基于非平行双目结构的三维坐标解算算法

理想情况下,双目立体视觉模型是平行放置的,三维坐标易于解算。但在实际安装摄像机的时候,光轴无法做到平行,标定所得的重投影矩阵和左右图像匹配都存在误差,影响了三维坐标解算精度。针对此种情况,对非平行双目结构三维坐标解算进行了深入的研究。传统的最小二乘法和归一化最小二乘法都是利用求解联立的超定方程组得到最优解,将最优解看作是空间物点的三维坐标,但是它们都没有考虑所建立的超定方程组所代表的几何意义。从几何学角度出发,推导出一种基于异面直线公垂线中点的三维坐标解算公式,通过在无人机平台上测距实验,验证了此方法比最小二乘法和归一化最小二乘法具有更高的精度。

Three-Dimensional Coordinate Solution Algorithm Based on Non-Parallel Binocular Structure

Ideally, the binocular stereo vision model is placed in parallel, and the three-dimensional coordinates are easyto be solved. However, when the camera is installed, the optical axis cannot be parallel. The reprojection matrix obtainedby calibration and the matching of left and right images have errors, which affect the accuracy of the three-dimensional co?ordinates. In view of this situation, this paper makes an in-depth study on three-dimensional coordinate solution of nonparallel binocular structure. The traditional least square method and the normalized least square method both get optimalsolutions by soluting simultaneous overdetermined equations. They regard the optimal solution as the three-dimensionalcoordinates of the space objects, without considering the geometric significance of the established overdetermined equa?tions. In this paper, from geometric angle, a three-dimensional coordinate solution formula based on the midpoint of thecommon vertical line of different planes is derived. Through the ranging experiment on UAV platform, it is verified thatthis method has higher accuracy than the least square method and the normalized least square method.