CONTOURLET TRANSFORM BASED ENHANCED BRAIN MR IMAGE SEGMENTATION

Arshad Javed1,2, Wang Yin Chai1, Narayanan Kulathuramaiyer1

1Faculty of Computer Science & Information Technology, Universiti Malaysia Sarawak (UNIMAS), MALAYSIA.2Faculty of Computer & Information Sciences, Al-Jouf University, SAUDI ARABIA

arsh_qau@hotmail.com, ycwang@fit.unimas.my, nara@fit.unimas.my

ABSTRACT

Interpretation of MR images is difficult due to their tendency to gain noise during acquisition. Segmentation is considered as vitally necessary step in medical image analysis and classification. In this paper, we have proposed a method for the automatic segmentation of brain from MR images using Contourlet Transform and K-means. De-noising is always a challenging problem in magnetic resonance imaging and important for clinical diagnosis and computerized analysis such as tissue classification and segmentation. Contourlet Transform has been used for noise removal and it also enhances the image quality. After enhancement, K-means has been used for segmenting the brain MR image. Proposed system is exclusively based on the information contained itself by the image. No extra information is needed and no human interventions are required in proposed system. Proposed method has been tested on different type of MR images like T1, T2 and PD brain MR images.

KEYWORDS: Magnetic resonance imaging (MRI), Silhouette, Image Segmentation, Laplacian Pyramid (LP), Directional Filter Bank (DFB), kmeans, Signal to Noise Ratio (SNR), Mean Squared Error (MSE).

1. INTRODUCTION

Magnetic resonance imaging (MRI) is a powerful diagnostic technique. However, merging of noise during image acquisition degrades the image quality and makes it difficult for human interpretation as well as computer-aided analysis of the images. Recently, because of technological development in image acquisition systems, magnetic resonance imaging (MRI) get benefited and now we can get MRI of increased resolution, reduced signal-to- noise ratio (SNR), and acquisition speed. However, there are many factors like resolution, speed, and SNR combined with scientific, clinical, and financial pressures to obtain resulting data more quickly. The researchers have to tradeoffs among all these factors. For instance, the need for shorter acquisition times for patients in certain clinical studies often undermines the ability to obtain images having both high resolution and high SNR in MRIs. The complexity of the organ that finds how a person thinks, remembers, feels and moves is overshadowed only by its unique vulnerability. The brain is concealed from direct view by the protective skull, which not only defends it from injury but also hinders the study of its function in both disease and health. The cells which supplies the brain in the arteries are tightly bound together thereby routine laboratory test are inadequate to analyze the chemistry of brain. Magnetic

resonance imaging and Computed tomography are two imaging modalities that allow the researchers and doctors to study the brain by looking at the brain non-invasively [1].Image segmentation is a course of action of partitioning an image into different homogeneous regions, so that significant information about the image can be retrieved and different analysis can be performed on that segmented image. There are three classes of tissue of human brain that are Gray Matter (GM), White Matter (WM) and Cerebrospinal Fluid (CSF). Precise segmentation of these tissue classes is a vital step for brain image processing. The fundamental aspect that makes segmentation a difficult problem is the complexity and variability of the anatomy that is being imaged. A major difficult matter in MR image segmentation is to label voxels according to these GM, WM and CSF tissue types within MRI and sometime tumor tissues. Proper classification of MR images is very momentous because most of the time MR images are not highly contrast thereby these classes can be easily overlapped with each other. It is clear from the fact that image segmentation can be efficiently used with striking results in different areas like ground surface [3], medical imaging [4] etc. In this paper we have applied image segmentation technique in the field of medical imaging to segment brain MR imagesIn this paper, we propose a system capable to perform segmentation of brain MR images in an automatic/unsupervised way. We used contourlets transform for noise removal, kmeans for segmentation and silhouette validation method to validate clusters for the automatic segmentation of brain MR images.

Major contributions of the proposed technique includes Contourlet Transform has been used for noise removal. It is fully automatic and completely unsupervised

method. No prior knowledge, information and assumptions are

required about the type, feature, model and contents of image.

Proposed technique calculates clusters/ segments automatically by using objective function and Silhouette validation method.

The paper is managed as follows. First, Section II comprises a survey on related research that is most closely related to the present work and find out problems. Section III holds a detailed description of the proposed system. Implementation and relevant results are represented in Section IV. Finally, conclusions and discussions are occurred in Section V.

