1313 
- V N, 
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
3.2.1 The 2D Polynomial equations 
x =Ÿ À a i X i Y {n - i) Y =Ÿ J b i X i Y (n ~ i) 
(1) 
Where (x,y) are image coordinates and (X,Y,Z) are object 
coordinates. 
3.2.2 Rational Function Model: In this model the image 
coordinates is determined from the ratio of two polynomials: 
ml m2 m3 
y y Y a m X l Y j Z k 
pi/ y v V\ !/* 
_ rl l A , I , _ /=Q j=Q k-0 
P1{X ’ Y ’ Z) SSI VfY'Z 
/=0 j=0 *=0 
ml m2 m3 
y £ ÿ c, k X‘ Y J Z k 
ni/ V V 7\ ljK 
y — r I 1 ^ ) _ /=0 y=0 Ar=0 
P4 ( X,V, Z) £££ dftX , pz 
i'=0 y=0 *=0 
(2) 
Where 
P1(X, Y, Z) = a 0 + a,X + a 2 Y + a 3 Z + 
a 4 XY + a$XZ +o 6 YZ +a 7 X~ + -ho t9 Z (3) 
Where (x,y) are normalized image coordinates and (X,Y,Z) are 
normalized object coordinates. 
4. THE EVALUATION RESULTS OF IRS-P5 IMAGES 
In this section we evaluate geometric accuracy and information 
contents of IRS P5 stereo images. 
4.1 Evaluation results of geometric accuracy of IRS-P5 
images 
NO. 
Check 
NO. 
Control 
RMSE 
(X) 
RMSE 
(Y) 
RMSE 
(X,Y) 
RMSE 
(Z) 
113 
0 
38.917 
128.318 
134.089 
8.0901 
112 
1 
1.4333 
1.8690 
2.3553 
3.9956 
111 
2 
1.4358 
1.7945 
2.2982 
3.9319 
110 
3 
1.5969 
1.4592 
2.1632 
2.9985 
109 
4 
1.5580 
1.3200 
2.0420 
2.8847 
108 
5 
1.5330 
1.3371 
2.0342 
2.8112 
Table 3: The results of geometric accuracy of IRS-P5 stereo 
images with using rational function model with RPC file 
-RMSE1XV) 
- RMSE(Z) 
13 5 7 
9 11 13 15 17 19 21 23 25 27 29 
No.Control 
Figure 4: The results of geometric accuracy of IRS-P5 stereo 
images with using rational function model with RPC 
As we see in table (3) because of using RPC, by choosing one 
control point, geometric accuracy increases significantly. By 
choosing 4 control points we achieved to desirable Accuracy. 
Also by using at least 3 control points, we achieved to height 
accuracy better than 3 meter that with regard to the height 
accuracy of 1:25000 scale maps, this result is in acceptable 
range. 
Figure 5: The results of geometric accuracy of IRS-P5 images 
with using rational function model without RPC file 
By using third equation of rational function model without 
RPC, we obtained more smooth results compared with other 
orders. By choosing 25 control points, the results of whole 
rational function models will become converge. 
-♦-OrderJ 
■ ♦ 0rder_2 
0rder_3 
Order 4 
Figure 6. The results of geometric accuracy of IRS-P5 images 
with using polynomial equations 
By using polynomial equations, approximately we achieve to 
the same results compared with rational function model without 
RPC. As we see the result of first order of polynomial equations 
is better than other orders.