# Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completion

arXiv: https://arxiv.org/abs/2111.12702 · HTML: https://mlsanity.com/paper/2111.12702/

## Key facts

- Cited by 112 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 44 references that are in the map.
- First posted on arXiv 24 Nov 2021.

## Builds on (most cited first, 30 of 35)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Cylindrical and Asymmetrical 3D Convolution Networks for LiDAR Segmentation](https://mlsanity.com/paper/2011.10033/) (2020)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [GRNet: Gridding Residual Network for Dense Point Cloud Completion](https://mlsanity.com/paper/2006.03761/) (2020)
- [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)
- [Point Cloud Completion by Skip-attention Network with Hierarchical Folding](https://mlsanity.com/paper/2005.03871/) (2020)
- [PointGrow: Autoregressively Learned Point Cloud Generation with Self-Attention](https://mlsanity.com/paper/1810.05591/) (2018)
- [Variational Relational Point Completion Network](https://mlsanity.com/paper/2104.10154/) (2021)
- [High-Resolution Shape Completion Using Deep Neural Networks for Global Structure and Local Geometry Inference](https://mlsanity.com/paper/1709.07599/) (2017)
- [Detail Preserved Point Cloud Completion via Separated Feature Aggregation](https://mlsanity.com/paper/2007.02374/) (2020)
- [Unsupervised 3D Shape Completion through GAN Inversion](https://mlsanity.com/paper/2104.13366/) (2021)
- [Improved Adversarial Systems for 3D Object Generation and Reconstruction](https://mlsanity.com/paper/1707.09557/) (2017)
- [Unpaired Point Cloud Completion on Real Scans using Adversarial Training](https://mlsanity.com/paper/1904.00069/) (2019)
- [On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithms](https://mlsanity.com/paper/1901.06482/) (2019)
- [Multimodal Shape Completion via Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2003.07717/) (2020)
- [Total Denoising: Unsupervised Learning of 3D Point Cloud Cleaning](https://mlsanity.com/paper/1904.07615/) (2019)
- [Point-set Distances for Learning Representations of 3D Point Clouds](https://mlsanity.com/paper/2102.04014/) (2021)

