  Symmetry detection, especially partial and extrinsic symmetry, is essential
for various downstream tasks, like 3D geometry completion, segmentation,
compression and structure-aware shape encoding or generation. In order to
detect partial extrinsic symmetries, we propose to learn rotation, reflection,
translation and scale invariant local shape features for geodesic point cloud
patches via contrastive learning, which are robust across multiple classes and
generalize over different datasets. We show that our approach is able to
extract multiple valid solutions for this ambiguous problem. Furthermore, we
introduce a novel benchmark test for partial extrinsic symmetry detection to
evaluate our method. Lastly, we incorporate the detected symmetries together
with a region growing algorithm to demonstrate a downstream task with the goal
of computing symmetry-aware partitions of 3D shapes. To our knowledge, we are
the first to propose a self-supervised data-driven method for partial extrinsic
symmetry detection.
