具有任意交叉切割的图形和非图形多边形拼图
Pictorial and apictorial polygonal jigsaw puzzles from arbitrary number of crossing cuts
AI总结：
本文提出了一种新的拼图问题，通过任意数量的直线切割生成一般凸多边形拼图，并通过多体弹簧质量动力系统和分层重建过程解决其中的挑战，实验表明可自动解决图形和非图形拼图。
摘要：
拼图求解，即从一组不重叠的无序视觉碎片中构建连贯整体的问题，是许多应用的基础，但过去二十年的文献大多集中在更不现实的拼图上，其拼图块是相同的正方形。在此，我们正式提出了一种新的拼图类型，其中拼图块是通过任意数量的直线切割通过一个全局多边形形状生成的一般凸多边形，这种生成模型受著名的Lazy caterer序列启发。我们分析了此类拼图的理论性质，包括在拼图块被几何噪声污染后解决它们的固有挑战。为应对这些困难并获得可处理的解决方案，我们将问题抽象为一个具有层次循环约束和分层重建过程的多体弹簧质量动力系统。我们定义了评估指标，并在图形和非图形拼图上展示了实验结果，证明它们可以完全自动解决。
英文摘要：
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 with an arbitrary number of straight cuts, a generation model inspired by the celebrated Lazy caterer 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
