一种用于空中和水下环境的低成本相机的物理和数学联合校准方法。

College of Information Technology, Shanghai Ocean University, Shanghai 201306, China.

School of Electronic and Information Engineering, Shanghai Dianji University, Shanghai 201306, China.

Sensors (Basel). 2023 Feb 11;23(4):2041. doi: 10.3390/s23042041.

Low-cost camera calibration is vital in air and underwater photogrammetric applications. However, various lens distortions and the underwater environment influence are difficult to be covered by a universal distortion compensation model, and the residual distortions may still remain after conventional calibration. In this paper, we propose a combined physical and mathematical camera calibration method for low-cost cameras, which can adapt to both in-air and underwater environments. The commonly used physical distortion models are integrated to describe the image distortions. The combination is a high-order polynomial, which can be considered as basis functions to successively approximate the image deformation from the point of view of mathematical approximation. The calibration process is repeated until certain criteria are met and the distortions are reduced to a minimum. At the end, several sets of distortion parameters and stable camera interior orientation (IO) parameters act as the final camera calibration results. The Canon and GoPro in-air calibration experiments show that GoPro owns distortions seven times larger than Canon. Most Canon distortions have been described with the Australis model, while most decentering distortions for GoPro still exist. Using the proposed method, all the Canon and GoPro distortions are decreased to close to 0 after four calibrations. Meanwhile, the stable camera IO parameters are obtained. The GoPro Hero 5 Black underwater calibration indicates that four sets of distortion parameters and stable camera IO parameters are obtained after four calibrations. The camera calibration results show a difference between the underwater environment and air owing to the refractive and asymmetric environment effects. In summary, the proposed method improves the accuracy compared with the conventional method, which could be a flexible way to calibrate low-cost cameras for high accurate in-air and underwater measurement and 3D modeling applications.

低成本相机标定在航空和水下摄影测量应用中至关重要。然而，各种镜头失真和水下环境的影响很难被通用的失真补偿模型所涵盖，并且在常规标定后仍然可能存在残余失真。在本文中，我们提出了一种用于低成本相机的组合物理和数学相机标定方法，该方法可以适应航空和水下环境。常用的物理失真模型被集成在一起，以描述图像失真。这种组合是一个高阶多项式，可以被视为基函数，从数学逼近的角度来连续逼近图像变形。标定过程会重复进行，直到满足某些标准，并且失真被降低到最小。最后，几组失真参数和稳定的相机内部定向（IO）参数作为最终的相机标定结果。佳能和 GoPro 的航空标定实验表明，GoPro 的失真比佳能大七倍。大多数佳能失真可以用 Australis 模型来描述，而 GoPro 的大多数偏心失真仍然存在。使用所提出的方法，经过四次标定，所有佳能和 GoPro 的失真都降低到接近 0。同时，还获得了稳定的相机 IO 参数。GoPro Hero 5 Black 的水下标定表明，经过四次标定后，得到了四组失真参数和稳定的相机 IO 参数。相机标定结果表明，由于折射和非对称环境的影响，水下环境与空气环境之间存在差异。总之，与传统方法相比，所提出的方法提高了精度，这可能是一种灵活的方法，可以用于高精度的航空和水下测量和 3D 建模应用中的低成本相机标定。