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 three components: (1) surface segmentation to separate fracture and original parts, (2) multi-parts matching to find correspondences among fracture surface points, and (3) 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.

翻译：三维碎片的自动组装在骨科、考古学及日常生活中至关重要。本文提出Jigsaw —— 一种用于从多块碎片中组装物理破碎三维物体的新型框架。我们的方法利用全局与局部几何层次化特征来匹配并对齐断裂表面。该框架包含三个组件：（1）表面分割——分离断裂部分与原始部分；（2）多部件匹配——寻找断裂表面点之间的对应关系；（3）鲁棒全局对齐——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，并无缝融合特征匹配与刚体约束。我们在Breaking Bad数据集上评估Jigsaw，性能优于现有最先进方法。该方法还能良好泛化至不同断裂模式、物体类型及未见实例。据我们所知，这是首个专为多碎片三维断裂装配设计的基于学习方法。