Brain image segmentation using semi-supervised clustering

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Highlights

  • Here multiple centers are used to represent a partitioning.

  • We have assumed that for 10% data points actual class labels are known.

  • Used objective functions are based on internal and external cluster validity indices.

  • AMOSA is used to optimize these three objective functions.

  • Three different mutation operators are used to obtain global Pareto front.

Abstract

The objective of brain image segmentation is to partition the brain images into different non-overlapping homogeneous regions representing the different anatomical structures. Magnetic resonance brain image segmentation has large number of applications in diagnosis of neurological disorders like Alzheimer diseases, Parkinson related syndrome etc. But automatically segmenting the MR brain image is not an easy task. To solve this problem, several unsupervised and supervised based classification techniques have been developed in the literature. But supervised classification techniques are more time consuming and cost-sensitive due to the requirement of sufficient labeled data. In contrast, unsupervised classification techniques work without using any prior information but it suffers from the local trap problems. So, to overcome the problems associated with unsupervised and supervised classification techniques, we have proposed a new semi-supervised clustering technique using the concepts of multiobjective optimization and applied this technique for automatic segmentation of MR brain images in the intensity space. Multiple centers are used to encode a cluster in the form of a string. The proposed clustering technique utilizes intensity values of the brain pixels as the features. Additionally it also assumes that the actual class label information of 10% points of a particular image data set is also known. Three cluster validity indices are utilized as the objective functions, which are simultaneously optimized using AMOSA, a modern multiobjective optimization technique based on the concepts of simulated annealing. First two cluster validity indices are symmetry distance based Sym-index and Euclidean distance based I-index, which are based on unsupervised properties. Last one is a supervised information based cluster validity index, Minkowski Index. The effectiveness of this proposed semi-supervised clustering technique is demonstrated on several simulated MR normal brain images and MR brain images having some multiple sclerosis lesions. The performance of the proposed semi-supervised clustering technique is compared with some other popular image segmentation techniques like Fuzzy C-means, Expectation Maximization and some recent image clustering techniques like multi-objective based MCMOClust technique, and Fuzzy-VGAPS clustering techniques.

Introduction

The major challenge in analyzing MR brain images is to classify the pixels of images into homogeneous regions. This type of problem is termed as clustering/segmentation problem (Gonzalez & Woods, 2001). The success of medical imaging system depends on proper segmentation of images. MR images have large number of applications in solving several neurodegenerative disorders like Alzheimer diseases, Parkinson related syndrome etc. To solve these problems, several unsupervised and supervised based classification techniques have been developed (Bhandarkar, Zhang, 1999, Saha, Bandyopadhyay, 2009). Most of the clustering techniques rely on some similarity/dissimilarity criteria of data points by using which points are assigned to different clusters. They evolve the partition matrix U(X) of size K × n in such a way that U = [uik], 1 ≤ iK, where, uij takes value “0” if pattern xk does not belong to cluster Ci(i = 1,,K), and can take value “1” if pattern xk belongs to cluster Ci(i = 1, ,K). Unsupervised classification techniques do not take into account any kind of supervised information (Gath, Geva, 1989, Kwan, Evans, Pike, 1999). They are used to partition the pixels based on some internal characteristics (Suckling, Sigmundsson, Greenwood, & Bullmore, 1999). Thus obtained partitioning may not be perfect always. Supervised classification techniques require large amount of labeled information to generate the models which are further utilized for classifying some unknown pixels (Pedrycz & Waletzky, 1997). But it is both time consuming and costly to generate huge amount of labeled information. In recent years a new classification technique, namely semi-supervised classification (Ebrahimi, Abadeh, 2012, Handl, Knowles, 2006), is developed to solve the difficulties of both unsupervised and supervised classification techniques. It utilizes the advantages of both supervised and unsupervised classification (Saha, Ekbal, & Alok, 2012). Here some small amount of labeled data and a huge collection of unlabeled data are used. The available labeled data is used to fine-tune the obtained partitionings. Several approaches have been developed to solve this type of semi-supervised classification problem. Literature survey shows that semi-supervised classification techniques are more powerful as compared to supervised or unsupervised classification techniques for solving different real-life problems (Saha et al., 2012).

