Abstract
Segmentation of brain tissues is an important but inherently challenging task in that different brain tissues have similar grayscale values and the intensity of a brain tissue may be confused with that of another one. The paper accordingly develops an ICKFCM method based on kernelized fuzzy -means clustering with ICA analysis for extracting regions of interest in MRI brain images. The proposed method first removes the skull region using a skull stripping algorithm. Through ICA, three independent components are then extracted from multimodal medical images containing T1-weighted, T2-weighted, and PD-weighted MRI images. As MRI signals can be regarded as a combination of the signals from brain matters, ICA can be used for contrast enhancement of MRI images. Finally, the three independent components are utilized as inputs by KFCM algorithm to extract different brain tissues. Relying on the decomposition of a multivariate signal into independent non-Gaussian components and using a more appropriate kernel-induced distance for fuzzy clustering, the proposed method is capable of achieving greater reliability in both theory and practice than other segmentation approaches. According to the experiment results, the proposed method is capable of accurately extracting the complicated shapes of brain tissues and still remaining robust against various types of noises.
1. Introduction
Along with the rapid advancement of medical imaging technologies, there has been a constant rise in the demand for more sophisticated visual means for inspection of anatomic structures, identification of disease, examination of the characteristics in a region of interest, and registration and reconstruction of images. Of the technologies developed to meet the demand, image segmentation plays an indispensable role. Medical images are mostly limited by low contrast, high noise, intensity inhomogeneity, and other imaging ambiguities greatly complicating the task of segmentation. In addition, compared with other types of images, medical images tend to pose greater difficulty in shape recovery. More accurate and effective techniques are therefore needed to assist medical image segmentation. Image segmentation refers to the technique that partitions an image into different regions and is typically used to identify regions of interest. Several algorithms have been reported in the literature for image segmentation, such as independent component analysis [1, 2], fuzzy clustering [3], level set method [4, 5], Markov random field [6], and neural network [7], each of which has its advantages and disadvantages.
Most medical images are acquired from special acquisition modalities, including magnetic resonance imaging (MRI), computed tomography (CT), single photon emission tomography (SPECT), positron emission tomography (PET), and ultrasounds (US). Because of its advantages over other diagnostic imaging techniques [8], MRI has been extensively used for image segmentation. To reduce the uncertainty widely present in medical images, this study strives to integrate independent component analysis (ICA), kernelized fuzzy -means clustering (KFCM), and image preprocessing as a computational technique for use in medical image segmentation.
A statistical and computational technique for revealing hidden factors that underlie sets of random variables, measurements, or signals, ICA defines a generative model for the observed multivariate data, which is assumed to be mixtures of some unknown latent variables. It was originally developed as a means to solve the problem of blind source separation (BSS) [9]. BSS refers to the problem of finding the original source signals from available mixtures, without having prior knowledge of the mixing mechanisms. For performing unsupervised classification, the data are modelled as a mixture of classes described by linear combinations of independent non-Gaussian densities. ICA has been successfully used to separate multivariate signals, yet two statistical limitations should be met. Lee and his colleagues [10] proposed the ICA mixture model (ICAMM) to overcome one of the ICA limitations, which is the assumption that the signal sources are independent. In such approach, the assumption is relaxed by using the concept of mixture models. The ICAMM algorithm finds the independent components and the mixing matrix for each class and computes the class membership probability for each pattern in the dataset. The learning rules for the ICAMM were derived using gradient ascent method to maximize the log-likelihood data function. Attempting to improve the ICAMM performance, Oliveira and Romero [1] proposed an enhanced ICA mixture model (EICAMM), which implements some modifications on the original ICAMM algorithm learning rules. EICAMM algorithm is similar to the original ICAMM algorithm as both are based on an information-maximization approach proposed by Bell and Sejnowski [11].