Proceedings of the IIEEJ Image Electronics 　　　　and Visual Computing Workshop 2012

Kuching, Malaysia, November 21-24, 2012

2. RELATED WORK

Zhang suggested a Hidden Markov Random Field Model and the Expectation-Maximization algorithm for segmentation of brain MR images [5]. This is a fully automatic technique for brain MR images segmentation. This method is based on estimation of threshold that is heuristic in nature. Thus most of the time, this method does not produce accurate results. Technique used in [5] is also computationally charging much. Bin Li proposed membership constraint FCM algorithm by including spatial information for image segmentation [6]. This proposed algorithm is quite similar or having a resemblance to conventional FCM algorithm but it gives better results for MR images on different noise level as compared to original FCM algorithm because it looks attentively at spatial information of MR images as well. T. Bala brought into service wavelets coefficient for segmentation and a fuzzy clustering method for classification [7]. T. Bala et al [7] measures strength of clusters using silhouette method. M. Masroor proposed segmentation of brain MR images for tumor extraction by combining K-means Clustering for grouping tissues and Perona Malik Anisotropic Diffusion Model [8] for image enhancement. This method also generates good results for segmentation. Ping proposed modified FCM algorithm by modifying membership weighting of every cluster and integrating spatial information [9]. Ping et al [9] applied this method on different MR images and their technique gives appropriate results for MR images of different noise type as compared to standard FCM algorithm.Sripama proposed fuzzy symmetry based genetic clustering technique [10] for MRI brain image segmentation. In [10] numbers of clusters are evolved by variable length genetic fuzzy clustering technique. For measuring quality of cluster fuzzy point symmetry based cluster validity index is proposed in this paper. Experiments are performed on different T1, T2 and PD brain images. This technique performs better than FCM and Expectation Maximization algorithm. But this technique does not consider spatial information and sometime does not segment brain image correctly. This technique also does not work properly for the data sets which have same point as a center for different clusters

2.1 Noise Model

MRI, Cancer and Brain images often composed of random noise that does not come directly from tissues but from other sources in the Electronics instrumentation during acquisition. The noise of an image gives it a gray appearances and mainly the noise is evenly spread and more uniform. In such situation it is very hard to diagnosis the particular disease. Therefore it is necessary to get rid of noise from the image.There are many types of noise like RF noise, Speckle noise, Gaussian noise and Salt & Pepper noise but salt & pepper noise frequently occurred in MR Images. Salt and pepper noise is a form of noise typically seen on images. It represents itself as randomly occurring white and black pixels. Salt and pepper noise is an impulse type of noise, which is also

referred to as intensity spikes. This is caused generally due to errors in data transmission. For an 8-bit image, the typical value for pepper noise is 0 and for salt noise 255. The salt and pepper noise is generally caused by malfunctioning of pixel elements in the camera sensors, faulty memory locations, or timing errors in the digitization process [18], [19].With this type of noise, one pixel is assigned either minimum or maximum intensity value. In case of impulse noise, this kind is considered to be most simple and most widely used. Other pixels can posses any value from allowed dynamic limit when we use random values impulse noise model. This type of noise is not easy to detect and separate as compared to simple salt and pepper noise. In our work, our main area of attention is separation of both these kind of noises from 8-bit gray scale images [20].

Let ),( jix and ),( jiy be the pixel values at position ),( ji of the original and noisy image, respectively. Where

p is the probability of impulse noise model. This can be described in this way.

pji

pjiojix

),(

1),(),(

…………… (1)

Where ),( ji is the noisy pixel at position ),( ji . The noisy

pixel ),( ji can get value between 0~255 for 8-bit grayscale image. Figure3 shows the histogram representation of original image and noisy image with salt & pepper noise image.

3. PROPOSED METHOD

The proposed system consists of two major modules, which includes a multi-resolution based technique for noise removal and kmeans technique for segmentation. Since noise corrupted images inherently contains uncertainty and ambiguity and can result in false segmentation, therefore, multi-resolution based noise removal is performed on the input image as a preprocessing step and then kmeans based technique is applied on the noise free image to automatically segment different objects present in image data. Complete system architecture of the proposed method is shown in figure 1. Details about the major components of the proposed algorithm are discussed in the following subsections one by one.

3.1 Preprocessing-Noise Removal

For achieving best possible diagnose, it is necessary that medical image should be sharp, distinct and free of noise. Major challenge in the study of medical image is to remove noise accurately while maintaining the image quality at best. Noise in MR images is very common. Noise can appear in MR images at acquisition time, transfer time and at image conversion time. So it is very important to remove noise from the images for good segmentation and correct classification.

