of the SCS GCPs design (Fig. 2b), the whole image was partitioned
into 16 compact strata, from which the centers of the strata were
selected as GCPs. The RMSE and the mean of z were 0.4417 and
0.2411, respectively. Compared with SRS, the SCS was far more
accurate. The UKMS GCPs design (Fig. 2c) was optimized with prior
information of SCS. GCPs were distributed more dispersedly than in
SCS throughout the image. The outer GCPs were closer than those
of the other spatial sampling designs to the boundary. The RMSE
and the mean of z were 0.4089 and 0.1674, respectively, which
were the smallest values among the three spatial sampling designs.
This result indicates that the UKMS GCPs sampling design provided
the most accurate geometric correction. In comparing the criterion
of the RMSE, UKMS was 24.5% and 7.43% more accurate than SRS
and SCS, respectively. The variogram of total residuals in UKMS is
given in Fig. 6c. This figure shows that for the UKMS, the residuals
of the geometric correction model do not have an autocorrelated
structure after GCP optimization.
In addition, SSRS statistical inference results were also calculated
to infer the geometric accuracy of population. Taking UKMS
GCPs spatial sampling design as an example, the mean and standard
deviation of the sum of two square errors z for each pixel in the
corrected image were 0.1674 and 0.1519, respectively. The t value
was 7.794, indicating that the estimation for the entire image was
significant. In a two-tailed test, at a 95% confidence interval of the
difference, the geometric error of z for each pixel in the corrected
image was between 0.1243 and 0.2106 pixels. The upper confidence
interval of z is less than 0.5 pixels. The UKMS thus provides
an accurate geometric corrected image.