International Journal of Academic Research in IJARCEijarce.org/archive/pdf/IJARCE_Vol1_No2_Nov2016_07.pdf · International Journal of Academic Research in Computer Engineering Print

International Journal of Academic Research in Computer Engineering

Print ISSN:2476-7638 and Online ISSN: 2538-2411 Vol. 1, No. 2, Pages. 57-67, November 2016

57

International Journal of Academic Research in

Computer Engineering

Volume 1, Number 2, Pages 57-67, November 2016

www.ijarce.org

IJARCE

A New Hybrid of Active Contour and Multiphase Level Set Models for

Segmenting of Medical Images: A Case Study

Siamak Abdehzadeh1*, Naser Sharifi2, Barfab Wafaee3, Majid Habibi4, and Mohammad

Hosntalab5

1. Department of Computer, Boukan Branch, Islamic Azad University, Boukan, Iran.

2. Department of Computer, Boukan Branch, Islamic Azad University, Boukan, Iran.

3. Department of Computer, Baneh Branch, Islamic Azad University, Baneh, Iran.

4. Department of Computer, Tabriz Branch, Islamic Azad University, Tabriz, Iran.

5. Faculty of Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.

Receive Date 2016.10.02; Accepted Date: 2016.11.15, Published Date: 2016.11.15

*Corresponding Author: S.Abdehzadeh ([email protected])

Abstract

Medical images segmentation due to the increasing volume of this images is difficult and in accessible to

human. with development of image processing we can use computers to help. Segmentation of the early stages

of image processing are very well regarded. In this paper, a combination method based on level set and active

contour models have been proposed to achieve more accurate image in image processing. The selected dataset

contains different slices that in this article 8 slices have been selected for testing. The proposed algorithm was

applied on these slices and it has been compared with previous methods. The results have been tested on MRI

images of the brain and this results show that the proposed method is better than other methods proposed

before.

Keywords: Medical Image Segmentation; Level Set Model; Active Contour; Brain MRI Image.

1. Introduction

Segmentation is a fundamental technique in image

processing, which is still being developed and

completed, Level set of the practical methods for

selecting region of interest. Enhance the accuracy

of segmentation methods in image processing is a

Specified target. Besides adding new techniques

such as multi-resolution and multi-phase can be

lead to achieve better results. In this study, the

addition of new methods noted, to Level set and

adjust its parameters lead to achieve better results.

This research is also being evaluated as a new

method by researchers [1,2,3]. Due to recent

advances, segmentation can be used directly in

treatment methods, Thus increasing the accuracy is

very clear [3]. Segmentation is done naturally in

the human visual system. The aim of threshold

algorithms, is to finding an ideal threshold value

for better segmenting of images. The threshold can

be adjusted either manually or automatically.

Manually choosing the threshold, one must

consider whether the threshold value is correct or

not. This process is time consuming. In choosing of

T, errors may occur and cause problems in image

analysis later. For this reason, many methods of

automatic threshold are introduced [4, 5, 6]. The

most popular active contour method introduced in

[7]. Kass named this method snakes. Because

during evolution, the contour moving toward

object that like a snake. According to the estimates

of the boundary of an object in an image, as initial

contour, snakes locate the actual border. In [8]

focus on reducing dependence on initial conditions

by defining a new external energy for improving

snake algorithm. Cohen et. al. in [9] proposed a

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new snake algorithm as balloon snake and added

second external force which is deform the contour

in the normal direction to the outer direction

(inflation) or inner direction (condensation). First,

the level set method was introduced in [10], then

by [11] changed. To getting moving front in a wide

range of issues, the level set method, is a powerful

numerical selection. The areas where the level set

method can be used are image processing,

computer vision and graphics. As noted by [12] It

is said, an implicit representation of the super

planes data, Set of PDE's which controls the

movement of planes manner, and related numerical

methods for implementing in computers make

elements of classical level set method.

