Balanced Chamfer Distance as a Comprehensive Metric for Point Cloud Completion

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 and robust evaluation. To tackle these problems, we propose a new similarity measure named Balanced Chamfer Distance (BCD). 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 robust evaluation over the whole test set. We evaluate the proposed BCD on the point cloud completion task, in which BCD is used to measure the similarity between the completion results and the high-fidelity ground truth. Experimental results show that BCD not only evaluates the accuracy of overall structures but also pays more attention to local geometric features by considering point density distributions. In particular, BCD can provide a more reliable evaluation, as CD and EMD often contradict each other. To enhance the balanced distribution of predicted complete point clouds, we incorporate a balanced design and propose a novel point discriminator module in our network, which achieves noticeable improvements under BCD together with competitive results for both CD and EMD. We hope our work could pave the way for a more robust and practical point cloud similarity evaluation.