segmentation of mr medical images by using multi-phase...

International Journal of Mathematics and Computer Sciences (IJMCS) ISSN: 2305-7661

www.scholarism.net 4201 April 28Vol.

267

Segmentation of MR Medical Images by Using multi-phase Level Set Method and Bias

Correction

1- SiamakAbdezadeh, Electrical and Computer Engineering Department- Islamic Azad University- Qazvin –

Iran

email: [email protected].

2- FarshidBabapour-Mofrad, Faculty of Engineering, Science and Research Branch, Islamic Azad

University (IAU), Tehran, Iran.

e-mail: [email protected]

3- Mohammad Hosntalab, Faculty of Engineering, Science and Research Branch, Islamic Azad University

(IAU), Tehran, Iran.

e-mail: [email protected]

Abstract: In this paper has been proposeda homogeneous method for image segmentation with bias correction in

images.Noise can usually cause inhomogeneity in images andcan lead to incorrect diagnosis. At first, we present a

model for the brightness distribution of each piece in the image and then we transfer it by converting to another

space in which region separation is done better. Finally it is possible toperform simultaneous segmentation and bias

correction by the level set method. Also the proportion method is robust than to initial state selection.

Keywords: Image segmentation, Level set, Bias Correction.

Introduction

Image segmentation is one of the basic images processing that have much applications in recognition affairs and

human machine.Image segmentation plays an important role in the field of analysis and medical images processing

due to the large volume and images. We know the heterogeneity in the brightness intensity of these images with

name bias [3-4].This heterogeneity is due to the lack of appropriate imaging tools andthe effect of magnetic fields on

it. By modeling the images and obtaining the bias, it can be removed that from the image to obtain the better

image.Among the bias correction methods, the methods together with segmentation are highly utilized and

parametric methods that use of the ML and MAP, are also used.

In [2] a method based on simultaneous bias correction and segmentation have been presented that have the

advantages such as robustness compared tothe initial start [9].Since in this method has been used of K-mean

weightedclustering, it is called WKVLS. It can be seen that WKVLS will be a special case of our method. In this

paper we try to implement the optimal values using unspecified starting states by definition of energy function and

using the maximum similarity.

The problem solutionapproach

We use the following method to model the received image:

(1)

https://mail.google.com/mail/h/l20747sx360/?&v=b&cs=wh&[email protected]://mail.google.com/mail/h/l20747sx360/?&v=b&cs=wh&[email protected]://mail.google.com/mail/h/l20747sx360/?&v=b&cs=wh&[email protected]



267

Where l is the observed image [6], b is bias, n is Gaussian noise with mean 0 and variance sigma and J is also the

original image without noise and bias. If we consider J as the average brightness of that region and equal to ci, then

weindicate each part with Ωiby considering N part of the image. Therefore it can be said that the brightness model

also follows of the Gaussian model with mean bJ and more accurate bci and variance sigma:

(2)

where

(3)

Formulating of the energy function will be in this way. For each point of the image define a neighborhood as

follows:

(4)

Then we transfer the image to another space usinga identity transformation:

(5)

Where

(6)

Because of the transformation, the new space will be also had a Gaussian distribution.

Since the brightness intensity changes smoothly in each part, we can apply the following estimation:

(7)

Also the multiplying of pdfs of Gaussian models would be Gaussian one:

(8)



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If we define D as follows:

(9)

For similar functionwe have:

(10)

Where:

(11)

If the similarity function is integrated over the entire image, we have:

(12)

The above energy function is obtained.Considering the neighborhood and K definition as follows:

(13)

We have:

(14)

In model WKVLS, the energy function is as follows:

(15)



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Where Gp is the segmented Gaussian function.It can be seen that if we equal to the specific values sigma and k in

the obtained energy function, then the energy function WKVLS will be achieved. Therefore, model WKVLS is a

special state of energy model that we obtained.

