本文为代尔夫特理工大学（作者：Teng Wu）的硕士论文，共119页。

本文提出了一种新的基于中轴变换（MAT）的点云可见性分析方法。这种基于MAT的方法具有几个优点，该方法避免了点云曲面重建，适用于输入点云中缺少曲面的情况。对于网格生成的点云、AHN3点云和稠密图像匹配生成的点云等不同的点云数据集，该方法都能成功地为它们提供良好的可见性结果。

本文所要克服的主要挑战是内外MAT分离。本文对两种方法，即正态重定位法和基于平分线的方法进行了实验研究。法向重定位方法仅适用于由网格生成的点云。基于平分线的方法适用于所有的数据集测试。当曲面缺失时，该方法能够成功地将内外MAT分开。为了加快查询速度，生成了内部MAT的空间索引。本文实现了KD树和R树两种空间索引。由于KD树实现的局限性，KD树并没有明显提高运行速度。KD树的实现还有待改进。R树大大提高了查询的运行时间。对于51567个点，基于R树的查询在1880ms内完成。总之，本文提出了一种有效的基于MAT的点云可见性分析方法。

This thesis proposes a novel medial axistransform (MAT) based method to achieve visibility analysis in a point cloud.There are several advantages of this MAT based method. This method avoidssurface reconstruction from a point cloud. It also works for the situation whenthere is surface missing in the input point cloud. For different point clouddatasets such as point cloud generated from meshes, AHN3 point cloud and pointcloud generated from dense image matching, this method successfully deliverdecent visibility result for all of them. The main challenge overcome in thisthesis is the interior and exterior MAT separation. Two approaches, normalreorientation approach and bisector based approach are experimented in thethesis to separate MAT. The normal reorientation approach only works for pointcloud generated from meshes. The bisector based approaches works for all thedatasets testes. It successfully separates the interior and exterior MAT whenthere is surfacing missing. To speed up of the query process, spatial index isgenerated for interior MAT. In this thesis, two spatial indices areimplemented, KD-Tree and R-Tree. Due to the limitation of my KD-Treeimplementation, the KD-Tree does not improve the running speed obvious. Thereis a room to improve the KD-Tree implementation. The R-Tree achieves sharplyimprovement on running time of the queries. For 51567 points, the query basedon R-Tree finished in 1880 ms. In a word, this thesis proposed an efficient MATbased method of visibility analysis in a point cloud.

1. 引言

2. 理论

3. 论文相关工作

4. 研究方法

5. 具体实现与实验

6. 结果与讨论

7. 结论与未来工作展望

附录A C++源代码

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