**Segmentation of Brain MRI**

Rong Xu1, Limin Luo2 and Jun Ohya1

*1Waseda University, 2Southeast University, 1Japan, 2China* 

#### **1. Introduction**

142 Advances in Brain Imaging

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Effective, precise and consistent brain cortical tissue segmentation from magnetic resonance (MR) images is one of the most prominent issues in many applications of medical image processing. These applications include surgical planning (Kikinis et al., 1996), surgery navigation (Grimson et al., 1997), multimodality image registration (Saeed, 1998), abnormality detection (Rusinek et al., 1991), multiple sclerosis lesion quantification (Udupa et al., 1997), brain tumour detection (Vaidyanathan et al., 1997), functional mapping (Roland et al., 1993), etc. Traditionally, the purpose of segmentation is to partition the image into non-overlapping, constituent regions (or called classes, clusters, subsets or sub-regions) that are homogeneous with respect to intensity and texture (Gonzalez & Woods, 1992). If the domain of the image is given by ߗ, then the segmentation problem is to determine the sets ܵ ؿ ߗ, whose union is the entire domain ߗ. Thus, the sets that make up a segmentation must satisfy

$$\Omega = \bigcup\_{k=1}^{K} S\_k \tag{1}$$

where ܵ ת ܵ ൌ for ്݆݇, and each ܵ is connected. Ideally, a segmentation method is to find those sets that correspond to distinct anatomical structures or regions of interest in the image (Pham et al., 2000).

For brain MR image segmentation, some studies aim to identify the entire image into subregions such as white matter (WM), grey matter (GM), and cerebrospinal fluid spaces (CSF) of the brain (Lim & Pfefferbaum, 1989), whereas others aim to extract one specific structure, for instance, brain tumour (M.C. Clark et al., 1998), multiple sclerosis lesions (Mortazavi et al., 2011), or subcortical structures (Babalola et al., 2008). Due to varying complications in segmenting human cerebral cortex, the manual methods for brain tissues segmentation might easily lead to errors both in accuracy and reproducibility (operator bias), and are exceedingly time-consuming, we thus need fast, accurate and robust semi-automatic (i.e., supervised classification explicitly needs user interaction) or completely automatic (i.e., nonsupervised classification) techniques (Suri, Singh, et al., 2002b).

Segmentation of Brain MRI 145

1. Noise: random noise associated with the MR imaging system, which is known to have a

2. Intensity inhomogeneity (also called bias field, or shading artefact): the non-uniformity in the radio frequency (RF) field during data acquisition, resulting in the shading of

3. Partial volume effect: more than one type of class or tissue occupies one pixel or voxel of an image, which are called partial volume effect. These pixels or voxels are usually

The evaluation of brain tissue classification also is a complex issue in medical image processing. Visual inspection and comparison with manual segmentation are very strenuous and are not reliable since the amount of data to be processed is usually large. Tissue classification methods can also be validated by using synthetic data and real brain MR images. The simulated brain MR data with different noise levels and different levels of intensity inhomogeneity, have been provided by Brainweb simulated brain phantom (Collins et al., 1998; Kwan et al., 1999) (http://www.bic.mni.mcgill.ca/brainweb/), and the ground truth for both the classification and partial volumes within the images is also available to estimate different methods quantitatively. The real brain MRI datasets with expert segmentations can be obtained from Internet Brain Segmentation Repository (IBSR) (http://www.cma.mgh.harvard.edu/ibsr/). A few surveys on this topic have been provided in (H. Zhang et al., 2008; Y.J. Zhang, 1996, 2001). Here, we depict three different

(1) The misclassification rate (MCR) is the percentage of misclassified pixels and is computed as (background pixels were ignored in the MCR computation) (Bankman, 2000)

<sup>×</sup> *number of misclassified pixels MCR = 100%*

(2) The root mean squared error (RMSE) is to quantify the difference between the true partial volumes and the algorithm estimations. The RMSE of an estimator ߠ with respect to

ˆ ˆˆ <sup>2</sup> *RMSE MSE E* ( ) ( ) [( ) ]

(3) Let ܰ be the number of pixels that do not belong to a cluster and are segmented into the cluster, ܰ be the number of pixels that belong to a cluster and are not segmented into the cluster, ܰ be the number of all pixels that belong to a cluster, and ܰ be the total number of pixels that do not belong to a cluster. Three parameters in this evaluation system

Under segmentation (*UnS*): ܷ݊ܵ ൌ ܰȀܰ, representing the percentage of negative false

Over segmentation (*OvS*): ܱݒܵ ൌ ܰȀܰ, representing the percentage of positive false

   

*total number of all pixels* (2)

(3)

Rician distribution (Prima et al., 2001);

effect (X. Li et al., 2003);

called mixels (Ruan et al., 2000).

