Edward M. Mikhail 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
The parameters estimated from invariance may then be coorc 
pro ar P CSI QR used as good approximations in a rigorous non-linear Mode 
30° side-look angle; Image Size: 240 rows, 320 cols photogrammetric solution. Table 2.1 shows the control phot 
point and check point RMS results for both the invariance select 
and the rigorous photogrammetric solutions. In this case, 
the recovered parameters for each camera included the 6 22V 
EO parameters, the three geometric IO parameters, and 
one radial lens distortion coefficient, K;. Although the One 
linear invariance technique was helpful in obtaining the tz 
: initial approximations for camera parameters, the use of resoli 
8 Control Points (red), 5 Check Points (blue), : : 
17 Pass Points (yellow) rigorous photogrammetry with added IO parameters 
significantly improved the RMS results. 2.2.1 
Figure 4. Invariance Applied to a Video Pair Ones 
result 
; interv 
Case Control Point RMS (m) Check Point RMS (m) 
X Y Z R X Y. Z R 
094 | 3.25 1.58 3.73 6]4 2:008 | 2:00 | 7.02 _ 
Invariance D 
0.45 | 0.84 1.69 1.94 143.|. 2:87 1-147 | 341 
Rigorous | nr 
Photogrammetry 
  
  
  
  
  
  
  
  
  
  
  
Table 2.1 Two-Frame Video Triangulation Results i 
  
Another useful application of invariance is in image transfer. Image transfer is an application performed on a triplet of 
images. Given two pairs of measured image coordinates, the third pair can be calculated using a previously established 3 
relationship among pairs of image coordinates on all three images. Six techniques, including two based on the F-matrix 
(see equation (1)), three based on the so-called trilinearity equations (Theiss, et al, 2000), and one collinearity 
technique, have been investigated for image transfer. As an example, a data set over Fort Hood consists of two near 
vertical aerial frame photographs taken at 1650 meters above mean terrain, and one low-oblique aerial frame 
photograph taken at a flying height of 2340 meters with a 25 degree (from the vertical) side-looking angle; see Figure 5. 
Nineteen reference points measured on each of the three photographs were used to establish the image coordinate 
Then, for 18 check points the image coordinates from two photographs were used to compute the 
  
  
  
  
  
  
  
relationships. 
transferred positions on the third, and the transferred positions were compared to their measured values. The results for E 
all of the models are shown in Table 2.2. Marke 
There 
gl 6 he ete fr i aa ree iL angles 
Model x RMS y RMS Positi 
Lom ___ | (pixels) Le the st: 
| Trilinearity 1* | -. za 058 | GPS € 
| Trilinearity 2** 0.47 0.61] 
| Trilinearity 3*# | 047 7 10.600 Roll, | 
| Collneaiy | 047 | 061 | every 
| F-matrix, 3F's [7054 | 062 74 Tespec 
| F-matrix, Ie 062 | ud 
EE SURE — EY orient; 
  
  
  
Table 2.2 Image Transfer Experiments with Fort Hood Data INS d. 
    
  
  
  
* After scaling image coordinates to range from The p 
E : — E -1t0+1. ow : exteric 
Figure 5. Fort Hood: Footprints of 2 ++ After rotating image coordinates by 90 degrees. divide 
Vertical Aerial Frames Overlaid on 1 Althoi 
Oblique Frame be too 
: : In the 
As noted by the asterisks below Table 2.2, the raw image coordinate data must be augmented for Models 1-3 in order t? each [ 
obtain those results. Since Model 1 does not rigorously linearize with respect to the observations, the imag image 
  
594 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.