基于工业CT切片数据的三角网格模型简化及优化方法研究
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摘要
工业CT技术能在对被检测产品无损伤的条件下，以二维或三维的形式，清晰、准确、直观的展现被检测产品内部的结构、组成、材质及缺损状况，该技术被誉为当今最佳的无损检测技术。但采用工业CT扫描被检测产品时，往往由于测量手段和技术的限制、被检测产品本身已有损坏等原因，使得工业CT切片数据重建的网格模型存在不封闭的现象，另外，对于复杂的被检测产品，重建模型还存在数据量大、三角形形状不规范等问题，这些问题的存在不利于重建模型的存储、传输以及网格模型的后续处理。
针对上述问题，本文以工业CT切片数据为研究对象，重点对网格模型的重建、网格模型的简化以及网格模型的优化进行了研究，主要的研究内容及研究成果包括以下几个方面：
①针对工业CT测量手段存在的问题，即扫描时只对被检测产品的有效区域进行扫描，而无法获得被检测产品上下端面处的数据信息，本文提出了一种修改端面处体元数据的方法，保证重建时端面处等值面的完整提取，实现被检测产品端面处的封闭。另外，本文采用改进的MC算法对所有体元数据进行重建，以消除MC算法的二义性，避免二义性所产生的孔洞。
②为了解决重建模型的庞大数据量给存储、传输等方面带来的困难，本文分别从边折叠和三角形折叠两个方面提出了两种三角网格模型的简化方法。这两种简化方法不仅在生成高质量简化模型的同时降低了简化模型的几何误差，而且还有效地保持了原始模型的几何特征，避免了目前大多数网格简化方法在简化网格模型时丢失模型特征的问题。
③提出了波前法和最小二乘拟合函数相结合的网格孔洞修补方法，以修补被检测产品因本身损坏、产品部位遮挡等原因所产生的孔洞。首先，该方法对识别出的孔洞边界进行预处理；然后，采用波前法对孔洞区域进行三角化；最后，通过最小二乘拟合函数的方法调整孔洞区域中各三角形顶点的位置。该孔洞修补方法实现了孔洞区域原始形貌的恢复，并保证了孔洞区域与周围原始网格的光滑过渡，初步优化了网格模型。
④经孔洞修补处理后，封闭的网格模型在孔洞区域中常存在三角形的形状、大小与孔洞周围的原始网格不一致的情形，此外，在整个网格模型中还存在大量狭长三角形。针对这些问题，本文提出了一种采用二阶加权伞算子局部优化网格模型的方法。该方法通过二阶加权伞算子对网格模型中的孔洞区域以及原始网格模型中的狭长三角形区域进行优化处理，改善网格模型中狭长三角形的质量，保证最终获得优化的网格模型。
本文的研究成果已集成到所开发的逆向软件系统中，并成功应用于具有复杂内腔产品的逆向设计。应用实例验证这些方法不仅能保证最终可获得简化的、高质量的网格模型，而且这些网格模型符合后续处理的需求。
Industrial CT (Industrial Computerized Tomography, ICT), owing to the feature ofbeing able to display the inner structure, composition, material and defect status of theinspected complex objects with2D slicing image or3D mesh model clearly, accurately,intuitively and without any damage to the inspected complex objects, is awarded as thebest non-destructive testing technology nowadays. But due to the limits ofmeasurements and technology, defect status of the inspected objects, and so on, themesh model reconstructed from industrial CT scanning data is often not closed, besides,the reconstructed mesh model with huge data and narrow triangle have the problem ofstorage, transmitting and subsequent processing.
To counter the problems above, this paper takes industrial CT scanning data as theresearch object, and focuses on mesh reconstruction, mesh simplification and meshoptimization. The main contents and achievements are listed as follows:
①To counter the existing problems of industrial CT measurement, that is, onlyvalid area of the inspected objects is scanned, the contour information about thebeginning and the end of the inspected objects can not be obtained. We present amethod of modifying voxels at end face, this method is benefit for the extraction ofcomplete iso-surface when reconstructing mesh model and the closure of the end face.Besides, an improved MC algorithm is used to reconstruct all voxels and avoid theambiguity of original MC algorithm.
②To solve the problem of storage, transmitting3D reconstruction models withhuge data, two triangular mesh simplification algorithms based on edge collapse andtriangle collapse are proposed in this paper. Compared to the majority simplificationalgorithms at present, the presented simplification algorithms work well for generatinghigh quality simplified model, reducing the error of the simplified model whilstpreserving the sharp geometric features of the original model, and making up defect oflosing features of the original model.
③In order to repair the hole derived from defect status of the inspected objects,the overlapping of the part of the inspected objects, and so on, a novel hole-fillingmethod is proposed. Firstly, identify all holes existed in the mesh model and performpreprocessing to boundary edges. Then the identified holes are triangulated by theimproved advancing front mesh method. Finally, adjust the position of triangle vertices existed in the patch meshes by the least square fit. The proposed hole-filling approachrestores the original shape and has smooth transition with the surrounding meshes, themesh model is optimized primarily.
④After hole filling, triangles in the area of the hole may be spiky, and can notadapt to the surrounding shape of the hole well. Besides, there are some irregularsituations in mesh model, such as narrow triangle, redundant triangle, and so on. Inview of these problems, a normalization method for mesh model is proposed. Firstly, inorder to improve the quality of mesh model, patch mesh and the area of the narrowtriangle are optimized by applying the weighted bi-umbrella operator, and then repairother defects to obtain normalization mesh model.
