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A novel semi-supervised fuzzy clustering method based on interactive fuzzy satisficing for dental x-ray image segmentation


Dental X-ray image segmentation has an important role in practical dentistry and is widely used in the discovery of odontological diseases, tooth archeology and in automated dental identification systems. Enhancing the accuracy of dental segmentation is the main focus of researchers, involving various machine learning methods to be applied in order to gain the best performance. However, most of the currently used methods are facing problems of threshold, curve functions, choosing suitable parameters and detecting common boundaries among clusters. In this paper, we will present a new semi-supervised fuzzy clustering algorithm named as SSFC-FS based on Interactive Fuzzy Satisficing for the dental X-ray image segmentation problem. Firstly, features of a dental X-Ray image are modeled into a spatial objective function, which are then to be integrated into a new semi-supervised fuzzy clustering model. Secondly, the Interactive Fuzzy Satisficing method, which is considered as a useful tool to solve linear and nonlinear multi-objective problems in mixed fuzzy-stochastic environment, is applied to get the cluster centers and the membership matrix of the model. Thirdly, theoretically validation of the solutions including the convergence rate, bounds of parameters, and the comparison with solutions of other relevant methods is performed. Lastly, a new semi-supervised fuzzy clustering algorithm that uses an iterative strategy from the formulae of solutions is designed. This new algorithm was experimentally validated and compared with the relevant ones in terms of clustering quality on a real dataset including 56 dental X-ray images in the period 2014–2015 of Hanoi Medial University, Vietnam. The results revealed that the new algorithm has better clustering quality than other methods such as Fuzzy C-Means, Otsu, eSFCM, SSCMOO, FMMBIS and another version of SSFC-FS with the local Lagrange method named SSFC-SC. We also suggest the most appropriate values of parameters for the new algorithm.

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Fig. 1
Fig. 2
Fig. 3


Spatial constraints:

Refer to the conditions regarding dental structure of a dental X-ray image. Some similar terms are: “spatial features”, “dental feature”


Fuzzy C-Means


Semi-Supervised Fuzzy Clustering algorithm with Spatial Constraints


Fuzzy Satisficing method


Lagrange method


Semi-Supervised Fuzzy Clustering algorithm with Spatial Constraints using Fuzzy Satisficing method

Membership matrix/degrees:

Refer to the level that a data point belongs to a given cluster


Semi-supervised Entropy regularized Fuzzy Clustering


Local Binary Patterns




Davies-Bouldin validity index


Simplified Silhouete Width Criterion validity index


A validity index


A spatial validity index


Ball and Hall index


Calinski - Harabasz index


The Banfeld - Raftery index


Difference-like index


Semi-Supervised Clustering technique using Multi- Objective Optimization


Fuzzy Mathematical Morphology for Biological Image Segmentation


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The authors are greatly indebted to the editor-in-chief, Prof. Moonis Ali and anonymous reviewers for their comments and their valuable suggestions that improved the quality and clarity of paper. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 102.05-2014.01.

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Correspondence to Le Hoang Son.



Matlab source codes of all algorithms and experimental data can be found at the URL:

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Tuan, T.M., Ngan, T.T. & Son, L.H. A novel semi-supervised fuzzy clustering method based on interactive fuzzy satisficing for dental x-ray image segmentation. Appl Intell 45, 402–428 (2016).

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  • Clustering quality
  • Dental X-Ray image segmentation
  • Fuzzy stochastic programming
  • Interactive fuzzy satisficing
  • Semi-supervised fuzzy clustering