2. Material and Methods

2.1. Multi-Stage Level Set Formulation and

Active Contour Model

We use multi-level set functions i, i = 1... n to

represent the regions Ωi, i = 1... N with N = 2n

as in [13]. That we consider Mi(φN(.))as

characteristic function of region Ωi, N (.)φ is a

function of φi, i=1… n, and called statistical

variable Multi-fuzzy level set (SVMLS) we can

present formulation of SVMLS in Equation (1) on

the basis of characteristic function [14].

(y) ( (y))

N

nSVMLSd M dy

i iN

(1)

Where d is equal to Equation (2):

(2)

We minimize the energy for four fuzzy level show

in the Equation (3).

𝑀1 = 𝐻(φ1)𝐻(φ2)

𝑀2 = 𝐻(φ1)(1 − 𝐻(φ2))

𝑀3 = (1 − 𝐻(φ1))𝐻(φ2)

𝑀4 = (1 − 𝐻(φ1))(1 − 𝐻(φ2)

(3)

In which H (φ) is heavy side function we often in

practice, use the regular version in Equation (4).

𝐻𝜀 = 1

2 [1 +

2

𝜋 arctan (

φ

휀)]

(4)

But the process of minimizing the energy includes

maintaining a variable constant, and changing the

other variable, we try to minimize energy that

Equation (5) and Equation (6) and Equation (7) to

calculate b, and 𝜎𝑖 , 𝑖 = 1,2,3,4 are listed:

𝑏 =

∑ (𝐾𝑝 ∗ (𝐼𝑀𝑖(φ4)) ∗𝑐𝑖𝜎𝑖2)

4𝑖=1

∑ (𝐾𝑝 ∗ (𝑀𝑖(φ4)) ∗𝑐𝑖𝜎𝑖2

4𝑖=1 )

(5)

𝐶𝑖 = ∫(𝐾𝑝 ∗ 𝑏) 𝐼𝑀𝑖(φ4)𝑑𝑦

∫(𝐾𝑝 ∗ 𝑏2) 𝑀𝑖(φ4)𝑑𝑦

(6)

𝜎𝑖 = √∬𝐾𝑝 (𝑦𝑥)((𝐼(𝑦) − 𝑏(𝑥)𝑐𝑗)2𝑀𝑖(φ4(𝑦))𝑑𝑦𝑑𝑥

∬𝐾𝑝 (𝑦𝑥)𝑀𝑖(φ4(𝑦))𝑑𝑦𝑑𝑥 (7)

Thus, by minimizing the energy function 𝐸φ4 𝛼𝑆𝑉𝑀𝐿𝑆

for φ1 and 𝜑2. We get gradient decline related to

that as Equation (8). 𝜕Φ1𝜕T

= −[(𝑑1 − 𝑑2 − 𝑑3 + 𝑑4)𝐻(φ2) + 𝑑2 − 𝑑4]𝜕(Φ1) (8) 𝜕Φ2

𝜕T= −[(𝑑1 − 𝑑2 − 𝑑3 + 𝑑4)𝐻(φ1) + 𝑑2 − 𝑑4]𝜕(Φ2)

Where δ (φ) is direct function that follows from

Equation (9).

𝛿𝜀(Φ) =1

𝜋∗

휀

휀2 + Φ2 (9)

But we must ensure that φ remained normalized.

That their vectors size is 1. This is done by

multiplying by a kernel function. The general trend

of the algorithm is as follows:

1. φ values, are randomly initialize.

2. φ values are considered constant and

update b, c and ϭ.

3. b, c and ϭ are considered constant and

update φ.

4. If convergence is not reached, go to 2.

We consider the kernel simple with a small

dimension (3*3). The Radius of ρ is also

considered 4.5. We keep the output of the model

SVMLS in order to combine it with active contour

model.

2.2. Level Set Method Two methods of statistical and variable Multi-fuzzy level set (SVMLS) and weighted K-means vibrational level set (WKVLS) which are from main methods of the level sets are shown in Figures 1 and 2 and then by combining this approach with active contour model we will see its results with SVMLS at the tests and results [14].

Figure 1. SVMLS Method [14]


59

Figure 2. WKVLS Method [14]

In the Figure (1) and Figure (2) from left to right,

we see the initialization value of the algorithm, the

second figure is an estimate of bias, the

segmentation result is shown in the third figure and

the fourth one is a figure in which the bias is

corrected. In general, it is observed that SVMLS

method compared to WKVLS is better segmented

the image (partly shown with the red mark).

