A Brain MR Images Segmentation Method Based on SOM Neural Network

Dan Tian, Linan Fan School of Information Shenyang University Shenyang ，China sddtian@sina.com

Abstract—Image segmentation is an indispensable process in the visualization of human tissues, particularly during clinical analysis of magnetic resonance （MR）images. In this paper, a novel brain MR images segmentation method is presented based on self-organizing map (SOM) neural network. The method comprises two main steps: feature extraction and pixel classification based on SOM neural network. In traditional techniques, neural network’s input is the feature vector extracted from the intensity of the pixel and of its n nearest neighbors, which introduces dependency on the gray levels spatial distribution，and thus the final segmentation results are prone to be effected by noise. To enhance the robustness of the method, we perform statistical transformation to the traditional feature vector as neural network’s input. Simulated brain MR images with different noise levels and intensity inhomogeneities are segmented to demonstrate the superiority of the proposed method compared to the traditional technique.

Keywords- MR images; tissue segmentation; SOM neural network; statistical transformation

I. INTRODUCTION Magnetic resonance (MR) imaging is widely used to obtain

high quality clinical images of the brain. Unlike other imaging tools, magnetic resonance acquisition parameters can be adjusted to vary dramatically the type and level of tissue contrast to yield exquisite differentiation between gray matter, white matter, cerebrospinal fluid (CSF), and various types of neuropathology. Post-processing of image data with segmentation methods can further aid in tissue visualization.

Methods for MR images segmentation can be categorized into thresholding methods [1], region growing methods [2], clustering methods [3], and neural network methods [4-7], etc. Since the distribution of tissue intensities in brain images is very complex, it leads to difficulties of threshold determination. Therefore, thresholding methods are generally restrictive and have to be combined with other methods. Region growing extends thresholding by combining it with connectivity conditions or region homogeneity criteria. Successful methods require precise anatomical information to locate single or multiple seed pixels for each region and together with their associated homogeneity. The most popular clustering methods are fuzzy c-means clustering and expectation-maximization

(EM) algorithms. A common disadvantage of EM algorithms is that the intensity distribution of brain images is modeled as a normal distribution, which is untrue, especially for noisy images. Neural network methods attract more and more attentions for its abilities of self-learning, fault tolerance, and optimum search. In this paper, a novel MR images segmentation method is presented based on Kohonen self-organizing map (SOM) neural network. The method comprises two main steps: feature extraction and pixel classification based on neural network. Particular attention has been devoted to feature extraction. In traditional techniques, the intensities of each pixel and of its n nearest neighbors are extracted as feature vector [8]. Segmentation results are prone to be effected by noise. The novel method performs statistical transformation to traditional techniques, obtains a promising result.

II. METHODOLOGY The choice of good features as neural network input is

essential in order to ensure an accurate and reliable segmentation. Features used in image segmentation usually include intensity, texture, shape, etc.

A. Feature extraction It is widely accepted that using a combination of MR

images obtained with different contrast properties will usually generate segmentation results superior to those obtained using single modality images [9]. Generally, some combination of T1-weighted, T2-weighted, and proton density (PD)-weighted images are used in multimodal methods. However, the time required to obtain more than one image series can lengthen the total MR images scan time, which may not be desirable in certain clinical or research MR images settings. It may be advantageous in these situations to extract enough information from a single modality image to make the segmentation based on it potentially comparable to a multimodal method. The method generally taken in such cases is to expand each pixel into a feature vector, characterizing the image data beyond simple pixel intensities.

In [8], a 9-dimensional feature vector extracted from each pixel neighborhood of T1-weighted images has been evaluated. Various combinations of the pixel and of its neighbors have been considered. Eventually the normalized intensity of the

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pixel and of its 8 nearest neighbors has been used, as it gave the best simulation results. Moreover, it introduces dependency on the gray levels spatial distribution in the final segmentation. To solve this problem, we extract a 2-dimention normalized statistical vector 1 2X [x , x ]= as feature vector. The statistical characteristic is composed of the normalized means and variances of a pixel and those of its 8 nearest neighbors. Applying this novel feature vector X as SOM neural network input can reduce the network size, and quicken network training and running.

B. SOM neural network Self-organizing map is one of the most fascinating topics in

the neural network field. The SOM introduced by Kohonen (1982), is a neural network that maps signals from a high-dimensional space to a one- or two-dimensional discrete lattice of neuron units. Each neuron stores a weight. The SOM organizes unknown data into groups of similar patterns, according to a similarity criterion (e.g. Euclidean distance). Such networks can learn to detect regularities and correlations in their input and adapt their future responses to that input accordingly. An important feature of this neural network is its ability to process noisy data.

The map preserves topological relationships between inputs in a way that neighboring inputs in the input space are mapped to neighboring neurons in the map space. A graphical representation illustrating the architecture of the SOM is shown in Fig. 1.

The SOM method follows two basic equations: matching and finding the winner neuron determined by the minimum Euclidean distance to the input as (1), and the update of the position of neurons inside the cluster as (2).

min ( ) ( ) .ij ijid x t w t= − (1)

( 1) ( ) ( )[ ( ) ( )] N

( 1) ( ) N .ij ij ij c

ij ij c

w t w t t x t w t iw t w t i

α+ = + − ∈

+ = ∉ (2)

where, for time t, and a network with n neurons:

x is the input.

