本文選題：多重網(wǎng)格 + 泊松方程　； 參考：《電子科技大學》2017年碩士論文

【摘要】：地質(zhì)資料解釋在地質(zhì)基礎研究以及地質(zhì)石油研究領域有著廣泛的應用,包括地質(zhì)構造學、地質(zhì)地層學等。而三維地質(zhì)曲面的重建過程又是在工區(qū)范圍內(nèi)的地質(zhì)資料解釋過程中非常重要的一個環(huán)節(jié),它可以將地質(zhì)采集到的散點數(shù)據(jù)以更形象的方式呈現(xiàn)給地質(zhì)分析人員,進而更好地了解地表以下的地質(zhì)形態(tài)以做出準確的分析和判斷�，F(xiàn)階段對于三維點云曲面重建有兩種解決方法:第一種方法是利用三維可視化的建模軟件Petrel等利用點云曲面上各點的標量函數(shù)值恢復出曲面;第二種方法則是利用點云中各點的法向量的方法重建出三維點云曲面,例如通過移動立方體算法進行三角面片的劃分進而提取出等值面的方法來恢復出被采樣物體的表面。在對三維地質(zhì)曲面的實際采樣過程中,往往會混入大量大噪聲點和冗余點,所在對點云曲面重建之前,先要對其進行預處理。然而現(xiàn)有的解決辦法都是將點云各部分區(qū)域看作是無厚度且均勻分布的,并且沒有結合能夠體現(xiàn)點云數(shù)據(jù)拓撲特征的信息,所以曲面恢復出的效果往往和實際需求有一定的差距。根據(jù)實際地質(zhì)曲面的情況,本文提出了相應的基于多重網(wǎng)格的點云預處理及其表面重建的方法,并利用實際工區(qū)中的地質(zhì)曲面信息對本文提出的方案進行了驗證。本文完成的主要工作如下:1.在對地質(zhì)中常見的三維幾何體采樣過程中會混入噪聲點和冗余點以及重復采樣的現(xiàn)象,導致閉曲面點云的局部區(qū)域會出現(xiàn)一定的厚度,且厚度不均勻,針對這種情況,本文結合多重網(wǎng)格的思想以及點云中各點到各網(wǎng)格之間映射的思想提出了一種基于泊松方程的曲面重建方法。首先對帶厚度的閉曲面點云進行一定的精簡處理,包括在三維空間構造立方體網(wǎng)格、將點云中各點至各單元網(wǎng)格映射、構造邊長為二倍步長的網(wǎng)格以及構造結構元素的方法對點云進行一系列的精簡。得到簡化后的點云之后,利用協(xié)方差法對點云中各點求法向量并使其方向朝向一致。然后將調(diào)整后的法向量的散度帶入三維泊松方程進行多重網(wǎng)格迭代求解。最后利用移動立方體算法將等值面提取出來。2.在對地質(zhì)勘探中常見的開曲面的采樣過程中,容易混入大量的噪聲點,導致采樣得到的開曲面點云表面非常不平滑。為了將曲面重建后得到滿意的效果,所以需要對開曲面點云進行平滑處理,具體步驟包括:在工區(qū)內(nèi)的地質(zhì)開曲面上進行網(wǎng)格剖分、計算點云中各點的曲率信息、構造二維泊松方程對點云坐標進行多重網(wǎng)格迭代。得到平滑后的點云之后,利用協(xié)方差法求出點云中各點的法向量信息并做一致化調(diào)整,并將調(diào)整后的法向量的散度帶入三維泊松方程進行多重網(wǎng)格迭代求解,最終利用移動立方體算法進行等值面的提取。3.本文結合實際的工區(qū)情況,將上述提出的不同地質(zhì)曲面的重建方案應用到真實地質(zhì)曲面中進行了仿真,得到了重建后的曲面形狀,發(fā)現(xiàn)重建后的效果滿足實際需求。
[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.

【學位授予單位】：電子科技大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：P628

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