Automatic Data Segmentation and Geometric Reasoning of Unorganized Point Cloud for Reverse Engineering of Precision Mechanical Objects

这笔赠款为开发必要的技术提供资金，这些技术支持在车间创建或修改原型时以及当计算机辅助设计模型不存在时，自动重建具有任意拓扑的现有对象的几何模型。特别是在重构的流形曲面上实现数据分割过程的自动化，并通过几何计算和推理实现精密机械零件的最佳几何模型重构。提出了一种从三维散乱的坐标点高效地重建三角形网格的算法，以最优地恢复物体的形状。重建的三角形网格捕捉对象的拓扑结构，并将关联的二维流形表示为组合结构，从而在数据点之间建立显式关系，并为后续的数据分割过程提供一个具有必要的微分几何特征的拓扑域。通过将分割概念从规则图像域扩展到不规则网格域，将基于边界的方法和区域生长方法相结合，提出了一种稳健的两步自动数据分割方法。最后，开发了几何计算和推理算法，将分割的面片自动分类为曲面元素，并推断出它们之间可能的拓扑关系和几何约束。如果研究成功，本研究的成果将对几何模型的自动重建和逆向工程产生重大的推动作用。通过自动数据分割和智能几何推理，可以消除用户干预，整个模型重建过程可以从几天缩短到几分钟。当与最先进的扫描设备集成时，开发的技术可以实现无缝的逆向工程过程，并支持高精度机械部件的快速设计和原型制作。该结果将在一系列工程问题中有潜在的应用，并对快速设计和原型、形状分析和虚拟现实产生重大影响。

This grant provides funding for the development of the necessary technologies that support automatic geometric model reconstruction of existing objects having arbitrary topology when the prototype is created or modified on the shop floor and when a computer-aided design model does not exist. Particularly, the focus is to automate the data segmentation process on the reconstructed manifold surface and to facilitate optimal geometric model reconstruction for precision mechanical parts by geometric computation and reasoning. An algorithm will be developed to efficiently reconstruct a triangle mesh from 3-dimensional unorganized coordinate points to optimally recover the object shape. The reconstructed triangle mesh captures object topology with the associated 2-manifold represented as a combinatorial structure, which establishes explicit relations among the data points, and provides a topological domain with necessary differential geometric characteristics for the subsequent data segmentation process. By extending segmentation concepts from the regular image domain to the irregular mesh domain, a robust two-step automatic data segmentation approach will be developed, combining the border-based approach and the region growing approach. Finally, algorithms for geometric computation and reasoning will be developed to automatically classify the segmented patches into surface elements and to infer possible topological relations and geometric constraints among them. If successful, the results of this research will lead to significant improvements in automatic geometric model reconstruction and reverse engineering. With automatic data segmentation and intelligent geometric reasoning, user intervention can be eliminated and the entire model reconstruction process can be shortened from days to minutes. When integrated with state of the art scanning devices, the developed technologies could lead to a seamless reverse engineering process and support rapid design and prototyping of high-precision mechanical components. The results will have potential application in a whole spectrum of engineering problems with a major impact on rapid design and prototyping, shape analysis, and virtual reality.