Reference control points (RCPs) used in establishing the regression model in the regis-tration 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 exten-sively 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. This paper introduces a consistent adjusted least squares (CALS) estimator and proposes relaxed consistent adjusted least squares (RCALS) estimator, with the latter being more general and flexible, for geometric correction or regis-tration. 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 proposed RCALS estimators is to improve the accuracy of measure-ment value by weakening the measurement errors. The conceptual arguments are substantiated by a real remotely sensed data. Compared to the OLS estimator, the CALS and RCALS estimators give a superior overall performance in estimating the regression coefficients and variance of measurement errors.
在遥感影像配准过程中,通常假设控制点是“完美的”。然而,在实际情况中,由于控制点本身不可避免的带有一定的误差导致这种假设在一定情况下并不成立,并且将会影响遥感影像几何校正的精度。普通最小二乘方法OLS(O rd inary Least Square)是遥感影像配准常用的校正估计模型,令人遗憾的是,在控制点存在误差的情况下,它的估计是有偏的,并且不能够正确传递和估计校正影像的误差大小。引入一致校正最小二乘方法CALS(ConsistentAd justed Least Squares),在此基础上提出的一个改进的方法,称之为松弛一致校正最小二乘方法RCALS(Relaxed ConsistentAd justed Least Squares)。这类回归模型具有改正控制点(解释变量)中的误差和跟踪回归模型中的误差传递的能力。为了验证CALS和RCALS模型的有效性,本文利用模拟影像进行分析。这里着重分析OLS,CALS和RCALS模型在几何校正过程中的比较。结果表明,RCALS和CALS的结果优于OLS估计结果。