ICA and its extension have been extensively applied in many research fields [12]. Jenssen and Eltoft [2] used ICA image model to generate a data dependent filter bank for texture segmentation. The filter bank consists of the ICA basis images which are learned from textured images. With the basis images capable of capturing the inherent structure of the texture, their method is able to segment the texture image. Tateyama et al. [13] proposed a method based on kernel independent component analysis (KICA) for classification of MRI datasets. KICA, a nonlinear approach for extracting independent components of images, appeared to produce significant enhancement in brain MRI datasets, and their experiment found the KICA-based classification method able to effectively classify brain tissues.
Among the other methods developed for MRI image segmentation, fuzzy clustering is of considerable benefits thanks to its ability to retain much more information from the original image than hard segmentation methods. Clustering algorithms attempt to classify a pixel to a tissue class by applying the notion of similarity to the class; they can thus be adopted for image segmentation. Unlike the crisp -means clustering algorithm [14], the fuzzy -means (FCM) algorithm allows pixels to belong to multiple clusters with varying degrees of membership; algorithms based on fuzzy clustering are therefore particularly suitable for handling an uncertainty problem concerning segmentation of multimodal medical images. Masulli and Schenone [15], after conducting a review of different clustering algorithms containing FCM algorithm, maximum entropy principle-based fuzzy clustering (MEP-FC) [16], and two versions of possibilistic -means algorithms (PCMs) [17, 18], introduced their clustering algorithm named possibilistic neurofuzzy -means algorithm (PNFCM). The KFCM algorithm [19, 20] was realized by replacing the original Euclidean distance in the FCM algorithm with a kernel-induced distance and a spatial penalty on the membership functions. Kannan et al. [21] proposed a kernel-induced fuzzy -means based on hypertangent function for segmenting breast MRI. The algorithm was developed by integrating kernel, hypertangent function, and Lagrangian methods with the basic objective function of the FCM algorithm to obtain proper effective segmentation. Gupta et al. [3] presented a hybrid segmentation method utilizing both features of Gaussian kernel-induced fuzzy -means (GKFCM) clustering [22] and active contour model driven by region scalable fitting (RSF) energy function [23] for ultrasound medical images. In this method, the result obtained from the GKFCM method is used to initialize the contour that spreads to identify the estimated regions. GKFCM also helps to estimate the controlling parameters used in the curve evolution process and achieve better results with the kernel-induced distance replaced by the Euclidean distance. The RSF formulation is responsible for attracting the contour toward the object boundaries and it does not require the reinitialization process when the level set curve is evolving. Gong et al. [24] proposed an improved FCM, called KWFLICM, by introducing a tradeoff weighted fuzzy factor and a kernel metric. The tradeoff weighted fuzzy factor depending on the space distance of all neighboring pixels and their gray-level difference is introduced into its objective function to guarantee noise insensitiveness and image detail preservation. To enhance segmentation robustness to noise and outliers, KWFLICM algorithm further incorporates a kernel distance measure in its objective function. The KWFLICM algorithm, which can accurately estimate the damping extent of neighboring pixels, yields good results in many cases of image segmentation and maintains fine robustness to various types of noises.
Despite their advantages in yielding regions more homogeneous than other crisp methods, reducing spurious blobs, and removing noisy spots, most of the fuzzy methods mentioned above still require prior knowledge about the number of clusters in the data that may not be known for new data. Instead of improving segmentation accuracy via enhancing the kernel function, eighteen different validity criteria [25] have been implemented to estimate the number of clusters to help achieve high-accuracy segmentation of a given image when they are performed with KFCM or SKFCM algorithm [26, 27].
2. Method
As shown in Figure 1, the proposed segmentation method comprises three stages: skull stripping, independent component analysis, and kernelized fuzzy -means clustering.
2.1. Skull Stripping
An essential step in most quantitative analyses of brain structure is removing the skull region, that is, the bones of skull and meninges, from the original image. To complete the task, a threshold that can separate brain and nonbrain tissues is calculated according to the histogram computed by image grayscale. With the thresholding, a binary image can be created. After creating the binary image, we eliminate isolated fake objects and holes by morphological operations from the binary image to produce another binary image, called binary morphological image (i.e., we remove the isolated fake objects outside the white portion and fill the holes inside the white portion in the first binary image). To remove the region boundaries from foreground pixels (i.e., white pixels), erosion operation is performed in the binary morphological image to obtain a binary eroded image. The last step is to mask the grayscale image using the binary eroded image. The mask operation leads to the creation of the skull stripped image; the skull image can then be obtained. The skull stripping algorithm is summarized as follows.
