多重网格的泊松目标体表面重建研究

发布时间：2018-05-11 17:54

本文选题：多重网格 + 泊松方程　；参考：《电子科技大学》2017年硕士论文

【摘要】：地质资料解释在地质基础研究以及地质石油研究领域有着广泛的应用,包括地质构造学、地质地层学等。而三维地质曲面的重建过程又是在工区范围内的地质资料解释过程中非常重要的一个环节,它可以将地质采集到的散点数据以更形象的方式呈现给地质分析人员,进而更好地了解地表以下的地质形态以做出准确的分析和判断。现阶段对于三维点云曲面重建有两种解决方法:第一种方法是利用三维可视化的建模软件Petrel等利用点云曲面上各点的标量函数值恢复出曲面;第二种方法则是利用点云中各点的法向量的方法重建出三维点云曲面,例如通过移动立方体算法进行三角面片的划分进而提取出等值面的方法来恢复出被采样物体的表面。在对三维地质曲面的实际采样过程中,往往会混入大量大噪声点和冗余点,所在对点云曲面重建之前,先要对其进行预处理。然而现有的解决办法都是将点云各部分区域看作是无厚度且均匀分布的,并且没有结合能够体现点云数据拓扑特征的信息,所以曲面恢复出的效果往往和实际需求有一定的差距。根据实际地质曲面的情况,本文提出了相应的基于多重网格的点云预处理及其表面重建的方法,并利用实际工区中的地质曲面信息对本文提出的方案进行了验证。本文完成的主要工作如下:1.在对地质中常见的三维几何体采样过程中会混入噪声点和冗余点以及重复采样的现象,导致闭曲面点云的局部区域会出现一定的厚度,且厚度不均匀,针对这种情况,本文结合多重网格的思想以及点云中各点到各网格之间映射的思想提出了一种基于泊松方程的曲面重建方法。首先对带厚度的闭曲面点云进行一定的精简处理,包括在三维空间构造立方体网格、将点云中各点至各单元网格映射、构造边长为二倍步长的网格以及构造结构元素的方法对点云进行一系列的精简。得到简化后的点云之后,利用协方差法对点云中各点求法向量并使其方向朝向一致。然后将调整后的法向量的散度带入三维泊松方程进行多重网格迭代求解。最后利用移动立方体算法将等值面提取出来。2.在对地质勘探中常见的开曲面的采样过程中,容易混入大量的噪声点,导致采样得到的开曲面点云表面非常不平滑。为了将曲面重建后得到满意的效果,所以需要对开曲面点云进行平滑处理,具体步骤包括:在工区内的地质开曲面上进行网格剖分、计算点云中各点的曲率信息、构造二维泊松方程对点云坐标进行多重网格迭代。得到平滑后的点云之后,利用协方差法求出点云中各点的法向量信息并做一致化调整,并将调整后的法向量的散度带入三维泊松方程进行多重网格迭代求解,最终利用移动立方体算法进行等值面的提取。3.本文结合实际的工区情况,将上述提出的不同地质曲面的重建方案应用到真实地质曲面中进行了仿真,得到了重建后的曲面形状,发现重建后的效果满足实际需求。
[Abstract]:Geological data interpretation is widely used in the field of geological research and geological petroleum research, including geological tectonics, geological stratigraphy, etc., and the reconstruction of 3D geological surfaces is a very important link in the process of interpretation of geological data within the scope of the work area. The image is presented to the geological analyst to better understand the geological form below the surface in order to make accurate analysis and judgment. At the present stage, there are two solutions to 3D point cloud surface reconstruction. The first method is to use the 3D visualization modeling software Petrel to use the scalar function value of each point on the point cloud surface. The second method is to reconstruct the 3D point cloud surface by using the normal vector of each point in the point cloud. For example, the surface of the sample is recovered by dividing the triangulation surface by the moving cube algorithm to recover the surface of the sampled object. A large number of large noise points and redundant points are preprocessed before the point cloud surface is reconstructed. However, the existing solution is to consider each part of the point cloud as a non thickness and uniform distribution, and do not combine the information that can reflect the topological features of the point cloud data, so the effect of the surface recovery is often and actually needed. There is a certain gap. According to the actual geological surface, this paper puts forward the corresponding method of point cloud preprocessing and surface reconstruction based on multi grid, and uses the information of geological surface in the actual work area to verify the proposed scheme. The main work done in this paper is as follows: 1. the common three dimensions in geology are as follows. For this case, a Poisson equation based on the thought of multi grid and the idea of the mapping between the points in the point cloud and the meshes in the point cloud is proposed. The method of surface reconstruction. First, a certain reduction is made for the closed surface cloud with thickness, including building a cube grid in three-dimensional space, mapping the points in the point cloud to the cell grid, constructing a grid with two times the length of the edge and a series of simplification of the point cloud. After that, the covariance method is used to find the normal vector and direction of the points in the point cloud. Then the divergence of the adjusted normal vector is brought into the three-dimensional Poisson equation to solve the multigrid iteration. Finally, the moving cube algorithm is used to extract the equivalent surface of the.2. in the sampling process of the common surface of the geological exploration. The surface of the open surface point cloud is very unsmooth. In order to get a satisfactory result after the surface reconstruction, it is necessary to smooth the open surface point cloud. The concrete steps include: the mesh generation on the surface of the geological surface in the work area, the curvature information of each point in the point cloud, and the construction of two The dimensional Poisson equation is used to iterate the multi grid of point cloud coordinates. After getting the smooth point cloud, the covariance method is used to obtain the normal vector information of the points in the point cloud and make the uniform adjustment. Then the divergence of the adjusted normal vector is brought into the three-dimensional Poisson equation to solve the multi grid iteratively. Finally, the moving cube algorithm is used to do so. .3. in this paper, based on the actual work area, the reconstruction scheme of different geological surfaces proposed above is applied to the real geological surface to simulate the surface. The shape of the reconstructed surface is obtained, and the results after the reconstruction are found to meet the actual needs.

【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P628

【参考文献】