chamfer Distance in 3D Shape Optimization](https://mlsanity.com/paper/2603.09925/) (2026)

## Abstract (arXiv)

As point clouds are 3D signals with permutation invariance, most existing works train their reconstruction networks by measuring shape differences with the average point-to-point distance between point clouds matched with predefined rules. However, the static matching rules may deviate from actual shape differences. Although some works propose dynamically-updated learnable structures to replace matching rules, they need more iterations to converge well. In this work, we propose a simple but effective reconstruction loss, named Learnable Chamfer Distance (LCD) by dynamically paying attention to matching distances with different weight distributions controlled with a group of learnable networks. By training with adversarial strategy, LCD learns to search defects in reconstructed results and overcomes the weaknesses of static matching rules, while the performances at low iterations can also be guaranteed by the basic matching algorithm. Experiments on multiple reconstruction networks confirm that LCD can help achieve better reconstruction performances and extract more representative representations with faster convergence and comparable training efficiency. The source codes are provided in https://github.com/Tianxinhuang/LCDNet.git.