Probabilistic region growing method for improving

This article was downloaded by: [E. A. Zanaty] On: 20 January 2014, At: 05:31 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

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Probabilistic region growing method for improving magnetic resonance image segmentation a

b

E.A. Zanaty & Ayman Asaad a

Computer Science Department, College of Science, Sohag University, Sohag, Egypt b

Mathematics Department, College of Science, Al-Azhar University, Assuit, Egypt Published online: 18 Nov 2013.

To cite this article: E.A. Zanaty & Ayman Asaad (2013) Probabilistic region growing method for improving magnetic resonance image segmentation, Connection Science, 25:4, 179-196, DOI: 10.1080/09540091.2013.854736 To link to this article: http://dx.doi.org/10.1080/09540091.2013.854736

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Connection Science, 2013 Vol. 25, No. 4, 179–196, http://dx.doi.org/10.1080/09540091.2013.854736

Probabilistic region growing method for improving magnetic resonance image segmentation E.A. Zanatya∗ and Ayman Asaadb

Downloaded by [E. A. Zanaty] at 05:31 20 January 2014

a Computer

Science Department, College of Science, Sohag University, Sohag, Egypt; b Mathematics Department, College of Science, Al-Azhar University, Assuit, Egypt (Received 18 June 2013; accepted 9 October 2013)

In this paper, we propose a new region growing algorithm called ‘probabilistic region growing (PRG)’ which could improve the magnetic resonance image (MRI) segmentation. The proposed approach includes a threshold based on estimating the probability of pixel intensities of a given image. This threshold uses a homogeneity criterion which is obtained automatically from characteristics of the regions. The homogeneity criterion will be calculated for each pixel as well as the probability of pixel value. The proposed PRG algorithm selects the pixels sequentially in a random walk starting at the seed point, and the homogeneity criterion is updated continuously. The proposed PRG algorithm is applied to the challenging applications: grey matter/white matter segmentation in MRI data sets. The experimental results compared with other segmentation techniques show that the proposed PRG method produces more accurate and stable results. Keywords: MRI; image segmentation; region growing; probability

1.

Introduction

Medical imaging includes modalities such as X-ray, computed tomography (CT), positron emission tomography (PET), single-photon emission computed tomography (SPECT), ultrasound, and magnetic resonance image (MRI) (Bandhyopadhyay & Paul, 2012). The X-ray, invented by Wilhelm in 1895, is based on the measurement of the transmission of X-ray through the body. But, because of the high level of radiation emitted by X-ray, it may cause diseases such as cancer, skin disease or eye cataract. In X-ray-based computer assistance tomography (CT), image is reconstructed from a large number of X-rays. In case of PET, radio nuclides are injected into patient’s body which attach to a specific organ. SPECT is a nuclear medicine-based tomographic imaging technique that uses gamma rays and is capable of producing three-dimensional (3D) image. The best modality for investigation of soft body tissues is ultrasound that measures the reflection of ultrasonic waves transmitted through the body, while MRI has several advantages over other imaging techniques enabling it to provide 3D data with high contrast between soft tissues. However, the amount of data is far too much for manual analysis/interpretation, and this has been one of the biggest obstacles in the effective use of MRI. The segmentation of medical images is an important first step for a variety of image-related application and visualisation tasks. It provides assistance for medical doctors to find out the diseases inside the body without ∗ Corresponding

author. Email: [email protected]

