Mathematical Problems in Engineering

Volume 2015, Article ID 240354, 9 pages

http://dx.doi.org/10.1155/2015/240354

## A Color Texture Image Segmentation Method Based on Fuzzy c-Means Clustering and Region-Level Markov Random Field Model

^{1}School of Computer & Information Engineering, Anyang Normal University, Anyang 455002, China^{2}Department of Geodesy and Geomatics Engineering, University of New Brunswick, Fredericton, NB, Canada E3B 5A3^{3}School of Software Engineering, Anyang Normal University, Anyang 455002, China

Received 24 October 2014; Accepted 1 January 2015

Academic Editor: Chih-Cheng Hung

Copyright © 2015 Guoying Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents a variation of the fuzzy local information c-means clustering (FLICM) algorithm that provides color texture image clustering. The proposed algorithm incorporates region-level spatial, spectral, and structural information in a novel fuzzy way. The new algorithm, called RFLICM, combines FLICM and region-level Markov random field model (RMRF) together to make use of large scale interactions between image patches instead of pixels. RFLICM can overcome the weakness of FLICM when dealing with textured images and at the same time enhances the clustering performance. The major characteristic of RFLICM is the use of a region-level fuzzy factor, aiming to guarantee texture homogeneity and preserve region boundaries. Experiments performed on synthetic and remote sensing images show that RFLICM is effective in providing accuracy to color texture images.

#### 1. Introduction

Image segmentation is one of the most important tasks in computer vision, and many other fields of application are closely related to it, including pattern recognition, remote sensing, and medical diagnostics. The purpose of segmentation is to partition an image into homogeneous regions. Although many methods have been proposed to solve this problem, the fuzzy c-means algorithm (FCM) [1] has been widely applied to image segmentation, because its fuzzy nature allows more original information being considered. FCM has some obvious advantages such as the straightforward implementation, the fairly robust behavior, the applicability to multichannel data, and the ability to model uncertainty within the data [2]. However, the traditional FCM failed to consider the spatial information, which may cause poor results when dealing with images corrupted by noise, outliers, and other image artifacts.

To compensate this drawback of FCM, many attempts have been proposed, including adding a preprocessing image smoothing step before clustering [3] or incorporating spatial context in different ways, for example, the fuzzy membership function refinement [4, 5], the dissimilarity function improvement [6], the objective function regularization [2, 7], and the fuzzy treatment of hidden Markov random field (MRF) model-based image segmentation (HMRF-FCM) [8]. More recently, following the method of objective function regularization, Krinidis and Chatzis [9] presented a robust image clustering method called fuzzy local information c-means (FLICM). In FLICM, the clustering is dependent on both the spectral and local spatial information which cooperate by using a fuzzy factor. However, this algorithm assumes that the label of one pixel is only related to the labels of its neighboring pixels. Therefore, only interactions between neighboring pixels can be used, which makes the algorithm defective in dealing with color texture images due to the lack of information of large scale interactions between image patches instead of pixels.

In recent years, there is an increasing trend to analyze images based on image regions in order to make use of different kinds of large scale local information (e.g., spectral, spatial, and structural information). The MRF model is one of the most popular methods to integrate these kinds of information together, because of its powerful capability of describing the continuity of image characteristics. Based on region-level MRF (RMRF), Yang and Jiang [10, 11] proposed a gray image segmentation method and showed good performance; Clausi et al.’s research group also presented algorithms to deal with gray images [12], multivariate images [13], and polarimetric SAR images [14]. All of these methods have shown the superiority to pixel-based ones.

Inspired by the success of RMRF-based image segmentation methods in image segmentation, this paper improves FLICM into a region-based version, named RFLICM. In RFLICM, a novel fuzzy factor is defined by the basic idea of RMRF and incorporated into the objective function of FCM. The fuzzy factor can simultaneously incorporate the region-level spatial, structural, and spectral information in a fuzzy way and helps to guarantee the texture homogeneity as well as preserving region boundaries. All these characteristics make RFLICM more general and suitable for color texture image segmentation.

The remainder of the paper is organized as follows. Section 2 briefly describes the fuzzy local information c-means algorithm, followed by the basic theory of RMRF-based image segmentation. The RFLICM algorithm is introduced in Section 3. Experimental results are presented in Section 4 and conclusions are drawn in Section 5.

#### 2. Related Work

##### 2.1. Fuzzy Local Information c-Means (FLICM) Clustering Algorithm

In [9], a fuzzy factor is used to incorporate local spatial and gray level information into the objective function of FCM:where denotes an -pixel image defined on a rectangular lattice set in the -dimensional vector space, is the number of image pixels, is the number of clusters with , is the degree of membership of in the th cluster, is the weighting exponent on each fuzzy membership, is the prototype of the center of cluster , is a distance measure between object and cluster center , and is the fuzzy factor which is defined aswhere th pixel is the center of the local window (e.g., 3 × 3), is the reference cluster, and pixel belongs to the set of neighboring pixels falling into the window around the th pixel (denoted as ). is the spatial Euclidean distance between pixel and and is the membership of the th pixel in the th cluster.

Local minimum extreme of is obtained iteratively as follows.

*Step 1. *Set clusters number , fuzzification parameter , and the stopping condition .

*Step 2. *Initialize randomly the fuzzy partition matrix.

*Step 3. *Set the loop counter .

*Step 4. *Calculate the cluster prototype using

*Step 5. *Compute membership values using

*Step 6. *If , then stop; otherwise, set and go to Step 4.

