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the curvature elements. s(i) only takes account 
neighbouring two pixels. After convoluting with 
g"(t), more pixels in the neighbourhood have been 
taken into the consideration, which yields more 
robust result. 
» Selecting high curvature points 
This is a thresholding procedure which compare 
each value from above convolution against certain 
threshold and high curvature points are selected. 
* Determining the position for the first node 
It is obvious that we can simply choose the 
starting point as the initial position of first node. 
Because our iteration procedure is much like the 
optimization by a steepest (gradient) descent, it can 
very often run into local minimum. To avoid such 
drawback, we change the initial status of 
optimization (in our situation, change the position 
of first node) several times, and compare the 
results from different initial statuses and choose 
the best result. Our experiment has proved that it 
is very efficient method to avoid local optimization 
for our application. 
* [nitial partition of boundary 
After the position of first node is decided, the 
positions of the rest of nodes can be determined 
along the boundary on the equal interval. 
* Optimize the position one by one node 
| updatingrange 
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Fig.5 
Because we don't use parallel processing, we have to 
update the position of nodes one by one, as indicated in 
Fig.5 (filled circle denotes fixed nodes and empty circle 
represents updating node). 
Model selection 
So far we have assumed that the number of line segments 
is known a priori. Such assumptions may be too strict for 
the method in Fig.4 to be applied into wide range of 
applications. Let's first relax the assumption of fixed 
725 
number of line segments to allow this number of 
segments within a limited number of choice. In this case, 
we still have no difficulty in applying the method 
described in Fig.4, only with more rounds, namely, we 
test each number by this iteration procedure and choose 
the number under which the difference between the 
original boundary and modeled line segments reaches the 
minimum. 
For the other type of generic models, like circle, ellipse, 
the method presented in the fig.4 is not valid any more. 
A lot of work have been done one this aspect, and the 
problem is how to integrate the available techniques into 
segmentation. Nevertheless, our current implementation of 
the shape modelling is still very useful in a lot of 
applications such as detecting human-made objects, 
industrial robots, indoor scene analysis, etc. 
6. EXPERIMENT 
We test a number of images, based on the principle and 
algorithms we have described in the previous sections. 
First image in our experiment is a simulated ideal image 
added with a gaussian noise (Fig.6a). The minimal 
difference between the regions is 20, and the standard 
deviation of the Gaussian noise is 20. We first use 
Kuwahara filter with 5 pixels of window size to suppress 
the noise (Fig.6b). In the main algorithm, a 4 thresholding 
value is used for initial segmentation, which forms the 
basic small regions, followed by the split-and-merge using 
only the statistic test (in this case only the mean) with 
threshold 12. MDL-based operations further groups the 
regions using the intensity information and shape 
constraint. After small regions with less than 20 area are 
removed, the final result is reached, as shown in Fig.6c. 
Fig.6d shows the region boundaries. 
We use the same procedure for the test of the second 
image (Fig.7), which is the part of a building wall image. 
a,b,c,d represent the original image, filtered image, 
segmented image and vectorized image respectively. 
7. CONCLUDING REMARKS 
In this paper, we have shown how the MDL principle can 
be adopted in such manner to integrate different 
knowledge for the purpose of image segmentation. The 
formulae for encoding image intensity and shape 
constraints of generic model have been described. In the 
implementation, we integrate the region growing, curve 
fitting and model selection in a unified procedure. We 
feel that it is a good trend which may lead to the general 
theoretical basis for the segmentation. The extension of 
this work includes the treatment of complex topological 
description of object model and integrate with other 
middle-level image analysis tasks, as indicated in one of 
our other papers [Zhang]. 
ACKNOWLEDGEMENT 
I owe my gratitude to Prof.dr.ir. M.J.M. Bogaerts for his 
consistent understanding and supporting to my work. This