2.3 Dataset

Selected image from dataset are of the size

181*217*181 pixel, image model T1, protocol of

the type ICBM, phantoms name is normal, Slice

thickness is 1 mm, noise in all three datasets is

equal to 0%, 3% and 9% respectively. Non-

uniform intensity in all three datasets is 20%. The

color scheme is gray in all three, all dataset is equal

except that their noise percentage varies, all

datasets saved in MINC format [15] and from each

dataset we choose 8 slice with numbers

86،87،88،89،90،91،92،95.

Comprised of brain images of 19 people with

dimensions of 136*189*157 pixels. Database sored

in .nii format and algorithms have tested on 72

slices of 19 selected brain images [15].

3. Proposed Method

The combination of SVMLS method with active

contour the following have explained. Overall

flowchart for segmentation methods and

calculation errors are shows in Figure (3).

Figure 3. Overall flowchart for segmentation methods

and calculation errors

One method of segmentation is using active contour

models. Here we are going to use a combination of

active contour models and methods obtained from

SVMLS and WKVLS to achieve better accuracy.

The study and use of active contour, will lead to

desirable results in segmentation. This approach is

based on the using variable contours which move

under the effect of this force and to tracking

boundaries and move are used. The idea of using a

flexible model to select specific features within an

image for the first time in [16] has been introduced,

nothing had not been done in this area. The goal is

to find an equation that can obtain a picture’s

contours .In other words, there must be a curve that

its boundaries segments the object. Since each

model requires a lot of steps to get good accuracy in

the segmentation, each method has its own time

needed to reach result. But this can be done with

fewer repetitions and combine them to achieve

better accuracy in less time. We use Chan-Vese

algorithm [19,20], An energy function is defined.

Aim will be to minimize the energy function and

minimizing the levels set Φ will do the

segmentation. In general, the energy function is

shown in the Equation (10).


60

F(Φ)=𝜇(∫ |∇𝐻(Φ)|𝑑𝑥Ω)𝑝 +

𝑣 ∫ 𝐻(Φ)𝑑𝑥 + 𝜆 ∫ |𝐼 − 𝑐1|2

ΩΩ𝐻(Φ)𝑑𝑥 +

𝜆2 ∫ |𝐼 − 𝑐2|2 (1 − 𝐻(Φ)𝑑𝑥

Ω

(10)

The parameters can be adjusted by the user. The

general case of Mumford-Shah function. In The

Mumford-Shah we set our parameters as P=1, v=0,

λ1=λ2=1 [17, 13]. H and I are defined as in the

previous step. C1 and C2, respectively, at the time

that ф is larger or smaller than zero it's defined as

Equation (11).

1 2

. ( ) .(1 H( ),

( ) (1 ( ))

I H dxdy I dxdyc c

H dxdy H dxdy

(11)

Using the Euler-Lagrange and gradient descent for

the level set function and the derivative we

minimize energy function as (12):

1

2 2

1 1 2 2

( )( )

( ) ( )

p

t

p div

I c p I c

(12)

After the discretization and linearization of

differential equations of minimizing the energy

function that is shown in Equation (13). 1

. ,

1

. 2

1

.

2 2 2 2

. . .

1

.

2 2 2 2

1. .

2

. 1 . 1 2

( ) ( . ( ) )

( ) / ( 1 1) / (2 )

( 1. ) / (2 ) ( ) / (2 )

( )( ( ( )) (

n n

i j i j

n n p

h i j

x n

i jx

x n n n

i j i j i j

x n

i jy

x n y n

i i j i j

n n

h i j i j i

t

p Lh

h h

j h h

I c I

2

. 2 ( )) .n

j c

(13)

δ is softened state of the delta function according to Equation (14).

2 2

1( )h

hx

h x

(14)

L is the length of the levels set in zero step and according to Equation (15) we have.

( ) ( )n n n

hL dxdy

(15)

We consider the Equation (16) constants for the

Equation (15).

