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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
3.1.2 Initial Value of the Temporal GCPs 
The Church method is one of methods to calculate exterior 
orientation parameters, and exterior orientation parameters of a 
tilted photo are calculated using 3 GCPs which have accurate 
3D ground coordinates (Wolf, 1983). 
In Figure 4, images p,, p» and p; of GCPs A, P, and Pj. 
Angle a, f... X are 
OR-OP, 
K, 2 (Xo - Xy KXo - X2) (Yo - Y o - 12) (7.1) 
*(Zo - AXZo - Z3) 
  
Kg vier o x ron RIRE) (7.2) 
* (Zo - Za YZo - Z3) 
K, 
COS — ————— 
OP,-OHR 
K, = (Xo - X35) Xo - X 0) + (%- Y, fn - x) (7.33 
*(Zo - ZAXZo - z) 
where: 
OR - (0 - XY «(s - n «(2 - AY 
OP, (Xy - Xs «(Y - Y «(Zo - Z) 
OP, » (Xo - X3 «0o - P + (Zo - 23) 
On the other hand, cose , cos/, and cosy are expressed with 
respect to focal length and image coordinates using the 
following geometry equations: 
Xpl Xp2 t3 "3 Yu Yp2 + £z 
  
  
cosa = (8.1) 
Op, Op, 
cos f n Xp2 . ps + Ypa -J . Y p3 + ^ (8.2) 
Op, - Ops 
2 
X XutYp'Yp* 
cosy = p3 "gut E p3 y! / (8.3) 
  
  
Ops - Op, 
In equation (8), Op, , Op, , and Op; are length from the 
camera position to the respective image point, and cosa , 
cos ff , and cosy in equation (7) are given by equation (8). 
Therefore, equation (7) consists of 3 unknowns (Xe, Yo, Zo), 
and equation (7) are solved with respect to unknowns using 
Taylor's theorem. 
However, Xj, Y;, and Z4 are unknowns in this paper. Therefore, 
in order to obtain these unknowns, the Church method was used 
inversely under assumption Z3 coordinate equal 0, and solved 
unknowns are given as initial values for the temporal GCP of 
P. 
Similarly, initial values for the other temporal GCPs are 
obtained by repeating the same procedures. 
3.1.3 Initial Values of Orientation Parameters 
The initial values of exterior orientation parameters are given as 
calculated values from the space resection using initial values 
for the temporal GCPs, which were obtained by the above 
procedures. 
3.2 Calibration Procedures 
In the above procedure, initial values for the exterior orientation 
parameters and 3D coordinates for the 6 temporal GCPs are 
given. Therefore, unknown parameters for the interior/exterior 
orientation parameters and 3D coordinates for temporal GCPs 
are calculated by the resection using collinearity conditions and 
space distances. 
Equation (9) shows collinearity conditions, and equation (10) 
shows distance conditions, and these equations for the both 
images are used simultaneously in calibration procedures. 
Consequently, 36 observation equations are acquired for 30 
unknown parameters, and unknown parameters are calibrated as 
the values that make the following function // minimum under 
the least-squares method (equation (11)). Furthermore, 3D 
coordinates for additional feature points are able to compute 
simultaneously. 
Collinearity condition: 
Ez (x Ea \i "J 
X Xo) mo(Y - x9) malz- Z) 
Bil Xo) amar - 95): m3(Z - 7.) 
= (y — yo \i + kr? 
AA X - Xo) maj(F Y)tanas(Z — 29) 
my (X = Xo) + mj(Y - 19 )+ m33(Z - Zo) 
where: x, y are image coordinates of temporal GCPs, r is 
  
(9) 
  
distance from principal point to image point, Æ, is lens 
distortion parameter, and 7; are rotation matrixes. 
Observation condition for the space distance: 
  
Ded, - Xy «(E - xy «(ZZ (10) 
Function with weight: 
nH=2n=6 m (11) 
H="Y Y nA 2+ Ay” 2), "5 > ^ pl, 2) min 
Eg yel 
where: Ax, Av : residual for the image coordinates, AD : 
residual for space distance. 
Weight values in equation (11) should be carefully considered 
under statistically or measurement accuracy, and calibration 
results were investigated using various weights. However, 
calibration results don't show any significant improvements 
compared with various weight values. Therefore, equal weight 
( p; = p2 =1 ) was adopted in this paper. 
4. PERFORMANCE EVALUATION 
In order to evaluate an accuracy of the IBIM, experiment was 
performed. Figure 5 shows test site, 20 circular points in Figure 
5 are temporal GCPs and check points. A stereo image was 
taken with 21.790m (left side), 21.957m flying height (right 
side) respectively and 8.44m base line under the fixed focal 
length. The 3D coordinates for all circular points and