Above-mentioned research results have been integrated into a prototype system ofreverse engineering, this system has been applied successfully in reverse design. Theapplied examples prove that the presented algorithm not only help obtain high qualitysimplified model, but also benefit subsequent processing.
针对上述问题，本文以工业CT切片数据为研究对象，重点对网格模型的重建、网格模型的简化以及网格模型的优化进行了研究，主要的研究内容及研究成果包括以下几个方面：
①针对工业CT测量手段存在的问题，即扫描时只对被检测产品的有效区域进行扫描，而无法获得被检测产品上下端面处的数据信息，本文提出了一种修改端面处体元数据的方法，保证重建时端面处等值面的完整提取，实现被检测产品端面处的封闭。另外，本文采用改进的MC算法对所有体元数据进行重建，以消除MC算法的二义性，避免二义性所产生的孔洞。
②为了解决重建模型的庞大数据量给存储、传输等方面带来的困难，本文分别从边折叠和三角形折叠两个方面提出了两种三角网格模型的简化方法。这两种简化方法不仅在生成高质量简化模型的同时降低了简化模型的几何误差，而且还有效地保持了原始模型的几何特征，避免了目前大多数网格简化方法在简化网格模型时丢失模型特征的问题。
③提出了波前法和最小二乘拟合函数相结合的网格孔洞修补方法，以修补被检测产品因本身损坏、产品部位遮挡等原因所产生的孔洞。首先，该方法对识别出的孔洞边界进行预处理；然后，采用波前法对孔洞区域进行三角化；最后，通过最小二乘拟合函数的方法调整孔洞区域中各三角形顶点的位置。该孔洞修补方法实现了孔洞区域原始形貌的恢复，并保证了孔洞区域与周围原始网格的光滑过渡，初步优化了网格模型。
④经孔洞修补处理后，封闭的网格模型在孔洞区域中常存在三角形的形状、大小与孔洞周围的原始网格不一致的情形，此外，在整个网格模型中还存在大量狭长三角形。针对这些问题，本文提出了一种采用二阶加权伞算子局部优化网格模型的方法。该方法通过二阶加权伞算子对网格模型中的孔洞区域以及原始网格模型中的狭长三角形区域进行优化处理，改善网格模型中狭长三角形的质量，保证最终获得优化的网格模型。
本文的研究成果已集成到所开发的逆向软件系统中，并成功应用于具有复杂内腔产品的逆向设计。应用实例验证这些方法不仅能保证最终可获得简化的、高质量的网格模型，而且这些网格模型符合后续处理的需求。
Industrial CT (Industrial Computerized Tomography, ICT), owing to the feature ofbeing able to display the inner structure, composition, material and defect status of theinspected complex objects with2D slicing image or3D mesh model clearly, accurately,intuitively and without any damage to the inspected complex objects, is awarded as thebest non-destructive testing technology nowadays. But due to the limits ofmeasurements and technology, defect status of the inspected objects, and so on, themesh model reconstructed from industrial CT scanning data is often not closed, besides,the reconstructed mesh model with huge data and narrow triangle have the problem ofstorage, transmitting and subsequent processing.
To counter the problems above, this paper takes industrial CT scanning data as theresearch object, and focuses on mesh reconstruction, mesh simplification and meshoptimization. The main contents and achievements are listed as follows:
①To counter the existing problems of industrial CT measurement, that is, onlyvalid area of the inspected objects is scanned, the contour information about thebeginning and the end of the inspected objects can not be obtained. We present amethod of modifying voxels at end face, this method is benefit for the extraction ofcomplete iso-surface when reconstructing mesh model and the closure of the end face.Besides, an improved MC algorithm is used to reconstruct all voxels and avoid theambiguity of original MC algorithm.
②To solve the problem of storage, transmitting3D reconstruction models withhuge data, two triangular mesh simplification algorithms based on edge collapse andtriangle collapse are proposed in this paper. Compared to the majority simplificationalgorithms at present, the presented simplification algorithms work well for generatinghigh quality simplified model, reducing the error of the simplified model whilstpreserving the sharp geometric features of the original model, and making up defect oflosing features of the original model.
③In order to repair the hole derived from defect status of the inspected objects,the overlapping of the part of the inspected objects, and so on, a novel hole-fillingmethod is proposed. Firstly, identify all holes existed in the mesh model and performpreprocessing to boundary edges. Then the identified holes are triangulated by theimproved advancing front mesh method. Finally, adjust the position of triangle vertices existed in the patch meshes by the least square fit. The proposed hole-filling approachrestores the original shape and has smooth transition with the surrounding meshes, themesh model is optimized primarily.
④After hole filling, triangles in the area of the hole may be spiky, and can notadapt to the surrounding shape of the hole well. Besides, there are some irregularsituations in mesh model, such as narrow triangle, redundant triangle, and so on. Inview of these problems, a normalization method for mesh model is proposed. Firstly, inorder to improve the quality of mesh model, patch mesh and the area of the narrowtriangle are optimized by applying the weighted bi-umbrella operator, and then repairother defects to obtain normalization mesh model.
Above-mentioned research results have been integrated into a prototype system ofreverse engineering, this system has been applied successfully in reverse design. Theapplied examples prove that the presented algorithm not only help obtain high qualitysimplified model, but also benefit subsequent processing.
引文
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