Select-Sliced Wasserstein Distance for Point Cloud Learning

Quantifying the discrepancy between point sets is a critical component for point cloud learning tasks. The mainstream point cloud learning tasks utilize Chamfer distance and Earth-Mover’s distance. Chamfer distance is computationally efficient but may not fully capture differences between sets of points. Earth-Mover’s distance, while precise, is computationally expensive and can be impractical to use with high-definition data. Several variants of Sliced Wasserstein distances (SW) are introduced to reduce the computation cost, but bring new problems to the situation: The vanilla SW treats sampled slices equally, resulting in redundant projections; Distributional Sliced Wasserstein distance requires gradient-based optimization, offsetting its benefits. To overcome this limitation and leverage the advantages of Sliced Wasserstein distance over EMD, we propose a novel metric, Select-Sliced Wasserstein distance. This new distance analyzes drawn samples of slices and quantifies their informativeness for each point in a single shot, which eliminates unnecessary projections as well as costly optimizations, but perpetuates the performance. Extensive experiments on various point cloud learning tasks to demonstrate the efficiency and effectiveness of the proposed distance metric. Our code is available at https://github.com/VideoProcessingLab/SSW_Distance