多视点中固定焦距值的全局优化求解

Global Optimal Estimate of Constant Focal Length for Self-Calibration from Multiple Views

相机标定是从二维图像获取三维信息的必要步骤,本文讨论了多视点图像中固定焦距的自标定问题.在绝对对偶二次曲面的成像方程基础上,把固定焦距作为独立未知量纳入到目标函数中,构造了带约束的多项式极值问题,其中约束条件既反映了绝对对偶二次曲面自身具有的代数性质,又包含了可成像的Cheirality约束.求解上述优化问题时,传统的建立在梯度计算基础上的优化方法容易陷入局部最优值,本文则通过使用基于LMI松弛的优化方法获得了焦距的全局最优解.合成数据和真实图像实验均表明本文方法是可行的,具有计算时间快和鲁棒性好的优点.

Camera calibration is an indispensable step to get three-dimensional information from images.In this paper constant focal length self-calibration from multiple views is under investigation.Our approach is based on explicit constraints which relate absolute dual quadric to its images.Two constrained polynomial minimization problems with respect to two types of parametrization on absolute dual quadric,whose properties are incorporated into the constraints,are proposed and solved by linear matrix inequality relaxation optimization method,which could avoid the local minimum.The difference with the other self-calibration approaches is that constant focal length is also an optimization variable besides the absolute dual quadric in the objective function.Experiments with simulated data and real images show that our approach works well.