In the current paper, the automatic MR brain image segmentation problem is posed as a multiobjective optimization (MOO) problem. Here we need to determine the number of clusters and the corresponding partitioning automatically from the given MR images using the search capability of any MOO based technique. During the clustering process, we have also assumed that some labeled information is also available. Thus the clustering problem is treated as a semi-supervised classification problem and a MOO based framework is developed to solve this problem. The proposed technique, namely Semi-MriMOO, utilizes a recently proposed simulated annealing based MOO technique, namely AMOSA (Bandyopadhyay, Saha, Maulik, & Deb, 2008), as the underline optimization strategy. Three objective functions are used to quantify the goodness of the obtained partitionings. These are simultaneously optimized using AMOSA (Bandyopadhyay et al., 2008). First two objective functions are some internal indices for cluster validity based on unsupervised properties of image data sets. These are: symmetry distance based Sym-index (Bandyopadhyay & Saha, 2008), and Euclidean distance based I-index (Maulik & Bandyopadhyay, 2002). Last one is an external index of cluster validity, Minkowski Score or MS-index (Ben-Hur & Guyon, 2003) based on supervised information or prior information of data set (Alok, Saha, Ekbal, 2012, Alok, Saha, Ekbal, 2014). This basically checks the compatibility of the obtained partitioning and the available supervised information. A new encoding schema is used to represent clusters in the form of a string. Clusters are divided into multiple small sub-clusters. Centers of these small clusters are then encoded in the form of a string. In the current paper, assignment of points to different clusters is done using the popular Euclidean distance. Different new perturbation operations are defined, and as supervised information, we have assumed that class labels of only 10% data points are available. The segmentation results obtained by the proposed Semi-MriMOO clustering technique for different brain MR images are analyzed quantitatively and visually. Those are further compared with the results obtained by some recent or popularly used clustering techniques like Fuzzy C-means (Bezdek, 1981), Expectation Maximization (Jain, Murty, & Flynn, 1999), MCMOClust (Saha & Bandyopadhyay, 2011) and Fuzzy-VGAPS (Saha & Bandyopadhyay, 2007) clustering techniques.

The contributions of the current paper are as follows:

  • To the best of our knowledge this is the first work where a semi-supervised based approach in multiobjective optimization framework is proposed to automatically segment the brain images.

  • Semi-supervised clustering is solved using a multiobjective optimization framework.

  • A new encoding strategy is proposed to represent the partitions in the form of a solution.

  • A set of internal and external cluster validity indices are used as the objective functions.

  • Search capability of a simulated annealing based multiobjective optimization technique, AMOSA, is utilized to automatically determine the appropriate partitioning from different brain images.

  • Effectiveness of the proposed technique is shown for segmenting several normal brain images and also brain images with multiple sclerosis lesions. Results are compared with several popular and recent image segmentation techniques. Experimental results and a thorough analysis of those results clearly demonstrate the effectiveness of the proposed technique.

Section snippets

Literature review

In recent years there have been several attempts to solve the brain image segmentation problem (Klauschen, Goldman, Barra, Meyer-Lindenberg, Lundervold, 2009, Ortiz, Górriz, Ramírez, Salas-Gonzalez, Llamas-Elvira, 2013). In Portela, Cavalcanti, and Ren (2014), authors have proposed clustering based semi-supervised classification technique to segment the MR brain images. Initially K-means clustering technique is applied on randomly selected MR brain slices. Thereafter, these clusters are labeled

Proposed framework for MR brain image segmentation

In the current paper in order to automatically segment magnetic resonance brain images, a multiobjective semi-supervised clustering technique is proposed. The proposed technique uses the search capability of AMOSA (Bandyopadhyay et al., 2008), a modern multiobjective optimization technique based on the concepts of simulated annealing to automatically determine the appropriate partitioning from MR brain image data sets. The proposed technique is a semi-supervised clustering technique; it

Discussion and experimental results

Here for MR brain images three bands are available: T1-weighted, T2-weighted and proton density weighted. This brain image data set can be downloaded from Brainweb database (brainWeb, 2013). The parameters for this brain image data set are: 1mm slice thickness, 3% noise and 20% intensity non-uniformity. The size of the image is 217 × 181 × 181. It consists of 181 different z planes. In the current paper we have executed the proposed algorithm on the intensity values corresponding to the pixels

Conclusion

The current work deals with the application of a semi-supervised clustering technique for segmenting the MR brain images. Here a semi-supervised based clustering approach is developed using the search capability of a multiobjective simulated annealing based approach. In general the existing literature of MR brain image segmentation mostly used some supervised and unsupervised based techniques. In recent years a new paradigm named semi-supervised classification which is a half-way between

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