三维重构不确定度的两阶估计方法

Two-stage uncertainty evaluation of 3D reconstruction

通过分析三维重构系统视场内3D点的重构不确定度,可以有针对性地优化系统配置,改善实验条件。给出了一种借助于不确定度传递原理估计三维重构不确定度的方法,该方法同时考虑了相机标定和重构3D点过程中的不确定度传递。相机模型参数既是相机标定过程的输出变量,又是重构3D点过程的输入变量,因此可将三维重构过程看作一个两阶系统。针对非线性相机模型给出了三维重构过程中不确定度传递的解析表达式。应用蒙特卡罗算法对文中提出的方法做了验证,并给出了一些典型的应用实例。实验结果表明,三维重构不确定度的估计值至少具有1位有效数字,同时也表明该方法是可行的。

The configuration of a 3D reconstruction system can be optimized by evaluating the reconstructed uncertainties of 3D points located in the working volume of stereo reconstruction system. An evaluation method considering camera calibaration and uncertainty propagation in reconstructing 3D points is presented for 3D reconstrution uncertainties,according to the law of uncertainty propagation. The procedure of 3D reconstruction involves two consecutive stages： calibrating camera models and reconstructing a 3D point from its image projections. The output quantities of the first stage,the parameters of camera models, constitute a part of the input quantities of the second stage. The analytical expressions for uncertainty propagation during reconstructing a 3D point are presented. The presented metrod is validated using Monte Carlo simulation,and some typical applications are given. The experimental results show that the evaluated uncertainties associated with the reconstructed coordinates of 3D point have one significant digit at least,and the presented algorithm is feasible.