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2.2 Definition of Coordinate Systems 
2.2.1 Camera Coordinate System O.-x'y'z ': O, is the perspective centre of the camera. z' is perpendicular to the focal 
plane of the camera. x' (y) is perpendicular (parallel) to the scanning line direction of the image and increases with the 
number of line (sample). (Note that x and y are usually defined with fiducial marks in metric film cameras) 
222 Image Coordinate System Orxy: x and y are parallel to x' and y' respectively. O; is some convenient reference 
point, usually, the top-left corner of the images for CCD cameras. For a point in the image plane, the image coordinates 
and camera coordinates are related by the equation below. 
x X - Xo 
Y= pad, 2-1 
z - f 
xo and yo are the image coordinates of the principal point which is the point in which O,z' meets the image plane. 
fis the principal distance of the camera. 
2.2.3 Telescope Coordinate System O-XYZ: O, is the 
rotational centre of the theodolite. X coincides with the 
tilting axis of the theodolite. Y coincides with the 
collimation axis and is positive as it points forward. The 
transformational relationship between this system and 
the camera coordinate system is denoted by the 
rotational matrix R, and the translational vector T, as 
below. 
    
  
X x : 
Y |-R.l Y' |* T. 22 DEIN axis 
Z z' x 
| A, 
Collimation axis Xt 
| 
au Ai a Fx 0 
Re. = au An az) T.Slr, 
90 
azı azı ass Fz 
|Vertical axis 
The rotational matrix is the function of three independent rotation angles. These three angles used in this paper are @, @, K as 
defined as that the reference (now the telescope) coordinate system turns into a system parallel to the camera coordinate 
X-axis by o, then about its current Y-axis by $ and finally about its current Z-axis by x. These 
lockwise when viewed from the positive ends of their respective axes. 
f œ, ®, can be found in most of the photogrammetric 
system by rotating about its 
three angles are defined as positive if they are counterc 
The expressions of the elements of the rotational matrix as functions o 
text books (Wolf 1983) 
2.2.4 Theodolite coordinate system O,-X,Y,Z, O, is the rotational centre of the theodolite. Z, coincides with the 
vertical axis and points upwards. Y, is parallel to the zero direction of the horizontal circle of the theodolite. The 
relationship between this system and the telescope coordinate system is as follows: 
X x 
Y,IlzRl.Yl|*T 23 
7 & 
where obviously T=0 and R is a function of horizontal reading h and the vertical angle v as follows: 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 389