Nc is the neighborhood of the winner, 1<Nc n< .

α is the gain sequence 0 1α< < .

ijw is any node weight,1 i n< < .

ijd is the Euclidean distance.

It can be noted from (2) that the updating process is a variation of the location of the node, proportional to the Euclidean distance from the node to the input multiplied by the gain sequence if the node lies inside of the neighborhood. If it is not inside the neighborhood, its position remains unaltered. The particular SOM method can be described as follows.

Step1: Initialize weights. Randomly initialize weights from N inputs. Set the initial radius of the neighborhood Nc .

Step2: Present new input.

Step3: Compute distance to all nodes.

Step4: Select output node with minimum distance. Select node *j as that output node with minimum distance ijd .

Step5: Update weights to node *j and neighbors according to (2).

Step6: If N 0c ≠ go back to step 2.

The basic idea behind the SOM method is to move the weights towards the center of clusters by updating the weights on each input value.

C. Pixel classification based on SOM If an image is to be used as input signal for a self-

organizing method, it is first read and transformed into an i*j matrix, where i*j is the dimension of pixels in the image. For each (i,j) position there exists a value in the range 0-255 depending on the grey level.

Based on grey level information, the statistical feature vector X can be constituted as network input. Then the self-organizing map neural network can realize unsupervised clustering function. For normal brain parenchyma, all pixels in the brain MR images belong to four classes, i.e. gray matter, white matter, CSF, and background. And for brain tumor images, all pixels in the brain MR images belong to six classes, i.e. normal tissues, tumor, edema and necrosis-if present. To mark each tissue classes, we extend the SOM neural network by adding an associative layer. This additional set of neurons does not participate in weight updating. After the self-organizing network terminates and weights are adjusted, the additional layer finds for each input the weight vector (prototype) closest to it and assigns the input to that class.

The mapping can be accomplished by using maximum likelihood training, a supervised learning scheme. The maximum likelihood approach suggests a simple training method which consists of counting the best matching units in the map corresponding to the training data. The output units are connected to the output nodes in the Kohonen layer corresponding to that class with greatest frequency of occurrence of training data. Usually the training dataset is small. For each class a few representatives are selected.

Figure 1. SOM architecture

Input

Output

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III. RESULTS In this section the network parameters and results of

segmentation of MR images based on different network input vector will be presented.

A. Images acquisition To test the segmentation methods’ stability against intensity

inhomogeneities and random noise, we downloaded two simulated brain MR images from Brainweb [10]. The images are based on an anatomical model of normal brain. Noise is 0% and 5% respectively, and intensity non-uniformity is 0% and 20% respectively. All datasets are T1-weighted MR images with a slice thickness of 1.0mm, and the sizes of the images are both 258*258.

B. Parameters setting and segmentation results One of the parameter that has to be set for a good mapping

is the form of the network topology. From several experiments the hexagonal grid was chosen for its better results. Different map sizes of 10*10, 11*11, 12*12, 13*13, 14*14, and 15*15 were tested. Results were improved when the map size was increased. However, no significant differences were observed when the size was increased from 12*12 to 13*13, 14*14, and 15*15. Therefore, the size of 12*12, i.e. 144 neurons, was selected for the best results.

The training set consists of 1000 randomly determined pixels empirically in order to provide sufficient generation capabilities while preserving the network from the effects of noise. As to the selected pixels, the statistical feature vectors and the traditional feature vectors can be constituted as neural network input. The number of network output nodes (additional layer) is 4 for normal brain MR images. The number of network iterations performed is set to 1000. In Fig.2 and Fig.3, the original images and the segmentation results are shown respectively.

Computer simulations show that the novel method can obtain more precise segmentation results, especially when random noise and intensity inhomogeneities exist.

IV. CONCLUSION Medical images generally contain unknown noise and

considerable uncertainty, and therefore clinically acceptable segmentation performance is difficult to achieve. In this paper, particular attentions have been devoted to MR images feature extraction. The traditional technique only considers the normalized intensity of the pixel and of its n nearest neighbors, which is prone to be effected by noise dramatically. To solve this problem, we compose the feature vector by using the statistical values of the pixel, e.g. the mean and the variance. Benefit from the regularity of feature vector SOM neural network can realize unsupervised clustering. To mask different brain tissues classes, we suggest adding an additional layer to the SOM neural network. Computational results with simulated brain MR images have shown the promising performance of our method.

Future work will be devoted to further testing of the proposed technique on a wider range of MR images.

ACKNOWLEDGMENT This work is supported by natural science fund of Liaoning

province, China, under Grant no.20052001.

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Figure 2. Segmentation results of a simulated MR image with 0% noise level and 0% inhomogeneity effect: (a) T1 image; (b) by the traditional method; (c) by the novel method.

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(b)

Figure 3. Segmentation results of a simulated MR image with 5% noise level and 20% inhomogeneity effect: (a) T1 image; (b) by the traditional method; (c) by the novel method.

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