曲面重建算法研究与实现
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摘要
近些年,随着三维数据获取技术的迅速发展,曲面重建及三维网格处理一直是计算机图形学领域的研究热点。本文对曲面重建及三维网格处理中存在的一些问题展开研究,主要内容包括多边形化隐式曲面的网格优化、隐式曲面的网格化、重新网格化、以及三维散乱点云的网格化。全文共分五章。
第一章对三维数据处理技术做了一个综述,着重阐述了曲面建模的研究现状及其在工业、医学等方面的应用。
第二章描述了两种多边形化隐式曲面的优化方法,分别是具有尖锐特征的多边形化隐式曲而的动态优化方法和基于二次误差度量的多边形化隐式曲面优化方法。给定一个初始粗糙的三角网格,对于动态优化方法,是通过调整网格顶点的位置、规则性和法向,使该三角网格逐步逼向隐式曲面；对于基于度量的方法,是通过对网格顶点进行重采样,顶点位置更新和曲率自适应网格细分,使该三角网格逐步逼向隐式曲面。提出了自适应曲率的隐式曲面多边形化方法,生成的三角形趋于等边,而且三角形大小自适应于隐式曲面的局部曲率,产生的网格质量较高,不需要做进一步的优化处理；并将该隐式曲而多边形化方法应用于具有复杂拓扑结构的血管三维几何建模。
第三章探讨了三角网格模型重新网格化的方法。在平面参数化的基础上,本文首先把三角网格的一些内在属性转化成一张张几何图像,然后采用图像处理技术对这些几何图像进行混合和重采样,再经过剖分和优化等处理,使可得到一张新的网格。
第四章探讨了三维散乱点云网格化处理的方法。由于三维扫描设备获取的点云数量巨大,一般方法很难对其进行处理。从工程实用角度出发,本文对其进行了快速、精确的网格化处理。首先生成一系列的包围球覆盖整个点云曲而,然后利用这些包围球内的辅助点生成三角网格。
第五章总结了本文所做的工作,同时展望了下一步工作。
In recent years, with the rapid development of three-dimensional(3D) data acquisition techniques, surfaces reconstruction remains a subject of intensive research in Computer Graphics(CG). This paper focused on the mesh methods of surfaces reconstruction from variational datasets. The main topics include the mesh optimization of polygonized implicit surfaces, the triangulation of implicit surfaces, the remeshing of triangular mesh and the triangulation of scattered point cloud. This presentation is divided into five chapters.
In chapter 1, a survey is given about surfaces reconstruction technology. We introduce the existing methods about how to mesh the surfaces and their applications in industry and medical domains.
In chapter 2, we discuss two methods about the optimization of polygonized implicit surfaces, including dynamic mesh optimization for polygonized implicit surfaces with sharp features, and triangulation optimization of polygonized implicit surfaces based on quadric error metrics, respectively; and describe the scale-adaptive surface modeling. Experimental results demonstrate that it can produce high quality triangulations which compared to those produced by traditional methods. Since the generated triangles mostly tend to equilateral and the triangles vary with the local curvature of the implicit surfaces, the output is appropriate for applications that require high quality triangulations. We have adapted the surface modeling approach to vessel surfaces reconstruction with complex topology.
In chapter 3, we propose a versatile method for remeshing irregular mesh with complex topology. First, a control geometry image is generated based on the parameterization and geometry properties of the input mesh. Then, an interactive resampling is applied on the control image using halftone technique. Finally, a binary image obtained from resampling is connected to construct a planar triangular mesh using Delaunay triangulation principle, and mesh optimization is performed to achieve a high quality mesh. This method is considerably flexible and can meet user-specified demands.
In chapter 4, we describe a hybrid approach to use a mesh for approximating a scattered point cloud over a piecewise smooth surface. Due to the large amounts of points obtained from 3D digital scans, it is difficult for traditional methods to triangulate those large datasets. Thus, from the view point of engineering, we design a fast and accurate approach for triangulating scattered point sets. First, an adaptive spherical cover and auxiliary corresponding to the cover elements are generated. Then the intersections between the spheres of the cover are analyzed and the auxiliary points are connected for generating mesh.
