**Automatic Vector Seeded Region Growing for Parenchyma Classification in Brain MRI**

Chuin-Mu Wang and Ruey-Maw Chen *National Chin-Yi University of Technology, Taiwan, R.O.C.* 

#### **1. Introduction**

Nuclear magnetic resonance (NMR) can be used to measure the nuclear spin density, the interactions of the nuclei with their surrounding molecular environment and those between close nuclei, respectively. It produces a sequence of multiple spectral images of tissues with a variety of contrasts using several magnetic resonance parameters. When tissues are classified by means of MRI, the images are multi-spectral. Therefore, if only a single image with a certain spectrum is processed, the goal of tissue classification will not be achieved because the single image can't provide adequate information. Consequently, it is necessary to integrate the information of all the spectral images to classify tissues. Multi-spectral image processing techniques [1-3] are hence employed to collect spectral information for classification and of clinically critical values. In this paper, a new classification approach was proposed, it is called unsupervised Vector Seeded Region Growing (UVSRG). The UVSRG mainly select seed pixel vectors by means of standard deviation and relative Euclidean distance. Through the UVSRG processing, the data dimensionality of MRI can be decreased and the desired target of interest can be classified which the brain tissue and brain tumor segmentation. A series of experiments are conducted and compared to the commonly used c-means method for performance evaluation. The results show that the proposed approach is a promising and effective technique for MR image classification.

Nuclear magnetic resonance (NMR) has recently developed as a versatile technique in many fields such as chemistry, physics, engineering because its signals provide rich information about material structures that involve the nature of a population of atoms, the structure of their environment, and the way in which the atoms interact with environment1. When NMR is applied to human anatomy, NMR signals can be used to measure the nuclear spin density, the interactions of the nuclei with their surrounding molecular environment and those between close nuclei, respectively. It produces a sequence of multiple spectral images of tissues with a variety of contrasts using three magnetic resonance parameters, spin-lattice (T1), spin-spin (T2) and dual echo-echo proton density (PD). By appropriately choosing pulse sequence parameters, echo time (TE) and repetition time (TR) a sequence of images of

Automatic Vector Seeded Region Growing for Parenchyma Classification in Brain MRI 3

Vector Seed Selection

MRI Multispectral Images

Region Growing

K-means Clustering

Seeded region growing starts from seeds, and each time, it expands around at the speed of one pixel. Hence, a seed point has to be selected in the beginning. In vector seed selection, the pixel vectors which can become seeds have to possess the following characteristics:

The seed points can be either a single pixel vector or a group of connected pixel vectors, which will be regarded as the same region in region growing. According to the aforesaid characteristics, there are two conditions for each pixel vector in the multi-spectral images to be selected to be a seed point. One is that the similarity between one pixel vector and the eight neighbors should be higher than one threshold. The other one is that the maximum relative Euclidean distance between a seed pixel vector and its eight neighbors should be smaller than a threshold. When the above two conditions are satisfied, a pixel vector

Similarity *H*, the first condition mentioned above, calculated the similarity between each pixel vector, composed of B1~B3, and its eight neighboring points. The standard deviation

9

*B i i*

*B i i*

*B i i*

1 9

<sup>1</sup> ( 1 1) <sup>9</sup>

*B B*

<sup>1</sup> ( 2 2) <sup>9</sup>

*B B*

<sup>1</sup> ( 3 3) <sup>9</sup>

*B B*

1 9

1

1

 

 

2

3

2

2

(1)

2

a. There should be high similarity between a seed pixel and the neighbors.

b. There should be at least one seed in the expected region. c. A seed should be unconnected to different regions.

of pixel vector was calculated by the following equation:

Fig. 1. Algorithmic procedures

**2.1 Vector seed selection** 

becomes a seed point.

specific anatomic area can be generated by pixel intensities that represent characteristics of different types of tissues throughout the sequence. As a result, magnetic resonance imaging (MRI) becomes a more useful image modality than X-ray computerized tomography (X-CT) when it comes to analysis of soft tissues and organs since the information about T1 and T2 offers a more precise picture of tissue functionality than that produced by X-CT2.