© 2013 Taylor & Francis


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the surgery procedure, to reduce the image reading time, to find the location of a lesion, and to determine an estimate of the probability of a disease. There are many types of image segmentation techniques (Liew & Hong, 2006), among which histogram-based (Chen, 2008; Otsu, 1979), graph cuts (Boykov & Jolly, 2001; Boykov & Kolmogorov, 2004), and region-based (Ayman et al., 2010; Del-Fresno, Vénere, & Clausse, 2009; Hsieh et al., 2011; Kavitha, Chellamuthu, & Rupa, 2012; Mehnert & Jackway, 1997; Mendoza, Acha, Serrano, & Gómez-Cía, 2012; Wu, Shih, Shi, & Wu, 2008; Yu, Zhu, Yang, & Zhu, 2006) techniques are most popular. The histogram-based techniques (Chen, 2008; Otsu, 1979) had been tried to solve threshold problem in histogram- and region-based methods. The histogram-based segmentation technique produces a binary image based on the threshold value. The intensities of object and background pixels tend to cluster into two sets in the histogram with threshold between these two sets (Otsu, 1979). For that, graph cut image segmentation techniques (Boykov & Jolly, 2001; Boykov & Kolmogorov, 2004) use two kinds of seed pixels as ‘object’ and ‘background’ to provide hard constraints for segmentation. The region-based segmentation techniques in Wu et al. (2008), Yu et al. (2006), Mehnert and Jackway (1997), Hsieh et al. (2011), Mendoza et al. (2012), Kavitha et al. (2012), Ayman et al. (2010), and Del-Fresno et al. (2009) segment an image which has strong boundaries into several small regions, followed by merge procedure using specific threshold. In both histogram-based and region-based segmentation techniques, if the threshold is not correct, the contour of object will be destroyed. Wu et al. (2008) described a top-down region-based image segmentation technique for medical images that contain three major regions: background and two tissues. This method can only segment 2D images and cannot segment 3D images or images which contain more than two tissues. Yu et al. (2006) described a hybrid model-based method for obtaining an accurate and topologically preserving segmentation of the brain MRI cortex. This approach is based on defining region and boundary information using, respectively, level set and Bayesian techniques, and fusing these two types of information to achieve cerebral cortex segmentation (Yu et al., 2006). The region growing (RG) technique can work efficiently in medical imaging segmentation if one can guarantee optimal initial seed (Mehnert & Jackway, 1997) and threshold criterion used to stop growing outside a region. In seeded RG, seed selection is crucial, but can be seen as an external task, often done by hand in medical image processing. Unseeded RG was also proposed. Hsieh et al. (2011) used an algorithm integrating fuzzy c-means and RG techniques for automated tumour image segmentation from patients with meningioma. Only non-contrasted T1- and T2weighted MRI are included in the analysis. The study’s aims where to correctly locate tumours in the images and to detect those situated in the midline position of the brain. Mendoza et al. (2012) proposed a self-assessed adaptive RG technique to segment bone CT image. They relied on a self-tuning approach to deal with a great variety of imaging conditions requiring limited user intervention (one seed). The detection of the optimal parameters was managed internally using a measure of the varying contrast of the growing region, and the stopping criterion was adapted to the noise level in the data set owing to the sampling strategy used for the assessment function. Moreover, they obtained similarity around 86% of segmentation results with the ground truth tissues. Kavitha et al. (2012) proposed an effective modified RG technique for detection of brain tumour. Modified RG included an orientation constraint in addition to the normal intensity constraint. The performance of this technique was systematically evaluated using the MRI brain images received from the public sources. For appropriate thresholds, Ayman et al. (2010) presented RG technique for medical image segmentation and obtained good results for low noise levels. But this method failed to extract the true tissue in the case of high noise levels and achieves similar results as Del-Fresno et al. (2009), more discussions can be found in Ayman et al. (2010). In spite of wide number of image segmentation techniques (Bandhyopadhyay & Paul, 2012) they failed in most cases largely because of unknown and irregular noise, inhomogeneity, poor contrast and weak boundaries which are inherent to medical images. MRI and other medical images


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contain complicated anatomical structures that require precise and most accurate segmentation for clinical diagnosis. The RG always used human users’ intervention by selecting initial seeds manually (Ayman et al., 2010); the problem here is that the selection of the homogeneity criterion is very important for influencing the accuracy of final segmentation especially MRI segmentation with weak boundaries. In this paper, we present a new RG algorithm called ‘probabilistic region growing (PRG) method’ in order to improve the medical image segmentation. The PRG is proposed to segment tissues with weak boundaries. It includes a threshold that can be varied over the image as a function of intensity probability to provide the better segmentation results. The proposed PRG algorithm technique stops when a pixel with its threshold function is described to be outside the region. The efficiency of the proposed PRG algorithm is demonstrated by extensive segmentation experiments using real MRIs, compared with other state-of-the-art algorithms. The rest of the paper is organised as follows. The MRI segmentation problem is discussed in Section 2. Section 3 presents RG techniques. The proposed approach is described in Section 4. The results obtained with both simulated brain and real magnetic resonance (MR) data are presented in Section 5. Our conclusion is presented in Section 6.

2. The MRI segmentation problem The basic idea of image segmentation can be described as follows. Given a set of data X = {x1 , x2 , . . . , xN } and uniformity predicates P, we desire to obtain a partition of the data into disjoint non-empty groups X = {v1 , v2 , . . . , vk } subject to the following conditions: (1) (2) (3) (4)

∪ki=1 vi = X, vi ∩ vj = φ, i = j, P(vi ) = TRUE, i = 1, 2, . . . , k, P(vi ∪ vj ) = FALSE, i = j.