Step 1. Calculate a threshold that can separate brain and nonbrain tissues based on the histogram computed by image grayscale.
Step 2. Apply the threshold to create a binary image.
Step 3. Eliminate isolated fake objects and holes from the binary image to create a binary morphological image.
Step 4. Remove layers of pixels to obtain a binary eroded image, where parameter is a constant and .
Step 5. Mask the grayscale image using the binary eroded image to achieve the skull stripped image.
2.2. Independent Component Analysis
In this section, we first briefly review the principle of the independent component analysis and then apply the ICA algorithm to analyze the multimodal MRI images, for extracting three independent components.
When the ICA algorithm is applied to the segmentation of brain tissues, three types of images, T1-weighted, T2-weighted, and PD-weighted images, are regarded as the observed signals and represented by , , respectively. The set of these images is described as
Brain tissues containing WM, GM, and CSF can be regarded as the source signals, respectively, represented by , . The set of these brain tissues is described asThe relation between images and brain tissues can then be represented as where is an unknown mixing matrix of size 3 × 3. If we can obtain the matrix , then the brain tissues can be obtained by the calculation of inverse matrix asHowever, according to the known condition, matrix is still unknown. By measurement, analysis of statistical independence of observed signals , and through mathematical operation, an approximation matrix can be estimated. With the inverse matrix (called demixing matrix) calculated, the approximation of , denoted by , can be predicted, and stands for the components of brain tissues. The approximation of (i.e., the components of brain tissues to be segmented) is presented asIn the paper, the FastICA algorithm is adopted to calculate the matrix and to further analyze each pixel in the multispectral image for correct classification of brain tissue.
FastICA [12, 28] uses a gradient descent method to maximize a measure of non-Gaussianity, thus accelerating the estimation of the independent components of source signals. Before applying this algorithm, two preprocessing steps, centering and whitening, are usually necessary.
(i) Center the Data. The first step is to center the observed data, that is, to subtract the mean from the observed data , where is a mixing matrix and is a latent source signal (data), so it has zero mean.
(ii) Whiten the Data Using Principal Components Analysis (PCA). After centering, PCA is performed on the zero-mean data to constrain the search of weights to an orthogonal space, that is, to transform observed data so that they are uncorrelated and have unit variance. Whitening is necessary as it makes it possible to search the independent components one by one and prevents the estimated weight vectors from converging to the same optimum. Moreover, finding the weight vectors one by one greatly improves the convergence speed.
The FastICA algorithm uses a gradient descent method to optimize the negentropy equation:where is a normalized random variable with zero mean and unit variance; is a mean function; is any nonquadratic function; and is a standard Gaussian variable with zero mean and unity variance. In the paper, the algorithm for FastICA is described as follows.
Step 1. Choose an initial random weight vector .
Step 2. Update demixing matrix by , where .
Step 3. Normalize weight matrix by .
Step 4. Set , and go back to Step if , where is the smallest constant.
After applying the FastICA algorithm to analyze the multimodal MRI images (a linear combination of T1-weighted, T2-weighted, and PD-weighted MRI images), we can extract three independent components. Compared with the original multimodal images, signals in two of the three independent components have been contrast enhanced. Therefore, the first independent component is used for the segmentation of WM and GM, while the second one is used for the segmentation of CSF to obtain more accurate segmentation results.