12 2/4

1. . , 1 . 1

22 2/4

1. . 1, 1 1. 1

32/4 2

1. 1. , 1 .

42/4 2

1. 1. , .

1

( ) ( )

1

( ) ( )

1

( ) ( )

1

( 1) ( 1)

n n n n

i j i j i j i j

n n n n

i j i j i j i j

n n n n

i j i j i j i j

n n n n

i j i j i j i j

C

C

C

C

(16)

Using the Equation (16) definition finally we

achieve the Equation (17).

1 2 3 4

2 41

1 1

. .

1 1

. .

1 1 1 1

1. 1. 3 , 1 . 1

.

2 2

1 . 1 2 . 2

1 ( ) ( . ( ) ( )

( ) ( . ( ) )

( )

( )

( ( )) ( ( ))

n n n p

i j h i j

n n n p

i j h i j

n n n n

i j i j i j i j

n

h i j

n n

i j i j

tp L C c c c

h

tp L

h

C c c c

t

I c I c

(17)

The algorithm presented in Equation (17) is Chan-Vese algorithm [18,19,20] for segmentation. To increase the accuracy of the segmentation, output of the model that is an image with the same size as the original image is multiplied Pixel by pixel to the result of the previous step that is also with the same size as original image, to obtain the final optimal results.

4. Evaluation and Results

In this section, we discuss and compare the results

between the proposed approach and methods of

SVMLS and WKVLS. The method will be tested

on a phantom circle. Figure 4 consists of six circles

with different illumination intensities of 60, 90,

120, 130, 200 160 and Gaussian noise with given

variance and mean intensity of the class is also

added. Figure 4 shows the phantom simulation of

the results. And Figure 5 shows diagram without

phantom noise.


61

Figure 4. Circle phantom simulation

Figure 5. Diagram Without Noise

According to the diagram, the green line shows

original image and red line shows the result of the

proposed method, and the black lines show

SVMLS method. It is clear that the proposed

algorithm has followed the behavior of the image

very well. Figure 6 shows phantom simulation with

noise and Figure 7 shows diagram phantom noise.

Figure 6. Diagram with phantom noise

Figure 7. Intensities of pixels of the image and noise

simulation phantom.

The implementation results are shown below. It

should be noted that the parameters required to

implement the algorithm that can be observed in

Table 1.

Table 1. Basic Parameters of the Proposed Algorithm

Values Parameters Name

4.5 sigma

1 epsilon

.45 time step

7 Iteration_No_of_Algorthim_Runs

1/9*ones(3) Regularizing_Kernel_Filter

ones(4*sigma+1) Initializing_SVMLS_Kernel

4 Seg_Regions_No

4 Max_No_of_Processing_Images

The parameters which are initialized in Table 1 are

from the initial parameters to implement the

algorithms that have been written within the

MATLAB software. At the following, we will do

the results on brain images dataset, which the

selected images contains without noise, noise,

noise 3% and 9% that the obtained results are

represented Figures 8 , 9 and 10.


62

Figure 8. Segmentation on T1-MRI images without the

noise

Figure 9. Segmentation on T1-MRI image with 3% noise

Figure 10. Segmentation on T1-MRI image with 9%

noise

If we assume, top left the first image and bottom

right the ninth image, Respectively, the first image

is the result of segmentation of all segments, the

next image is sum of all the segments with equal

weight and the next of that is the sum of all

weighted image with same weight and in fact the

output of segmenting algorithm SVMLS. The

fourth image shows the original image, fifth Image,

displays active contour model and the sixth image

illustrates the combinative output and thus the

proposed method. Bottom row from left, shows the

result of masked SVMLS with ideal mask. This

action for result of the proposed method illustrated

in the middle of the bottom row. Finally, in the

lower right hand manually segmentation is

presented. It is clear that the proposed method

compared to SVMLS method is less different than

the manually segmentation method is.