The first condition ensures that every data value must be assigned to a group, while the second condition ensures that a data value can be assigned to only one group. The third and fourth conditions imply that every data value in one group must satisfy the uniformity predicate, while data values from two different groups must fail the uniformity criterion. Medical tissue has a complex structure, and its segmentation is an important step for deriving the computerised anatomical atlases as well as pre- and intra-operative guidance for therapeutic intervention. 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: (1) Noise: random noise associated with the MRI system, which is known to have a Rician distribution (Prima,Ayache, Barrick, & Roberts, 2001). The noise comes from the stray current in the detector coil due to the fluctuating magnetic fields arising from random ionic currents in the body, or the thermal fluctuations in the detector coil itself (Buxton, 2002; Chakeres & Schmalbrock, 1992). When the level of noise is significant in an MRI, tissues that are similar in contrast could not be delineated effectively, causing error in tissue segmentation. (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 effect (Li, Li, Lu, Chen, & Liang, 2003). In MRIs, intensity non-uniformity can affect computational analysis of the image due to the variance in signal intensity. It is manifested as smooth spatially varying signal intensity across the image and caused by several factors including inhomogeneous RF

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There is no universal algorithm for segmentation of every medical image. Each imaging system has its own specific limitations. The proposed PRG algorithm is introduced to solve the above problems in steps 1–3, by modifying the threshold function with the homogeneity criterion in the RG algorithm. Of course, the proposed method is more general when compared with specialised algorithms and can be applied to a wider range of data. A brief survey of some medical image segmentation techniques had been provided by Withey and Koles (2007).

3.

RG method

The RG is an approach to image segmentation in which neighbouring pixels are examined and added to a region class. This technique used only a few seed pixels as ‘object’ and described each pixel in the object to belong to the edges of this object (Figure 1). The simple RG technique consists in merging neighbouring pixels Px to pixels Py inside the region, according to |I(Px ) − I(Py )| ≤ T , where T is a fixed threshold and I(·) is the pixel intensity value. The algorithm of RG technique can be described by iteratively merging similar pixels into sets or merging sub-regions into larger regions in three main steps: (1) choice of the seed pixels; (2) neighbourhood analysis according to a similarity rule; (3) growing the seed regions by including adjacent pixels that satisfy the similarity rule. The steps (1) and (2) are repeated until there are no more adjacent pixels to be included in a seed region. In the next section, we will solve the choice of threshold problem. The major problems of RG technique are (1) the chaining effect especially for images with pixel intensities changing gradually and (2) the choice of the threshold. The first problem can be solved by using the homogeneity test f (Ii,j ) = |Ii,j − RA| ≤ T , where RA is the average pixel (the summation of pixel intensities over the number of pixels inside the region). Now, the challenge that faces the RG technique is to select a threshold capable to segment images containing weak boundaries. However, it is really difficult to find a general threshold for all cases. The second

Background

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f(I i,j) & T


fields (caused by distortion of the RF field by the object being scanned or non-uniformity of the transmission field). (3) The boundaries among tissues become weak (when pixels around the boundaries have very similar intensities). The boundaries become strong if there is big difference between the pixels inside and outside the tissues and become weak if the difference is small (Buxton, 2002). (4) 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 called mixels (Ruan, Jaggi, Xue, Fadili, & Bloyet, 2000).

T

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Figure 1. The function f (Ii,j ) with fixed threshold.

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Weak boundaries

Figure 2. The histogram of slice #91.

problem is addressed in this paper to achieve high segmentation accuracy of images of weak boundaries. The proposed PRG technique uses different fixed thresholds for each tissue in the image. The fixed threshold crosses the function f (Ii,j ) between two points (a < RA and b > RA see Figure 1) with the same distance from RA, if T is a small prescribed value, then pixels inside the tissue will be described as outside, and if it is big, some pixels outside the tissue will be added to the region especially when the tissue has weak boundaries as shown in Figure 2.

4. The proposed PRG method As known, the MRI contains several regions with weak boundaries (very similar pixel values around the boundaries). RG techniques cannot segment the tissues with weak boundaries because the growing of the region will not stop on the boundaries and will add outside pixels of a tissue to the organ. Furthermore, the number of pixels that have the same intensity inside or outside the tissue(s) is bigger than the number of pixels on the boundaries. The probabilities of these pixel intensities, Ii ∈ [0, 1), in the tissue or in other tissues have higher value than pixel intensities on the boundaries. To solve this problem, we propose a new idea; under the assumption that the pixel values along the boundaries usually have lower probability of pixels than the other pixels in the tissue, we can use the probability of pixels (in the whole image) for the growing region to stop to add pixels from other tissues to a region. The proposed method uses the probability of pixel defined as the number of pixels that have the same intensities. We assume that T is a threshold function, and it will cut or cross the image f (Ii ) only at one pixel, in backward pixel intensity if Ii < RA and in forward pixel intensity if Ii > RA (Figure 1). We suppose that f (Ii ) = |Ii − RA| ≤ T (Ii , Pr(Ii )). (1) In fact, the similar pixels need smaller threshold to add them to seed pixel rather than the pixels on boundary. This means that f (Ii ) takes a value smaller than at the boundary pixels. To extract a tissue with weak boundaries, the region must be stopped growing in the first pixel outside the tissue(s).

