Huang, Yi Dong 
1 0 Ol(cosh -sinh 0 
R'(hv)=|0 cosv sinvl|sinh cosh 0 
0 -sinv cosv 0 0 1 
cosA -sinh 0 
=| cosvsinh cosvcosh sinv 24 
-sinvsinh -sinvcosh cosv 
2.2.5 Object Coordinate System O,-X, Y, Z,: 
Its transformation with the theodolite coordinate system is denoted as follows: 
Xw X; 
Y, | Ri] Y:|* Ti 2-5 
Zw Zi 
miu mi mi T. 
Rı = mi m» ms» TT, 2-6 
ms; ms ms p 
2.3 The Principle of Three Dimensional Measurement Using Video-Theodolites 
When the camera of the video-theodolite is used as the major measuring device and works on photogrammetric principles, 
the camera exterior orientation can be determined directly by means of theodolite observations. To explain this, the camera 
orientation is represented by a rotation matrix R,,, and a translation vector T,, , and the transformation between the camera 
coordinate system and the object coordinate system is written in the following equation (see the notation in 2.1.1): 
Aw xt 
ys = Rew y + Tew 2-7 
Zw z 
By substituting Eq.2-7 with Eq.2-5, Eq. 2-5 with Eq.2-3, and Eq.2-3 with Eq.2-2, the following is obtained 
Rew - RR R. 3 2-8 
Tw = R: RT. FT T: 2-9 
It can be seen from the above that the camera orientation can be broken down into three separate steps: 
1) System calibration to determine R, and T, . These, as defined before, represent the transformation between the camera 
system and the telescope system. They form part of the constants of the video-theodolite and can be determined together 
With the camera interior orientation parameters using the camera-on-theodolite calibration method (Huang, 1989); 
2) System orientation to determine R, and T. . These represent the transformation between the theodolite coordinate system 
and the object coordinate system. They are constants for each set-up station. Its methods are the subject of section 4. 
3) Theodolite reading on image capture to determine R. This represents the transformation between the telescope system 
and the theodolite system. It is the function of theodolite the horizontal and vertical angular readings of the theodolite only, 
as stated in 2-4. 
It can be seen that after system calibration and system orientation have been completed, the orientation parameters of the 
cameras with respect to the object coordinate system can be found using theodolite readings and Eq. 2-9 and 2-10. It is then 
possible to use the space intersection algorithm to compute the three dimensional coordinates of unknown object points. 
  
390 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 
: defined in accordance with the specification of a particular application. 
tU). ne Cth A ot 
A oN Ls Nw 6 "5 wl 
FA^ 
ab a. db i