We propose an efficient and effective method to learn convolutions for non-uniformly sampled point clouds, as they are obtained with modern acquisition techniques. Learning is enabled by four key novelties: first, representing the convolution kernel itself as a multilayer perceptron; second, phrasing convolution as a Monte Carlo integration problem, third, constructing an unstructured Poisson disk hierarchy for pooling, and fourth, using Monte Carlo convolution as pooling and upsampling operation at different resolutions simultaneously. The key idea across all these contributions is to guarantee adequate consideration of the underlying non-uniform sample distribution function from a Monte Carlo perspective. To make the proposed concepts applicable for real-world tasks, we furthermore propose an efficient implementation which significantly reduces the required GPU memory. By employing our method in hierarchical network architectures we can outperform most of the state-of-the-art networks on established point cloud segmentation, classification and normal estimation benchmarks. Furthermore, in contrast to most existing approaches, we can also demonstrate the robustness of our method with respect to sampling variations even when only trained on uniformly sampled models.

本文提出了一种有效的深度学习方法，可用于非均匀采样的点云，通过将卷积核本身表示为多层感知机，将卷积视为蒙特卡罗积分问题，使用匹配多级采样的信息，并使用泊松盘采样进行点云学习。 最终，作者通过在分级网络架构中应用该方法，赢得了大多数基于点云的任务的最佳成绩，并且本方法具有强大的鲁棒性。

蒙特卡罗卷积用于不均匀采样点云学习