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For that, we define the threshold function as follows: T (Ii , Pr(Ii )) = T1 (Ii )T2 (Pr(Ii )); where

T1 (Ii ) =

2γ

Ii (1 − Ii )2α

0 ≤ Ii < 1,

Ii ≤ 0.5, Ii > 0.5,

(2)

(3)

where γ and α are 1/2


γ = γ1 Ii

and

α = α1 (1 − Ii )1/2 .

Here γ1 and α1 are prescribed parameters. These parameters are more stable along a test set of images and the change of their values do not affect the final results. The values of these parameters are selected by trial or experiment one image in the volume and then these values are fixed for whole images in the volume. The range of pixel value is between 0 and 1, that is, Ii ∈ [0, 1). The 2γ threshold T1 takes two values Ii for brightest pixels and (1 − Ii )2α for dark pixels. By using the new threshold functions, we will get the values and opposite values in the range of Ii , therefore when Ii = 0.5, the threshold function is controlled by the γ1 . γ takes very small value in very dark tissue and this value increases when the dark tissue is extracted. To increase the total threshold function with the pixels that lie very close to the boundaries, another probability threshold function is used similar to Equation (3). However, we need a new threshold to force the threshold to be small at the boundaries. This threshold can be described as T2 (Pr(Ii, j )) = eβ ,

β = −β1 [log(Pr(Ii, j ))]−1 ,

(4)

where β1 is a prescribed value. We will use T1 to find very dark pixel intensity that is outside the tissue. T2 takes the smallest value when pixels have the highest probability. Therefore, this function will increase when Pr(Ii ) decrease to help T1 to find Ii such that T < f (Ii ). The behaviour of T2 can be shown in Figure 3 over an intensity Ii .

Figure 3.

(a) Brain MRI, (b) histogram of (a), and (c) new threshold function T2 with intensity Ii .

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Figure 4.

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Pixel and its neighbour pixels for 2D and 3D.

For example, Figure 2 shows MRI slice #91 in (a), the histogram of this image in (b) and the threshold function from Equation (2) in (c); T2 function will increase when Pr(Ii ) increases, and it has minimum value on the boundaries. The histogram is calculated as shown in Figure 1. We can calculate T1 and T2 from Equations (3) and (4), respectively. Then, the T threshold can be computed from Equation (1) to examine the neighbouring pixels to the initial seed. In the proposed algorithm, the 4- and 8-pixel neighbour pixels of 2D and 3D are used, respectively, as shown in Figure 4. 4.1. The proposed algorithm The proposed PRG algorithm starts with some seed pixel(s) and subsequently adds neighbour’s pixel to a region. The algorithm adds pixels which are very close to RA. Then, RG will continue to grow by adding new neighbour pixels satisfying Equation (1) through Equation (4). The details of the proposed PRG algorithm can be described as follows: Algorithm (1) Input MRI, β1 and γ1 . (2) Let the image S = {Ii |i = 1, 2, . . ., N} be the set of seed pixel(s) and set the counter k := 0. (3) While S = φ, apply Equation (1) by calculating the threshold T (Ii , Pr(Ii )) using Equations (2)–(4). 3.1 Set k := k + 1, Rk = φ, RA = 0 and J = φ. 3.2 Choose a seed Ik ∈ S. 3.3 Update S, where S = S − {Ik }. 3.4 Update Rk , where Rk = Rk ∪ {Ik }. 3.5 Update RA, where RA = average(RA ∪ {Ik }). 3.6 Update J, where J = J ∪ neighbours(Ik ). 3.7 Compute f (J), where f (J) = {|RA − Ii |, Ii ∈ J}, and set Z = min(f (J)). 3.8 If Z satisfy Equation (1), then set Ik = Z. 3.9 Update J, where J = J − {Ik } and go to step 3.3. (4) Stop. (5) Return by the regions Ri , i = 1, 2, . . ., k. (6) End 4.2. Numeric example In this section, we try to apply the proposed PRG algorithm on an image. Let us have a 6 × 6 discrete image on the square grid after applying the median filtering to enhance a given image by reducing noise. The pixels of an image are converted into grey values between 0 and 1, that is, the pixel values ∈ [0, 1] (Figure 5) while the initial seeds S are selected (using mouse selection in PRG program). The main algorithm is described in step 3; we can describe the computation of this step as follows.