To better illustrate the obtained results and to better

assess the results, we will use the curve of Receiver

operating characteristics (ROC) That the results of

ROC curve on the circle phantom without noise

and taking into consideration the noise are shown

in Table 2 and Figures 11 and 12. The parameters

of the ROC among other parameters used for the

analysis scan be noted these parameters are

including Sensitivity, Specificity, Precision,

Accuracy and Mean error rate. To obtain this

parameter you must convert image to binary, as

well as to obtain the parameter values of the ROC,

for each image, we have two thresholding step. We

have done this for masked result of the proposed

method, SVMLS method and manually

segmentation. And the values of TP, TN, FP and

FN calculated and from the values obtained here,

the five analytical components for the images of

circle simulating phantom and T1-MRI were

calculated. The Image of phantom of circle with

noise and without noise threshold with value of 0.2,

0.3 and 0.4. And results of thresholding for

SVMLS method, proposed method and for

manually segmented image (standard criterion) is

calculated. For the phantom of simulating circle

with noise and without noise, obtained point

calculated in Table 2 and it can be observed there.


63

Table 2. ROC PARAMETRS CANCULATED BY THE PROPOSED METHOD AND THE METHOD SVMLS FOR

CIRCLE PHANTOM

ROC curve for without noise circle phantom represented in Figure 11 and ROC curve for noisy circle phantom represented in Figure 12.

Figure 11. ROC curve for without noise circle phantom with proposed method and SVMLS method

Figure 12. ROC curve for noisy circle phantom with

proposed method and SVMLS method

In this part, the ROC curve results are done on the

brain images whose results are presented in Tables

3, 4 and 5. We have three T1-MRI dataset of the

brain (without noise, 3% noise, 9% noise) from

Circle phantom Without Noise

SVMLS Method Proposed Method

Mean

error rate

Accurac

y

Precisio

n

Specificit

y

Sensitivit

y

Mean

error rate

Accurac

y

Precisio

n

Specificit

y

Sensitivi

ty Threshold

0.0469 0.9531 0.7196 0.9467 1 0.007

4 0.9926 1 1 0.9385 0.2 Circle

withou

t noise 0.0469 0.9531 0.7196 0.9467 1 0.007

4 0.9926 1 1 0.9385 0.3

Circle phantom 0.001 Noise


Mean error rate

Accuracy

Precision

Specificity

Sensitivity

Mean

error

rate

Accuracy

Precision

Specificity

Sensitivity

Threshold

0.0322 0.9678 0.8969 0.9870 0.8270 0.023

4 0.9766 1 1 0.8058 0.2

Circle

0.001

noise

0.0333 0.9667 0.8860 0.9854 0.8295 0.022

9 0.9771 1 1 0.8093 0.3

0.0314 0.9686 0.9040 0.9880 0.8264 0.023

1 0.9769 1 1 0.8083 0.4



Mean

error rate

Accurac

y

Precisio

n

Specificit

y

Sensitivit

y

Mean

error rate

Accurac

y

Precisio

n

Specificit

y

Sensitivi

ty Threshold

0.0276 0.9724 0.9334 0.9919 0.8302 0.023

1 0.9769 1 1 0.8080 0.2

Circle

0.004

noise

0.0309 0.9691 0.9047 0.9880 0.8305 0.023

5 0.9765 1 1 0.8048 0.3

0.0295 0.9705 0.9208 0.9903 0.8257 0.023

6 0.9764 1 1 0.8035 0.4



Mean

error rate

Accurac

y

Precisio

n

Specificit

y

Sensitivit

y

Mean

error

rate

Accurac

y

Precisio

n

Specificit

y

Sensitivi

ty Threshold

0.0303 0.9697 0.9167 0.9898 0.8232 0.025

1 0.9749 1 1 0.7915 0.2

Circle

0.008 noise

0.0298 0.9702 0.9209 0.9903 0.8226 0.025

1 0.9749 1 1 0.7909 0.3

0.0284 0.9716 0.9249 0.9908 0.8311 0.023

9 0.9761 1 1 0.8013 0.4


64

each 8 slices of brain image selected and test has

been done on them and to convert to binary we use

thresholding, and for each image slices we have

done thresholding two time with values 0.3 and 0.4

and result of this thresholding were calculated for

SVMLS method, proposed method and manual

method(standard) and parameters calculated and

represented in Table 3 and 4 and 5.

