Measurement Errors and their Propagation in the Registration of Remote Sensing Images (?)

Reference control points (RCPs) used in establishing the regression model in the registration or geometric correction of remote sensing images are generally assumed to be ?perfect?. That is, the RCPs, as explanatory variables in the regression equation, are accurate and the coordinates of their locations have no errors. Thus ordinary least squares (OLS) estimator has been applied extensively to the registration or geometric correction of remotely sensed data. However, this assumption is often invalid in practice because RCPs always contain errors. Moreover, the errors are actually one of the main sources which lower the accuracy of geometric correction of an uncorrected image. Under this situation, the OLS estimator is biased. It cannot handle explanatory variables with errors and cannot propagate appropriately errors from the RCPs to the corrected image. Therefore, it is essential to develop new feasible methods to overcome such a problem. In this paper, we introduce the consistent adjusted least squares (CALS) estimator and propose a relaxed consistent adjusted least squares (RCALS) method, with the latter being more general and flexible, for geometric correction or registration. These estimators have good capability in correcting errors contained in the RCPs, and in propagating appropriately errors of the RCPs to the corrected image with and without prior information. The objective of the CALS and our proposed RCALS estimators is to improve the accuracy of measurement value by weakening the measurement errors. The validity of the CALS and RCALS estimators are first demonstrated by applying them to perform geometric corrections of controlled simulated images. The conceptual arguments are further substantiated by a real-life example. Compared to the OLS estimator, the CALS and RCALS estimators give a superior overall performances in estimating the regression coefficients and variance of measurement errors. Keywords: error propagation, geometric correction, ordinary least squares, registration, relaxed consistent adjusted least squares, remote sensing images.