Flexible-weighted Chamfer Distance: Enhanced Objective Function for Point Cloud Completion

TL;DR

The paper addresses the instability of using Chamfer Distance with fixed, equal weights for its local and global components in point cloud completion. It proposes Flexible-weighted Chamfer Distance (FCD), which treats the CD components as two learning objectives with adaptable weights, allowing a global-distribution–first training regime through Preset Adaptive Weighting and Uncertainty Weighting strategies. Empirical results on ShapeNet55 and PCN datasets using AdaPoinTr and SeedFormer show that FCD improves global distribution (lower DCD/EMD) while maintaining or enhancing local fidelity (CD, F-Score), corroborated by qualitative visualizations. The approach is plug-and-play and generalizable to other CD-based objectives, offering a practical route to better complete point clouds with balanced global structure and local detail.

Abstract

Chamfer Distance (CD) comprises two components that can evaluate the global distribution and local performance of generated point clouds, making it widely utilized as a similarity measure between generated and target point clouds in point cloud completion tasks. Additionally, CD's computational efficiency has led to its frequent application as an objective function for guiding point cloud generation. However, using CD directly as an objective function with fixed equal weights for its two components can often result in seemingly high overall performance (i.e., low CD score), while failing to achieve a good global distribution. This is typically reflected in high Earth Mover's Distance (EMD) and Decomposed Chamfer Distance (DCD) scores, alongside poor human assessments. To address this issue, we propose a Flexible-Weighted Chamfer Distance (FCD) to guide point cloud generation. FCD assigns a higher weight to the global distribution component of CD and incorporates a flexible weighting strategy to adjust the balance between the two components, aiming to improve global distribution while maintaining robust overall performance. Experimental results on two state-of-the-art networks demonstrate that our method achieves superior results across multiple evaluation metrics, including CD, EMD, DCD, and F-Score, as well as in human evaluations.

Figures (6)

• Figure 1: The structural features of $\mathcal{P}_1$ and $\mathcal{P}_2$ with identical CD metric. (a) and (c) illustrate the assignment strategies from the predicted point cloud $\mathcal{P}_1$ to the ground-truth point cloud $\mathcal{G}$ and vice versa, respectively. (b) and (d) depict the assignment strategies from the predicted point cloud $\mathcal{P}_2$ to the ground-truth point cloud $\mathcal{G}$ and vice versa, respectively.
• Figure 2: Preset Adaptive Weighting approaches.
• Figure 3: Overview of our point cloud completion processes. In our experiments, SeedFormer (with several upsample layers) and AdaPoinTr are used as the baseline models, and the results they generate include both the coarse and fine point clouds. To investigate the impact of different FCD weighting strategies on the final generated results, we apply a statically scheduled Preset Adaptive Weighting to compute the loss for the coarse point cloud. For the final point cloud, we use Preset Adaptive Weighting with various schedules, as well as Uncertainty Weighting, to calculate the loss.
• Figure 4: Visual results using $\mathcal{L}_{part}$ as objective function.
• Figure 5: Visual comparisons using CD or FCD as the objective function on the PCN dataset. Employing FCD for model training guidance can produce outcomes featuring superior global structure and finer local details in contrast to utilizing CD.