**1.3 Evaluation of segmentation techniques** 

measures for quantitatively evaluating segmentation results.

the estimated parameter ߠ is defined as (Bankman, 2000):

may now be defined as follows (Shen et al., 2005).

segmentation;

segmentation;

#### **1.1 MR imaging (MRI)**

MR imaging (MRI), invented by Raymond V. Damadian in 1969, and was firstly done on a human body in 1977 (Damadian et al., 1977). MR imaging is a popular medical imaging technique used in radiology to visualize detailed internal structures. It provides good contrast between different soft tissues of the body, which makes it especially useful in imaging the brain, muscles, the heart and cancers when compared with other medical imaging techniques, such as computed tomography (CT) or X-rays (Novelline & Squire, 2004). According to different magnetic signal weighting with particular values of the echo time (ܶா) and the repetition time (ܶோ), three different images can be achieved from the same body: ܶଵ-weighted, ܶଶ-weighted, and PD-weighted (proton density).

In the clinical diagnosis, one patient's head is examined from 3 planes showed in Fig.1 (a), and they are axial plane, sagittal plane and coronal plane. The ܶଵ-weighted brain MR images from different planes are respectively showed in Fig.1 (b), (c), and (d).

Fig.1. Brain MR images from (b) axial plane, (c) sagittal plane and (d) coronal plane.

#### **1.2 Difficulties in segmentation of brain MRI**

Even though cortical segmentation has developed for many years in medical research, it is not regarded as an automated, reliable, and high speed technique because of magnetic field inhomogeneities:

MR imaging (MRI), invented by Raymond V. Damadian in 1969, and was firstly done on a human body in 1977 (Damadian et al., 1977). MR imaging is a popular medical imaging technique used in radiology to visualize detailed internal structures. It provides good contrast between different soft tissues of the body, which makes it especially useful in imaging the brain, muscles, the heart and cancers when compared with other medical imaging techniques, such as computed tomography (CT) or X-rays (Novelline & Squire, 2004). According to different magnetic signal weighting with particular values of the echo time (ܶா) and the repetition time (ܶோ), three different images can be achieved from the same

In the clinical diagnosis, one patient's head is examined from 3 planes showed in Fig.1 (a), and they are axial plane, sagittal plane and coronal plane. The ܶଵ-weighted brain MR images

(a)

(b) (c) (d)

Even though cortical segmentation has developed for many years in medical research, it is not regarded as an automated, reliable, and high speed technique because of magnetic field

Fig.1. Brain MR images from (b) axial plane, (c) sagittal plane and (d) coronal plane.

**1.2 Difficulties in segmentation of brain MRI** 

inhomogeneities:

body: ܶଵ-weighted, ܶଶ-weighted, and PD-weighted (proton density).

from different planes are respectively showed in Fig.1 (b), (c), and (d).

**1.1 MR imaging (MRI)** 


#### **1.3 Evaluation of segmentation techniques**

The evaluation of brain tissue classification also is a complex issue in medical image processing. Visual inspection and comparison with manual segmentation are very strenuous and are not reliable since the amount of data to be processed is usually large. Tissue classification methods can also be validated by using synthetic data and real brain MR images. The simulated brain MR data with different noise levels and different levels of intensity inhomogeneity, have been provided by Brainweb simulated brain phantom (Collins et al., 1998; Kwan et al., 1999) (http://www.bic.mni.mcgill.ca/brainweb/), and the ground truth for both the classification and partial volumes within the images is also available to estimate different methods quantitatively. The real brain MRI datasets with expert segmentations can be obtained from Internet Brain Segmentation Repository (IBSR) (http://www.cma.mgh.harvard.edu/ibsr/). A few surveys on this topic have been provided in (H. Zhang et al., 2008; Y.J. Zhang, 1996, 2001). Here, we depict three different measures for quantitatively evaluating segmentation results.

