[Paper Review] Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completion

Tong Wu, Liang Pan+4 more|arXiv (Cornell University)|Nov 24, 2021

3D Shape Modeling and AnalysisEngineering38 references68 citations

TL;DR

Introduces Density-aware Chamfer Distance (DCD), a bounded, density-sensitive metric derived from Chamfer Distance to better evaluate and train point cloud completion, complemented by a point discriminator and guided down-sampling.

ABSTRACT

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 .

Motivation & Objective

• Identify limitations of Chamfer Distance (CD) and Earth Mover’s Distance (EMD) in point cloud completion evaluation.
• Propose Density-aware Chamfer Distance (DCD) to capture density distribution and local detail while remaining efficient and bounded.
• Demonstrate DCD as a reliable evaluation metric and effective loss function for training.
• Develop a point discriminator module to enable guided down-sampling and balanced point distributions during completion.

Proposed method

• Derive DCD by applying a first-order Taylor expansion to CD to bound the per-point contribution between 0 and 1.
• Incorporate a density-aware term by weighting each point’s contribution with its query frequency n_y and a temperature parameter alpha.
• Introduce a two-term symmetric loss using DCD to provide bounded, gradient-stable optimization.
• Design a neural point discriminator that predicts a density-aware signal g(x) to identify point importance.
• Use the discriminator output to perform guided down-sampling, reducing outliers and balancing density during two-stage completion.
• Optionally replace CD loss with DCD loss during training to improve both global structure and local detail.

Experimental results

Research questions

• RQ1 Can a density-aware modification of Chamfer Distance provide more consistent evaluation across varying local densities and noise levels in point clouds?
• RQ2 Does DCD outperform CD and EMD as both an evaluation metric and a training loss for point cloud completion tasks?
• RQ3 Can a density-aware discriminator plus guided down-sampling improve completion quality and stability across datasets?
• RQ4 What are the practical effects of using DCD as a loss function on common PCN-family architectures?
• RQ5 How does DCD balance global structure preservation with fine local details compared to CD and EMD?

Key findings

• DCD provides bounded, [0,1]-normalized distances that correlate with both global structure and local geometry.
• DCD is more consistent and reliable than CD and EMD, especially when CD and EMD disagree.
• Training with DCD as a loss reduces EMD and can also reduce CD compared with CD-trained models.
• A two-stage completion framework with a density-aware point discriminator and guided down-sampling yields improved visual quality and balanced point distributions.
• Replacing CD loss with DCD loss in competitive baselines achieves favorable trade-offs across CD, EMD, and DCD metrics.