3.1.1 Adaptive Thresholding Conventionally, noisy image coefficients are compared to a threshold value for noise reduction. The value of those coefficients is obtained through using trial and error method. It must be noted that threshold values depend on noise variance and noise level, and the noise intensity at different frequencies doesn’t line up because high frequency coefficients have higher noise intensity and low frequency coefficients have lower noise intensity, so we consider adaptive threshold value. The aim of adaptive threshold is to offer a compromise between hard and soft thresholding by changing the gradient of the slope. This scheme [21] requires two thresholds, a lower threshold λ1 and an upper threshold λ2 where λ2 is estimated to be twice the value of lower threshold λ1. The criterion of each scheme is described as follows. Given that λ denotes the threshold limit, Xw denotes the input transformcoefficients and Yt denotes the output transform coefficients after thresholding, we define the following thresholding functions:

…………………….. (2)3.1.2 Contourlet Transform using Laplacian pyramid and the directional decompositionThe multiscale decomposition is handled by a Laplacian pyramid [13][14][16] and the directional decomposition is handled by a directional filter bank (DFB)[15]. The laplacian pyramid first captures the point discontinuities and then followed by a directional filter bank to link the discontinuities into linear structures.The architecture of contourlets via laplacian pyramid and directional filter is as follows:

1. Input image consists of components like LL (Low Low), LH (Low High), HL (High Low) and HH (High High).

2. The laplacian pyramid at each level yields a low pass output (LL) and a band pass output (LH, HL, HH).

3. The band pass output is then passed into directional filter bank, which results in contourlets coefficients. The low pass output is again passed through the laplacian pyramid to obtain more coefficients and this process is continued until the fine details of the image are retrieved. This process is shown in the figure 4.

The image is then reconstructed by applying inverse contourlets transform (CT). The figure5 shows the decomposition of Brain MR Image and figure2 shows the architecture of contourlets transform (CT). Table 1 Shows the experimental results of Contourlet

Figure 1: Block Diagram of Proposed Method

3.2 Segmentation

Segmentation is performed for extracting the tumorous brain portion from the brain MRI. This process segments the brain MR image into two portions. One segment contains the normal brain tissues and the second segment contains the tumorous cells. The segment which contains the tumorous cells is the desired region which is known as tumorous region.After removing noise, the K-Means algorithm was used to segment the image. This illustrates the image using only the pixel intensity feature. For accurately finding the number of clusters, K-Mean algorithm is iterated for a range of hypothesized numbers of clusters. And best option for clusteris chosen based on cluster validity measure. Some cluster validity measures, the silhouette validity method [11] yielded amazingly good results for some of the test images. This might be partially due to the special nature of the data, which is not common in clustering problems: the data is 1-D and at least one entry exists at each possible point. On the other hand, accepting the fact that different values might fit the given data (e.g., for segmentation at different detail), a threshold on the validity measure should be chosen below/above which is accepted.In Fig 6 first noise is added in the original image and then image is restored using Contourlets transform.

Figure 2: Block Diagram of Contourlets Transform as Preprocessing

(a). Original Image (b). Noisy Image (SNR = 3.55 dB)

(c). Histogram of Original Image a (d). Histogram of Noisy Image b

Figure3: Histogram representation of Original image and Image with Salt & Pepper Noise

Figure4: Illustration of Contourlets Transform Figure5: Decomposition of Brain MR Image

(a) Original (b) Image with Noise (c) Restored

(1.a) Histogram of image a (1.b) Histogram of image b (1.c) Histogram of image c

(d) Original (e) Image with Noise (f) Restored

(1.d) Histogram of image d (1.e) Histogram of image e (1.f) Histogram of image f

(g) Original (h) Image with Noise (i) Restored

(1.g) Histogram of image g (1.h) Histogram of image h (1.i) Histogram of image i

Figure 6: Image De-noising using Contourlets Transform with histograms (Left to right)

3.3 Kmeans Clustering

K-means clustering is an unsupervised clustering technique which is used to partition the data set n into K groups [8][17].

K-means clustering algorithm initially set centers of each cluster which is known as centeroids of clusters. K-means algorithm minimizes the intra cluster distance and maximize

the inter cluster distance. Each instance is assigned to the cluster which has closest center value with it. Each cluster center Cj is updated to be the mean of its constituentinstances. This algorithm aims at minimizing an objective function. The objective function for K-means is

…………..(3)

Where is a chosen distance measure between a

data point and the cluster centre , is an indicator of the distance of the n data points from their respective cluster centers.

