yields a variance component that represents the variance of the 
spatial offset between the two bundles along the image plane. A 
relative comparison between the computed variance component 
and the expected variance of image coordinate measurements 
would reveal whether the two bundles are significantly different 
from each other or not. The above methodology is denoted as 
the rotation (ROT) method in image space comparison. 
The comparison in image space provides meaningful measures 
of the degree of similarity between two bundles of light rays, 
defined by two sets of IOP, sharing the same origin (perspective 
center). However, it is possible that the IOP and EOP might be 
correlated. Therefore, the object space comparison method is an 
alternative technique for comparing the bundles in terms of 
their fit at a given object space. 
3.2.2 Object Space Comparison 
In contrast to the image space comparison method, two bundles 
of light rays are compared by permitting spatial and rotational 
offsets between them while observing their fit at a given object 
space. Hence, the two bundles might not share the same 
perspective center. The methodology for evaluating the degree 
of similarity between the two bundles in terms of their fit at a 
given object space can proceed as follows: 
i. Define a regular grid in the image plane. 
ii. Derive distortion-free coordinates of the grid vertices using 
two IOP sets. . 
iii. Define a bundle of light rays for the first IOP set using the 
perspective center together with the distortion-free grid 
vertices. 
iv. Intersect the bundle of the first IOP set with an arbitrary 
object space to produce a set of object points, as shown in 
Figure 3. 
v. Use the object points and the corresponding distortion-free 
grid vertices, according to the second set of IOP, in a Single 
Photo Resection (SPR) procedure to estimate the position 
and the attitude of the second bundle that fits the object 
space as defined by the given set of object points. The 
variance component resulting. from the SPR procedure 
represents a quantitative measure of the spatial offset 
between the distortion-free grid vertices, defined by the 
second set of IOP, and the computed coordinates from back 
projecting the object points. 
    
RC il 
A 
PC a if 
to / 
a y 
OQ Original Grid vertices 
€ Distortion-tree Grid vertices 
i N 
À X 
/ n X 
— Bundle | f 
Bundle II y 
Figure 3 — Object Space Comparison between bundles by allowing 
spatial and rotational offsets 
A relative comparison between the computed variance 
component and the expected variance of the image coordinate 
measurements will reveal whether the two bundles fit at the 
object space. A good fit signifies that the two bundles defined 
by the two sets of IOP are similar. The above methodology is 
   
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004 
denoted as the SPR method in this paper. There is one factor in 
the SPR method that will affect the quality of fit of the object 
points, and that is the choice of the object space. A relatively 
flat terrain is expected to have high correlations between the 
IOP and EOP, and yield a better fit between the two bundles at 
the object space, even if the two IOP sets are significantly 
different from each other. On the other hand, a rugged terrain 
would allow for the de-correlation between the IOP and EOP, 
and give a more reliable measure for the degree of similarity 
between the two bundles. Therefore, the type of terrain must be 
chosen in such a way that it is similar to the expected object 
space to be photographed by the calibrated camera. 
4. EXPERIMENT DESCRIPTION 
To perform calibration and stability analysis on a camera, a 
specific detailed procedure is carried out. A two-dimensional 
test field consisting of straight lines and points was used for 
calibration, Figure 4. Lines and points were established on a 3.5 
x 7.0 meter section of a white wall. The lines are thin, dark 
ropes that are stretched between nails on the wall, and the 
points are in the form of crosses that are signalized targets used 
as tie points in the calibration procedure. The datum for the 
calibration procedure is established by fixing six coordinates of 
three points as well as a few measured distances. For the 
conducted camera calibration experiments, eighteen converging 
and overlapping images are captured at locations that are 
roughly four to five meters away from the closest point on the 
test field. The position and orientation of each captured image 
are shown in Figure 4. 
  
  
  
  
  
  
Ode^ Oe Dio | 
005 Ms Me 
  
Figure 4 — Calibration Test Field and Position and orientation of 18 
: P. . : 9 
images captured for a calibration dataset 
The cameras implemented for calibration and stability analysis 
are digital cameras ranging in price from $500 to $6000 USD. 
They are all Single-lens Reflex (SLR) cameras with Charged- 
coupled Device (CCD) sensors. Table | summarizes the 
characteristics of the implemented cameras. 
  
  
Max. 
ripe Biss Rt Effective 
Camera I fice Range Output Pixel Size Pixels 
(S US) Resolution (mm/pixel) MPixels 
(pixels) (Mpixels) 
Canon EOS ID $5000 2464x1648 0.0115 4.15 
Nikon 4500 $500 - $600 2272x1704 0.0031 3.87 
Rollei d 7 metric $6000 2552x1920 0.004 4.90 
Sony DSC-F707 $650 - $800 2560x1920 0.004 4.92 
Sony DSC-P9 $500 2272x1704 0.004 3.90 
  
  
Table 1 — Characteristics of Implemented Cameras 
  
   
   
    
   
   
     
    
  
    
   
   
    
     
     
   
     
     
   
   
    
    
   
  
  
  
   
   
        
  
    
   
  
    
   
      
        
      
   
   
      
   
   
    
[nternationc 
A total of n 
stability ov 
exception 0 
acquired ir 
cameras, tw 
simply swit 
As mention 
the estimat 
the adjustm 
the two bu 
significantl 
measureme 
approximat 
deemed sim 
The stabilit 
their exper 
method img 
four distanc 
. Canon( 
of the 
which c 
to be c 
all IOP 
— 
Table 
(X 
ii. Canon’ 
compar 
over a 
0.0077 
Table 
(N 
iii. Rollei - 
of the I 
within 
accurac