Monte Carlo Convolution for Learning on Non-Uniformly Sampled Point Clouds
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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.
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