【作者】 潘如刚；

【导师】 叶修梓；

【作者基本信息】 浙江大学 ， 计算机应用技术， 2004， 硕士

【摘要】 本文主要关注基于轮廓数据的三维物体对象曲面重构问题，轮廓表示着一系列通过物体对象的断层截面形状。基于轮廓数据的三维物体重构问题有着广泛的应用背景，在生物医学研究、地质勘探、工业检查、实体建模和快速原型制造等方面是主要的建模手段。这个问题可以分为四个子问题，即轮廓对应问题、分叉问题、拼接问题和曲面拟合问题。本丈主要在对应、分叉和拼接三个基本问题的解决上提出了新方法，并对已有算法作了重要改进。解决了这三个问题就可以得到基于轮廓数据的三角网格模型，它是原始轮廓对应的曲面的分片逼近表示。 本文总结了在对应、分叉和拼接三个基本问题上已有的研究成果。研究并改进了一些轮廓线相关的基础算法，包括平面多边形的方向判别、点在多边形内外位置关系判别、同平面内两个多边形间的相互位置关系判别、轮廓多边形的特征骨架计算、轮廓线数据的精简。 轮廓对应问题的解决是基于轮廓数据曲面重构的关键工作，是保证重建网格模型拓扑关系正确性的基础。由于实际物体的拓扑复杂性，相邻断层轮廓线之间的对应关系有一对一、一对多、多对多等多种情况。本文全面分析了相邻断层间轮廓对应问题。改进了两个基本算法，包括相邻两个轮廓对应关系判别算法和相邻断层间轮廓对应关系的快速匹配算法。在轮廓对应合法性规则的基础之上提出了四个优化准则，并给出了完整的建立相邻断层轮廓对应关系的步骤。 骨架线能有效刻画轮廓的特征形状。本文通过引入图象处理技术中提取骨架线的概念，提出一种基于骨架的拼接方法。这个方法通过插入中间断层，建立轮廓间的一对一对应关系，可以解决多种分叉类型情况下的拼接问题。与先构造复合轮廓再拼接的方法相比，具有更广的适用性和更令人满意的拼接效果。通常，对末端轮廓都是以平面三角剖分封闭端面。本文提出的基于骨架的末端封闭方法，可以得到更符合物体自身形状的三角网格模型。更多还原

【Abstract】 This dissertation is concerned with the problem of reconstructing the surfaces of 3-D objects from a collection of planar contours representing cross sections through the objects. This problem has important applications in diverse fields, including biomedical research, geology, industrial inspection, solid modeling, and rapid prototyping manufacturing. The problem can be decomposed into four sub-problems, the correspondence problem, the branching problem, the tiling problem and the surface fitting problem. The main work of this dissertation is developing the new solutions to the three fundamental problems of correspondence, branching, and tiling problems in surface-based reconstruction and improving the quality of some existing algorithms. The result after solution of the correspondence, branching and tiling problems is a triangular mesh that is a piecewise planar approximation of a surface consistent with the contours.This dissertation gives a survey of previous research on the correspondence, branching, and tiling problems. Then, studies and improves some basic algorithms, including determining orientation of planar polygon, determining point inclusion of polygon, determining relationship of location between contours in the same plane, extracting skeleton of contour, reducing the data for contours.The solution to the correspondence problem is important for reconstruction of surface from contours, especially for validity of topology of the reconstructed triangular mesh. Because an actual object has complex topology, it may have many cases for correspondence relationship of contours between adjacent sections, for example one-to-one, one-to-many, many-to-many. This dissertation makes a complete analysis of the correspondence problem. The two basic algorithms are improved for determining direct correspondence relationship between two contours and matching contours between adjacent sections. The four criteria and the detailed steps for establishment of entire correspondence relationship between adjacent sections are proposed on the base of the eligibility rules.The skeleton is an effective representation of object shapes. This dissertation introduces the idea of extracting skeleton in digital image processing, develops a skeleton-based approach for solving the tiling problem that inserts intermediate section and establishes aone-to-one correspondence of contours between sections. This approach applies to many types of branches. It has extensive applicability and produces a better result than previous approach of constructing a composite contour. Generally, a planar triangulation method is used to enclose the unmatched contours. A new skeleton-based method for tiling the unmatched contours is developed that will produce a more natural physical model.更多还原