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.

Jigsaw puzzle solving, the problem of constructing a coherent whole from a set of non-overlapping un-ordered fragments, is fundamental to numerous applications, and yet most of the literature 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 with an arbitrary number of straight cuts. 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 sys-tem endowed with hierarchical loop constraints and a layered reconstruction process that is guided by the pictorial content of the pieces. We define evaluation metrics and present experimental results on both apictorial and pictorial puzzles to indicate that they are solvable completely automatically.