##### 2.2. RMRF-Based Image Segmentation

Assume the image has been over-segmented previously into disjoint regions. In region-level methods [11–14], all pixels in the same region are assumed to have the same label. Let be the label image. In the Bayesian image segmentation framework, the segmented image is:where and are the class conditional probability and prior probability, respectively. With the assumption that the noise in the image is independent Gaussian white noise, can be written as follows:where is the Gaussian probability density function with mean value and covariance matrix . And if RMRF is used to model the prior probability, can be described as:where is a normalizing constant and is an energy function defined as:where is the set of neighboring regions of , and is defined as [10]:where is the length of the common boundaries between region and , is the boundary length of region , is the area of region , and are the mean value of region and , respectively, and is the Kronecker function.

Then the configuration of can be determined bywhere is the potential function. Equation (10) can be solved by simulated annealing (SA) [16] or iterative conditional mode (ICM) [17]. For the sake of efficiency, ICM is a good choice. In this paper, we denote the ICM algorithm based on the RMRF as RICM. By using a RMRF model-based prior probability, RICM can make use of the large scale local spectral, spatial, and structural information during the segmentation process.

#### 3. Region-Level Fuzzy Local Information c-Means (FLICM) Clustering Algorithm

Motivated by the successful application of RMRF to image segmentation, we propose, in this paper, a novel framework for image clustering by extending FLICM to a region-based version, called RFLICM.

For each region, some region-level features are extracted firstly. For example, and are the mean value and covariance matrix of , respectively, and are the area and boundary length of , respectively, and is the common boundary length between and , satisfying the constraint of .

##### 3.1. The Region-Level Fuzzy Factor

In order to overcome the defect of FLICM on using large scale information, the new fuzzy factor should take into account the region-level spatial, spectral, and structural information. Following the basic idea of RMRF, the fuzzy factor for each region is only determined by its direct neighboring region set . So, in this paper, the novel region-level fuzzy factor for region is defined aswhere is the membership value of belonging to th cluster.

It is easy to see that the factor makes the influence of regions within the direct neighborhood , to change flexibly according to their areas, boundary lengths, and mean values. Therefore, more region-level information can be used to deal with color texture segmentation. In (11), acts like a normalizing coefficient preventing to have a too large value. Similar to , (2), also reflects the damping extent of the neighboring regions to be assigned to different labels. So the designed fuzzy factor has the ability to force neighboring regions to be equally labeled.

##### 3.2. General Framework of RFLICM

We assume that all pixels in the same region have the same membership value belonging to different clusters. So the objective function RFLICM is defined aswhere is a constant weighting parameter, it has the similar function as the potential function in RMRF-based image segmentation, (10). The first term in the right part of (12) depicts the fidelity of clustering result to image data, and the second term is a smooth term that forces neighboring regions to have the same label. The parameter controls the contribution of these two terms.

In this paper, we assume that pixels in each cluster follow a Gaussian distribution. So the distance measure is defined aswhere and are the mean value and covariance matrix of the th cluster, respectively, and is the spectral number of the image being processed.

Similar to FLICM, a solution of the objective function of RFLICM, (12), can be obtained through an iterative process, which is carried as follows.

*Step 1. *Get the initial partition of the input image.

*Step 2. *Set the number of the cluster prototypes, fuzzification parameter , weighting parameter , and the stopping condition .

*Step 3. *Set the loop number , perform FCM clustering on image pixels, and get the initial region level fuzzy partition matrix based on the minimizing membership the rule:where is the membership value of pixel belonging to the th cluster.

*Step 4. *Calculate the cluster prototypes using

*Step 5. *Calculate the membership functions using

*Step 6. *If , then stop; otherwise, set and go to Step 4.

When the algorithm has converged, a defuzzification process of maximum membership is employed to convert the partition matrix to a segmentation result:

A constraint is imposed on the membership value in (15) to avoid the underfitting of Gaussian parameters:

Another issue that is worthy to be pointed out is the determination of the weighting parameter . It controls the smooth strength of the region-level fuzzy factor. In this paper, we employ an increasing schedule for to guarantee the accuracy of parameter estimation and the homogeneity of segmentation result. It increases with the iterative procedure:At the first stage of the iteration, takes a small value to depress the influence of the region-level fuzzy factor , which forces the estimated Gaussian parameter to fit well the image data. As increases, more large scale local spectral, spatial, and structural information is introduced into the clustering procedure. Finally, reaches its limitation, the iteration procedure arrives at a balance state, and begins to help to refine the final result.

#### 4. Experimental Results

In this section, we show the performance of the proposed method by presenting results on synthetic images and remote sensing images. Furthermore, we compare the efficiency of RFLICM with HMRF-FCM [8], FLICM [9], and RICM described in Section 2.2. For FLICM, we set the window size as 3 × 3. For HMRF-FCM, we use the 2nd neighborhood. For both RICM and our proposed RFLICM, mean shift algorithm (MS) [18] is chosen to get the initial partition. In this experiment, we set for our algorithm and set different for RICM using the trial-and-error method (we select the parameter in the range of with the interval of 0.5, and the one with the highest segmentation accuracy is recorded and is listed in Table 1). For MS, it is difficult to choose the optimal parameter set. How to choose good parameters is out of the scope of this paper. Intuitively, if parameters are set too large, there will be a risk of losing useful information in the initial oversegmentation; otherwise, large scale interactions cannot be obtained and employed properly. In this paper, we just experimentally choose both the spatial resolution parameter and the range resolution parameter to be 6 and the size of the smallest segment to be 10.