QO =~ nn 5S 0 
ao Uu 
ISPRS Commission III, Vol.34, Part 3A Photogrammetric Computer Vision“, Graz, 2002 
In summary, for bundle adjustment with self-calibration using 
straight lines, the end points (points 1 and 2 in the above 
example) can be selected in any of the images where the straight 
line appears. These points need not be identifiable or even 
visible in other images. Four collinearity equations will be 
written using the measured end points for each line. The 
intermediate points (point 3 in the above example) can be 
measured in any one of the overlapping images. Those 
intermediate points need not be conjugate. A constraint is 
written for each intermediate point according to Equation 6. A 
schematic drawing to clarify the different scenarios for the end 
point selection is shown in Figure 3. Figure 3-A shows a case 
where the end points of the straight line are selected in one 
image (image 1); while in Figure 3-B, they are selected in 
different images (images 1 and 4). Intermediate points are 
shown in the same figure. 
The same approach can be extended to include higher-order 
primitives (for example, conic sections). In addition, it is 
applicable for line cameras as well. The only difference is that 
the platform motion perturbations during the scene capture as 
well as the above mentioned distortion sources cause deviation 
from straightness in the imagery. 
3.2 Optimal configuration 
Two types of configurations of straight lines, box-type (Figure 
4) and X-type (Figure 5), are used to test the effects of previous 
distortion models. The optimum configuration is the one that 
will cause more deviations from straightness in the image space. 
Figures 4 and 5 illustrate the effects of various distortion 
sources for both configurations. 
(A) (B) (C) 
Figure 4. Distortions in box-type configuration 
(A) Radial distortion, (B) Decentric distortion, 
(C) Affine deformation. 
(A) (B) (C) 
Figure 5. Distortions in X-type configuration 
(A) Radial distortion, (B) Decentric distortion, 
(C) Affine deformation. 
By analysing Figures 4 and 5, one can see that the box-type 
configuration is more useful since it causes larger deviation 
from straightness (compare Figure 4-A and 5-A). Therefore, to 
successfully recover the radial distortion parameters (the most 
significant distortion component), we need a test field 
composed of a grid of straight lines along the rows and columns 
of the captured calibration images. We also need some point 
targets to derive the camera constant (principal distance). These 
   
targets need not be surveyed with a theodolite or total station. 
Only distances between those targets should be measured. An 
example of such a test field can be seen in Figure 6. 
4. EXPERIMENTAL RESULTS 
Conducted experiments using real data are primarily focused on 
achieving the following objectives: 
e Determine the required distortion parameters to 
sufficiently describe the IOP of the involved camera. 
e Compare the performance of the suggested approach to the 
traditional approach using distinct ground control points. 
e Inspect the accuracy of the reconstructed object space 
using the derived IOP. 
In those experiments, we used a SONY DSC-F707 digital 
camera, with a maximum resolution of 2560 x 1920 pixels. A 
total of forty-eight images have been acquired in four different 
sessions (A-D). Using a shutter speed of 125, images used for 
experiment A and B were acquired with an f/number of 3.5. 
Then, an f/number of 11 is applied for experiments C and D. 
Each session consists of twelve exposures at six different 
locations with 90? rotation around the Z-axis at each exposure 
station. The camera was switched off/on after each session. We 
built a test field based on the optimal configuration discussed 
before, Figure 6. The test field is composed of nine straight 
lines (black robes on a white background). Also, distances 
between five targets (highlighted by black circles) have been 
measured (+2.0mm). We developed an automated procedure for 
measuring intermediate point coordinates along the lines in the 
involved imagery. 
  
  
  
Figure 6. New test field 
The test field has been augmented to allow for traditional point 
based camera calibration. A total of 30 signalised targets are 
precisely surveyed using a total station (x0.5mm), Figure 7-A. 
In the bundle adjustment with self-calibration, we can consider 
the following deformation/distortion parameters: 
e Radial distortion parameters K;, Ko. 
e  Decentric distortion parameters P,, P». 
e Affine deformation parameters A;, A». 
We carried out several experiments, using both point-based and 
line-based self-calibration, to investigate the most appropriate 
model that sufficiently describes the internal characteristics of 
the camera. Considering K;, Ky, P;, P», A;, A» resulted in high 
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