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Mathematical Problems of Computer Science 30, 71--75, 2008. 

71 
 

 
 
 

Stop Rule for Image Hierarchical Segmentation Algorithm 

David Asatryan, Grigor Sazhumyan 

Institute for Informatics and Automaation Problems of NAN RA 
e-mail dasat@ipia.sci.am 

 

Abstract 

In this paper we consider an important problem of stopping the hierarchical 
segmentation procedure when the appropriate segmentation is achieved. This 
problem arises at every segmentation procedure, which uses a searching algorithm 
for selection of acceptable decision. We propose an algorithm for stopping the 
hierarchical segmentation procedure. Stop-rule is based on the segmentation 
homogeneity measure, and uses a ratio of special sum of squares. The first sum 
equals to summarized variance of pixel intensity relative to the centers of intervals, 
being determined by thresholds, the second one expresses variance of mean values of 
the segments relative to the same centers. Examples of segmentation results to 
demonstrate the features and properties of proposed technique are considered.  

 
     References 
 

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3. Q. Luo, and T. M. Khoshgoftaar, “Unsupervised Multiscale Color Image Segmentation Based on 
MDL Principle”. IEEE Transactions on Image Processing, Vol. 15, No 9, pp. 2755-2761, 2006. 

4. NASA. “Recursive Hierarchical Segmentation (RHSEG) Pre-processing Software”, 
[http://techtransfer.gsfc.nasa.gov/rhseg - 21.06.2006]. 

5. Д. Г. Асатрян, Г. С. Сажумян, “Об одном методе пороговой локальной сегментации 
изображения”, Mathematical Problems of Computer Science, vol. 26, pp. 15-20, 2006.  

6. Д. Г. Асатрян, Г. С. Сажумян, “Метод когерентной сегментации и его приложение к 
восстановлению поврежденных изображений”, Вестник ГИУА, сер. Моделирование, 
оптимизация, управление, вып. 9, т. 2, с. 15-21, 2006. 

7. D. G. Asatryan, G. S. Sazhumyan, and H. S. Shahverdyan, “Technique for Coherent 
Segmentation of Image and Applications”, Mathematical Problems of Computer Science, vol. 28, 
pp. 88-93, 2007. 

 
 
 
 
 
 

 



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