Chasing clouds: Differentiable volumetric rasterisation of point clouds as a highly efficient and accurate loss for large-scale deformable 3D registration

Learning-based registration for large-scale 3D point clouds has been shown to improve robustness and accuracy compared to classical methods and can be trained without supervision for locally rigid problems. However, for tasks with highly deformable structures, such as alignment of pulmonary vascular trees for medical diagnostics, previous approaches of self-supervision with regularisation and point distance losses have failed to succeed, leading to the need for complex synthetic augmentation strategies to obtain reliably strong supervision. In this work, we introduce a novel Differentiable Volumetric Rasterisation of point Clouds (DiVRoC) that overcomes those limitations and offers a highly efficient and accurate loss for large-scale deformable 3D registration. DiVRoC drastically reduces the computational complexity for measuring point cloud distances for high-resolution data with over 100k 3D points and can also be employed to extrapolate and regularise sparse motion fields, as loss in a self-training setting and as objective function in instance optimisation. DiVRoC can be successfully embedded into geometric registration networks, including PointPWC-Net and other graph CNNs. Our approach yields new state-of-the-art accuracy on the challenging PVT dataset in three different settings without training with manual ground truth: 1) unsupervised metric-based learning 2) self-supervised learning with pseudo labels generated by self-training and 3) optimisation based alignment without learning. https://github.com/mattiaspaul/ChasingClouds