點雲配准是三維點雲處理研究領域中的一個技術難題和典型問題，其目的在於比較或者融合針對同一對象在不同視場角下獲取的點雲。比如，對於一組點雲數據集中的兩幀點雲，通過尋找一種空間變換把一幀點雲經過旋轉平移移動到另一幀點雲，使得兩幀點雲中對應於空間同一位置的點一一對應起來，從而達到拼接點雲實現點雲融合的目的。本篇論文提出了一種基於點雲在多面體上的分佈來改進ICP的方法。利用點雲在多面體上的分佈和點雲的法向量，來描述點雲的形狀，從而避免傳統的ICP會陷入局部最優值的情況。

Point cloud alignment is a typical problem and technical difficulty in the field of three-dimensional point cloud processing research, which aims at comparing or fusing the point clouds obtained for the same object under different conditions. Specifically, for two frames of a point cloud data set, by finding a spatial transfor-mation to move one frame of the point cloud to the other frame through rotational translation, the two frames of the point cloud corresponding to the same position in space correspond to each other, so as to achieve the purpose of information fusion. This makes the points in the two frames correspond to the same position in space one by one, so as to achieve the purpose of information fusion. In this paper, we propose a method to improve the ICP based on the distribution of point cloud on a polyhedron. The distribution of the point cloud on the polyhedron and the normal vectors of the point cloud are used to describe the shape of the point cloud to avoid the traditional ICP from falling into the local optimal value.

Acknowledgement I
Abstract II
III
List of parametersIV
1 Preliminary1
1.1 Normal vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 SVD decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Point cloud alignment accuracy evaluation index . . . . . . . . . . . . 2
1.3.1 Root Mean Squared Error . . . . . . . . . . . . . . . . . . . . 3
1.3.2 Hausdorff Distance . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3.3 Chamfer Distance,CD . . . . . . . . . . . . . . . . . . . . . . 3
1.3.4 Earth Mover’s Distance . . . . . . . . . . . . . . . . . . . . . . 4
2 Introduction 5
3 Related Works 9
3.1 ICP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 NDT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4 Implementation 17
4.1 Project Point Cloud on Polygon . . . . . . . . . . . . . . . . . . . . 17
4.1.1 Histogram and cosine similarity . . . . . . . . . . . . . . . . . 18
4.2 Spherical Triangle Subdivision . . . . . . . . . . . . . . . . . . . . . . 20
4.3 Describing point clouds with normal vectors . . . . . . . . . . . . . . 23
4.3.1 Principal Component Analysis . . . . . . . . . . . . . . . . . . 24
4.3.2 Determine the orientation of the normal vector . . . . . . . . 24
4.3.3 Normal vectors histogram . . . . . . . . . . . . . . . . . . . . 25
4.4 Polyhedron ICP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5 Experiments 28
5.1 Compare with ICP and NDT. . . . . . . . . . . . . . . . . . . . . . . 31
5.2 The Impact of the Number of Point Clouds . . . . . . . . . . . . . . . 32
5.3 Impact of Noise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.4 Impact of Convergence Threshold. . . . . . . . . . . . . . . . . . . . . 33
6 Conclusions and future work 34

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