3.4 Cluster Validity

The Silhouette validation technique calculates the silhouette width for each sample, average silhouette width for each cluster and overall average silhouette width for a total data set. Using this approach each cluster could be represented by so-called silhouette, which is based on the comparison of its tightness and separation. The average silhouette width could be applied for evaluation of clustering validity and also could

be used to decide how good is the number of selected clusters, validity criteria is defined as

……..(4)

where a(i) –average dissimilarity of i-object to all other objects in the same cluster; b(i) – minimum of average dissimilarity of i-object to all objects in other cluster (in the closest cluster).

It is followed from the formula that . If silhouette value is close to 1, it means that sample is “well-clustered” and it was assigned to a very appropriate cluster. If silhouette value is about zero, it means that that sample could be assign to another closest cluster as well, and the sample lies equally far away from both clusters. If silhouette value is close to –1, it means that sample is “misclassified” and is merely somewhere in between the clusters. The overall average silhouette width for the entire plot is simply the average of the S(i) for all objects in the whole dataset.The largest overall average silhouette indicates the best clustering (number of cluster). Therefore, the number of cluster with maximum overall average silhouette width is taken as the optimal number of the clusters.

iter phase num sum 1 1 512 3.79553e+006 2 1 17 3.76e+006 3 1 4 3.75416e+006 4 1 2 3.75273e+006 5 1 2 3.75205e+006 6 2 0 3.75205e+0066 iterations, total sum of distances = 3.75205e+006

Figure 7(a): Cluster Validity by equation (4) Figure 7(b): Total sum of distances by equation (3)

Table 1: Results Validation of Contourlet Transform

TransformNoisy image

SNR (dB)Noisy imagePSNR (dB)

Noisy imageMSE

Restored imageSNR (dB)

Restored image

PSNR (dB)

Restored imageMSE

Wavelet9.54 34.74 21.8185 17.48 35.91 20.998.48 32.23 23.7752 15.53 33.44 22.743.52 29.67 26.6741 13.30 30.03 26.43

Curvelet9.54 34.74 21.8185 17.59 36.11 19.348.48 32.23 23.7752 15.95 33.98 21.113.52 29.67 26.6741 14.21 31.12 23.51

Contourlet9.54 34.74 21.8185 17.70 36.76 18.718.48 32.23 23.7752 16.29 34.21 18.933.52 29.67 26.6741 14.67 31.89 22.31

4. EXPERIMENTAL RESULTS AND DISCUSSION

The proposed system was implemented by using the MATLAB environment. We acquired some images from internet and some images from brain web [12]. First, we have performed contourlet transform for noise removal. After that, Kmean has been used for segmenting the images. Fig 8 (b),(d),(f),(h),(j),(l) shows the result of our proposed technique when applied on different T1,T2 weighted and PD brain MR images. From results it is manifest that the proposed system produces much better results than the schemes that have been used former. Nearly all previous techniques don’t perform segmentation accurately when there are less contrast images and WM, GM and cerebrospinal fluid are overlapped in an image. However, our proposed technique shows promising results on different MR images. Our proposed technique shows improve result as compared to previous techniques. Our proposed system can segment the WM, GM and cerebrospinal fluid tissues for different MR images. We have just showed our results qualitatively in the form of visualization. As so far there is not any standard quantitative measure for determining the quality of segmented medical image.

5. CONCLUSION AND FUTURE WORK

We have presented an iterative method for automatic segmentation of brain MR images. Contourlets transform is performed on the images for the purpose of removing noise from the MR image as a preprocessing step. Kmeans performs segmentation process and the objective function, is the core of this proposed system. Kmeans is based on human heuristic that what a “good” partition should be like. This is just the first step of a Computer Aided Diagnosis System (CAD) which is still under development. The results of the proposed system are shown on various MR images. One great advantage of our proposed system is that there is no need of any prior information about the input image type and it does not need any human expert interference.The further step we are working is on brain tumor detection. At the moment, our method is just at an experimental/ demonstrational stage and needs to be evaluated through a double blind procedure by a number of radiologists, with comparison with their current method of brain tumor detection.

(a) Original Image (b) Proposed Method (c) Original Image (d) Proposed Method

(e) Original Image (f) Proposed Method (g) Original Image (h) Proposed Method

(i) Original Image (j) Proposed Method (k) Original Image (l)Proposed Method

Figure 8: Results of our Proposed System

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