Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completion (2111.12702v1)

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 .

• The paper introduces Density-aware Chamfer Distance as a novel metric that overcomes limitations of traditional metrics like CD and EMD in evaluating point cloud completion.
• It employs a query frequency fraction and Taylor Expansion to integrate global efficiency with local density sensitivity, enhancing structure evaluation.
• Experimental results show DCD produces consistent and improved performance across various metrics in point cloud completion tasks.

An Analysis of Density-aware Chamfer Distance for Point Cloud Completion

The paper "Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completion" introduces a novel metric, namely Density-aware Chamfer Distance (DCD), aimed at addressing deficiencies in conventional point cloud similarity metrics. The extant metrics, Chamfer Distance (CD) and Earth Mover's Distance (EMD), exhibit limitations such as insensitivity to local density variations and excessive sensitivity to global distribution, respectively. The proposed DCD metric amalgamates the advantages of both CD and EMD while mitigating their shortcomings.

Core Contributions and Findings

1. Enhanced Sensitivity to Density Distributions: DCD introduces a mechanism to detect density distribution discrepancies by incorporating a query frequency fraction. This allows DCD to more critically evaluate point clouds by accounting for mismatched density distributions, which is often overlooked by CD.
2. Balance Between Global and Local Structures: While retaining the computational efficiency of CD, DCD adds computational rigor to finer structures and local details, similar to EMD, but alleviates the computational overhead associated with EMD. This balance is achieved through an approximation using Taylor Expansion which bounds the metric's value and thus controls outlier influence.
3. Consistency Over Point Set Variations: The experimental evidence suggests that DCD maintains consistent evaluations between competing models where CD and EMD might contradict each other. This attribute is particularly highlighted through the point cloud completion tasks, where DCD outperforms when employed as a training loss, providing superior results across three different metrics.
4. Practical Implementation and Evaluation: The experimental results demonstrate that DCD offers a more robust evaluation compared to CD and EMD when examining the quality of generated shapes. Its capability as both a metric and a training loss function is unequivocally established, outperforming models trained with conventional metrics.

Theoretical and Practical Implications

The DCD metric has substantial implications in both theory and application. Theoretically, DCD provides an enriched framework for redefining distance metrics in point cloud analysis, potentially influencing further developments in distance functions that account for local density and distribution metrics. Practically, the employment of DCD in point cloud tasks such as completion, upsampling, and denoising could enhance model performance by encouraging generation outputs that are faithful to both local and global point distributions.

Future Prospects in AI and Computer Vision

The paper positions DCD as a stepping stone towards more comprehensive and context-sensitive evaluation metrics in the field of 3D point cloud tasks. As AI systems increasingly intersect with 3D data, metrics such as DCD could significantly influence the fidelity and effectiveness of geometric deep learning, benefiting applications in areas like autonomous driving, AR/VR systems, and robotics.

In summary, the Density-aware Chamfer Distance metric emerges as a meaningful advancement in point cloud completion tasks, addressing the limitations of current metrics and paving the way for more detailed and balanced model evaluations. Its innovation lies in captivating a nuanced balance between efficiency, structure sensitivity, and robustness against distribution anomalies, thereby offering novel avenues for research and application in AI.