Point Cloud Completion with Landau Distribution: A Probabilistic View
Keywords: Point Cloud Completion, Landau Distribution, Loss Function Design
TL;DR: We propose a new distribution-based loss function for point cloud completion, namely LandauCD
Abstract: Point clouds are fundamental discrete representations used in computer vision, robotics, etc. Chamfer Distance (CD) is widely adopted as a metric and training loss to evaluate the similarity between two point clouds. However, the vanilla CD is sensitive to outliers, which means a few widely distributed points can disproportionately affect the final similarity score. Besides, CD calculates the simple average of distances of matched point pairs between two sets, which does not take into account the underlying point-wise distance distribution across two point clouds (same weights assigned for short- and long-distance pairs by using uniform distribution). To mitigate these issues, we analyze the effect of prioritizing short- and long-distance pairs with Gaussian distributions obtained with grid search, and based on the findings, we take an indirect approach to find Landau distribution, out of many distributions, fits in the form of bimodal Gaussian mixture model which balances two types of pairs. Based on this observation, we propose LandauCD, an innovative loss function grounded in the Landau distribution. We conduct comprehensive experiments using LandauCD and observe significant improvements consistently over all the popular baseline networks trained with CD-based losses, leading to new state-of-the-art results on several benchmarks (PCN, Shapet-55/34, ShapeNet-Part). We also delve into the theoretical explanation behind the consistent improvements of LandauCD. Code and weights will be released upon acceptance.
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Submission Number: 2158
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