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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
a) Perform bundle block adjustment on a block of virtual 
images. 
b) Compute mean image residuals per square cell (about 
256x256 pixels). Each image cell should have at least 40 
points in order to have a reliable correction grid. 
c) Compute some sort of smoothing of the trend surface with 
either low-pass Gaussian kernel or least square surface 
splines. 
d) Refine image coordinates with this “Correction Grid” 
using bi-linear interpolation. 
e) Repeat steps (a-d) 3 to 4 times until maximum residual 
trend increment per cell drops to lower than 0.5[um], 
f) Use the correction grids in the DMC Postprocessing 
software to generate “distortion free” virtual images. 
Repeat steps (a-d) 3 to 4 times until the maximum residual trend 
increment per cell drops lower than 0.5[um], Use the correction 
grids in the DMC Postprocessing software to generate 
“distortion free” virtual images. 
Alternatively, correction grids can be generated from self- 
calibration bundle adjustments. Exported correction grids 
should cover the entire virtual image format. Otherwise, image 
coordinates outside the correction grid must be extrapolated, 
which will give wrong results. These correction grids can be 
imported in the DMC Postprocessing software for refining 
virtual images, in the image observation refinement process, 
and in the object to image projection (real-time math model of 
the digital photogrammetry workstations). 
5. NUMERICAL RESULTS 
5.1 DMC50 Calibration and Testing 
In the following sections, only results of the DMC50 block are 
presented. Results and conclusions of other test blocks were 
similar; therefore, they are not reported here. 
Ima^eStation Automatic Triangulation is used to generate 
tie/pass points (Madani, 2001) for the DMC50 block. This 
block is then adjusted by using GPS with block shift correction 
(no IMU is used) and 10 microns for standard deviation of 
image points (tight constraints in object space and loose ones in 
image space force all the errors to go into the image space, 
where it will be captured by the collocation model). The general 
adjustment statistics are given in Table 2 and distributions of 
control/check points are given in Figure 3. 
Sigma =2.9, RMS x=2.7, 
RMS y = 2.6 [urn] 
Xfm] 
Y[m] 
Z[m] 
RMS of 8 Control Points 
0.017 
0.029 
0.019 
RMS of 6 Check Points 
0.020 
0.032 
0.047 
MAX of 8 Control Points 
0.035 
0.043 
0.030 
MAX of 6 Check Points 
0.036 
0.049 
0.067 
RMS GPS 
0.007 
0.009 
0.019 
GPS Block Shift 
-0.028 
-0.033 
0.218 
6.16 6.160 617 6.175 6 10 6 100 6 19 
«10* 
Figure 3. Distribution of control “red circles”, check “blue 
squares”, and photo centers “red circles” 
5.1.1 Correction Grid generation 
For a reliable estimation of the residual trend surface that is 
almost free from influence of clusters of small outliers, the 
recommended density of image residuals per 256x256-pixel cell 
should be between 20 to 40 points. A histogram of image points 
per cell and spatial distribution of cumulative redundancy 
number per cell (which serves as weight factor in collocation fit) 
are given in Figure 4. 
mean count: 58; max count: 97 
Redundancy Number 
50 I 
150 
100 
50 
50 
100 
10 20 30 
Figure 4. Histogram of image points and cumulative 
redundancy number distribution per cell 
The collocation fit has converged to a trend surface after 4 
iterations performed with the previously adjusted reference 
block. The estimated systematic distortion and the remaining 
residual trend are given in Figure 5. 
Dilionxxi PmtiT r.i* X 3.03|ijm) mu Y 3 S3|um! Owwtw P«n«m m.i X 0 «Hum) m« Y 0 U[urn! 
J0 •» fl » <0 « 
RmsX“ 1 03|UfTi] PmfY» 1 67(umj 
« -20 0 M 4fi £C 
HHum). Rm»Y < D 13j«m| 
Table 2. DMC50 general adjustment statistics 
Figure 5. DMC50 VIR correction grid and the remaining 
distortion trend