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

• URL: http://arxiv.org/abs/2305.16314v2
• Date: Fri, 26 May 2023 14:28:26 GMT
• Title: Banana: Banach Fixed-Point Network for Pointcloud Segmentation with Inter-Part Equivariance
• Authors: Congyue Deng, Jiahui Lei, Bokui Shen, Kostas Daniilidis, Leonidas Guibas
• Abstract summary: 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. Our formulation naturally provides a strict definition of inter-part equivariance that generalizes to unseen inter-part configurations.
• Score: 31.875925637190328
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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