  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/.