Table 3. ROC Parameters Calculated By the Proposed Method and the Method SVMLS for Without Noise T1-MRI Image

T1-MRI Without Noise


Mean

error

rate

Accuracy Precision Specificity Sensitivity

Mean

error

rate

Accuracy Precision Specificity Sensitivity Threshold

0.0432 0.9568 0.9921 0.9929 0.9195 0.0156 0.9844 0.9817 0.9823 0.9866 0.3 T1-MRI Slice -

86 0.0467 0.9533 0.9926 0.9934 0.9117 0.0176 0.9824 0.9817 0.9823 0.9824 0.4

0.0423 0.9577 0.9920 0.9928 0.9213 0.0144 0.9856 0.9816 0.9821 0.9893 0.3 T1-MRI

Slice - 87

0.0443 0.9557 0.9922 0.9930 0.9170 0.0153 0.9847 0.9816 0.9821 0.9874 0.4

0.0437 0.9563 0.9918 0.9927 0.9186 0.0147 0.9853 0.9816 0.9821 0.9886 0.3 T1-MRI

Slice - 88

0.0458 0.9542 0.9922 0.9931 0.9140 0.0159 0.9841 0.9816 0.9821 0.9862 0.4

0.0438 0.9562 0.9917 0.9926 0.9185 0.0142 0.9858 0.9817 0.9822 0.9895 0.3 T1-MRI

Slice -

89 0.0458 0.9542 0.9923 0.9931 0.9139 0.0152 0.9848 0.9818 0.9823 0.9874 0.4

0.0464 0.9536 0.9924 0.9932 0.9125 0.0154 0.9846 0.9816 0.9821 0.9871 0.3 T1-MRI Slice -

90 0.0487 0.9513 0.9927 0.9936 0.9074 0.0164 0.9836 0.9816 0.9821 0.9851 0.4

0.0492 0.9508 0.9936 0.9944 0.9057 0.0134 0.9866 0.9815 0.9820 0.9913 0.3 T1-MRI Slice -

91 0.0513 0.9487 0.9940 0.9947 0.9011 0.0142 0.9858 0.9816 0.9820 0.9898 0.4

0.0569 0.9431 0.9944 0.9952 0.8892 0.0121 0.9879 0.9816 0.9820 0.9941 0.3 T1-MRI

Slice - 92

0.0601 0.9399 0.9947 0.9954 0.8823 0.0131 0.9869 0.9816 0.9820 0.9919 0.4

0.0605 0.9395 0.9960 0.9966 0.8804 0.0117 0.9883 0.9815 0.9819 0.9949 0.3 T1-MRI

Slice -

95 0.0626 0.9374 0.9963 0.9968 0.8758 0.0122 0.9878 0.9816 0.9820 0.9937 0.4

In Table 3 estimates the comparison and the results

of evaluation parameters at images without noise

for the proposed method and SVMLS method that

their results show that the classification accuracy of

the proposed method is better than SVMLS.

Table 4. ROC Parameters Calculated By the Proposed Method and the Method SVMLS for %3 Noise T1-MRI Image

T1-MRI 3% Noise

SVMLS Method Proposed Method Mean

error

rate

Accuracy Precision Specificity Sensitivi

ty

Mean

error rate

Accurac

y

Precisio

n Specificity Sensitivity

Thresho

ld

0.0405 0.9595 0.9917 0.9925 0.9254 0.0140 0.9860 0.9816 0.9821 0.9901 0.3 T1-MRI

Slice - 86 0.0430 0.9570 0.9922 0.9930 0.9198 0.0152 0.9848 0.9817 0.9822 0.9875 0.4

0.0430 0.9570 0.9910 0.9919 0.9208 0.0146 0.9854 0.9816 0.9821 0.9888 0.3 T1-MRI

Slice - 87 0.0455 0.9545 0.9917 0.9926 0.9150 0.0157 0.9843 0.9815 0.9821 0.9865 0.4

0.0430 0.9570 0.9907 0.9916 0.9212 0.0140 0.9860 0.9815 0.9820 0.9903 0.3 T1-MRI

Slice - 88 0.0452 0.9548 0.9915 0.9924 0.9159 0.0150 0.9850 0.9815 0.9820 0.9881 0.4

