【作者】 王世东；

【导师】 张佑生；

【作者基本信息】 合肥工业大学 ， 计算机应用技术， 2006， 硕士

【摘要】 现在,应用三维扫描所得物体表面的散乱点集合进行曲面重建和重建后的网格优化,已成为计算机图形学领域的一个热门研究课题,其研究成果对于机械制造、医学诊断和虚拟现实等许多领域具有重要的实用价值。 曲面重建的传统算法如零集法、α-shape法和Voronoi法等,都取得了不错的效果。不过,零集法生成的近似曲面和真实曲面之间存在较大的误差,而α-shape法和Voronoi法生成插值网格曲面的网格密度大,所需存储空间大;且当散乱点的数量增大时,这些算法的处理速度迅速下降。网格优化的传统算法如边交换、边瓦解、边劈裂等只是对网格进行局部的优化,效果不是很好。因此,十分需要在这方面开展进一步的研究。 本论文的主要工作如下: 1、研究使用成长型神经网络的曲面快速重建方法。神经网络在处理输入数据时一次只采样一个点,计算速度独立于输入数据量,而且能很好地处理含噪声的数据,因而特别适合基于三维扫描散乱点集的曲面重建。这为基于学习的曲面重建方法开辟了一条新途径,具有广阔的应用前景。我们在曲面重建过程中采用线性组合的方式分裂节点,使用一种简化的方法计算节点的Voronoi区域面积用于分配新增节点的计数器值,并对生成的曲面作进一步的综合优化。 2、提出使用基于能量最小化的网格优化算法:对于给定的三维散乱点集合和初始三角网格,使用能量最小化算法对网格顶点位置优化,使网格更好地逼近三维散乱点。 3、提出一种新颖的网格综合优化算法:对某一形体表面的三维散乱点集给定一个初始三角网格,使用神经网络中自组织映射算法对网格顶点位置优化,使网格更好地逼近三维散乱点,使网格中节点的分布更符合散乱点数据的空间概率分布,并分裂网格中度数特别大的节点,使网格的空间形状更加平滑。 4、进行了曲面重建与网格优化实验,实验结果表明,上述算法可取得曲面重建与优化的良好效果,处理速度快。更多还原

【Abstract】 At present, it is a hot research topic in Computer Graphics (CG) field to realize surface reconstruction and mesh optimization using a set of 3D scattered data points obtained by scanning object surface. The research findings have great practical value in many fields, such as machine building, virtual reality and so on.The traditional algorithms of surface reconstruction, including Zero-Set algorithm, a -shape algorithm, Voronoi algorithm, etc., have obtained good results. But, the errors are large between the actual surface and the reconstructed one by Zero-Set algorithm. And the memory space, required by the interpolation mesh surfaces by a -shape and Voronoi algorithms, is rather big. Furthermore, the speed of above algorithms drops quickly when amount of scattered data points increasing. The traditional algorithms of mesh optimization, such as Edge exchanging, Edge collapse and Edge splitting, etc., can only partially optimize a mesh with not very good result. So it is necessary to do further research about approaches of surface reconstruction and mesh optimization.The main works in this dissertation are as follows:1 、 The method of fast surface reconstruction using Growing Cell Structure (GCS) is studied. When dealing with input data, GCS samples just one point a time. Its speed of processing is independent of amount of input data. And it is very effective to deal with the noisy data . So, it is well suited for surface reconstruction based on a set of scattered data points and has a good foreground of applications. During surface reconstruction, the method of linear combination is used to split nodes, and a simple method to calculate the area of Voronoi cells to assign a value to the signal counter of the new node. And the surface is further optimized by a method in the end.2、 An algorithm of mesh optimization based on energy minimization is presented. For a set of 3D scattered data points and an initial triangular mesh, the energy minimization method is used for mesh optimization to make all vertex position approach the scattered data points.3、 A new algorithm for integrated mesh optimization is proposed. For a set of3D scattered data points of an object surface and an initial triangular mesh, we use a mesh optimization algorithm based on Self-Organizing Mapping(SOM) to make all vertex position approach the scattered data points and make the distribution of vertices close to the probability distribution, of scattered data points. The vertices with very high valence are splitted in order to make the shape of mesh more smooth. 4n Some experiments have been done about surface reconstruction and mesh optimization, the results of which show that the methods presented in this dissertation are effective and rapid in surface reconstruction.更多还原