Novel Point Cloud Distance Metric with Adjustable Error Sensitivity and Shape Compensation

Point distance metrics such as Chamfer Distance (CD) and Earth Mover’s Distance (EMD) play a key role in evaluating the quality of reconstructed point clouds and computing training loss in point cloud reconstruction. However, the metrics show their own characteristics in evaluation, stemming from differences in their sensitivity to point cloud error traits, which, in turn, causes differences in their performance of point cloud evaluation and reconstruction. In this study, we analyzed in detail the sensitivity of distance metrics to such error traits as density imbalance and point dispersion. We showed how the sensitivity difference in metrics affects their performance in point cloud evaluation and reconstruction. Recognizing that the sensitivity of a metric is correlated with the level of bijective one-to-one point correspondence embedded in the metric, we proposed a new metric, the nestedChamfer distance (NCD-n), that allows to adjust its sensitivity to error traits through the nested CD cycle, n, by which the level of bijective one-to-one point correspondence is controlled. In addition, we analyzed the effect of shape-induced point density difference on distance metrics and proposed taking shape compensation into account in metrics. Based on extensive experiments, we verified the difference of metrics in their sensitivities to error traits, the capability of the proposed NCD-n for adjusting its sensitivity effectively, and the effect of sensitivity adjustment and shape-compensation on the performance of point cloud evaluation and reconstruction.