Image segmentation using PSO and PCM with Mahalanobis distance

doi:10.1016/j.eswa.2011.01.041

Expert Systems with Applications

Volume 38, Issue 7, July 2011, Pages 9036-9040

https://doi.org/10.1016/j.eswa.2011.01.041 Get rights and content

Abstract

Fuzzy clustering algorithm is widely used in image segmentation. Possibilistic c-means algorithm overcomes the relative membership problem of fuzzy c-means algorithm, and has been shown to have satisfied the ability of handling noises and outliers. This paper replaces Euclidean distance with Mahalanobis distance in the possibilistic c-means clustering algorithm, and optimizes the initial clustering centers using particle swarm optimization method. Experimental results show that the proposed algorithm has a significant improvement on the effect and efficiency of segmentation comparing with the standard FCM clustering algorithm.

Research highlights

► An image segmentation method based on PSO and PCM is proposed. ► The proposed method replaces Euclidean distance with Mahalanobis distance in the possibilistic c-means clustering algorithm. ► The proposed method optimizes the initial clustering centers using particle swarm optimization method.

Introduction

Image segmentation is an important technology for image processing, and also is a fundamental process in many image, video, and computer vision applications. The goal of image segmentation is to cluster pixels into salient image regions, such as regions corresponding to individual surfaces, objects, or natural parts of objects. Most computer vision and image analysis problems require a segmentation stage in order to detect objects or divide the image into regions, which can be considered homogeneous according to a given criterion, such as color, motion, texture, etc. Using these criteria, image segmentation can be used in several applications including video surveillance, medical imaging analysis, image retrieval and object classification (Luis, Eli, & Sreenath, 2009).

Cluster analysis is the process of classifying objects into subsets. Clustering has a place of honor in many engineering fields such as pattern recognition, image processing, system modeling, data mining, and so on. Bezdek (1981) proposed fuzzy c-means (FCM) clustering algorithm based on fuzzy theories. Fuzzy clustering technology is widely used in image segmentation for its simplicity and applicability. Furthermore, on the basis of FCM, much more optimized clustering methods have been proposed. Wu and Yang (2002) have proposed an alternative fuzzy c-means clustering algorithm Xing and Hu (2008) have proposed an adaptive FCM-based mixtures of expert model to improve the unlabeled data classification. Kang, Min, and Luan (2009) have proposed the improved fuzzy c-means algorithm based on adaptive weighted average to solve noise samples.

However, FCM-type algorithms share the problem of sensibility to noise and outliers as do all the least squares approaches. In addition, due to the constraints in FCM, the membership is interpreted as degrees of sharing, but not as degrees of possibility of a point belonging to a class. A degree of typicality or possibility of belonging may be better suited for classical fuzzy set theory. Possibilistic c-means (PCM) algorithm, proposed by Krishnapuram and Keller (1993), overcomes the relative membership problem of fuzzy c-means (FCM) algorithm and has been shown to have satisfied the ability of handling noises and outliers. Moreover, many algorithms are based on Euclidean distance which can only be used to detect spherical structural clusters. So, accuracy dealing with high dimensional data is not fine. To improve these problems, this paper replaces Euclidean distance with Mahalanobis distance in the PCM algorithm.

Usually, fuzzy clustering algorithm gave better results only when the initial partitions were close to the final solution. In other words, the results of fuzzy clustering depend highly on the initial state and reach to local optimal solution. In order to overcome this problem, a lot of studies have been done in clustering. For instance, Mualik and Bandyopadhyay (2000) have proposed a genetic algorithm based method to solve the clustering problem and experiment on synthetic and real life datasets to evaluate the performance. Ng and Wong (2002) have proposed a tabu search based clustering algorithm to find a global solution of the fuzzy clustering problem. Niknam, Amiri, Olamaie, and Arefi (2009) have presented a hybrid evolutionary algorithm based on PSO and SA to find optimal cluster centers, and also have presented a cluster analysis optimization algorithm based on the combination of PSO, ACO and k-means (Niknam & Amiri, 2010).

