1ations 
ility of 
nd the 
16. 
  
  
Figure 7 is a test image from the OEEPE-test on the feature- 
based segmentation. The image is 64 x 64 pixels large and 
has the Gaussian noise with the variance o = 20. The seg- 
mented results for both models are nearly the same, but by 
a = 0.196 the part inside the letter D is treated as three 
small regions for the horizontal plane function model and 
the planar function model segments this part into the same 
region as the letter D itself. Figure 8 shows the segmented 
results of the horizontal function model, figure 9 is the re- 
sults after the region-merging from figure 8, and figure 10 
the boundaries graph. 
   
Fig.11 the 4. image from CCD camera Fig. 12 the coarse segmentation 
  
   
  
  
  
  
Fig. 13 results after region-merging Fig. 14 regions boundaries of Fig. 11 
Figure 11 is a real image taken by a CCD camera. The image 
has 128 x 128 pixels and the range of the grayvalues is from 0 
to 255. We can see from the segmented results figure 12 that 
there are a few small regions at the boundaries. After the 
elimination of the small regions we have the results shown 
in the figure 13. Figure 14 shows again the boundaries of 
the regions. 
5. CONCLUSIONS 
From the above discussions and examples we can see the 
method of image segmentation based on parameter estima- 
tion has not only a perfect theoretical and mathematical 
basis, but also great prospects in applications. With this 
method we can treat the image noise quite perfectly. We 
can also quantitatively judge the separability of the regions. 
The results of the simple horizontal plane function model 
are not worse than the planar function model, but the for- 
mer works much faster. Usually there will be more regions 
segmented with the larger risk error a. 
À further work is how better to solve the problem of the 
prevention and mergence of the superfluous small regions at 
the boundaries. It may be better solved together with the 
edge-based method or by using an iterative approach. More 
experiments should be carried out on the real images in order 
to examine the effects of the method and to evaluate which 
function model and which risk error œ are more suitable. 
  
REFERENCES 
1. Sanz, J.L.C., 1989, Advances in Machine Vision, Springer 
Verlag. 
2. Boyle, R.D., 1988, Thomas, R.C., Computer Vision, 
Blackwell Scientific Publications LTD. 
3. Koch, K.R., 1980, Parameterschätzung und Hypothesen- 
tests in linearen Modellen, Dümmler Verlag, Bonn. 
4. Li, D., 1985, Theorie und Untersuchung der Trennbarkeit 
von groben Paßpunktfehlern und systematischen Bildfehlern 
bei der photogrammetrischen Punktbestimmung, Disserta- 
tion, University of Stuttgart. 
5. Grün, A., 1988, Towards Real-Time Photogrammetry, 
Photogrammetia(PRS), 42. 
6. Maitre, H., et al., 1990, Range Image Segmentation based 
on function approximation, Close Range Photogrammetry 
Meets Machine Vision, SPIE Volume 1395. 
7. Wang, Y., Jacobsen, K., 1991, Model Based Fast Recog- 
nition of the Structure of Industrial Workpieces, In B. Radig 
(editor), Mustererkennung 1991, Informatik Fachberichte 
290, Springer Verlag.