Converting point clouds into concise polygonal meshes in an automated manner is an enduring problem in computer graphics. Prior works, which typically operate by assembling planar shapes detected from input points, largely overlooked the scalability issue of processing a large number of shapes. As a result, they tend to produce overly simplified meshes with assembling approaches that can hardly digest more than 100 shapes in practice. We propose a shape assembling mechanism that is at least one order of magnitude more efficient, both in time and in number of processed shapes. Our key idea relies upon the design of a kinetic data structure for partitioning the space into convex polyhedra. Instead of slicing all the planar shapes exhaustively as prior methods, we create a partition where shapes grow at constant speed until colliding and forming polyhedra. This simple idea produces a lighter yet meaningful partition with a lower algorithmic complexity than an exhaustive partition. A watertight polygonal mesh is then extracted from the partition with a min-cut formulation. We demonstrate the robustness and efficacy of our algorithm on a variety of objects and scenes in terms of complexity, size, and acquisition characteristics. In particular, we show the method can both faithfully represent piecewise planar structures and approximate freeform objects while offering high resilience to occlusions and missing data.

中文翻译：

---

动力学形状重建

以自动方式将点云转换为简洁的多边形网格是计算机图形学中一个长期存在的问题。先前的工作通常通过组装从输入点检测到的平面形状来操作，很大程度上忽略了处理大量形状的可扩展性问题。结果，他们倾向于使用组装方法生成过于简化的网格，实际上几乎无法消化超过 100 种形状。我们提出了一种形状组装机制，无论是在时间上还是在处理形状的数量上，效率都至少提高了一个数量级。我们的关键思想依赖于将空间划分为凸多面体的动力学数据结构的设计。而不是像以前的方法那样详尽地切片所有平面形状，我们创建了一个分区，其中形状以恒定速度增长，直到碰撞并形成多面体。这个简单的想法产生了一个更轻但有意义的分区，其算法复杂度比穷举分区低。然后使用最小切割公式从分区中提取防水多边形网格。我们展示了我们的算法在复杂性、大小和采集特性方面对各种对象和场景的鲁棒性和有效性。特别是，我们展示了该方法既可以忠实地表示分段平面结构，又可以近似自由形式的对象，同时提供对遮挡和丢失数据的高弹性。然后使用最小切割公式从分区中提取防水多边形网格。我们展示了我们的算法在复杂性、大小和采集特性方面对各种对象和场景的鲁棒性和有效性。特别是，我们展示了该方法既可以忠实地表示分段平面结构，又可以近似自由形式的对象，同时提供对遮挡和丢失数据的高弹性。然后使用最小切割公式从分区中提取防水多边形网格。我们展示了我们的算法在复杂性、大小和采集特性方面对各种对象和场景的鲁棒性和有效性。特别是，我们展示了该方法既可以忠实地表示分段平面结构，又可以近似自由形式的对象，同时提供对遮挡和丢失数据的高弹性。