Particle swarm optimization (PSO), proposed by Kennedy and Eberhart (1995), has been successfully applied to various optimization problems. This new optimization algorithm combines social psychology principles in socio-cognition human agents and evolutionary computations. The PSO algorithm is motivated by the behavior of organisms. This algorithm begins with generating an initial population of random solutions. Each individual, also called a particle, is assigned with a randomized velocity according to its own and companions’ flying experiences, and the individuals are flown through hyperspace. The PSO algorithm can produce high-quality solutions within shorter calculation time and more stable convergence characteristics than other stochastic methods. Due to the good features of PSO algorithm, nowadays it has been emerged as a new and attractive optimization tool and successfully applied in variety of different fields (El-Zonkoly, 2006, Chen and Zhao, 2009, Zhao, 2010).

This paper replaces Euclidean distance with Mahalanobis distance in the possibilistic c-means algorithm, and optimizes the initial clustering centers using particle swarm optimization method. Experimental results in image segmentation show the proposed algorithm is effective and advantageous. The remainder of this paper is organized as follows. Section 2 briefly introduces the related work. We propose image segmentation method based on particle swarm optimization and PCM method with Mahalanobis distance in Section 3. The experimental results are reported in Section 4. Section 5 concludes this paper.

Section snippets

Particle swarm optimization

Inspired by social behavior in nature, PSO is a population-based search algorithm that is initialized with a population of random solutions, called particles. Each particle in the PSO flies through the search space at a velocity that is dynamically adjusted according to its own and its companion’s historical behavior.

Particle swarm optimization is an evolutionary computation technique. Similar to genetic algorithms, PSO is a population-based optimization tool. It is inspired by social behavior

PCM algorithm based on Mahalanobis distance

Distance metric is a key issue in many machine learning algorithms, such as clustering problems (Yang and Lin, 2006, Weinberger et al., 2006, Globerson and Roweis, 2006, Torresani and Lee, 2007). Many methods are based on Euclidean distance metric and only be used to detect the data classed with same super spherical shapes. The Euclidean distance metric assumes that each feature of data point is equally important and independent from others. This assumption may not be always satisfied in real

Experimental results

This section provides three images to verify the efficiency of the proposed method. We evaluated our proposed method on three images, and compared it with PCM algorithm. Experiments were done in Matlab 7.0.

Suppose that the initial parameters in PCM algorithm with Mahanabois distance are weighting exponent m = 2, iteration limit T = 100, number of clusters c = 3, and termination threshold ε = 1e − 5. In addition, the related parameters of the PSO algorithm are given by population size N = 50, inertia weight

Conclusions

In this paper, an image segmentation method based on PSO and PCM algorithm with Mahalanobis distance is presented. The proposed method uses possibilistic c-means to overcome the relative membership problem of fuzzy c-means algorithm in image segmentation. We first replace Euclidean distance with Mahalanobis distance in the possibilistic c-means algorithm, and then optimize the initial clustering centers using particle swarm optimization method. Experimental results in image segmentation show

Acknowledgments

This work is supported by Liaoning Doctoral Research Foundation of China (Grant No. 20081079), and Dalian Science and Technology Plan Foundation of China (Grant No. 2010J21DW019).

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Short CommunicationImage segmentation using PSO and PCM with Mahalanobis distance

Abstract

Research highlights

Introduction

Section snippets

Particle swarm optimization

PCM algorithm based on Mahalanobis distance

Experimental results

Conclusions

Acknowledgments

Expert Systems with Applications

Expert Systems with Applications

Digital Signal Process

Pattern Recognition

Applied Soft Computing

Pattern Recognition

Neurocomputing

Metric learning by collapsing classes

Short Communication
Image segmentation using PSO and PCM with Mahalanobis distance