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Fig. 5: Convergence of the closest point matching algorithm 
Subsampling. Searching the closest point is the most time consuming part of the algorithm and grows with O(Np-Nx). For a 
better performance we are thus interested in reducing the number of points representing the objects. In this experiment the 
number of points building the corners faces are subsampled uniformly to see if the matching still succeeds. As before we 
allow only translations. Figure 6 shows the results where, first, the number of points of the test has been reduced by two and, 
secondly, also the number of points of the model. 
  
  
  
  
original test subsampled model and test subsampled 
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Fig. 6: Matching with objects subsampled in space 
A reduction by a factor of two of the test has no influence on the result. If both the test and the model are subsampled in 
space the performance degrades. This fact will allow us to work with a test at a relatively poor resolution, which again will 
enhance speed in the recognition process. 
Geometry. The next experiments investigate the influence of object geometry on the matching. We repeat the first 
experiment with an asymmetric corner. The corner faces have edge lengths with a ratio x:y:z of 10:7:5. The left drawing in 
figure 7 shows the positions for which the matching is successful. These positions differ from the symmetric corner (figure 4) 
and there are slightly more failures. 
The results of the matching of puzzle subparts showed that convergence depends largely on the starting position. To see if 
the same problem occurs in space we compare a small corner to a larger one. The subpart matching works only for a few 
initial conditions (see right drawing in figure 7). These cases have an interesting characteristic. All successful starting points 
are located near to the symmetric axe of the model corner. 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995