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.
Abstract (translated)
一致性作为一个重要的网络属性，本身就确保了稳健泛化。然而，在与复杂的系统，如多关节疼痛对象或多对象场景时，有效地捕捉部分之间的变换面临着挑战，因为它与整体结构和局部变换交织在一起。部分分配和每个部分的独立行动需要一种独特的一致性定义，以便它们的协同演化。在本文中，我们介绍了banana，一个由Banach fixed-point网络构建的一致性分割网络，具有部分一致性。我们的关键发现是解决一个固定点问题，该问题点部分分配标签和每个部分的SE(3)一致性同时演化。我们提供了每个步骤的一致性和全球收敛的理论推导，导致一致性最终的收敛状态。我们的定义自然地提供了部门一致性的严格定义，可以泛化到未知的部门配置。通过在多关节疼痛对象和多对象扫描的实验中实施，我们证明了我们的方法在部分变换下实现稳健泛化的有效性，即使面对点云几何和拓扑的重大变化。
URL
https://arxiv.org/abs/2305.16314
