基于全局性极小化二维反投影误差的射影重建方法

A New Method for Projective Reconstruction Based on Global Minimization of 2D Re-Projection Error

建立1种新的射影重建方法。该方法以全局性极小化射影三维空间点的二维反投影误差平方和为准则,相对于缩小SVD反投影误差的方法,具有更为明确合理的物理意义。实现过程是以奇异值分解为基本工具的分步线性迭代计算,避免了传统射影重建方法复杂的非线性优化环节。它无需估计投影深度,避免了基础矩阵计算的复杂性问题,因而也不受相机特殊运动的限制。文中利用虚拟物体图像和真实物体图像进行了实验验证,证明该方法具有计算简单、准确性和鲁棒性高等方面的特点,具有较高的实用价值。

A new method to recover 3D projective reconstruction is presented in this paper. Firstly, unlike the factorization-based methods that minimize the SVD （singular value decomposition） re-projection error, the method uses the minimization of mean 2D re-projection error of projective points as a criterion, therefore it has a clearer physical meaning and enhances the accuracy of projective reconstruction results. Secondly, the method applies a linear iterative procedure in calculation and the SVD is used as a main tool, avoiding complex nonlinear optimization processes. In addition, it does not need the computation of the projective depth and consequently the fundamental matrix. Several experiments on simulated and real image data show that the proposed method is more accurate, robust and faster.