(1) The misclassification rate (MCR) is the percentage of misclassified pixels and is computed as (background pixels were ignored in the MCR computation) (Bankman, 2000)

$$\text{MCR} = \frac{number\text{ of misclassified pixels}}{\text{total number of all pixels}} \times 100\,\%\tag{2}$$

(2) The root mean squared error (RMSE) is to quantify the difference between the true partial volumes and the algorithm estimations. The RMSE of an estimator ߠ with respect to the estimated parameter ߠ is defined as (Bankman, 2000):

$$RMSE(\hat{\theta}) = \sqrt{MSE(\hat{\theta})} = \sqrt{E[(\hat{\theta} - \theta)^2]} \tag{3}$$

(3) Let ܰ be the number of pixels that do not belong to a cluster and are segmented into the cluster, ܰ be the number of pixels that belong to a cluster and are not segmented into the cluster, ܰ be the number of all pixels that belong to a cluster, and ܰ be the total number of pixels that do not belong to a cluster. Three parameters in this evaluation system may now be defined as follows (Shen et al., 2005).


Segmentation of Brain MRI 147

and are spatially separated, and also it generates connected regions (Bankman, 2000). Instead of region merging, it is possible to start with some initial segmentation and subdivide the regions that do not satisfy a given uniformity test. This technique is called splitting (Haralick & Shapiro, 1985). A combination of splitting and merging adds together the advantages of both approaches (Zucker, 1976). However, the results of region growing depend strongly on the selection of homogeneity criterion. Another problem is that different starting points may not grow into identical regions (Bankman, 2000). Region growing has

In edge detection techniques, the resulting segmented image is described in terms of the edges (boundaries) between different regions. Edges are formed at intersection of two regions where there are abrupt changes in grey level intensity values. Edge detection works well on images with good contrast between regions. A large number of different edge operators can be used for edge detection. These operations are generally named after their inventors. The most popular ones are the Marr-Hildreth or LoG (Laplacian-of-Gaussian), Sobel, Roberts, Prewitt, and Canny operators. Binary mathematical morphology and Watershed algorithm are often used for edge detection purposed in the segmentation of brain MR images (Dogdas et al., 2002; Grau et al., 2004). However, the major drawbacks of these methods are over-segmentation, sensitivity to noise, poor detection of significant areas with low contrast boundaries, and poor detection of thin structures, etc. (Grau et al., 2004).

Classifier methods are known as supervised methods in pattern recognition, which seek to partition the image by using training data with known labels as references. The simplest classifier is nearest-neighbour classifier (NNC), in which each pixel is classified in the same class as the training datum with closest intensity (Boudraa & Zaidi, 2006). Other examples of classifiers are *k*-nearest neighbour (*k*-NN) (Duda & Hart, 1973; Fukunaga, 1990), Parzen window (Hamamoto et al., 1996), Bayes classifier or maximum likelihood (ML) estimation (Duda & Hart, 1973), Fisher's linear discriminant (FLD) (Fisher, 1936), the nearest mean classifier (NMC) (Skurichina & Duin, 1996), support vector machine (SVM) (Vapnik, 1998). The weakness of classifiers is that they generally do not perform any spatial modelling. This weakness has been addressed in recent work extending classifier methods to segment images corrupted by intensity in-homogeneities (Wells III et al., 1996). Neighbourhood and geometric information was also incorporated into a classifier approach in (Kapur et al., 1998). In addition, it requires manual interaction to obtain training data. Training sets for

Clustering is the process of organizing objects into groups whose members are similar in certain ways, whose goal is to recognize structures or clusters presented in a collection of unlabelled data. It is a method of unsupervised learning, and a common technique for

each image can be time consuming and laborious (Pham et al., 2000).

statistical data analysis used in many fields.

been exploited in many clinical applications (Cline et al., 1987; Tang et al., 2000).

**2.3 Edge detection techniques** 

**2.4 Classifiers** 

**2.5 Clustering** 

 Incorrect segmentation (*InC*): ܫ݊ܥ ൌ ሺܰ ܰሻȀܰ, representing the total percentage of false segmentation.

The purpose of this chapter is to render a review about existing segmentation techniques and the work we have done in the segmentation of brain MR images. The rest of this chapter is organized as follows: In Section 2, existing techniques for human cerebral cortical segmentation and their applications are reviewed. In Section 3, a new non-homogeneous Markov random field model based on fuzzy membership is proposed for brain MR image segmentation. In Section 4, image pre-processing, such as de-noising, the correction of intensity inhomogeneity and the estimation of partial volume effect are summarized. In Section 5, the conclusion of this chapter is given.
