Robust level set image segmentation algorithm using local correntropy-based fuzzy c-means clustering with spatial constraints
Introduction
Image segmentation is one of the most difficult topics in image understanding and pattern recognition. The purpose of image segmentation is to divide an image into a number of non-overlapping regions and extract interest targets. Until now, many segmentation algorithms have been proposed, such as edge detection [1], [2], clustering [3], [4], [5], [6], level set [7], [8], [9], graph cut [10], [11], and so on. Among the clustering segmentation methods, fuzzy c-means (FCM) algorithm [12], [13] has been broadly applied to image segmentation. The main characteristic of fuzzy clustering is that it allows pixels belonging to multiple clusters with different degrees of membership. Thus, the FCM algorithm retains more information from original images. However, it is very sensitive to noise and other imaging artifacts, since it does not consider any spatial information.
To solve these problems, many improved algorithms which introduce local spatial information into the original FCM algorithm were applied to improve the segmentation performance [14], [15], [16], [17], [18]. Ahmed et al. [14] presented FCM_S algorithm by introducing the spatial information to the objective function of FCM which enabled every pixel to be influenced by its immediate neighborhood. However, FCM_S is very time-consuming because of the calculation of the spatial neighborhood term in each iteration step. Subsequently, in order to reduce the time consumption of FCM_S, Chen and Zhang [15] proposed two variants, FCM_S1 and FCM_S2. These two algorithms substituted the neighborhood term by utilizing the mean-filtered image and median-filtered image respectively. Thus, the computational times are reduced significantly. Moreover, based on the fact that the number of gray-levels is smaller than that of the pixels of the summed image, Szilagyi et al. [16] proposed the enhanced fuzzy c-mean (EnFCM) algorithm. In this algorithm, a linearly-weighted sum image is obtained from both the original image and its neighborhood average image. Hence, the computational time of EnFCM algorithm is dramatically reduced. More recently, Cai et al. [17] proposed the fast generalized fuzzy c-means algorithm (FGFCM). This algorithm utilizes local spatial and gray-level information to form a nonlinearly-weighted sum image. The quality of the segmented image is well enhanced. However, EnFCM and FGFCM, still lack enough robustness to noise and intensity inhomogeneity.
The level set method, originally introduced by Osher and Sethian [19], has been extensively applied to image segmentation with noise and intensity inhomogeneity. In [20], [21], Li et al. proposed an efficient region-based level set method by introducing a local binary fitting (LBF) energy with a kernel function. The LBF model which draws upon spatially varying local image information as constraints, can well segment objects with intensity inhomogeneities. Some related methods which have similar capabilities of dealing with intensity inhomogeneity as the LBF model were recently proposed in [22], [23]. Wang and Pan [22] proposed a novel segmentation algorithm via a local correntropy-based K-means (LCK) clustering and it can be robust to the outliers. In [23], Huang et al. presented a level set model using local region robust statistics and correntropy-based K-means method. This model can efficiently segment images with intensity inhomogeneity and noise. However, as pointed out in [22], [23], these two methods are still sensitive to the noise to some extent.
In this paper, we propose a novel level set algorithm for image segmentation by introducing the local correntropy-based fuzzy c-means clustering with spatial constraints (LCFCM_S) and then simplify it, to corresponding robust version LCFCM_S1. In the proposed models, the correntropy criterion can reduce the weights of the samples that are away from their corresponding cluster centers. As a result, LCFCM_S and LCFCM_S1 based clustering algorithm can provide enough robustness to noise and outliers. In addition, we have also made some comparisons with several state-of-the-art models to show the superiority of our methods.
The remainder of this paper is organized as follows. In Section 2, we review several related backgrounds. Our model is presented in Section 3. The experimental results are provided in Section 4, followed by some discussions in Section 5. Finally, this paper is summarized in Section 6.
Section snippets
Backgrounds
Given a dataset , the K-means clustering is to minimize the following objective function:where is the number of clusters, is the total number of pixels, is the center of each cluster, and represents the membership function of the ith pixel, with respect to the cth cluster center. The membership function satisfies two conditions as and . The objective function of Eq. (1) uses the mean square error (MSE) criterion to
The proposed method
Motivated by individual strengths of FCM_S1 and FCM_S2 [15], in this paper, a novel level set algorithm for image segmentation called local correntropy-based fuzzy c-means clustering algorithm with spatial constraints (LCFCM_S) and its simplified model (LCFCM_S1) are proposed.
Experimental results
In this section, we describe the experimental results on several synthetic and real images in the presence of slight or severe intensity inhomogeneity. There are a total of five algorithms used in this section, namely, LBF [21], LGDF [25], LCK [22], LCFCM_S and LCFCM_S1. All the methods were implemented Matlab2011a on the PC with Pentium CPU 2.50 and 4 GB of RAM, Windows 7 64-bit. Unless otherwise specified, we use the following default setting of the parameters in the experiments: time step
Discussions
In this section, we simply discuss the parameters which need to be adjusted to obtain appropriate segmentation results. There are six parameters which need to be manually set, including the time step , the standard deviation of Gaussian kernel , the positive constant to approximate the Heaviside function, the weighting coefficient of the neighborhood term , two constants and for the length and regularity terms, respectively. Generally, larger time step can speed up the level set
Conclusions
In this paper, we propose a robust level set model for images segmentation by taking the local correntropy-based fuzzy c-means clustering with spatial constraints into consideration and then simplify it, to corresponding robust version LCFCM_S1. The models efficiently utilize the advantages of fuzzy clustering with spatial constraints and the correntropy criterion, which can reduce the effects of noise and outliers. Hence, our models can handle images caused by noise, low contrast and intensity
Acknowledgments
The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve this paper. Besides, this work is supported by the National Natural Science Foundation of China (Nos. 51305368 and 30800263), Cultivation Program for the Excellent Doctoral Dissertation of Southwest Jiaotong University (No. A0920502051410-3), Science and technology support project of Sichuan province (2013GZ0032 and 2014GZ0005).
Xiao-Liang Jiang received his M.S. in mechanical design from the Southwest Jiaotong University, Chengdu, China, where he is currently a Ph.D. candidate in the College of Mechanical Engineering, Southwest Jiaotong University. His research interests include image processing and image recognition.
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Xiao-Liang Jiang received his M.S. in mechanical design from the Southwest Jiaotong University, Chengdu, China, where he is currently a Ph.D. candidate in the College of Mechanical Engineering, Southwest Jiaotong University. His research interests include image processing and image recognition.
Qiang Wang received his M.S. in mechanical design from the Southwest Jiaotong University, Chengdu, China, where he is currently a Ph.D. candidate in the College of Mechanical Engineering, Southwest Jiaotong University. His research interests include detection and computer vision.
Biao He received his B.Eng. degree from the Southwest Jiaotong University of Mechanism Design, Manufacturing and Automatization, Chengdu, China, in 2013. he is currently a Ph.D. student of Southwest Jiaotong University, major in Mechanical Engineering. His current research interests include image processing and image recognition.
Shao-Jie Chen is currently a M.S. candidate in the College of Mechanical Engineering, Southwest Jiaotong University. His research interests include image processing and image recognition.
Bai-Lin Li received his B.S. in cargoes handling machines and M.S. in construction machinery and Ph.D. in Rolling Stock from the Southwest Jiaotong University, Chengdu, China. From 1994 to 2006, he was a professor in the Department of Mechanical Engineering. His research interests include image processing and image recognition, Robot mechanism and optimization techniques, etc.