MRI shares many image structures and characteristics with remotely sensed imagery. They are acquired as image sequences by spectral channels at different specific wavelengths remotely. Most importantly, they produce a sequence of images which explore the spectral properties and correlation within the sequence so as to improve image analysis. One unique feature for which both multispectral MR images and remote sensing images are in common is spectral properties contained in an image pixel that are generally not explored in classical image processing. Since various material substances can be uncovered by different wavelengths, an MR or remote sensing image pixel is actually a pixel vector, of which each component represents an image pixel acquired by a specific spectral band. There are mainly four types of segmentation techniques, namely global thresholding, boundary-based segmentation, region-based segmentation, and mixed segmentation. Seeded Region Growing is an integrated method brought up by Adams and Bischof [4-13], in which few initial seeds are generated, and more similar neighboring regions are then combined to achieve region growing [14-21]. In addition, the method of unsupervised vector seeded region growing suitable for medical multi-spectral images was established. Vector seed selection mainly selects seed pixel vectors by means of standard deviation and relative Euclidean distance. Seeds emerge from even and smooth regions, so the smaller the standard deviation is, the more concentrated the data distribution is. In terms of image, it indicates that the difference between a pixel vector and the eight neighbors is smaller, and the pixel vector is suitable for the seed pixel vector. Furthermore, relative Euclidean distance is employed to more carefully select the seed pixel vector to accomplish unsupervised classification.

## **2. Vector seeded region growing**

First of all, the multi-spectral images of a brain section were obtained. There wee five images belonging to the same section but different spectrums, respectively Band1, Band2, and Band3. When tissue classification is conducted, the characteristic information of a single image is too insufficient to achieve effects upon tissue classification if only a single image of a particular spectrum is processed. Thus, the images from Band1 to Band3 in order were combined into 3D eigenspace to acquire the 3D eigenvector of every pixel.

Vector seed selection was applied to the aforementioned eigenspace images, or multispectral images, to obtain initial seeds. The algorithm of seeded region growing was further adopted to divide the multi-spectral images into many small regions. The algorithm of region merging was employed to merge similar regions as well as to combine smaller regions with the nearest neighboring regions. Finally, all the regions eventually segmented by means of region growing were classified, and the algorithm of K-means clustering was used, in which it was assumed that K=3, to divide the regions into three categories. After the classification was accomplished, the regions in the same category were namely the same type of brain tissues. Figure 1 indicates the algorithmic procedures.

Fig. 1. Algorithmic procedures

#### **2.1 Vector seed selection**

2 Advances in Brain Imaging

specific anatomic area can be generated by pixel intensities that represent characteristics of different types of tissues throughout the sequence. As a result, magnetic resonance imaging (MRI) becomes a more useful image modality than X-ray computerized tomography (X-CT) when it comes to analysis of soft tissues and organs since the information about T1 and T2

MRI shares many image structures and characteristics with remotely sensed imagery. They are acquired as image sequences by spectral channels at different specific wavelengths remotely. Most importantly, they produce a sequence of images which explore the spectral properties and correlation within the sequence so as to improve image analysis. One unique feature for which both multispectral MR images and remote sensing images are in common is spectral properties contained in an image pixel that are generally not explored in classical image processing. Since various material substances can be uncovered by different wavelengths, an MR or remote sensing image pixel is actually a pixel vector, of which each component represents an image pixel acquired by a specific spectral band. There are mainly four types of segmentation techniques, namely global thresholding, boundary-based segmentation, region-based segmentation, and mixed segmentation. Seeded Region Growing is an integrated method brought up by Adams and Bischof [4-13], in which few initial seeds are generated, and more similar neighboring regions are then combined to achieve region growing [14-21]. In addition, the method of unsupervised vector seeded region growing suitable for medical multi-spectral images was established. Vector seed selection mainly selects seed pixel vectors by means of standard deviation and relative Euclidean distance. Seeds emerge from even and smooth regions, so the smaller the standard deviation is, the more concentrated the data distribution is. In terms of image, it indicates that the difference between a pixel vector and the eight neighbors is smaller, and the pixel vector is suitable for the seed pixel vector. Furthermore, relative Euclidean distance is employed to more carefully select the seed pixel vector to accomplish unsupervised

First of all, the multi-spectral images of a brain section were obtained. There wee five images belonging to the same section but different spectrums, respectively Band1, Band2, and Band3. When tissue classification is conducted, the characteristic information of a single image is too insufficient to achieve effects upon tissue classification if only a single image of a particular spectrum is processed. Thus, the images from Band1 to Band3 in order were