Finally, we conclude in chapter 5. The main points in future works are briefly introduced.
第一章对三维数据处理技术做了一个综述,着重阐述了曲面建模的研究现状及其在工业、医学等方面的应用。
第二章描述了两种多边形化隐式曲面的优化方法,分别是具有尖锐特征的多边形化隐式曲而的动态优化方法和基于二次误差度量的多边形化隐式曲面优化方法。给定一个初始粗糙的三角网格,对于动态优化方法,是通过调整网格顶点的位置、规则性和法向,使该三角网格逐步逼向隐式曲面；对于基于度量的方法,是通过对网格顶点进行重采样,顶点位置更新和曲率自适应网格细分,使该三角网格逐步逼向隐式曲面。提出了自适应曲率的隐式曲面多边形化方法,生成的三角形趋于等边,而且三角形大小自适应于隐式曲面的局部曲率,产生的网格质量较高,不需要做进一步的优化处理；并将该隐式曲而多边形化方法应用于具有复杂拓扑结构的血管三维几何建模。
第三章探讨了三角网格模型重新网格化的方法。在平面参数化的基础上,本文首先把三角网格的一些内在属性转化成一张张几何图像,然后采用图像处理技术对这些几何图像进行混合和重采样,再经过剖分和优化等处理,使可得到一张新的网格。
第四章探讨了三维散乱点云网格化处理的方法。由于三维扫描设备获取的点云数量巨大,一般方法很难对其进行处理。从工程实用角度出发,本文对其进行了快速、精确的网格化处理。首先生成一系列的包围球覆盖整个点云曲而,然后利用这些包围球内的辅助点生成三角网格。
第五章总结了本文所做的工作,同时展望了下一步工作。
In recent years, with the rapid development of three-dimensional(3D) data acquisition techniques, surfaces reconstruction remains a subject of intensive research in Computer Graphics(CG). This paper focused on the mesh methods of surfaces reconstruction from variational datasets. The main topics include the mesh optimization of polygonized implicit surfaces, the triangulation of implicit surfaces, the remeshing of triangular mesh and the triangulation of scattered point cloud. This presentation is divided into five chapters.
In chapter 1, a survey is given about surfaces reconstruction technology. We introduce the existing methods about how to mesh the surfaces and their applications in industry and medical domains.
In chapter 2, we discuss two methods about the optimization of polygonized implicit surfaces, including dynamic mesh optimization for polygonized implicit surfaces with sharp features, and triangulation optimization of polygonized implicit surfaces based on quadric error metrics, respectively; and describe the scale-adaptive surface modeling. Experimental results demonstrate that it can produce high quality triangulations which compared to those produced by traditional methods. Since the generated triangles mostly tend to equilateral and the triangles vary with the local curvature of the implicit surfaces, the output is appropriate for applications that require high quality triangulations. We have adapted the surface modeling approach to vessel surfaces reconstruction with complex topology.
In chapter 3, we propose a versatile method for remeshing irregular mesh with complex topology. First, a control geometry image is generated based on the parameterization and geometry properties of the input mesh. Then, an interactive resampling is applied on the control image using halftone technique. Finally, a binary image obtained from resampling is connected to construct a planar triangular mesh using Delaunay triangulation principle, and mesh optimization is performed to achieve a high quality mesh. This method is considerably flexible and can meet user-specified demands.
In chapter 4, we describe a hybrid approach to use a mesh for approximating a scattered point cloud over a piecewise smooth surface. Due to the large amounts of points obtained from 3D digital scans, it is difficult for traditional methods to triangulate those large datasets. Thus, from the view point of engineering, we design a fast and accurate approach for triangulating scattered point sets. First, an adaptive spherical cover and auxiliary corresponding to the cover elements are generated. Then the intersections between the spheres of the cover are analyzed and the auxiliary points are connected for generating mesh.
Finally, we conclude in chapter 5. The main points in future works are briefly introduced.
引文
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[13]Kazhdan M, Bolitho M, Hoppe H. Poisson surface reconstruction. In proc. of the fourth Eurographics symposium on geometry processing,2006,61-70
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