This paper proposes the RePAIR dataset that represents a challenging benchmark to test modern computational and data driven methods for puzzle-solving and reassembly tasks. Our dataset has unique properties that are uncommon to current benchmarks for 2D and 3D puzzle solving. The fragments and fractures are realistic, caused by a collapse of a fresco during a World War II bombing at the Pompeii archaeological park. The fragments are also eroded and have missing pieces with irregular shapes and different dimensions, challenging further the reassembly algorithms. The dataset is multi-modal providing high resolution images with characteristic pictorial elements, detailed 3D scans of the fragments and meta-data annotated by the archaeologists. Ground truth has been generated through several years of unceasing fieldwork, including the excavation and cleaning of each fragment, followed by manual puzzle solving by archaeologists of a subset of approx. 1000 pieces among the 16000 available. After digitizing all the fragments in 3D, a benchmark was prepared to challenge current reassembly and puzzle-solving methods that often solve more simplistic synthetic scenarios. The tested baselines show that there clearly exists a gap to fill in solving this computationally complex problem.

Abstract Jigsaw puzzle solving, the problem of constructing a coherent whole from a set of non-overlapping unordered visual fragments, is fundamental to numerous applications, and yet most of the literature of the last two decades has focused thus far on less realistic puzzles whose pieces are identical squares. Here we formalize a new type of jigsaw puzzle where the pieces are general convex polygons generated by cutting through a global polygonal shape/image with an arbitrary number of straight cuts, a generation model inspired by the celebrated Lazy caterer’s sequence. We analyze the theoretical properties of such puzzles, including the inherent challenges in solving them once pieces are contaminated with geometrical noise. To cope with such difficulties and obtain tractable solutions, we abstract the problem as a multi-body spring-mass dynamical system endowed with hierarchical loop constraints and a layered reconstruction process. We define evaluation metrics and present experimental results on both apictorial and pictorial puzzles to show that they are solvable completely automatically.