Full text: XVIIIth Congress (Part B3)

   
    
     
  
    
  
    
    
  
  
    
  
  
    
      
   
   
   
   
    
   
    
    
    
     
  
   
   
    
    
    
   
   
  
6. TESTS AND ANALYSES 
In this section we first describe the implementation 
of our algorithm and then report the test results with 
an aerial stereo. 
The primary step in this algorithm is to determine the 
fundamental martix E. As only the ratios among the 
entries of E could be determined, we may simply let 
one of its component equal to one. It is proper to set 
635 = 1 as it is approximately equal to Bx 55 which 
may never be zero. All image correspondences are in- 
cluded to determine E. Moreover, since there are only 
seven degrees of freedom in the fundamental matrix, 
the condition 
|E| 2 0 (34) 
may also be included in the solution procedure 
(Barakat et al,1994). 
In exterior orientation, the entries of matrix A' is 
determined with six known points by Eq.(30). Other 
four parameters are then obtained by Eq.(31). After 
that the object could be fully reconstructed. 
We use an aerial stereo to evaluate our algorithm. Its 
primary parameters and the distribution of the six 
ground control points (GCPs) are shown in Fig.1 and 
Tab.1 respectively 
  
  
  
  
  
  
  
  
  
  
  
  
Tab.1 Photographic parameters 1 2 3 
Flight height: ca. 2250m 
Principle length: 88.94mm 
Frame size: 230mm*230mm 
Camera: RC-10 3 
Overlap: ca. 65% | 4 "B6 
Fig.1 GCPs 
distribution 
Altogether 36 image points as well as their 3D ground 
coordinates are measured with an analytical plotter. 
The latter are treated as "best values" to check the 
validity of our algorithm. Moreover, the DLT algo- 
rithm and the traditional collinear algorithm are also 
implemented. In order to check the efficiency of our 
algorithm, results under different control configura- 
tions and various image deformations are presented 
respectively in Tab.2 and Tab.3, in which all numerics 
are relative to the "best values". 
In Tab.2, the DLT algorithm and collinear algorithm 
are implemented with all six conjugate GCPs, while 
our algorithm is evaluated with different GCPs con- 
figuration on the second image and six common GCPs 
on the first image. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
   
It is no wonder that the collinear algorithm holds 
the best results (c.f., item Colli. in Tab.2). Item a 
and item DLT in Tab.2 show our algorithm obtains 
essentially the same rigorous results as the DLT algo- 
rithm when they have the same GCPs configuration. 
Through item b to fof Tab.2 where the DLT algorithm 
is not applicable, our algorithm behaves completely 
robust to various GCPs configurations. The small 
differences, rarely up to maximum decimeters, are 
within the tolerance of GCPs themselves. Moreover, 
the most encouraging is in each minimum GCPs con- 
figuration we could still reach the same accuracy as 
the full GCPs configuration - a benefit due to the 
complete employment of the imformation within a 
stereo. 
Tab.2 Results under different GCPs (in meters) 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
GCPs config. on | RMSE to best values 
the second image | ox oy cz 
a: 1-2-3-4-5-6 1.936 | 1.595 | 1:722 
b: 2-3-4-6 1.892 11.455 | 1.722 
e: 1-2-4-5 1.944 | 1.648 | 1.723 
d: 2-3-5-6 1.887 | 1.444 | 1.722 
e: 2-4-5-6 1.915 | 1.539 [ 1.722 
f: 1-2-3-5 1:054 11.633 | 1.722 
DLT algorithm 1.954 | 1.580 | 1.736 
Colli. algorithm | 1.376 | 1.365 | 1.745 
  
  
  
Tab.3 shows the results of our algorithm under dif- 
ferent affine image deformations, where s, a and d 
refer to the scale factor, rotation angle and the dis- 
parity of the principal point respectively. In order to 
testify the validity of our algorithm, simulated affine 
deformations based on these parameters are added to 
the original image observations, where the first and 
second image take different signs of the parameters 
respectively. The GCPs configuration for this table 
is item b in Tab.2. Since the DLT algorithm presents 
the same result under different image deformations, it 
is appended there only in the last row. 
Tab.3 Results under image deformations (in meters) 
Amount of image defor- RMSE to best values 
mation parameters ox oy oz 
1. no deformation 1.892 | 1.455 | 1.722 
2. s=1.1,0 = 10°,d=10mm | 1.926 | 1.460 | 1.715 
3. s=0.9,0 = 207,d=20mm | 1.907 | 1.466 | 1.719 
4. s=1.3,0 = 30°,d=30mm | 1.923 | 1.465 | 1.748 
9. 
D 
  
  
  
  
  
  
  
  
  
  
  
  
s=0.7,0 = 40°, d=40mm | 1.911 | 1.488 | 1.743 
| 1.954 | 1.580 | 1.736 | 
  
  
LT algorithm 
It could be clearly seen that our algorithm is practi- 
cally invariant and robust to different amount of affine 
image deformations, since only trivial changes (maxi- 
mum up to centimeters) might occur among them. 
   
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