Abstract: Advancing Large-scale Deformable 3D Registration with Differentiable Volumetric Rasterisation of Point Clouds

3D point clouds are an efficient and privacy-preserving representation of medical scans highly suitable for complex segmentation and registration tasks. Yet, current loss functions for training self-supervised geometric networks are insufficient to handle largescale clouds and provide robust derivatives. Here, we present Differentiable Volumetric Rasterisation of Point Clouds (DiVRoC) that overcomes those limitations and provides highly accurate learning- or optimisation-based deformable 3D registration [1]. The key contribution is the derivation of a reverse grid-sampling operation with gradients for the motion vectors that can rapidly transform between grid-based volumetric and sparse point representations. It enables scalable regularisation and loss computation on 3D point clouds with >100k points being orders of magnitude faster than a Chamfer loss. The concept includes geometric registration networks that can be robustly trained in an unsupervised fashion and act on sparser point clouds. This is followed by a regularisation model that enables extrapolation for high-resolution distance metrics. Our experiments on the challenging PVT1010 lung dataset [2] that includes large motion of COPD patients between inspiration and expiration demonstrate state-of-the-art accuracies for training a PointPWC-Net and/or alignment based on Adam instance optimisation. The model reduces registration errors to approx. 2.4 mm and runs on very large point clouds in one second. The DiVRoC module can also be used to learn shape models for 3D surfaces [3]. Implementation details to use DiVRoC as drop-in replacement for point distances, a new out-of-domain dataset for evaluation and demos for realtime inference can be found at https://github.com/mattiaspaul/ChasingClouds.