﻿ 基于非量测相片的三维模型重建

基于非量测相片的三维模型重建Three-Dimensional Model Reconstruction Based on Non-Measured Photo

Abstract: With the development of science, the requirement of visual feeling is improved, an increasing number of three-dimensional image products enter life. Nevertheless, the three-dimensional model reconstruction is subject to many restrictions, and does not meet the public requirement. In recent years, three-dimensional reconstruction with non-measurement photos has become one of the popular ways of 3D model reconstruction. This paper mainly introduces the process of 3D model reconstruction, including the use of non-measurement photos for camera calibration, extraction and matching of feature points, line constraint and intrinsic matrix calculation, three-dimensional reconstruction, error analysis. Lastly, the paper briefly analyzes the prospect of this method.

1. 引言

2. 基于相片的三维几何信息计算方法

2.1. 相机标定

2.1.1. 坐标系转换

2.1.2. 内参提取

$Z\left[\begin{array}{c}x\\ y\\ 1\end{array}\right]=\left[\begin{array}{ccc}f& 0& {c}_{x}\\ 0& f& {c}_{y}\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]$ (1)

2.1.3. 外参提取

$sx=K\left[\begin{array}{cc}R& T\end{array}\right]\left[\begin{array}{c}X\\ 1\end{array}\right]$ (2)

2.2. 特征点提取与匹配

2.3. 极线约束与本征矩阵

$0={{x}^{\prime }}_{2}E{{x}^{\prime }}_{1}$ (3)

$\begin{array}{l}{{x}^{\prime }}_{1}={K}^{-1}{x}_{1}\\ {{x}^{\prime }}_{2}={K}^{-1}{x}_{2}\\ E={\stackrel{⌢}{T}}_{2}{R}_{2}\end{array}$ (4)

3. 三维重建方法

3.1. 双目重建

$s{x}_{2}=K\left(RX+T\right)$ (5)

$\stackrel{⌢}{x}K\left[\begin{array}{cc}R& T\end{array}\right]\left[\begin{array}{c}X\\ 1\end{array}\right]=0$ (6)

3.2. 多目重建

OpenCV中拥有solvePnP和solvePnPRansac函数，只需知道空间中部分点的坐标和其对应点的像素坐标，就可以通过solvePnP计算获得相机的空间坐标。进行多目重建的过程原理是首先对最初的两张相片进行双目重建，获得了空间中的一些点，然后加入第三张相片，令此相片与第二张相片进行特征点的匹配，在形成的匹配点中包含相片二与相片一之间的部分匹配点，同时在第三张相片中这些点的像素坐标已知，即可通过solvePnP得到第三个相机的空间位置，得到相机三到相机一的变换矩阵。

4. 实验与分析

4.1. 数据准备

4.2. 三维重建结果

Figure 1. Flow chart of multi-purpose reconstruction

Figure 2. Two-dimensional non-measuring photo

Figure 3. Sparse reconstruction

Figure 4. 3D reconstruction of the image

5. 结束语

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