2.3. Kernelized Fuzzy -Means Clustering
A kernelized FCM (KFCM) algorithm [20, 25] is constructed with the following objective function as where fuzzifier is a real number greater than 1, is an implicit nonlinear mapping, and and are, respectively, the th measured data and center of the th cluster in the original space. The implicit nonlinear mapping is defined as follows. From the data space to the mapped feature space, Φ: (, ), a dataset (input data has low -dimensional vector space) is mapped into a potentially much higher -dimensional feature space or inner product . The purpose of this mapping is to turn the original nonlinear problem in the input space into a potentially linear one in a rather high dimensional feature space. A kernel in the feature space can be represented aswhere denotes the inner product operation. In the study, Gaussian radial basis function (GRBF) kernel [29] is adopted and described as where is a parameter of Gaussian kernel.
Based on the kernel substitution trick, we haveSince , , and , (7) can be rewritten as
As shown in a previous study [30], the GRBF kernel tends to achieve better segmentation results on simulated MRI images corrupted by noise and other artifacts than polynomial kernel. Thus, the GRBF kernel is adopted as a distance metric replacing the standard Euclidean distance for reliable KFCM clustering.
Like the FCM algorithm, the objective function in (11) can be minimized under the constraint of (i.e., ). The fuzzy membership matrix can thus be obtained by where is the number of clusters; and are the cluster centers of fuzzy groups and , respectively; and the parameter (fuzzifier) is a weighting exponent on each fuzzy membership. The cluster center can be obtained by
3. Results and Discussion
All the algorithms were implemented in MATLAB and C# programming language. Simulated MRI images downloaded from BrainWeb website [31] were used as the test images. To obtain more realistic experiment results, medical images provided by the National Library of Medicine [32] and the Department of Medical Imaging and Radiological Technology at YPU (the Yuanpei University of Medical Technology) [33] had also been used.
Five parts of the experiments are reported: preprocessing for skull stripping, extraction of independent components by ICA, qualitative comparison with state-of-the-art segmentation methods, quantitative comparison of segmentation accuracy, and image segmentation using real medical images.
Figure 2 presents three types of original simulated T1-weighted, T2-weighted, and PD-weighted MRI brain images, and the image size is 181 × 217 pixels. At first, the skull stripping algorithm was used to strip the skull region of the brain image. Original T1-weighted MRI brain image, binary image, binary morphological image, binary eroded image, skull region image, and skull stripped image are shown in Figures 3(a)–3(f), respectively. As indicated, the approach can accurately strip the skull region from the examined brain image. Moreover, when applied to other types of medical images, the skull stripping was also capable of achieving fine results.
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To demonstrate that ICA can be adopted for contrast enhancement of MRI images, the FastICA algorithm was used to extract the independent components in multimodal medical images (a linear combination of T1-weighted, T2-weighted, and PD-weighted MRI images). Figures 4(a)–4(c) present three simulated images, T1-weighted, T2-weighted, and PD-weighted MRI brain images of the 94th slice, where image size = 181 × 217, slice thickness = 1 mm, and noise = 0% (the noise was calculated relative to the brightest tissue), with intensity nonuniformity (“RF”) with 0%. Figures 4(d)–4(f) show the results of the images without skull region after centering and whitening. Visual inspection finds only a slight difference between these two sets of images (two rows in Figure 4). Using the FastICA algorithm to extract the independent components and then rescaling the intensity range of the independent components, we obtained three independent components as shown in Figures 4(g)–4(i). It can be seen that the contrast of WM is enhanced in the first component (Figure 4(g)), while the contrast of CSF is enhanced in the second component (Figure 4(h)). Similarly, as in the previous experiment, the three simulated images were added by different noises with 3% and 5% as shown in Figures 5 and 6, respectively; the FastICA algorithm was then used to extract the independent components. As indicated by the results of applying the FastICA algorithm, ICA can enhance the contrast of images despite the presence of noise corruption. Moreover, after the algorithm was applied, a small part of the noise in the independent components disappeared as shown in Figures 5(g), 5(h), 6(g), and 6(h).
