Heikkinen, Jussi 
  
  
* 
a 
a 
a 
a 
a 
Figure 5 Poor intersection geometry. 
Based on this aspect we should estimate both image blocks simultaneously. This way we can get good observations 
from convergent images. The number of additional unknowns respect to photo parameters is 5+n,. The first five 
unknown parameters consist rotation angles of the first camera position on the second block, radius r, and angle 
between x-axes of first and second blocks. The rest n, unknowns are 8; angles from first camera position of the first 
image block. The number of tie points does not need to increase much as both sequences will include more or less the 
same scenery. 
As we will construct our own coordinate system and we do not have any exterior knowledge we have to have a scale for 
our measurements. Though in a closed image block we do get the scale without any auxiliary measurements. The scale 
will be based on the interior orientation of a calibrated camera. This scale derived from interior orientation might not be 
the most reliable and auxiliary distance measures will be necessary to support our estimation process. Distance 
measures can be included in estimation as constraint equation or as a normal observation with a high weight. We chose 
to use the later alternative. 
4 SIMULATION 
In order to analyse the precision of the image block construction we created a simulated situation. The point set 
presenting the tie points was evenly distributed about 5m from the revolution centre. There were altogether 240 points 
in a set. Thirty photos were taken evenly spaced on the circular trajectory. The camera model resembles a video camera 
type device with resolution 572 x 720 (PAL standard). The camera constant was 900 pixels. 
We created the observations by projecting 3D points on the focal plane. The camera positions were equally spaced on 
the circle with radius of 0.3m and orientations were calculated according to equation ( 8 ). The distance between 
subsequent camera poses in a single block was 62mm and angular difference 12 degrees. For the 3D point initial values 
we generated some error to evaluate how sensitive the system is to initial values. We found that initial values from few 
decimetres up to a meter from correct values were still acceptable. 
We tested the case where only one circular block was present in estimation and a case where both image blocks were 
estimated simultaneously. Also cases with and without an auxiliary distance measure were tested. A couple of times 
with distance observations we came across a situation where iterations began to divergence when distance measure was 
weighted too much. The reason was that the system corrected the parameter values too much, so that the angle 0; was 
greater than the angle 05,,. The situation was unbearable and caused the system to fail. In order to avoid such a situation 
we must take care that subsequent camera poses cannot change places during the estimation. Adding the following 
constraint will do this: 
(14) 
n-i 
Yo, ot; + lo, - a, = 21 
i=1 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 363