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.

翻译：对称性检测，特别是局部对称与外蕴对称，对于三维几何补全、分割、压缩以及结构感知的形状编码或生成等下游任务至关重要。为检测局部外蕴对称性，我们提出通过对比学习为测地点云块学习旋转、反射、平移和尺度不变的局部形状特征，这些特征在多个类别中具有鲁棒性，并能泛化到不同数据集。我们证明了该方法能够为此歧义问题提取多个有效解。此外，我们引入了一个用于局部外蕴对称性检测的新基准测试来评估我们的方法。最后，我们将检测到的对称性与区域生长算法结合，展示了以计算三维形状对称感知分区为目标的下游任务。据我们所知，我们是首个提出用于局部外蕴对称性检测的自监督数据驱动方法。