Formulating of level set is as follows:

We use the multi-level set function as in [8]. If we consider that the following function is the characteristic function

of the region ith

(16)

Therefore, the energy function that is called the multilevel statistical function (SVMLS) is defined as follows:

(17)

Where

(18)

In this paper we have taken advantage of minimizing the energy for the four stages. In the fourth stage model we

have:

(19)

Where H is the Heaviside function that we consider it here as usual as follows:

(20)

Minimizing the energy function is performed by considering a variable constantly and minimizing the other. [7-8]

Then we have:



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(21)

Where

(22)

For minimizing compared to other variable, we have:

(23)

Dirac function has been used as follows:

(24)

It proves that it is enough for staying normalized and uniform the perpendicular vectors to the surfaces, we

convolvethem in a simple Gaussian kernel with limited size.

The main steps of the algorithm are as follows:

1- We select the initial state vectors 1ф and 2ф in such way that they are normalized. It can be considered the

same size and the one in inside and the other in outside of the contour.

2- We update the variables c, b, ϭ by considering the parameters 1ф and 2ф constantly.

3- We update 1ф and 2фby considering variables c, b, ϭconstantly.

4- We stop when the stopping condition has been satisfied.

The output of this step include image segmentation. However, to acquire high accuracy is required to do more

iteration of algorithm that requires much more time to do. for this reason, we use a simpleactive contour model. We



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form the active contour model with a simple initial state. Then we reverse the result, and multiply it to the result of

the previous step. So we increase the accuracy by using image segmentation hybrid model.

Implementation and results

We have considered in implementation the size of kernel is 3, the level number is 4, and the neighborhood

radius is equal to 4.5. the method result has been compared to with method WKVLS. For both models, the

initial states have been given the same to do the better comparison. Here we have four different levels.

Cerebrospinal fluid, the white section, the gray section and background. Drawing the histogram illustrates that

the image histogram have the stronger peaks and better ability to separate in the proposed model space. The

segmentation results have been also presented. Also the image of MRI has been presented with intensity 7

teslain the following that indicates the available bias has been complicated the diagnosis in image. The result of

bias correction for it has been given in the following.



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Conclusions

In the proposed method the smoothing of the bias will be able by convolvea simple kernel function. This

simplifies the working with MRI images. Also the proposed model is robust than the initial state. Therefore it

can be utilized for the fully automatic methods. The accuracy has been improved in comparison to the before

methods.

References

[1] K.Leemput, F.Maes, D.Vandermeulen, and P.Suetens. “Automated model-based biasfield correction of MR

images of the brain”, IEEE Trans.Med.Imag.,vol.18, pp.885-896, Oct.1999.

[2] C.Li, R.Huang, Z.Ding, C.Gatenby, D.Metaxas, and J.Gore, “A variational level set approach to segmentation

and bias correction of medical images with intensity inhomogeneity”, MICCAI., vol. LNCS 5242, pp. 1083-1091,

2008.

[3] U.Vovk, F.Pernus, and B.Likar,“ A review of methods for correction of intensity inhomogeneity in MRI”, IEEE

Trans.Med.Imag.,vol.26, pp.405-421, Mar.2007.

[4] W.Wells, E.Grimson, R.Kikinis, and F.Jolesz, “ Adaptive segmentation of MRI data”, IEEE Trans. Med. Imag.,

vol.15, pp.429-442, 1996.

[5] H. Knutsson and C.-F. Westin,“Normalized and Differential Convolution: Methods for Interpolation and

Filtering of Incomplete and Uncertain data”, CVPR.,pp.515-523,1993.

[6] T.Brox,“From pixels to regions: partial differential equations in image analysis”, Ph.D. Thesis, Saarland

University, Germany, 2005.

[7] K.Zhang, H.Song, L.Zhang, “Active contours driven by local image fitting energy”, Pattern Recognition,2010.

[8] Vese.L, Chan.T, “A multiphase level set framework for image segmentation using the mumford and shah

model”, IJCV., vol.50,pp.271-293, 2002.

[9] C. Li, C.Xu, C.Gui, M.Fox, “Level Set Evolution Without Re-initialization: A New Variational Formulation”,

CVPR., 2005.

[10] S. Zhu and A.Yuille, “Region competition: Unifying snakes, region growing, and bayes/mdl for multiband

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