Internal and External Parameter Calibrations of a Camera Based on Convex Relaxation Optimization Algorithm

Abstract

Abstract:

The similarity between the real object and the reconstructed model and the precision of the 3D point cloud were determined by the accuracy of the internal and external parameters of the camera. A convex relaxation algorithm was proposed to deal with the problems of camera calibration. Each monomial in the polynomial optimization problem was replaced by its corresponding linear item and some semi-definite matrix inequalities were added. The global optima could be approximated or achieved by solving one or more semi-definite programming problems. The experimental results confirm the feasibility and the accuracy of this algorithm. Moreover, the algorithm can be applied to the problems of camera calibration and some other polynomial optimization problems in multiple view geometry.

Key words: optimization, camera calibration, 3D reconstruction, semi-definite programming, global optimum

摘要：

相机内外参数标定的准确性直接影响后期三维重建与真实被测物之间的相似性和三维点云的精度。针对该情况，提出了一种基于凸松弛多项式优化方法来对相机进行标定。该方法通过对优化问题中的高阶单项式进行线性化处理并添加相应的半正定矩阵约束，从而将原非凸优化问题转换为可以快速并准确求解的半正定规划问题，通过求解一次或多次的半正定规化问题来逼近或求解出原优化问题的全局最优解。实验数据证明了该方法的可行性与精确性。对于其他多视角几何中的多项式优化问题，该方法同样存在着良好的通用性与适应性。

关键词: 最优化, 相机标定, 三维重建, 半正定规划, 全局最优解

CLC Number:

TP751.1

Ke Fengkai, Chen Youping, Xie Jingming, Zhang Dailin. Internal and External Parameter Calibrations of a Camera Based on Convex Relaxation Optimization Algorithm[J]. China Mechanical Engineering, 2016, 27(05): 634-639,657.

柯丰恺, 陈幼平, 谢经明, 张代林. 基于凸松弛优化算法的相机内外参数标定[J]. 中国机械工程, 2016, 27(05): 634-639,657.

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