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Figure 5. An image with three seeds after using median filtering.

Figure 6.

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k

Growing step: (a) input image after smoothing and (b) region with value k label.

In step 3.1, the counter k is set to 1 to label the first region. In addition, the three empty sets are given as follows: Rk is the target k region; RA is the average of pixels in Rk , and J is a set of neighbour pixels of a pixel in Rk . In the proposed PRG algorithm, the pixel’s neighbour pixels in 2D and 3D are selected to be 4 and 6 pixels. In step 3.2, the algorithm will start to grow with first seed pixel (Ik = 0.504,2 ) as in Figure 6(a). In step 3.3, if Ik ∈ S, remove it from S (i.e. S = {0.322,5 , 0.506,5 }). In step 3.4, Rk is updated by adding Ik to the region (Rk = {0.504,2 }). Moreover, the algorithm will label all pixels in Rk with k value as in Figure 6(b). Step 3.5 updates RA by recalculating the average of pixel’s grey values in Rk (RA = 0.50/1). In step 3.6, the set J is given and can be updated by adding the neighbour pixels of Ik to J. Step 3.7 computes f (J) for all pixels in J; for instance in Figure 6(a), J and f (J) are computed as follows: ⎧ ⎫

⎧ ⎫

⎧ ⎫

⎪0.483,2 ⎪

⎪0.023,2 ⎪ 0.483,2 ⎪ ⎪ ⎪ ⎪

⎪

⎪ ⎪ ⎪ ⎨ ⎬

⎨0.514,1 ⎬

⎨0.014,1 ⎬ 0.514,1

J= f (J) =

− 0.50 = . 0.484,3 ⎪ 0.484,3 ⎪ 0.024,3 ⎪ ⎪ ⎪ ⎪

⎪ ⎪

⎪ ⎪ ⎪ ⎪ ⎩ ⎭ ⎩ ⎭ ⎩ ⎭

0.515,2 0.515,2 0.015,2 In the above example, Z = {Ji |f (Ji ) = 0.01}, so Z = J2 = 0.514,1 . In step 3.8, the algorithm will calculate T1 from Equation (3) (T1 = (1 − 0.51)2α , α = γ1 (1 − 0.51)1/2 ), T2 from Equation (4) (T2 = eβ , β = −βx [log(4/36)]−1 ), and substitute in Equation (2) to compute T . Therefore, if the homogeneity test is satisfied, we put Ik = J2 . In addition, in step 3.9, J is updated by removing new Ik from it as follows:

After that, go to step 3.3, select new Ik , we note that Ik ∈ / S, so the S set does not change. In step 3.4, Rk will be updated by adding new Ik to the region (i.e. Rk = {0.504,2 , 0.514,1 }). In step 3.5, update RA = (0.50 + 0.51)/2. In step 3.6, the algorithm will update the set J by adding the

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neighbour pixels of new Ik to J as follows: ⎫

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⎪ ⎪ ⎪ ⎬ ⎨0.484,3 ⎪ ⎬ ⎨0.0254,3 ⎪ ⎬ ⎨0.484,3 ⎪

J 2 = 0.515,2 f (J) =

0.515,2 − 0.505

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⎪ ⎪

⎪ ⎪0.0853,1 ⎪ ⎪ ⎪ ⎪ ⎪0.423,1 ⎪ ⎪ ⎪ ⎪0.423,1 ⎪ ⎪

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In step 3.7, the algorithm will compute new f (J) as above. Moreover, Z = J3 = 0.515,2 since Z = {J3 |f (J3 ) = 0.005}. In step 3.8, the algorithm will calculate T for J2 . Therefore, if homogeneity test is satisfied, then Ik = J3 . In step 3.9, update J by removing new Ik = J3 as follows:

Then, go to step 3.3. The algorithm will repeat these steps until the pixel Z that has minimum f (J) with its threshold does not satisfy Equation (1), while all pixels in J will also not satisfy Equation (1) as follows:

Figure 7 shows 2nd, 3rd, and 12th pixels added to Rk . When the algorithm returns to step 3.3, the set S has only one seed pixel {0.322,5 }, since the seed pixel {0.506,5 } is removed from this set and added to the region with label k. In this case, the algorithm will test the set S to select the next seed to start a new region.

