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Jigsaw puzzle solving, the problem of constructing a coherent whole from aset of non-overlapping unordered visual fragments, is fundamental to numerousapplications and yet most of the literature of the last two decades has focusedthus far on less realistic puzzles whose pieces are identical squares. Here weformalize a new type of jigsaw puzzle where the pieces are general convexpolygons generated by cutting through a global polygonal shape/image with anarbitrary number of straight cuts, a generation model inspired by thecelebrated Lazy caterer's sequence. We analyze the theoretical properties ofsuch puzzles, including the inherent challenges in solving them once pieces arecontaminated with geometrical noise. To cope with such difficulties and obtaintractable solutions, we abstract the problem as a multi-body spring-massdynamical system endowed with hierarchical loop constraints and a layeredreconstruction process. We define evaluation metrics and present experimentalresults on both apictorial and pictorial puzzles to show that they are solvablecompletely automatically.

Pictorial and apictorial polygonal jigsaw puzzles: The lazy caterer model, properties, and solvers