Hence, UKMS performs best in both simulation and actual-image geometric correction experiments.
As in the UKMS GCPs optimization, the quality measure of MUKV
does not depend on the data values themselves but merely on the
spatial pattern of the predictors and the covariance structure of the
residuals. This allows us to compute the MUKV before collecting
the GCPs coordinates. However, the UKMS needs the variogram of
regression residuals to calculate the covariance of samples and predictors
before samples optimization. In this paper, the variogram
was provided by the SCS geometric correction. Therefore, it needs
to collect GCPs for twice: the first time is to collect the GCPs for
SCS geometric correction which in order to obtain the regression
form and regression residual variogram; the second time is to collect
GCPs for UKMS geometric correction based on the results of
SCS. As a result, this method becomes less efficient, even though
UKMS achieves the most accurate geometric correction. Besides
this, the variogram of regression residuals always contains uncertainty,
which will propagate into UKMS optimization and affect
the GCP configuration. Hence, dealing with the situation that no
prior variogram is known or the variogram has uncertainty is a
key problem in UKMS optimization. Diggle and Ribeiro (2007) provided
a way to solve this problem through utilizing a model-based
geostatistical approach. In this approach, the residual variogram
can be modeled from expert judgment or empirical experience.
Then one treats the variogram as being uncertain and estimates its
parameters using a Bayesian approach (Diggle and Lophaven, 2006;
Diggle and Ribeiro, 2007). Therefore, this model-based geostatistical
method can be adopted in the GCPs spatial pattern optimization
when no variogram is known or variogram has uncertainty.