Vector seed selection was applied to the aforementioned eigenspace images, or multispectral images, to obtain initial seeds. The algorithm of seeded region growing was further adopted to divide the multi-spectral images into many small regions. The algorithm of region merging was employed to merge similar regions as well as to combine smaller regions with the nearest neighboring regions. Finally, all the regions eventually segmented by means of region growing were classified, and the algorithm of K-means clustering was used, in which it was assumed that K=3, to divide the regions into three categories. After the classification was accomplished, the regions in the same category were namely the same

combined into 3D eigenspace to acquire the 3D eigenvector of every pixel.

type of brain tissues. Figure 1 indicates the algorithmic procedures.

offers a more precise picture of tissue functionality than that produced by X-CT2.

classification.

**2. Vector seeded region growing** 

Seeded region growing starts from seeds, and each time, it expands around at the speed of one pixel. Hence, a seed point has to be selected in the beginning. In vector seed selection, the pixel vectors which can become seeds have to possess the following characteristics:


The seed points can be either a single pixel vector or a group of connected pixel vectors, which will be regarded as the same region in region growing. According to the aforesaid characteristics, there are two conditions for each pixel vector in the multi-spectral images to be selected to be a seed point. One is that the similarity between one pixel vector and the eight neighbors should be higher than one threshold. The other one is that the maximum relative Euclidean distance between a seed pixel vector and its eight neighbors should be smaller than a threshold. When the above two conditions are satisfied, a pixel vector becomes a seed point.

Similarity *H*, the first condition mentioned above, calculated the similarity between each pixel vector, composed of B1~B3, and its eight neighboring points. The standard deviation of pixel vector was calculated by the following equation:

$$\begin{cases} \sigma\_{B1} = \sqrt{\frac{1}{9} \sum\_{i=1}^{9} (B1\_i - \overline{B1})^2} \\ \sigma\_{B2} = \sqrt{\frac{1}{9} \sum\_{i=1}^{9} (B2\_i - \overline{B2})^2} \\ \sigma\_{B3} = \sqrt{\frac{1}{9} \sum\_{i=1}^{9} (B3\_i - \overline{B3})^2} \end{cases} \tag{1}$$

Automatic Vector Seeded Region Growing for Parenchyma Classification in Brain MRI 5

pixel vectors connecting with but uncovered by regions. Because the pixel vectors connecting with each other are the priority, these uncovered pixel vectors usually have the judgment upon the distance difference with the connected regions conducted to carry out region growing. It is the major reason why CSF is covered by GM and eroded. Therefore, it is necessary to modify the pixel vector, simultaneously calculate the distance difference with all the regions, and grow it into one of the regions with the minimum difference. The minimum distances were found out from the distances between the pixel vectors and all the regions, each corresponding region with the minimum distance was recorded, and the minimum distances were arranged in the order from small to large in Table T. Due to the order from small to large, the first point 'p' in Table T possessed the minimum difference and the highest similarity with the regions it connected among the pixel vectors in the rims of all the regions. Hence, p is more qualified than all the other uncovered pixel vectors to

The algorithm of K-means clustering was employed to mainly classify the results of region segmentation in the previous stage. The brain MR images were classified into three categories, respectively GM, WM, and CSF. Because there were many fragmentary regions, it was necessary to classify all the regions, in which all the regions were divided into three categories, it was assumed that K=3, and the region was regarded as a unit to conduct the algorithm of K-means clustering. After the algorithm was accomplished, the regions in the

The real MR images were used for performance evaluation. They were acquired from ten patients with normal physiology. One example is shown in Fig. 2(a)-(e) with the same parameter values in Table 1. Band 1 is the PD-weighted spectral image acquired by the pulse sequence TR/TE = 2500ms/25ms. Bands 2, 3 and 4 are T2-weighted spectral images were acquired by the pulse sequences TR/TE = 2500ms/50ms, TR/TE = 2500ms/75ms and TR/TE =2500ms/100ms respectively. Band 5 is the T1-weighted spectral image acquired by the pulse sequence TR/TE = 500ms/11.9ms. The tissues surrounding the brain such as bone, fat and skin, were semiautomatically extracted using interactive thresholding and masking. The slice thickness of all the MR images are 6mm and axial section were taken from GE MR

