Rotation-Invariant Hierarchical Segmentation on Poincare Ball for 3D Point Cloud

Pierre Onghena, Leonardo Gigli, Santiago Velasco-Forero; Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) Workshops, 2023, pp. 1765-1774

Point clouds are a set of data points in space to represent the 3D geometry of objects. A fundamental step in the processing is to achieve segmentation of the point cloud at different levels of detail. Within this context, hierarchical clustering (HC) breaks the point cloud down into coherent subsets to recognize the parts that make up the object. Along with classic approaches that build a hierarchical tree bottom-up using linkage criteria, recent developments exploit the tree-likeness of hyperbolic metric space, embedding data into the Poincare Ball and capturing a hierarchical structure with low distortion. The main advantage of this kind of solution is the possibility to explore the space of discrete binary trees using continuous optimization. However, in this framework, a similarity function between points is assumed to be known, while this cannot always be granted for point cloud applications. In our method, we propose to use metric learning to fit at the same time the good similarity function and the optimal embedding into the hyperbolic space. Furthermore, when arbitrary rotations are applied to a 3D object, the pose should not influence the segmentation quality. Therefore, to avoid extensive data augmentation, we impose rotation invariance to ensure the uniqueness of the hierarchical segmentation of point clouds. We show the performance of our method on two datasets, ShapeNet and PartNet, at different levels of granularity. The results obtained are promising when compared to state-of-the-art flat segmentation