0.0434 0.9566 0.9915 0.9923 0.9196 0.0144 0.9856 0.9816 0.9821 0.9892 0.3 T1-MRI

Slice - 89 0.0458 0.9542 0.9921 0.9929 0.9141 0.0157 0.9843 0.9816 0.9821 0.9866 0.4

0.0472 0.9528 0.9919 0.9928 0.9114 0.0153 0.9847 0.9815 0.9820 0.9875 0.3 T1-MRI Slice - 90 0.0496 0.9504 0.9924 0.9933 0.9059 0.0165 0.9835 0.9815 0.9820 0.9849 0.4

0.0508 0.9492 0.9935 0.9943 0.9025 0.0138 0.9862 0.9815 0.9820 0.9905 0.3 T1-MRI

Slice - 91 0.0540 0.9460 0.9940 0.9947 0.8955 0.0151 0.9849 0.9815 0.9820 0.9879 0.4

0.0562 0.9438 0.9944 0.9951 0.8907 0.0135 0.9865 0.9815 0.9820 0.9911 0.3 T1-MRI

Slice - 92 0.0606 0.9394 0.9949 0.9956 0.8812 0.0150 0.9850 0.9815 0.9820 0.9880 0.4

0.0588 0.9412 0.9956 0.9962 0.8843 0.0111 0.9889 0.9816 0.9819 0.9961 0.3 T1-MRI

Slice - 95 0.0614 0.9386 0.9959 0.9965 0.8787 0.0116 0.9884 0.9816 0.9820 0.9950 0.4


65

In Table 4 estimates the comparison and the results

of evaluation parameters at images 3% noise for the

proposed method and SVMLS method the results

show that the classification accuracy of the

proposed method is better than SVMLS.

Table 5. Roc Parameters Calculate by the Proposed Method and the Method SVMLS for 9% Noise T1-Mri Image

T1-MRI %9 Noise

SVMLS Method Proposed Method Mean

error

rate

Accuracy Precision Specificity Sensitivity

Mean

error

rate

Accuracy Precision Specificity Sensitivity Thre

shold

0.0109 0.9891 0.9822 0.9959 0.9825 0.0103 0.9897 0.9816 0.9977 0.9819 0.3 T1-MRI Slice - 86 0.0452 0.9548 0.9911 0.9161 0.9921 0.0158 0.9842 0.9815 0.9865 0.9820 0.4

0.0107 0.9893 0.9827 0.9958 0.9830 0.0103 0.9897 0.9816 0.9977 0.9819 0.3 T1-MRI

Slice - 87 0.0471 0.9529 0.9911 0.9124 0.9921 0.0158 0.9842 0.9815 0.9864 0.9820 0.4

0.0144 0.9856 0.9834 0.9874 0.9839 0.0105 0.9895 0.9816 0.9974 0.9819 0.3 T1-MRI

Slice - 88 0.0443 0.9557 0.9911 0.9181 0.9920 0.0141 0.9859 0.9816 0.9898 0.9820 0.4

0.0206 0.9794 0.9861 0.9718 0.9867 0.0107 0.9893 0.9816 0.9968 0.9819 0.3 T1-MRI

Slice - 89 0.0468 0.9532 0.9912 0.9129 0.9922 0.0159 0.9841 0.9816 0.9862 0.9821 0.4

0.0136 0.9864 0.9839 0.9886 0.9843 0.0104 0.9896 0.9816 0.9976 0.9819 0.3 T1-MRI

Slice - 90 0.0500 0.9500 0.9926 0.9050 0.9934 0.0154 0.9846 0.9815 0.9874 0.9820 0.4

0.0136 0.9864 0.9844 0.9879 0.9848 0.0104 0.9896 0.9816 0.9976 0.9819 0.3 T1-MRI Slice - 91 0.0544 0.9456 0.9929 0.8957 0.9938 0.0149 0.9851 0.9815 0.9883 0.9820 0.4

