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1. 洛阳师范学院 信息技术学院，河南 洛阳 471022;
2. 广东工业大学 自动化学院，广东 广州 510090

3-D scene plane reconstruction based on multiple views
LI Jing1, YANG Yimin2, CAI Shuting2
1. Academy of Information Technology, Luoyang Normal University, Luoyang 471022, China ;
2. School of Automation, Guangdong University of Technology, Guangzhou 510090, China
Abstract: With consideration to the problems including low accuracy of the 3-D scene plane reconstruction by using the traditional 3-D reconstruction method, two kinds of 3-D scene plane reconstruction models based on multiple views are presented. One is the model of a scene plane reconstruction based on minimizing the reverse projection error. The other is the model of a scene plane reconstruction based on minimizing the transfer error. The first model uses the knowledge that the reverse projection lines should not only intersect with a scene plane but should also meet at one point in a scene plane, so as to minimize the reverse projection error in the scene plane. The second model uses the transfer relationship between the image plane and the scene plane, so as to minimize the transfer error in the scene plane. Finally, the optimized value is computed by the genetic algorithm. The basic principles of the two methods are the same, and the difference between them is in regard to the computational complexity. The experimental results show that the accuracy of the two methods is almost the same and the accuracy of the 3-D scene plane reconstruction is improved greatly.
Key words: 3-D scene plane     reconstruction     homography     constraint condition     intelligent algorithm     genetic algorithm

1 基于两视图的三维景物中平表面重建

 图 1 由景物平表面诱导的单应矩阵H(π) Fig. 1 The homography H(π) induced by a scene plane

xi=[ui vi 1]Tx′i=[u′i v′i 1]T是空间平表面上的点在2幅图像上的对应点对，π为未知景物平表面，空间景物平表面参数化为

3-D点X投影到第2幅图像上可得到

 (1)

2 基于多视图的三维景物中平表面重建

2.1 基于最小化反投影误差的平表面重建模型

 (2)

 (3)
 图 2 反投影线不交于一点 Fig. 2 Reverse projection lines don't intersect in a point
 图 3 反向投影线与一个空间平面相交 Fig. 3 Reverse projection lines intersect in a scene plane

2.2 基于最小化转移误差的平表面重建模型

 (4)

2.3 基于多视图的三维景物中平表面重建

 (5)

 (6)

1)输入N个空间点对应的图像点数据，摄像机的投影矩阵Pi, i=1, 2, …, M

2)将式(4)和式(3)转换为如式(6)所示的无约束优化函数，设置惩罚因子β=500，即构造关于式(4)和式(3)的适应度函数；

3)初始化种群，每一个染色体都是N个空间点和场景平面法线向量n，以及参数αij(见式(3))的组合，采用实数编码，设定种群个数，即染色体个数Nind=50，并设置边界条件；

4)选择操作，计算种群中每个染色体的适应度值，采用轮盘赌的方法进行选择复制，即各个染色体按照适应度值所占总适应度值的比例组成面积为1的一个圆盘，指针转动停止之后，指向的染色体将被复制到下一代，适应度好的染色体被选择的概率大，每个染色体被选中的概率为

5)交叉操作，以交叉概率pc=0.6进行一点交叉，把2个父代个体的部分基因进行交换而生成新的个体，直到所有个体都被选择过；

6)变异操作，选变异概率pm=0.02，即全部染色体位串上的每位基因按变异概率pm进行随机改变；

7)保存当前适应度函数的最小值，以及对应的染色体位置；

8)直至达到最大迭代次数，最大迭代次数为100，若满足，则停止迭代，否则转4)；

9)输出当前适应度函数最小值对应的最优染色体，即空间点的最优坐标值，平面法向量n以及αij

3 实验与结果分析

3.1 仿真实验与结果分析

 图 4 仿真实验环境示意图 Fig. 4 The schematic diagram of simulation environment

 方法名称 噪声标准差(σ) 重投影均方根误差 空间位置均方根误差 0.2 0.013 0 0.005 1 0.4 0.017 1 0.016 2 L∞ 0.6 0.020 1 0.0183 0.8 0.031 1 0.025 1 1.0 0.045 2 0.038 3 0.2 0.020 1 0.000 8 0.4 0.063 3 0.001 1 RPE-GA 0.6 0.085 2 0.001 3 0.8 0.096 4 0.0017 1.0 0.104 2 0.002 3 0.2 0.018 4 0.000 7 0.4 0.059 4 0.001 0 TE-GA 0.6 0.083 3 0.001 4 0.8 0.095 4 0.001 6 1.0 0.109 1 0.002 0

3.2 真实图像实验与结果分析

 图 5 平面模版的5幅图像 Fig. 5 Five images of a planer pattern

 图 6 平面模版的重建结果 Fig. 6 Reconstruction of the planar pattern

 方法名称 重投影均方根误差 空间位置均方根误差 L∞ 0.063 5 0.058 3 RPE-GA 0.081 2 0.001 3 TE-GA 0.081 5 0.001 2

5 结束语

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DOI: 10.3969/j.issn.1673-4785.201309029

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#### 文章信息

LI Jing, YANG Yimin, CAI Shuting

3-D scene plane reconstruction based on multiple views

CAAI Transactions on Intelligent Systems, 2014, 9(4): 454-460
http://dx.doi.org/10.3969/j.issn.1673-4785.201309029