The existence of several unnecessary and highly correlated coefficients in the rational function model (RFM), known as rational polynomial coefficients (RPCs), leads to an ill-posed design matrix. Under such a condition, any small perturbation, including errors in the problem’s input, causes drastic changes in the final results. The ill-posedness of the design matrix, intrinsic to the RFM problem, can be amplified due to the errors in the ground and image coordinates of the control points. The principal component analysis (PCA)-based RFM optimization method has already been applied to reduce the impact of ill-posedness of the design matrix. Despite its efficacy, the existence of a case-sensitive tunable threshold value in this method has overshadowed its efficiency. To address this problem, we propose an automated PCA-based RFM optimization, called APCA-RFM method, which is based on the thresholding ridge ratio criterion. In APCA-RFM, the data itself is used to obtain the threshold value and hence to separate the noise from the signal. Experiments conducted on different data sets demonstrated the high performance of the proposed method to come up with a solution to the challenge of an appropriate threshold value. Additionally, the experimental results proved the superiority of the proposed APCA-RFM in comparison with recently published methods dealing with the ill-posedness problem of RFM.

有理函数模型（RFM）中存在几个不必要且高度相关的系数，称为有理多项式系数（RPCs），导致设计矩阵不正确。在这种情况下，任何小的扰动，包括问题输入中的错误，都会导致最终结果发生急剧变化。由于控制点的地面和图像坐标中的误差，RFM问题所固有的设计矩阵不适定性可以得到放大。基于主成分分析（PCA）的RFM优化方法已被应用来减少设计矩阵不适定的影响。尽管具有有效性，但是此方法中存在区分大小写的可调阈值，这已经掩盖了其效率。为解决此问题，我们提出了基于PCA的自动RFM优化，称为APCA-RFM方法，该方法基于阈值脊比率标准。在APCA-RFM中，数据本身用于获取阈值，从而将噪声与信号分离。在不同数据集上进行的实验证明了所提出方法的高性能，从而提出了应对阈值挑战的解决方案。另外，实验结果证明了与最近发表的解决RFM不适性问题的方法相比，所提出的APCA-RFM的优越性。在不同数据集上进行的实验证明了所提出方法的高性能，从而提出了应对阈值挑战的解决方案。此外，实验结果证明了与最近发布的解决RFM不适性问题的方法相比，所提出的APCA-RFM的优越性。在不同数据集上进行的实验证明了所提出方法的高性能，从而提出了应对阈值挑战的解决方案。此外，实验结果证明了与最近发布的解决RFM不适性问题的方法相比，所提出的APCA-RFM的优越性。