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- 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.