International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
achieve the improved coordinates (X’, Y’, Z’). It requires at least 
one GCP. The second model uses three additional scale factors (a, 
bi, ci) to correct non-homogeneous scale distortions. An affine 
transformation and a second-order polynomial transformation are 
applied to the third and fourth models, respectively. In image 
space, the image coordinates (I, J) are improved by four similar 
models to compute the corrected image coordinates (l', J^). 
However, these models are simplified by dropping the parameters 
associated with the third dimension. The implementation and 
  
IMPROVEMENT RESULTS AND DISCUSSION 
Tables 5 and 6 show improvements in accuracy achieved by the 
three different methods performed in the object space for both 
IKONOS and QuickBird stereo images, respectively. It should be 
noted that the minimum number of control points is not met with 
the available GCPs for the second-order polynomial model. In the 
GCP distribution column of both tables, each digit (from 0 to 8) 
represents a control point ID (as indicated in Figure 1). 
Improvement results for the models performed in the image space 
are summarized in Tables 7 and 8. A discussion of the results of 
each method is given below. 
  
  
  
Maximum 
RMSE (m) Difference (m) 
X YZ |X |Y_ Z 
No. GCP 
Method \GCPsDistribution 
  
  
  
— 
Translation 1 0.43700.631/0.815/0.719]1.0031|1.361 
  
  
  
  
2 
S 8 |2-7 9.8431.152]1.131/1.283]2.286|1.553 
«Ft 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
2 
Scale and 2 x 
Translation 2 s | 3-6 0.3081.071/0.912/0.383/1.384|1.328 
© = 
4 0-3-5-7 0.2720.612/0.523/0.396/0.724|0.650 
6 |5-6-3-7-2-0 0.44770.243|0.624/0.447|0.243|0.624 
Aff 4 0-3-5-7 | .2060.794/0.809/0.308/1.130/0.955 
ine 
6 |5-6-3-7-2-0 0.2800.570/0.429/0.280/0.570/0.429 
  
  
  
assessment processes are the same as those in the object space. 
Min. No. 
ID Adjustment Models 
J of GCPs 
|] | Translation 1Y'za,.Y'z5,.Z'zc, l 
Scaleand |^ ^ *^* 
: Y'=b, +bY 2 
2 | Translation]. ^ ^ 
Fo te 
X'= a, +a, À +a,Y +a;2 
Object | 3 Affine |1'=b,+bX+bY+b2Z 4 
Space ZG BOÀATOlT0 A 
X'=a, va, X+a,Y +a, Z +a, XY +a, XZ 
+a Yl va, XP +a ¥ «aZ 
4 Second-order |y'=p, +b.X +6, +b,2 +b, XY +b. XZ 10 
Polynomial +b YZ +b, X +b)’ +b,Z° 
Z'=c, +e, X +e, ¥Y +e, +e XY +e XZ 
+e YZ +e, X +6,17 +052 
1 | Translation |I'=a,,J'=b, I 
2 Scale and |/- ay t aM ) 
Image Translation |J'- 5, € ^,J - 
Space 3 Affine I'=a, +a, +a,J 3 
J'=b, +b! +b,J 
4 Second-order |/'=a, +a, +a a, a P! au? 6 
Polynomial M'zb + bf + b,J tb b, tJ 
  
  
  
  
  
  
  
Table 6. Accuracy of ground points improved by three object 
space-based models for QuickBird stereo images 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Table 4. Adjustment models defined in object and image space No. GCP RMSE (m) Maximum 
Method \GcPsDistribution Difference (m 
The experiment starts with each model using the minimum X Y Z X Y Z 
number of GCPs (see Table 4). Additional GCPs are then added Translation| 1 5 1.3650.631/1.355/3.702/1.53013.219 
to improve accuracy. Various combinations of the number and ES : 
distribution of GCPs are also tested to determine the effectiveness Ss 9 1-3 11.20211.21412.85513.85612.577 7.786 
of different configurations. > <= 
Scale and | 2 4 . 2 CA 
Translation e 8|5-I [.3180.653|1.272|4.099]1.385|2.821 
Maximum Ve 
No. GCP RMSE (m) d 
Method istributi Difference (m) 4 | 2-3-5-6 |1.3660.658|1.163|4.017|1.531|2.757 
GCPsbDistribution X Y Z X Y Z 
6 |1-3-4-5-7-8|1.35000.651]1.233/|4.225|1.448/2.872 
7 . nn ^A 2 
Translation] 1 1 1.000/0.733|2.264|3.424|2.079|4.606 # 4 13.5.7 37310 50011 28815 88811.17013.006 
oh 2 ine > p 
5 S 3-9 |1.11810.69312.18713.859|1.81615.524 6 | 1-3-4-5-7-8 |1.43110.597|1.137/4.230}1.502|2.787 
A Second- | 6 |0-2-3-4-6-8 [1.52411.287]1.537/5.9155.167]4.505 
Scale and 25 |, > » Order 
Translation & & 8L0320.8220.2223.6732.867 5.984| — |bolynomial| 10 | evenly |1.3660.557]1.362 3.681]1.531/3.860 
4 1-3-5-7 |1.192/[0.626/2.008|3.824|1.650|4.945 
^ Table 7. Accuracy of ground points improved by four image 
6 |0-2-4-5-6-8|1.068/0.712|1.941|3.926|2.034|4.639 space-based models for IKONOS Stereo images 
Aff 4 1-3-5-7 .|1.525/0.645|3.217|4.871|1.488|5.850 
ine 6 |1-3-4-5-7-8|1.179/0.736/1.678|4.498|2.098|4.195 
  
  
  
  
  
  
  
  
  
  
  
Table 5. Accuracy of ground points improved by three object 
space-based models in IKONOS stereo images 
Translation Model: This model offers a simple way to improve 
accuracy by a translation in either object or image space. Using 
one GCP, reasonable accuracies can be achieved. For IKONOS 
images, RMSE generally is less than 1 m in the horizontal and 2.5 
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