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In step 4, the growing will be stopped if there is no more seed in the set S. In step 5, the algorithm will return with all regions Ri , i = 1, 2, . . . , k, where k is the total number of regions obtained in the image(s).

5.

Experimental results


In this section, we will use T1-weighted MRI phantoms which are essential for the detection and characterisation of many abnormalities using MRI (Chakeres & Schmalbrock, 1992). A T1weighted MRI is created typically by using short echo time (TE) and repetition time (TR). The final image is a reflection of more than one of these pulse sequence parameters, weighted according to

Slice#

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Segmentation of GM

62

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Figure 8. Original slice from the 3D simulated data (Web): segmentation results of WM and GM obtained by the proposed PRG after using median filtering (3% noise and 20% RF level) from slice #62 to slice #67.


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the type of sequence and its timing. During this relaxation, a RF signal is generated, which can be measured with receiver coils. Our study is related to 3D images from simulated brain database of McGill University (Web) and from Digital Imaging and Communications in Medicine (DICOM) (Web). MRI from simulated brain database has several advantages over other imaging techniques enabling it to provide 3D data with high contrast between soft tissues, while DICOM defines the formats for medical images that can be exchanged with the data and quality necessary for clinical use. Finally, to further quantitatively evaluate the performance of the algorithm, our method is realised to segment the digital MR phantoms with different noise levels. There are many advantages of using digital phantoms rather than real image data for validating segmentation methods. In these tests, T1-weighted MRI phantom will be used with slice thickness of 1 mm, generated at various noise levels and spatial intensity non-uniformity RF levels (DICOM; Web). We generate various inhomogeneities and boundary weakness by controlling noise and RF, respectively. Four data sets from Web and DICOM are used in order to prove the efficiency of the proposed PRG

Figure 9. Original slice from the 3D simulated data (Web): slice #62 and its segmentation results of WM at noise levels 0%, 1%, 3%, 5%, 7%, and 9% and RF levels 0%, 20%, and 40%.


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Figure 9.


Continued.

method. First set is generated at noise level 3% and spatial RF 20% containing six slices from slice #62 to slice #67 (see the second column of Figure 8), where the original slices are 181 × 217 × 181 voxels). The second set contains slice #62 with various noise levels (0%, 1%, 3%, 5%, 7%, and 9%) and RF levels (0%, 20%, and 40%) (see the second column of Figure 9). The third set (brain MRI) is created at noise level 0%, 3%, 6% and spatial RF 20% containing six slices from slice #121 to slice #126, the original slices are 256 × 256 × 192 voxels (see the second column of Figure 10). The fourth set includes 3D foetus MRI of heart, lung, liver, and foetus (original slices are 168 × 352 × 120 voxels) from slice #61 to slice #70 (see the first row of Figure 10) (Web). Although the concerns in pregnancy are the same as for MRI in general, but the foetus may be more sensitive to the effects, particularly to heating and to noise. The segmentation is used here to show the efficiency of the proposed algorithm to extract small tissues such as foetal tissues. Especially, the feasibility and significance of 3D visualisation of the postmortem foetus using MRI is needed for more investigation in the future (Estroffm, 2009). Seed selection could be done manually or automatically. In this work, seed selection will be done semi-automatically. The principle is a use of the image view and based on the personal

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Figure 10. Original slice from the 3D simulated data (Web): segmentation results of WM obtained by the proposed PRG after using median filtering (noise 0%, 3%, 6% and RF 20%) from slice #21 to slice #26.

judgement, choose the seed point by a mouse-based point and click mechanism. Some MATLAB functions are employed in order to obtain an initial seed point. The proposed algorithms were implemented in MATLAB simulations on a PC with an Intel Core 2, 3 GHz processor and 3 GB of RAM memory. In these algorithms, we set γ1 = α1 = 3.2

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and β1 = 2.2 which appear the best choice after performing several tests. We use 4 and 8 neighbour pixels for 2D and 3D data, respectively (Figure 4). In order to demonstrate the advantage of the proposed PRG in terms of accuracy, we use average overlap metric (AOM) (Dice, 1945; Jaccard, 1912) as a metric to evaluate the performance of image segmentation algorithms. The AOM is computed as follows: 2|A ∩ B| , AOM(A, B) = (|A| + |B|) where A represents the set of results obtained by the proposed PRG technique and B represents the set of the ground truth data. These metrics reach a value of 1.0 for results that are very similar and is near 0.0 when they share no similarly classified voxels.


5.1.