## Built on by (most cited first, 30 of 112)

- [Comprehensive Review of Deep Learning-Based 3D Point Cloud Completion Processing and Analysis](https://mlsanity.com/paper/2203.03311/) (2022)
- [ProxyFormer: Proxy Alignment Assisted Point Cloud Completion with Missing Part Sensitive Transformer](https://mlsanity.com/paper/2302.14435/) (2023)
- [3D Face Reconstruction with the Geometric Guidance of Facial Part Segmentation](https://mlsanity.com/paper/2312.00311/) (2023)
- [Entity-Centric Reinforcement Learning for Object Manipulation from Pixels](https://mlsanity.com/paper/2404.01220/) (2024)
- [Advancements in Point Cloud Data Augmentation for Deep Learning: A Survey](https://mlsanity.com/paper/2308.12113/) (2023)
- [Spatial Reasoning in Multimodal Large Language Models: A Survey of Tasks, Benchmarks and Methods](https://mlsanity.com/paper/2511.15722/) (2025)
- [SuperPC: A Single Diffusion Model for Point Cloud Completion, Upsampling, Denoising, and Colorization](https://mlsanity.com/paper/2503.14558/) (2025)
- [NeuralVDB: High-resolution Sparse Volume Representation using Hierarchical Neural Networks](https://mlsanity.com/paper/2208.04448/) (2022)
- [Bayesian Diffusion Models for 3D Shape Reconstruction](https://mlsanity.com/paper/2403.06973/) (2024)
- [High Fidelity 3D Hand Shape Reconstruction via Scalable Graph Frequency Decomposition](https://mlsanity.com/paper/2307.05541/) (2023)
- [NeuSDFusion: A Spatial-Aware Generative Model for 3D Shape Completion, Reconstruction, and Generation](https://mlsanity.com/paper/2403.18241/) (2024)
- [RibSeg v2: A Large-scale Benchmark for Rib Labeling and Anatomical Centerline Extraction](https://mlsanity.com/paper/2210.09309/) (2022)
- [Taming Anomalies with Down-Up Sampling Networks: Group Center Preserving Reconstruction for 3D Anomaly Detection](https://mlsanity.com/paper/2507.03903/) (2025)
- [TCDM: Transformational Complexity Based Distortion Metric for Perceptual Point Cloud Quality Assessment](https://mlsanity.com/paper/2210.04671/) (2022)
- [Multi-View Partial (MVP) Point Cloud Challenge 2021 on Completion and Registration: Methods and Results](https://mlsanity.com/paper/2112.12053/) (2021)
- [CP3: Unifying Point Cloud Completion by Pretrain-Prompt-Predict Paradigm](https://mlsanity.com/paper/2207.05359/) (2022)
- [PICASSO: A Feed-Forward Framework for Parametric Inference of CAD Sketches via Rendering Self-Supervision](https://mlsanity.com/paper/2407.13394/) (2024)
- [SCARP: 3D Shape Completion in ARbitrary Poses for Improved Grasping](https://mlsanity.com/paper/2301.07213/) (2023)
- [Neural Garment Dynamics via Manifold-Aware Transformers](https://mlsanity.com/paper/2407.06101/) (2024)
- [OP-Align: Object-level and Part-level Alignment for Self-supervised Category-level Articulated Object Pose Estimation](https://mlsanity.com/paper/2408.16547/) (2024)
- [Hyperbolic-constraint Point Cloud Reconstruction from Single RGB-D Images](https://mlsanity.com/paper/2412.09055/) (2024)
- [LAM3D: Large Image-Point-Cloud Alignment Model for 3D Reconstruction from Single Image](https://mlsanity.com/paper/2405.15622/) (2024)
- [Toward Mesh-Invariant 3D Generative Deep Learning with Geometric Measures](https://mlsanity.com/paper/2306.15762/) (2023)
- [High-Resolution Cranial Defect Reconstruction by Iterative, Low-Resolution, Point Cloud Completion Transformers](https://mlsanity.com/paper/2308.03813/) (2023)
- [BuilDiff: 3D Building Shape Generation using Single-Image Conditional Point Cloud Diffusion Models](https://mlsanity.com/paper/2309.00158/) (2023)
- [ADoPT: LiDAR Spoofing Attack Detection Based on Point-Level Temporal Consistency](https://mlsanity.com/paper/2310.14504/) (2023)
- [Arbitrary-Scale Point Cloud Upsampling by Voxel-Based Network with Latent Geometric-Consistent Learning](https://mlsanity.com/paper/2403.05117/) (2024)
- [Shape Completion with Points in the Shadow](https://mlsanity.com/paper/2209.08345/) (2022)
- [LD-SDM: Language-Driven Hierarchical Species Distribution Modeling](https://mlsanity.com/paper/2312.08334/) (2023)
- [Learnable Chamfer Distance for Point Cloud Reconstruction](https://mlsanity.com/paper/2312.16582/) (2023)

## Abstract (arXiv)

Chamfer Distance (CD) and Earth Mover's Distance (EMD) are two broadly adopted metrics for measuring the similarity between two point sets. However, CD is usually insensitive to mismatched local density, and EMD is usually dominated by global distribution while overlooks the fidelity of detailed structures. Besides, their unbounded value range induces a heavy influence from the outliers. These defects prevent them from providing a consistent evaluation. To tackle these problems, we propose a new similarity measure named Density-aware Chamfer Distance (DCD). It is derived from CD and benefits from several desirable properties: 1) it can detect disparity of density distributions and is thus a more intensive measure of similarity compared to CD; 2) it is stricter with detailed structures and significantly more computationally efficient than EMD; 3) the bounded value range encourages a more stable and reasonable evaluation over the whole test set. We adopt DCD to evaluate the point cloud completion task, where experimental results show that DCD pays attention to both the overall structure and local geometric details and provides a more reliable evaluation even when CD and EMD contradict each other. We can also use DCD as the training loss, which outperforms the same model trained with CD loss on all three metrics. In addition, we propose a novel point discriminator module that estimates the priority for another guided down-sampling step, and it achieves noticeable improvements under DCD together with competitive results for both CD and EMD. We hope our work could pave the way for a more comprehensive and practical point cloud similarity evaluation. Our code will be available at: https://github.com/wutong16/Density_aware_Chamfer_Distance .