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Before the experiments of qualitative and quantitative comparisons of different methods, we listed the ground truth of brain tissue segmentation of the simulated MRI images of the 94th slice obtained from the same BrainWeb website [31] in Figure 7. It presents the several different anatomical regions in the human brain in terms of WM, GM, CSF, muscle/skin, skin, skull, connective tissue, fat, glial matter (glial matter is a connective tissue in the brain and a CSF-WM interface with an image intensity intermediate between WM and GM), and background. To qualitatively compare segmentation performance, a total of six methods were used for the simulated MRI images: -means, FCM, KFCM, KWFLICM, FCM with ICA analysis (ICFCM), and the proposed KFCM with ICA analysis (ICKFCM).
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In our experiments, a brain image was segmented into only four major regions: WM, GM, CSF plus glial matter, and the skull region. Figure 8 illustrates the case of tissue segmentation when the simulated MRI images do not suffer noise corruption. The segmentation results are reported in Figures 8(a)–8(c) using -means algorithm, Figures 8(d)–8(f) using FCM algorithm, Figures 8(g)–8(i) using KFCM algorithm, Figures 8(m)–8(o) using KWFLICM algorithm, Figures 8(p)–8(r) using ICFCM algorithm, and Figures 8(s)–8(u) using ICKFCM algorithm. The three independent components extracted from multimodal medical images are also shown in Figures 8(j)–8(l) for visual inspection.
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Figure 9 illustrates the case of tissue segmentation with the simulated MRI images at a noise level of 3%. The segmentation results are reported in Figures 9(a)–9(c) using -means algorithm, Figures 9(d)–9(f) using FCM algorithm, Figures 9(g)–9(i) using KFCM algorithm, Figures 9(m)–9(o) using KWFLICM algorithm, Figures 9(p)–9(r) using ICFCM algorithm, and Figures 9(s)–9(u) using ICKFCM algorithm. The three independent components extracted from multimodal medical images are also shown in Figures 9(j)–9(l) for visual inspection. Figure 10 presents another case of tissue segmentation when the simulated MRI images have a 5% noise level. The segmentation results are reported in Figures 10(a)–10(c) using -means algorithm, Figures 10(d)–10(f) using FCM algorithm, Figures 10(g)–10(i) using KFCM algorithm, Figures 10(m)–10(o) using KWFLICM algorithm, Figures 10(p)–10(r) using ICFCM algorithm, and Figures 10(s)–10(u) using ICKFCM algorithm. The three independent components extracted from multimodal medical images are also shown in Figures 10(j)–10(l) for visual inspection. In all the equations of segmentation methods based on fuzzy clustering, , , and maximum iteration = 80. In addition, Gaussian kernel parameter , and (i.e., the number of clusters) is normally not known in advance. However, as a brain image without skull region is usually delineated into three regions, was set at 3. As indicated by the results of the qualitative comparison, no matter in the noiseless or noise case, the proposed method (i.e., ICKFCM algorithm) emerged to be capable of extracting the brain tissues in a more accurate manner than the other four comparable methods.
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For further visual comparison of segmentation results (Figure 8) based on ICKFCM, KWFLICM, and KFCM algorithms, Figure 11 presents an example illustrating the ability of the proposed method for brain tissue extraction, where red boxes denote the regions of interest (ROI). Figure 11(a) shows the ground truth of GM. Figures 11(b)–11(d) show the segmentation results of GM using ICKFCM, KWFLICM, and KFCM algorithms. Figures 11(e) and 11(i) show the enlargement regions of ROI in ground truth of GM. Figures 11(f) and 11(j) show the enlargement regions of ROI in Figure 11(b). Figures 11(g) and 11(k) show the enlargement regions of ROI in Figure 11(c). Figures 11(h) and 11(l) show the enlargement regions of ROI in Figure 11(d). As indicated by the extraction results, the proposed ICKFCM method can accurately extract the complicated shapes of GM with the longitudinal fissure clearly delineated. Moreover, when applied to extract other brain tissues such as WM, CSF, and glial matter, the proposed method can also achieve fine segmentation results compared with other segmentation methods.
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To quantitatively evaluate the accuracy of the segmentation methods, Jaccard coefficient (measure similarity) [34] was used as a measure of similarity between the region delineated by the computerized method and the ground truth, and it is defined as where refers to the binary mask of the ground truth, indicates the region segmented by the computerized method, and denotes the cardinality of a set. The value of this measure varies between 0 and 1, and a higher value of Jaccard coefficient indicates a better match between the segmented region and the ground truth.