MRI segmentation

In this section, four tests are performed using the proposed PRG technique. The first three tests are focused on segmenting the challenge applications white matter (WM) and grey matter (GM) tissues. The proposed PRG algorithm is applied to these data sets. First data set consists of six slices of 181 × 217 × 181 voxels (from slice #62 to slice #67). Figure 8 shows segmentation results of WM and GM of slice #62 to slice #67 with 3% noise and 20% RF level, the second column contains the original images, where the third and fourth columns contain the segmentation results of WM and GM, respectively. Second data set includes one slice corrupted noise with different noise and different RF levels. Figure 9 shows the segmentation results of WM of slice #62 at noise levels 0%, 1%, 3%, 5%, 7%, and 9% and RF levels 0%, 20%, and 40%. While third data set consists of six slices (from slice #121 to slice #126) with different noise and 20% RF levels. Figure 10 shows the segmentation results of WM from slice #121 to slice #126 with 0%, 3%, and 6% noise and 20% RF levels, the original slices in the second column are 256 × 256 × 192 voxels. Table 1. AOM segmentations accuracy of slice #62 to slice #66 with 3% noise and 20% RF levels. MRI slices

WM

GM

62 63 64 65 66 67

0.97 0.97 0.98 0.99 0.99 0.95

0.98 0.96 0.98 0.98 0.97 0.96

Table 2. AOM segmentations accuracy of slice #62 with different noise and RF levels. RF Noise

0%

20%

40%

0% 1% 3% 5% 7% 9%

0.97 0.97 0.96 0.95 0.93 0.92

0.96 0.96 0.95 0.93 0.92 0.90

0.94 0.94 0.93 0.91 0.90 0.90

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To prove the efficiency of the proposed PRG algorithm, AOM average is evaluated at each test image. The segmentation accuracy (AOM) of WM and GM is described in Table 1 for the first set. Table 1 shows the slice numbers in the first column, and the AOM of WM and GM of slice #62 Table 3. AOM for segmentations of WM on seven T1-weighted MRI slices (slice #121 to slice #126) at 0%, 3%, and 6% noise and 20% RF levels.


Noise MRI slices

0%

3%

6%

121 122 123 124 125 126

0.98 0.98 0.97 0.98 0.99 0.98

0.97 0.96 0.98 0.97 0.97 0.97

0.97 0.96 0.96 0.95 0.97 0.96

Figure 11. Original slice from DICOM: the proposed PRG segmentation, row 1: real foetus 3D MRIs from slice #61 to slice #70 and from row 2 to row 5: 3D segmentation results of heart, lung, liver, and foetus, respectively.


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to slice #67 with noise level 3% and RF level 20% is presented in the second and third columns, respectively. Table 2 shows the AOM of WM with the proposed PRG technique applied to MRI at various noise levels (0%, 1%, 3%, 5%, 7%, 9%) and RF levels (0%, 20%, and 40%). While Table 3 shows AOM for segmentations of WM on seven T1-weighted MRI slices (containing six slices from slice #121 to slice #126) at 0%, 3%, and 6% noise and 20% RF levels. These results indicate that the proposed PRG algorithms are very robust to noise and intensity homogeneities and inhomogeneities. The segmentation accuracy (using AOM) is evaluated. According to Zijdenbos’s (1994) statement AOM > 0.7 indicates excellent agreement; the proposed PRG has desired performance in cortical segmentation. The best AOM is achieved for low noise and RF levels, for which values of AOM are higher than 0.96. According to the results which are in Tables 1–3, the proposed PRG is stable at 90%, at noise level 9% and RF level 40%; this result is satisfactory for segmenting the WM tissues. Lastly, the proposed PRG method is applied to the fourth image test. It is used to segment the images in row 1 which contains real foetus 3D MRIs from slice #61 to slice #70. The segmentation results are presented in row 2, heart; row 3, lung; row 4, liver; and row 5, foetus (Figure 11). It is shown that the proposed PRG method appears stable and good in all clinical MRI segmentation. 5.2.

Comparison results for WM and GM measurements

The fourth data set is tested using the proposed PRG as well as recent methods such as Ayman et al. (2010), Del-Fresno et al. (2009), and Yu et al. (2006), while the WM and GM segmentations are computed by applying them to the challenge application WM and GM segmentation (Web). The segmentation accuracy (using AOM) of these methods is computed. Tables 4 and 5 show AOM of WM and GM, respectively, after performing the proposed PRG, Ayman et al. (2010), Del-Fresno et al. (2009), and Yu et al. (2006) techniques to the test image. Although the segmentation quality logically deteriorates in the presence of noise and variations in intensity, the robustness of the proposed technique is highly satisfactory when compared with the results of the others. The Table 4. AOM of Ayman et al. (2010), Del-Fresno et al. (2009), Yu et al. (2006), and the proposed PRG for segmentation of WM on slice #91 with different noise and RF levels. Noise

