Banana: Banach Fixed-Point Network for Pointcloud Segmentation with Inter-Part Equivariance

作者：Congyue Deng, Jiahui Lei, Bokui Shen, Kostas Daniilidis, Leonidas Guibas · 发表于：arXiv (Cornell University) · 年份：2023 · DOI：10.48550/arxiv.2305.16314 · 被引用次数：6 · 研究领域：3D Shape Modeling and Analysis、Robotics and Sensor-Based Localization、Computer Graphics and Visualization Techniques

Equivariance has gained strong interest as a desirable network property that inherently ensures robust generalization. However, when dealing with complex systems such as articulated objects or multi-object scenes, effectively capturing inter-part transformations poses a challenge, as it becomes entangled with the overall structure and local transformations. The interdependence of part assignment and per-part group action necessitates a novel equivariance formulation that allows for their co-evolution. In this paper, we present Banana, a Banach fixed-point network for equivariant segmentation with inter-part equivariance by construction. Our key insight is to iteratively solve a fixed-point problem, where point-part assignment labels and per-part SE(3)-equivariance co-evolve simultaneously. We provide theoretical derivations of both per-step equivariance and global convergence, which induces an equivariant final convergent state. Our formulation naturally provides a strict definition of inter-part equivariance that generalizes to unseen inter-part configurations. Through experiments conducted on both articulated objects and multi-object scans, we demonstrate the efficacy of our approach in achieving strong generalization under inter-part transformations, even when confronted with substantial changes in pointcloud geometry and topology.