The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
• Scale and Translation Model: If only GCPs are em
ployed without redundancy, their distribution affects plane ac
curacy greatly mainly because the calculation error by the small
denominator during solution. Rotation of the coordinates by 45
degrees can solve this problem and get stable solutions. Stan
dardization is employed in the calculation to convert all the in
put data between -0.5 and 0.5, which can reduce the calculation
error caused by big difference of data. The plane accuracy is 2
m to 5 m with 2 m for the best, while height accuracy is within
0.6 m. Increase of GCP number does not count much when the
number is more than 6.
• Affine Model: At least 4 GCP are needed in affine
model, and adjustment is needed when the GCP are redundant.
Results with only 4 GCP are not stable. When GCP number is
more than 8, accuracy is not sensitive to the GCP number.
About 0.7 m in plane direction can be achieved when 16 well
distributed GCP are employed, and the height accuracy is about
0.5 m.
• Second-order Affine Model: 10 GCP are needed for
the model, and this is the most unstable model. One cannot get
stable solutions when the GCP is 10, 12, 14, respectively, which
means it has high requirement for GCP distribution. For this
model, if the square items of height in plane direction equations
are omitted (Equation 8.), the solution would be more stable,
the right figure is the result of this simplified model. We can
learn from the figure that for this model, with 16 well distrib
uted GCP, the plane accuracy is within 0.6 m, and height accu
racy is also within 0.6 m.
P = Qq + o^X + + q 3 Z + q 4 XY + a 5 XZ + YZ + a 2 X + q%Y
■ L = b 0 + b x X + b 2 Y + b 3 Z + b 4 XY + b 5 XZ + b 6 YZ + b,X 2 + b e Y 2
H = c 0 + c t X + c 2 Y + c 3 Z + c 4 XY + c 5 XZ + c 6 YZ + c n X 2 + c s Y 2 + c 9 Z 2
Figure 6. Figures of Accuracy with different GCP Number in image space:
(a) .translation model; (b) scale and translation model; (c) affine model; (d) second-order affine model.
3.3.2 Accuracy improvement in image space
• The translation model is the simplest model and the
minimum GCP number is 1. Providing one GCP, the accuracy
is about 3 meters in plane direction and 4.5 meters in height di
rection. Accuracy improves when more GCPs are available.
With 6 or more GCPs available, accuracy in both directions are
stable, about 2.2 m in Plane direction and 3.2 m in height direc
tion can be achieved. The accuracy in latitude direction is much
better than that in longitude direction. High accuracy can be ob
tained when the GCPs are in the middle of the test region.
• The minimum GCP number for translation and scale
model is 2 and iterative calculation is needed for the solution of
this model. When 2 GCPs are used in this model without redun
dancy, accuracy is about 6 meters in plane direction and 16 me
ters in height, thus for this model redundancy is necessary. With
the increase of GCP number, accuracy in plane direction can
achieve about 1 meter. With more than 8 GCPs, the accuracy in
plane direction can be less than 1 m, up to about 0.85 m, and
the height direction is about 1 meter. The maximum error in
plane direction is about 2.5 meter and slightly less than that in
height direction which is about 2.7 meter.
• 3 GCPs are necessary for the affine model with itera
tion needed for the solution. However, accuracy is also not sat
isfying when only 3 GCPs are used in this model without re
dundant number. With one more GCP, the accuracy is much
better, about 1 meter in plane direction and 1.5 meter in height