0.0126 0.9874 0.9842 0.9903 0.9846 0.0103 0.9897 0.9816 0.9977 0.9819 0.3 T1-MRI Slice - 92 0.0587 0.9413 0.9942 0.8856 0.9950 0.0137 0.9863 0.9815 0.9909 0.9819 0.4

0.0356 0.9644 0.9915 0.9356 0.9922 0.0104 0.9896 0.9816 0.9975 0.9819 0.3 T1-MRI

Slice - 95 0.0615 0.9385 0.9954 0.8788 0.9960 0.0119 0.9881 0.9817 0.9942 0.9821 0.4

In Table 5, estimates the comparison and the results

of evaluation parameters at images 9% noise for the

proposed method and SVMLS method the results

show that the classification accuracy of the

proposed method is better than SVMLS. At the

following, we will compare and study the

important performance of ROC curve parameters

that the results and the obtained data are

represented at 6, 7 and 8.

Table 6. Performance Measurement Parameters By

Proposed Method And The Method SVMLS For Without

Noise T1-MRI Image

T1-MRI Without Noise

Propose

d

Method

(%)

Svmls

Metho

d

)%(

Definition Measure

98.90 90.55 TP/(TP+FN) Sensitivit

y

98.21 99.39 TN/(TN+FP) Specificit

y

98.16 99.31 TP/(TP+FP) Precision

98.55 95.05 (TP+TN)/(TP+TN+FP+FN

) Accuracy

1.44 4.94 (FP+FN)/(TP+TN+FP+FN

)

Mean

error rate

According to Table 6, it is determined that the performance measurement of the proposed method was better in terms of classification accuracy. Also to better assess and view the results, we can see the results on graphs in Figure 13.

Table 7. Performance measurement parameters by

proposed method and the method SVMLS for %3 noise

T1-MRI image

T1-MRI 3% Noise

Proposed

Method

(%)

Svmls

Method

)%(

Definition Measure

98.92 90.63 TP/(TP+FN) Sensitivity

98.20 99.36 TN/(TN+FP) Specificity


98.55 95.07 (TP+TN)/(TP+TN+FP

+FN) Accuracy

1.44 4.92 (FP+FN)/(TP+TN+FP

+FN)

Mean

error rate

According to Table 7, it is determined that the performance measurement of the proposed method was better in terms of classification accuracy. Also to better assess and view the results, we can see the results on graphs in Figure 14.

Table 8. Performance measurement parameters by

proposed method and the method SVMLS for 9% Noise

T1-MRI image

T1-MRI 9% Noise

Proposed

Method

(%)

)%(

Svmls

Method

Definition Measure

98.19 98.92 TP/(TP+FN) Sensitivity

99.31 94.23 TN/(TN+FP) Specificity


98.74 96.62 (TP+TN)/(TP+TN+FP+FN) Accuracy

1.25 3.37 (FP+FN)/(TP+TN+FP+FN) Mean

error rate


66

According to Table 8, it is determined that the

performance measurement of the proposed method

was better in terms of classification accuracy. Also

to better assess and view the results, we can see the

results on graphs in Figure 15. ROC curves for

eight noise-free image of the brain with the

proposed method showed in figure 13 and with 3%

and 9% noise showed in Figure 14 and 15

respectively.

Figure 13. ROC curves for eight without noise image of

the brain with the proposed method and SVMLS

Figure 14. ROC curves for eight with 3% noise image of


Figure 15. ROC curves for eight with 9% noise image of


5. Conclusions and Future Works In this paper, a multi-stage level set method and the active contour was presented so that the bias correction and images segmentation is able to be done simultaneously. Smoothing bias is inherently guaranteed without any additional cost by using normalized convolution. According to the generally accepted model, images with non-uniform intensity and obtained local intensity clustering features, we define an energy function of the level set functions that shows one part of image domain and a bias field for none-uniform intensities. Thus, the segmentation and bias field estimation by minimizing an energy function to be implemented jointly. Slowly changing bias field feature obtained from the proposed energy naturally given expression is guaranteed in our framework, Without having to enter a clear Flattening value in bias field. Finally make the method stronger by combining with active contour model in order to obtain more accurate results. The results showed that this method improves the accuracy more than the other methods.

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