The results of the corresponding measured similarity for Figures 8–10 using the six methods with three classes are shown in Tables 1–3, and the level of noise varies from 0 to 5%. Note that the noise was calculated relative to the brightest tissue with image size = 181 × 217, slice thickness = 1 mm, and intensity nonuniformity (“RF”) with 0%. In all cases with different noise levels, the -means method failed to correctly classify the brain tissue, demonstrating the worst performance especially for GM segmentation with a Jaccard coefficient lower than 0.13. As ICA analysis can be used for contrast enhancement of MRI images, the two methods (ICFCM and ICKFCM) based on ICA signals decomposition are assumed to be able to achieve better performance than a method without ICA analysis. The assumption was confirmed by the quantitative evaluation of the experiments as the Jaccard coefficients evaluated by ICFCM and ICKFCM appeared to be greater than those of FCM, KFCM, and KWFLICM. Moreover, in all tables, it can be observed that the proposed ICKFCM algorithm reports the largest Jaccard coefficient among the six methods; that is, the proposed method delivers the best segmentation result.
To validate the suitability of the proposed method for segmentation of multimodal MRI images, we also examined the ability of brain tissue extraction when the original images were degraded by several processes in terms of 3 × 3 averaging, Gaussian smoothing of and , and adding 15% uniform random noise to the original images. Figures 12(a)–12(c) show the simulated MRI images, T1-weighted, T2-weighted, and PD-weighted images of the 98th slice. The segmentation results of averaging operation, Gaussian smoothing, and adding uniform random noise are shown, respectively, in Figures 12(d)–12(f), Figures 12(g)–12(i), and Figures 12(j)–12(l). The ground truth, segmentation on noiseless original images, and skull region of the T1-weighted image are shown in Figures 12(m)–12(t) for qualitative comparison. The quantitative performance of the proposed method was also calculated when the original images were corrupted by the processes mentioned above. As indicated in Table 4, the proposed method can extract the complicated shape of brain tissues and suppress various types of noise.
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In addition to segmenting the simulated MRI images, the proposed method was further applied to real medical images as shown in Figures 13(a)–13(c). Figures 13(d)–13(f) show the images after skull stripping. Figures 13(g)–13(i) show the three independent components extracted by the FastICA algorithm. Figures 13(j)–13(m) show that the skull region, WM, GM, and CSF plus glial matter were segmented by the proposed method. Finally, real MRI images, provided by the Yuanpei University of Medical Technology as shown in Figures 14(a)–14(c), were used to verify the performance of the proposed method. The skull stripped images and the independent components extracted by the FastICA algorithm are, respectively, shown in Figures 14(d)–14(i). As indicated by the segmentation results presented in Figures 14(j)–14(m), the brain tissues were correctly extracted by the proposed ICKFCM algorithm.
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4. Conclusions
The study proposes an ICKFCM method integrating skull stripping, ICA, and KFCM clustering for brain MRI image segmentation. The skull region of the original images is firstly removed by a skull stripping algorithm. Since MRI signals can be considered as a combination of the signals from each brain matter, with the FastICA algorithm, MRI images can be transformed into contrast-enhanced images (the independent components extracted by the FastICA algorithm). KFCM is then used to segment the major brain tissues (WM, GM, and CSF plus glial matter).
In the experiments, we discuss the segmentation performance of six methods (-means, FCM, KFCM, ICFCM, KWFLICM, and ICKFCM) for the simulated MRI images in noiseless case, noise case, and real medical images. To quantitatively compare the six segmentation methods, we further evaluate segmentation accuracy using JSI similarity measure. The results of both qualitative and quantitative comparison indicate that, compared to other segmentation methods, the proposed ICKFCM method can extract the complicated shape of brain tissues and is robust against various types of noise.
Competing Interests
The author declares that there are no competing interests regarding the publication of this paper.