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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXX V, Part B7. Istanbul 2004 
show that this checking method can efficiently detect and 
eliminate most blunders and false match. 
4. FAST AND ACCURATE RECTIFICATION OF 
RSIHR 
After acquiring the image parameters and DEM, the RSIHR can 
be rectified to orth-image, which is geo-referenced and is the 
base of quantificational processing and analysis. The common 
method of the rectification is indirect algorithm as following. 
4.1 Computation of ground coordinates 
If the coordinates of a point P on orthoimage are (X^ Y^ Its 
plane coordinates on the ground can be calculated by the 
coordinates (Xj, Y,) of the down-left corner and the scale M of 
orthoimage: 
X=Xp+MX' 
Y=Yy +MY’ (11) 
4.2 Computation of image coordinates 
The height of point P is interpolated based on DEM and (X, Y). 
Then the image coordinates of the point P can be computed by 
the ground coordinates (.X, Y, Z) and image parameters. 
4.3 Interpolation of gray level 
Because the image point is usually not in the center of a pixel, 
the gray level g(x, y) should be interpolated by bilinear 
polynomials. 
4.4 Gray level mapping 
Final, the gray level g(x, y) by the interpolation will be put to 
the pixel of orthoimage: 
GN, Y) = 2t, y) (12) 
In order to accelerate the rectification, the rectified unit is a 
facet instead of pixel by pixel in fact. Only the image 
coordinates (x;, y;) (x», y») (x3, V3) (x4, yy) of the four corners in 
each grid of the DEM are computed by image parameters and 
ground coordinates, and the image coordinates x(i,j) and y(i,j) 
of the points within the grid are interpolated by bilinear 
polynomials respectively. 
x, f= A ir nc 7 *in- j)x, *(n- i)jx, +JX;] 
H^ 
(13) 
(5,7) 2 — [0 - Dn - j)y, +i(n- j)y, *(n-i)jy, * jy] 
n 
  
Where n is the number of rows and columns in the window 
corresponded to the DEM grid, and i, j are the number of row 
and column of the pixel. 
5. RESULTS OF EXPERIMENTS 
Table 1 shows the accuracy of parameter computation in 14 
cases for one IKONOS image pair. There are 25 known points 
in the pair. Case 0 is using only RPC parameters, and cases 1.1 
to 1.6 are applying the block adjustment based on RPC 
parameters, selecting 1, 2, 3, 4, 5 and all of the 25 points as 
control points respectively. Case 2.1 to 2.5 are utilizing the 
strict geometric model based on affine transformation with 23, 
18, 12, 8 and 6 control points respectively. Case 3.1 is the 
RMSE from measured and known coordinates of 77 feature 
points, and case 3.2 is height RMSE of 95 points in DTM. 
Table 2 shows the accuracy of parameter computation in a 
block with 14 IKONOS images, which are from 3 orbits and 
1099 
  
generate 9 modelswith 9 known points. Table 3 shows the 
accuracy of parameter computation for SPOT images, which 
parts are shown in figure 2. Figure 2 shows the matching results 
of a SPOT image pair by the method presented above. Figure 
3(a) shows the orthoimage correspounding with the image in 
Figure 2 by the method discribed above. Figure 3(b) is the 
orthoimage from IKONOS image. 
Tab.1 Parameter calculation of IKONOS stereo image pair 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
case Control points(m) Check points(m) 
N Mx My Mz N Mx My Mz 
0 0 13 3.055 3.155 16.085 
1.1 1 0.000 0.000 0.000 24 0.567 1.478 1.581 
1.2 2 0.190 0.598 0.232 23 0.609 0.580 1.522 
1.3 3 0.016 0.317 0.001 22 0.774 0.548 0.967 
1.4 4 0.179 0.561 0.097 21 0.583 0.674 1.006 
1.5 5 0.425 0.540 0.571 20 0.614 0.575 0.973 
1.6 25 0.532 0.527 0.901 0 
2.1 25 0.031 0.028 0.088 0 
22 8 0.030 0.029 0.094 0 0.044 0.031 0.082 
2.3 12 0.030 0.030 0.081 0 0.037 0.028 0.096 
2.4 8 0.022 0.034 0.084 0 0.044 0.028 0.107 
2.5 6 0.024 0.012 0.034 0 0.042 0.037 0.125 
3:] 25 0.031 0.028 0.088 77 1.098 0.774 0.852 
32 25 0.031 0.028 0.088 95 : 1.30 
  
  
  
  
  
  
  
  
  
  
Tab.2 Parameter calculation of IKONOS image block 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Case Control points(m) Check points(m) 
asc 
N Mx My Mz N Mx My Mz 
4.1 1 0.118 0.109 0.191 8 1.477 1.132 0.927 
4.2 2 0.125 0.146 0.215 7 0.631 0.578 0.883 
4.3 3 0.395 0.115 0.396 6 0.609 0.849 0.866 
4.4 5 0.481 0.107 0.521 4 0.484 | .0.522 0.592 
4.5 9 0.521 0.315 0.436 0 
Tab. 3 Parameter calculation of SPOT image 
Control points(m) Check points(m) 
N Mx My Mz N Mx M Mz 
67 9.401 11.745 5.311 11 7.745 15.282 4.753 
  
49 9.537 10.898 5.378 29 11.242 15.397 6.374 
30 9.456 10.148 4.172 48 10.553 13.853 7.111 
10 3.487 5.856 3.989 68 11.749 15.553 6.072 
  
  
  
  
  
  
  
  
  
  
  
  
  
(a) SPOT image 
Fig. 3 Orthoimage 
(b) IKONOS image