【作者】 莫堃；

【导师】 尹周平；

【作者基本信息】 华中科技大学 ， 机械电子工程， 2010， 博士

【摘要】 曲面重构是复杂曲面建模的关键技术,是将测量设备采样获取的点云数据转换为光滑、封闭曲面的过程,广泛应用于诸多领域。虽然曲面重构方法众多,但在工程实际中仍面临巨大挑战,存在一些重要问题需要解决。工业现场测量的诸多因素会导致点云包含噪声、孔洞以及层叠等缺陷。缺陷数据使得现有大多数重构方法很难获得所依赖的点云一致性法矢或三角网格,需要耗时的预处理、曲面修补以及人工操作等复杂过程。对于工业中有特定功能要求的零件产品,现有重构方法只能保证重构曲面的几何精度,很难使重构曲面符合相应的功能要求。为此,本文针对这些工程应用中存在的问题,研究曲面重构的数学模型,基于隐式函数理论提出了多种有效的曲面重构和点云分割方法,并应用到工程实例中。第一,现有重构方法没有统一的数学模型,曲面质量以及重构方法缺乏合理的评价标准,大多数方法依赖点云定向信息,其估算过程复杂,很难适用于缺陷点云重构。本文对现有方法进行总结,提出了基于度量函数和各种约束条件的曲面重构模型,对其分类、使用条件、求解方法等作详细分析与讨论。在此基础上,将数学形态学方法扩展到三维空间中,提出了一种新的点云定向信息的快速估算方法,能利用较少的步骤去除点云孔洞和层叠缺陷的影响,避免复杂的三角网格重构和预处理过程,提高了估算效率。第二,传统点云分割方法往往依赖点云的三角网格,很难有效分割含缺陷的点云,需借助复杂的数据结构或算法。本文提出了基于活动轮廓模型的点云自动分割方法,能有效去除点云缺陷的影响,实现点云的高效分割。将中值滤波方法扩展到三维空间窄带内,实现点云噪声影响的有效去除。扩展二维空间的活动轮廓模型理论,建立了基于点云平均曲率的能量函数优化模型,通过空间曲线的自适应拓扑演化来实现点云的边界提取和区域划分。此方法采用简单的数据结构,能避免三角网格重构,在保证分割精度的基础上极大提高分割效率。第三,针对诸多隐式曲面重构方法依赖于点云一致性法矢或三角网格,很难合理重构缺陷数据的不足,提出了一种基于双梯度场的间接重构方法。此方法不直接拟合点云,而通过构造双梯度函数来高效且合理的修复点云孔洞缺陷,融合层叠区域,避免了复杂的一致性法矢和三角网格构造过程。基于数学形态学集合运算的双梯度函数构造,利用了简单的立方网格数据结构和快速傅里叶变换的数值求解方法保证了很高的重构效率。数值试验表明,本方法对缺陷点云有很好的重构效果,既保证了重构的精度也合理的去除了点云缺陷的影响。第四,现有曲面重构方法很难重构出具有相应性能要求的功能曲面,需要大量的拼接、人工修改等后续处理。为此,以流曲面为例,提出了结合流场约束的隐式曲面重构方法。将流体速度场作为整体约束加入到传统的隐式曲面重构方法中,配合点云的距离函数,通过曲面演化共同求解出最终曲面,不仅保证了重构曲面的几何精度要求,而且实现了曲面的流线型造型和全局光顺。解决了流体速度计算中的边界条件以及曲面演化收敛条件设定问题。结合工程实际中的发动机进气道点云实例,详细讨论了重构模型中两类约束的控制参数对最终结果的影响,数值试验证明了本方法的有效性和鲁棒性。最后,基于曲面重构数学模型,利用VC++6.0和MATLAB平台的混合编程环境,将提出的多种重构方法整合到统一的数值仿真平台。以偏微分方程求解为核心,包含了功能选择、数学库函数添加以及输入输出接口等功能,并将多种类型的测量硬件设备和商业软件包整合,能有效处理工程实际中的点云重构和分割问题。通过此平台基础上的一系列数值试验说明了平台的实用性,为扩展今后的研究及实现工程化提供了基础。更多还原

【Abstract】 Surfaces reconstruction is a key technology used for complex surface modeling, which is a process transforming the point clouds into continuous and watertight surface and widely used in many research fields. There are many reconstruction methods, but the most challenge comes from the defective sample points due the measurements in practice. The point clouds often have large amount data with noise, holes and overlapping regions. These defective samples make the existing surface reconstruction difficulty to evaluate the oriented information or construct triangular meshes, which is necessary for reconstruction. The know methods only guarantee the accurate result of function surface with geometric standard, but can not realize the physical performance. Aiming at the problems existing above, this paper mainly researches the surface reconstruction modeling, and proposes some effective methods based on implicit function theory for application.Firstly, the known existing methods are lacking in the mathematical description and the suitable standard. Most methods are based on complex oriented information evaluation, hard to apply in practice. Based on the summary of the existed reconstruction methods, a general extremum model based on the metric function and constrains conditions is proposed. This paper analyzes many kinds of metric functions including the definition, conditions, resolving methods. Based on the modeling, a efficient estimation methods for oriented information of defective point clouds is proposed. The approach can handle the holes and overlapping regions, avoiding constructing triangular mesh and pre-processing, which can increase the efficiency.Secondly, many segmentation methods rely on the triangular mesh and are hard to segment defective samples, requiring complex algorithm or data structure. This paper proposes an efficient and automatic segmentation methods based on active contour model, which can reduce the defective influence. The median filter is extended into a narrowband in 3D space to handle the noisy samples. The active contour model in image processing is also extended to create a segmentation model based on curvature and the segmentation is performed by propagating the space curves with adaptive topological changes. This method can avoid reconstruct triangular mesh, not only guarantee the accurate segment results, but also increase the efficiency with simple data structure.Thirdly, many known reconstruction methods need the oriented information previously, however the information is often hard to evaluate automatically and accurately. For avoiding this problem, this paper proposes an implicit surface reconstruction based on dual off-set gradient functions. It does not fit the clouds, instead, it generates dual surfaces which construct a minimal surrounding space to the point clouds firstly and reconstruct the final surface then. The dual gradient functions are constructed by the mathematical morphology quickly, they are then combined as a novel minimal model, and finally the corresponding PDE is solved by fast Fourier transform (FFT) efficiently. Since this method needs not the normals estimation or the triangular mesh construction, it saves lots steps. For the FFT implementation, the compute time of reconstruction is reduced. Through the numerical examples, this method shows much effectiveness to the noise point clouds.Fourthly, the know reconstruction method can not guarantee the physical performance of resulting surface and need complex post-processing including smoothing, modification et.al. Therefore, this paper takes stream surface as example and proposes a stream surface reconstruction method with the fluid velocity function. The main idea is to compute the fluid velocity as global constraint to the traditional minimal model, and use the surface evolution to reconstruct the final surface. It can not only generate a global smooth and accurate resulting surface, but also keep the surface as a corresponding stream modeling. The influences of each parametric are also discussed with an engine intake ports in real world.Finally, based on the general extremum model and the methods proposed in the paper, a numerical platform is developed. The platform is programmed by the combination of VC++and MATLAB environment. It contains many function modules, such as input/output, mathematical function library, many kinds of measurement equipment and software package. Series numerical examples, which all sample from industrial products in real world, are adopted to prove these methods in the paper.更多还原