Partial Symmetry Detection for 3D Geometry using Contrastive Learning with Geodesic Point Cloud Patches

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.

Octree Transformer: Autoregressive 3D Shape Generation on Hierarchically Structured Sequences

Autoregressive models have proven to be very powerful in NLP text generation tasks and lately have gained popularity for image generation as well. However, they have seen limited use for the synthesis of 3D shapes so far. This is mainly due to the lack of a straightforward way to linearize 3D data as well as to scaling problems with the length of the resulting sequences when describing complex shapes. In this work we address both of these problems. We use octrees as a compact hierarchical shape representation that can be sequentialized by traversal ordering. Moreover, we introduce an adaptive compression scheme, that significantly reduces sequence lengths and thus enables their effective generation with a transformer, while still allowing fully autoregressive sampling and parallel training. We demonstrate the performance of our model by comparing against the state-of-the-art in shape generation.