Abstract
Abstract. The rational polynomial coefficients (RPC) model is a generalized sensor model, which can achieve high approximation accuracy. And it is widely used in the field of photogrammetry and remote sensing. Least square method is usually used to determine the optimal parameter solution of the rational function model. However the distribution of control points is not uniform or the model is over-parameterized, which leads to the singularity of the coefficient matrix of the normal equation. So the normal equation becomes ill conditioned equation. The obtained solutions are extremely unstable and even wrong. The Tikhonov regularization can effectively improve and solve the ill conditioned equation. In this paper, we calculate pathological equations by regularization method, and determine the regularization parameters by L curve. The results of the experiments on aerial format photos show that the accuracy of the first-order RPC with the equal denominators has the highest accuracy. The high order RPC model is not necessary in the processing of dealing with frame images, as the RPC model and the projective model are almost the same. The result shows that the first-order RPC model is basically consistent with the strict sensor model of photogrammetry. Orthorectification results both the firstorder RPC model and Camera Model (ERDAS9.2 platform) are similar to each other, and the maximum residuals of X and Y are 0.8174 feet and 0.9272 feet respectively. This result shows that RPC model can be used in the aerial photographic compensation replacement sensor model.
Highlights
The new generation of commercial high-resolution satellite imagery will open a new era for digital mapping (Zhou G, 2000)
The Tikhonov regularization method is equivalent to the approximate deformation of the least square method
In order to evaluate the fitting accuracy of rational polynomial coefficients (RPC) model, the pixel coordinates of each checkpoint were calculated by strict sensor model and RPC model, and the error is calculated on the basis of the difference between the two
Summary
The new generation of commercial high-resolution (up to one meter ground resolution) satellite imagery will open a new era for digital mapping (Zhou G, 2000). The RPC model is widely applied to geometry processing of remote sensing images of high-resolution satellite and has become a sensorindependent generalized geometry processing model that can replace the strict geometry processing model (Zhang G, 2006). In the process of solving RPC of aerial images, the normal equations are prone to pathological conditions. The Tikhonov Regularization can be a good solution to the pathological equation. The key of this regularization method is to determine its effective regularization parameters. L-curve method is used to determine regularization parameters. Experiments and error analysis show that the third-order RPC model can replace the rigorous imaging model to complete the orthorectification of images.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