In this experiment, there was one type of real brain MR images. In order to evaluate the performance of the UVSRG, the widely used c-means method (also known as k-means) is used for comparative analysis. The reason to select the c-means method is because it is a spatial-based pattern classification technique. In order to make a fair comparison, the implemented c-means method always designates the desired target signature d as one of its

In order to enhance classification of these MR images, the interfering effects resulting from tissue variability and characterization must be eliminated. However, to identify the sources that cause such interference is nearly impossible unless prior information is provided. On the other hand, in many MRI applications, the three cerebral tissues, GM, WM and CSF are of

become a region.

**3. Experimental results** 

class means with d fixed during iterations.

1.5T Scanner.

**2.3 Applying K-means to region classification** 

same category belonged to namely the same sort of brain tissue.

In the equation, *BB B* 1 , 2 and 3 indicates the mean of the selected 3×3 range, calculated as follows:

$$\begin{cases} \overline{B1} = \frac{1}{9} \sum\_{i=1}^{9} B1\_i \\ \overline{B2} = \frac{1}{9} \sum\_{i=1}^{9} B2\_i \\ \overline{B3} = \frac{1}{9} \sum\_{i=1}^{9} B3\_i \end{cases} \tag{2}$$

The overall standard deviation is calculated as follows:

$$
\sigma = \sigma\_{B1} + \sigma\_{B2} + \sigma\_{B3} \tag{3}
$$

The standard deviation was further normalized by [0, 1] as follows:

$$
\sigma\_N = \sigma \ne \sigma\_{\text{max}} \tag{4}
$$

 max indicated the maximum standard deviation in the image. The similarity between a pixel vector and its eight neighbors was calculated as follows:

$$H = 1 - \sigma\_N \tag{5}$$

Furthermore, according to the second condition, the relative Euclidean distance between each pixel vector and its eight neighboring points was calculated as follows:

$$d\_i = \frac{\sqrt{\left(B1 - B1\_i\right)^2 + \left(B2 - B2\_i\right)^2 + \left(B3 - B3\_i\right)^2}}{\sqrt{B1^2 + B2^2 + B3^2}}\tag{6}$$
 
$$i = 1, 2, \dots, 8$$

According to the experiment by Shih & Cheng [11], the efficacy of employing relative Euclidean distance is better than that of using normal Euclidean distance. Therefore, the maximum distance between each pixel and its eight neighboring points was calculated by the following equation:

$$d\_{\max} = \max\_{i=1}^{8} (d\_i) \tag{7}$$

The two aforementioned conditions have to be satisfied in order for a pixel vector to be selected as a seed point. The first condition aims at examining whether or not there is considerably high similarity between a seed pixel vector and its neighbors whereas the second condition focuses on ensuring that a seed pixel vector is not in the boundary between two regions.

#### **2.2 Region growing**

The traditional method of region growing can not successfully classify brain tissues. Consequently, this paper modified the principle of region growing and recorded all the pixel vectors connecting with but uncovered by regions. Because the pixel vectors connecting with each other are the priority, these uncovered pixel vectors usually have the judgment upon the distance difference with the connected regions conducted to carry out region growing. It is the major reason why CSF is covered by GM and eroded. Therefore, it is necessary to modify the pixel vector, simultaneously calculate the distance difference with all the regions, and grow it into one of the regions with the minimum difference. The minimum distances were found out from the distances between the pixel vectors and all the regions, each corresponding region with the minimum distance was recorded, and the minimum distances were arranged in the order from small to large in Table T. Due to the order from small to large, the first point 'p' in Table T possessed the minimum difference and the highest similarity with the regions it connected among the pixel vectors in the rims of all the regions. Hence, p is more qualified than all the other uncovered pixel vectors to become a region.

#### **2.3 Applying K-means to region classification**

The algorithm of K-means clustering was employed to mainly classify the results of region segmentation in the previous stage. The brain MR images were classified into three categories, respectively GM, WM, and CSF. Because there were many fragmentary regions, it was necessary to classify all the regions, in which all the regions were divided into three categories, it was assumed that K=3, and the region was regarded as a unit to conduct the algorithm of K-means clustering. After the algorithm was accomplished, the regions in the same category belonged to namely the same sort of brain tissue.
