Page 204 - Digital Analysis of Remotely Sensed Imagery

Image Geometric Rectification 169

The overall accuracy of the transformation is evaluated by inte-
grating residuals in both the easting and northing directions at all the
GCPs utilized. The final accuracy indicator RMSE is calculated
EN
using the following formula:

1 n
RMSE = ∑ (δ 2 + δ 2 ) (5.20)
EN n Ni Ei
i=1
The accuracy of image rectification is affected by the following
factors:

• The quantity of GCPs and their reliability, which in turn is
controlled by the quality of the GCP source.
• The precision in locating these GCPs in the image being rec-
tified. It is much easier and more accurate to locate these
points in imagery of a fine spatial resolution than in a coarse
one. Similarly, image coordinates are more reliably deter-
mined from imagery of a fine spatial resolution. The accu-
racy is even higher if the points are more conspicuous (e.g.,
road intersections amid agricultural fields).
• Accuracy of the ground coordinates. They are more accurate
if logged with a GPS unit than read from a topographic map.
• Finally, the order of transformation. A high order of transforma-
tion is usually associated with a more accurate rectification.

There is no theoretic guideline as to what RMSE value is the
acceptable minimum. The conventional wisdom, or rule of thumb,
is that overall RMSE should not exceed one pixel size in value. For
instance, it should be less than 20 m for SPOT multispectral bands
or smaller than 30 m for Landsat TM data. This tolerance level is
justified by the rationale that within a pixel it is impossible to
locate the GCP precisely. If the actual RMSE of a rectification
exceeds this limit, it can be reduced to within the one-pixel limit
by using the following two approaches:

• First, the GCPs with a relatively large residual are excluded
from the transformation. Worse than average GCPs may be
sequentially removed from the transformation until RMSE
falls within one pixel for the first time. It must be emphasized
that removal of any selected GCPs reduces control over
certain parts of the image being rectified. Deletion of more
carefully selected GCPs from a rectification creates an
increasingly imbalanced spatial distribution of GCPs. The
geometric accuracy achieved is thus spatially more uneven.
Geometric uncertainty rises in areas where GCPs have been
removed.