Huang, Yi Dong 
: = T 
ertical C=(C, Cy c) =RT. 54 
ds are 
hat of where the subscripts P and p are omitted and x' are the camera coordinates as stated by Eq.2-1. Now, adopting the 
nts to following notation 
and eliminating s in Eq.4-2, we obtain the collinearity equations below: 
  
  
:veled 
ses u _ Mi(Xy-T)*mn(Yw-T,)+ mrs(Z»-T:)-Cz 5-5a 
int à w msi( Xw-Tx) * ms(Ys-T,) * ms( Ze- T:)- C. 
) point kyon mu Xs-T.)t ma(Ys-T;,)* mu(Z.-T.)-C, 5-5b 
Ww. mu( Xs-T.)* mo(Ys- T,) * ms( Zv- T.)- C. | 
Video- It can be seen that by using these equations, it is possible to solve for the theodolite orientation parameters R, and T, ina 
e two similar way to the analytical space resection or relative orientation when the theodolite readings at the time of image 
exposure are used as well as the image coordinates of the measured points. An experiment on using these equations for 
  
  
  
n, th 
e theodolite relative orientation is detailed in Section 6. These equations can also be applied to a multiple stations bundle 
adjustment. 
or tie 
nined 
rs are 6 EXPERIMENTS 
olved 
An experiment has been carried out to test the validity of the new collinearity equations for video-theodolite orientation. A 
calibrated video-theodolite was used at two stations to capture multiple images of 28 targets (Fig.1). Theodolite readings 
were recorded on capture of each image. The target images were measured to 0.3 pixel accuracy. Six of the targets were 
used to determine relative orientation between the two stations using the new collinearity equations. Space intersection was 
then performed for the rest targets using the same collinearity equations. The root mean squares of residual image position 
errors from space intersection were computed to assess the overall accuracy of the whole operation. 
ad to The camera used is a zoom CCD camera set and a Targets Distribution | 
calibrated at 65mm. With a 1/3 inch chip and 576*480 ds | 
digitization resolution, it gives a pixel angle of about 30" s | 
ges at of arc. The target images were measured manually to 0.3 Sat. v e e s 95 | 
earity | pixel which is equivalent to 10” in angle. Compared with 25 e? . uw v | 
| this, the Geodimeter theodolite has an 3" arc angular es 2? 8 e oc «7 ua 
precision and thus can be treated as error free in this N M 9 e em 28 [e Targets 
i N 15% 4d e 014 9 eu © 
experiment. 2 | 
Calibration was performed using the  camera-on- gs | 
le the theodolite method and achieved higher than 0.1 and 0.3 oi. 1 
wing pixel in the line and sample direction respectively. This 0 1 2 3 4 5 | 
| accuracy is poorer than average previously achieved due p X (m) d 
  
  
| probably to the heavey linejitter encountered recently 
with the camera and frame grabber. The repeatability was assessed to be about 0.3-0.4 pixel using the method described in 
(Huang 1999). The calibrated values were used as known constants in orientation and space intersection. 
Both theodolite stations were levelled and dual axial compensation was on. Relative orientations with three parameter (x, 
By, Bz) and five parameters (®,9,k, By,Bz) were performed respectively using the new collinearity equations with 6 widely 
spread points captured on 6 different frames of image at different theodolite pointings from each station. The 6 points used 
were No. 1,5,10,19,25,28. Space intersection was then carried out using the new collinearity equations again to determine 
3D coordinates of all target points. 
The root mean squares image position residual errors from space intersection were 0.35 and 0.51 pixel for the 3-parameter 
and 5-parameter relative orientations respectively. These accuracies are consistent and believed to improve with the 
calibration accuracy. A similar experiment to this but with simulated data has also been carried out. That has validated the 
correctness of the algorithm and computation. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 393