  We present a new method for the unsupervised detection of geometric anomalies
in high-resolution 3D point clouds. In particular, we propose an adaptation of
the established student-teacher anomaly detection framework to three
dimensions. A student network is trained to match the output of a pretrained
teacher network on anomaly-free point clouds. When applied to test data,
regression errors between the teacher and the student allow reliable
localization of anomalous structures. To construct an expressive teacher
network that extracts dense local geometric descriptors, we introduce a novel
self-supervised pretraining strategy. The teacher is trained by reconstructing
local receptive fields and does not require annotations. Extensive experiments
on the comprehensive MVTec 3D Anomaly Detection dataset highlight the
effectiveness of our approach, which outperforms the next-best method by a
large margin. Ablation studies show that our approach meets the requirements of
practical applications regarding performance, runtime, and memory consumption.