3%

9%

RF

0%

40%

0%

40%

Ayman et al. (2010) Del-Fresno et al. (2009) Yu et al. (2006) The proposed PRG

0.91 0.94 0.90 0.97

0.90 0.89 0.90 0.95

0.90 0.91 0.88 0.94

0.90 0.87 0.88 0.95

Table 5. AOM of Ayman et al. (2010), Del-Fresno et al. (2009), Yu et al. (2006), and the proposed PRG for segmentation of GM on slice #91 with different noise and RF levels. Noise

3%

9%

RF

0%

40%

0%

40%

Ayman et al. (2010) Del-Fresno et al. (2009) Yu et al. (2006) The proposed PRG

0.90 0.90 0.89 0.95

0.90 0.89 0.90 0.94

0.90 0.90 0.89 0.94

0.89 0.86 0.88 0.92

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proposed PRG gives the best performance. With the AOM of WM and GM at noise level 9% and RF = 40, PRG exceeded by factors of 5% and 4%, 8% and 6%, and 7% and 4% over Ayman et al. (2010), Del-Fresno et al. (2009), and Yu et al. (2006) techniques, respectively.


6.

Discussions and conclusions

In this paper, we have proposed a PRG method to segment MRIs which contain weak boundaries. The proposed approach has several advantages compared to previous segmentation strategies. One of the most important improvements is that the method gives an automatic threshold for different volumes of data by using the pixel probability from the whole image. The growing process incorporates information of the local neighbourhood and probability of each voxel of the region. The proposed method starts by adding pixels that are closest to the initial seed at a region. The growing will stop at the first pixel outside the region. Furthermore, this method relies on the pixel probability, so that the threshold at the border increases to add some pixels that will help to get higher accuracy. The proposed algorithm has been experimented using MRI data and implemented on PC i3, 3 GHZ. We have used the parameters γ1 , α1 and β1 to be 3.2, 3.2, and 2.2, respectively. During the RG phase, the error in selecting the parameters (if they have very different values) can slightly affect the neighbour pixels of seed which can be added to the region and thereby to a connected region. For that this parameters can be fixed at values in the whole MRI volume (a voxel contributes in multiple tissue types). Four tests are performed using the proposed technique to prove its efficiency. For the first set, WM and GM of slice #62 to slice #67 with noise level 3% and RF level 20% are segmented. For the second data set, the proposed PRG is applied to MRI with various noise levels (0%, 1%, 3%, 5%, 7%, and 9%) and RF levels (0%, 20%, and 40%). For the third set, it is applied to MRI volume containing six slices from slice #121 to slice #126. In these data sets, the accuracy (AOM) is computed after applying the proposed method for each resultant WM or GM segments. We noted that the best AOM is achieved for low noise and RF levels, for which values of AOM are higher than 0.97 and reached 90% for the highest noise and RF levels. In addition, these results indicate that the proposed PRG algorithm is very robust to segment most of the brain image data with different noise and intensity homogeneities and inhomogeneities levels. The proposed PRG is more stable at 90% and the accuracy reaches 99% for MRI segmentation of brain images. The proposed method is also applied to real foetus images in order to improve the prenatal diagnostic capability and diagnostic confidence MRI. Because MRI uses magnetic waves and not X-rays (ionising radiation) it has been shown to be safe to use in pregnancy. The output results prove that the proposed PRG gives high accuracy for extracting the liver, lung, heart, and body of the foetus of real MRIs. As an independent test, we have experimented the proposed algorithm using T1-weigthed MRI with 6% noise while the score accuracy AOM of each segment is evaluated. The superiority of the proposed algorithm is demonstrated by comparing its performance against the existing methods: Ayman et al. (2010), Del-Fresno et al. (2009), andYu et al. (2006). The WM and GM segmentations are measured to ensure the faithfulness of the proposed algorithm when applied to the challenge application WM and GM segmentation. The proposed method achieves better performance of WM and GM segmentations than the existing methods by factors of 5% and 4%, 8% and 6%, and 7% and 4% over Ayman et al. (2010), Del-Fresno et al. (2009), and Yu et al. (2006) techniques, respectively. This study has reflected the fact that these results are promising, but the study is limited by the limited clinical experimentation and that more testing is needed to establish reproducibility

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and stability of these results in the future work. Moreover, the further research can be directed towards the improvement of the 3D version of the algorithm with the consideration of the geometry structure of interesting objects and the statistical characteristics of sub-regions.


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