Automated assembly of 3D fractures is essential in orthopedics, archaeology, and our daily life. This paper presents Jigsaw, a novel framework for assembling physically broken 3D objects from multiple pieces. Our approach leverages hierarchical features of global and local geometry to match and align the fracture surfaces. Our framework consists of four components: (1) front-end point feature extractor with attention layers, (2) surface segmentation to separate fracture and original parts, (3) multi-parts matching to find correspondences among fracture surface points, and (4) robust global alignment to recover the global poses of the pieces. We show how to jointly learn segmentation and matching and seamlessly integrate feature matching and rigidity constraints. We evaluate Jigsaw on the Breaking Bad dataset and achieve superior performance compared to state-of-the-art methods. Our method also generalizes well to diverse fracture modes, objects, and unseen instances. To the best of our knowledge, this is the first learning-based method designed specifically for 3D fracture assembly over multiple pieces. Our code is available at https://jiaxin-lu.github.io/Jigsaw/.

翻译：三维断裂物体的自动化装配在骨科、考古学及日常生活中至关重要。本文提出Jigsaw——一种新颖的框架，用于将物理断裂的三维物体从多个碎片中组装起来。我们的方法利用全局与局部几何的层次化特征来匹配并对齐断裂表面。该框架包含四个组件：(1) 基于注意力机制的前端点特征提取器；(2) 表面分割以区分断裂面与原始表面；(3) 多碎片匹配以建立断裂面点间的对应关系；(4) 鲁棒全局对齐以恢复碎片的全局姿态。我们展示了如何联合学习分割与匹配，并无缝集成特征匹配与刚性约束。在Breaking Bad数据集上的评估表明，Jigsaw取得了优于现有方法的性能，并且能够良好泛化至多种断裂模式、物体类别及未见实例。据我们所知，这是首项专门针对多碎片三维断裂装配设计的基于学习方法。代码已开源至https://jiaxin-lu.github.io/Jigsaw/。