In this paper, we have compared three level setbased active contour (LSAC) methods on inhomogeneous MR image segmentation which is known as an important role of brain diseases to diagnosis and treatment in early. MR image is often occurred a problem with similar intensities and weak boundaries which have been causing many segmentation methods. However, LSAC method could be able to segment the targets such as the level set based on the local image fitting energy, the local binary fitting energy, and local Gaussian distribution fitting energy. Our implemented and tested the subcortical image segmentations were the corpus callosum and hippocampus and finally demonstrated their effectiveness. Consequently, the level set based on local Gaussian distribution fitting energy has obtained the best model to accurate and robust for the subcortical image segmentation.
1. INTRODUCTION
Segmentation is an important task in medical image analysis for the process of partition a given image into interested regions for a specific purpose. However, the medical image is often corrupted by noise, lack of boundaries, and also inhomogeneity due to technical limitations or artifacts introduced by the object being imaged. In particular, the inhomogeneities in magnetic resonance images arise from the nonuniform magnetic fields which produced by radiofrequency coils as well as from variations in object susceptibility. Especially the intensity of the hippocampus and corpus callosum are difficult to distinguish with other tissues located around them that cause misclassification between interested region and background. Therefore, the segmentation is challenging difficulty in medical images.
In previous research, the level setbased active contour methods have been extensively used in medical image segmentation because of its advantageous properties such as they can achieve subpixel accuracy of object boundaries. They also can be easily formulated under principled energy minimization framework, and allow incorporation of various prior knowledge. Moreover, they can provide smooth contours to the object being segmented
[1
,
2]
. The level set methods can be categorized into two types: firstly the edgebased model which is used image gradient to stop the contours on the boundaries of interested regions and attract the contours to the desired boundaries, even the controlling contours to expend or shrink
[3

5]
. Secondly, the regionbased model is used the image statistical information to construct constraints but more powerful than the edgebased model for image segmentation on the interested object with lack of boundaries or even without boundaries
[6

8]
. Zhang et al. proposed a novel active contour model that embeds the image information which can be used to segment images with inhomogeneous intensity, by utilizing the local image information to construct a local image fitting (LIF) energy functional
[9]
. The similar previous studies are also found in literatures for the differences between the fitting image and the original image
[10]
. Moreover, a novel method is used to regularize the level set function by using Gaussian kernel filtering for the smoothness of the level set function which is avoided the reinitialization step that causes computationally expensive. Recently, local intensity information has been incorporated into the active contour models
[11
,
12]
for more accurate segmentation, especially in the presence of inhomogeneous intensity. For example, Li et al.
[13]
proposed a local binary fitting (LBF) energy in a regionbased model for more accurate and efficient segmentation. The LBF model draws upon local intensity means, which enables it to cope with reinitialization. In order to make possibility of the image reinitialization segmentation Wang et al.
[14]
also proposed an active contour driven by local Gaussian distribution fitting (LGDF), starting from a point of the local image data then the local energy integrated over the entire image domain by using Gaussian distributions with different means and variances to described the local image intensities. The LGDF energy then incorporated into a variation level set formulation with a level set regularization term. There are two variables of the energy functional such as local intensity means and variances which are derived from a variational principle
[14
,
15]
. Izmantoko. et al
[16]
presented an active shape model (ASM) which uses a prior knowledge from sample images with the object in different shape and size to make a model for segmenting another image. The evaluation of active contour and active shape model for medical image segmentation is also presented in
[17]
.
In our study, we have evaluated three level setbased active contour models for subcortical MR brain images to the local image fitting model
[9]
, local binary fitting model
[13]
, and local Gaussian distribution fitting model
[14]
, by applying them to the corpus callosum and hippocamus. These models are based on a level set evolution and variation framework. In the rest part of this paper is organized as follows. In section II, we briefly describe a few level setbase active contour method that uses in this study. Section III shows implementation results to demonstrate the effectiveness of the chosen level setbased active contour methods. Finally the conclusion of this paper is served in section IV.
2. METHODOLOGY
In this section, we provide the brief introduction of the models which used in our study. The three level setbased active contour models were used such as the local image fitting (LIF), the local binary fitting (LBF), and the local Gaussian distribution fitting (LGDF) models to segment MR brain images. In order to evaluate these models are able to the suitable model for the MR brain image segmentation.
 2.1 The LIF model
The local image fitting (LIF) model was recently proposed by Zhang et. al
[9]
for segmenting images with the intensity inhomogeneity. It provides less computational complexity than the classical active contour. The major contribution of this model is to introduce a local image fitting energy into a variation framework. The LIF energy function was also used the Gaussian filtering. However, the reinitialization is still necessary for this method. The LIF energy functional defines as follows:
where
ϕ
is a level set function,
I
(
x
) is the original image, and
I^{LFI}
is the local fitted image defined as follows:
Heaviside function
H_{ε}
(
ϕ
) is usually approximated by a smoothing function defined as
the weighting parameters (
m
_{1}
,
m
_{2}
) are defined as
where
W_{k}
(
x
) is a rectangular window function, in this study a truncated Gaussian window with size (4
k
+1) by (4
k
+1) is used which is smaller than the standard deviation.
Minimizing energy function
E^{LIF}
(
ϕ
) with respect to
ϕ
, one can get the level set formulation of the LIF model as
where
δ_{ε}
(
ϕ
) is regularized Dirac function, the derivative of
H
_{ε}
is the following smooth function defined as
 2.2 The LBF model
The local binary fitting (LBF) model has been recently proposed by Li et al
[13]
for segmenting images. By utilizing image information in local regions and incorporating a local binary fitting energy with a kernel function
K
(
x
) as a Gaussian kernel into a level set formulation, the model is able to extract interested region with inhomogeneous intensity and using two fitting functions
f
_{1}
(
x
) and
f
2(
x
) to localize the inside and outside intensity of the contour. The LBF energy function can be written as:
The kernel function
K
(
x
) chooses as a Gaussian kerne
K_{σ}
(
x
) with a localization property such that
K_{σ}
(
xy
) decreases and approaches zero as y goes far away from
x
.The LBF energy function with Heaviside function
H_{ε}
(
ϕ
) is defined in Eq. (3) which approximates by a smoothing function e.g., rewritten as:
where
λ
_{1}
and
λ
_{2}
are the weighting positive constants. The distance regularizing term is added to ensure the level set evolution which is stable
the level set regularization term used to penalize the deviation of the level set function
ϕ
from a signed distance function. To regularize the zero level contour of
ϕ
, which is given by
the term in (10) is the length of the zero level set contour of
ϕ
.
δ
(
ϕ
) is regularized Dirac function as defined in Eq. (6). The entire energy functional can be defined as
Minimizing the energy function in Eq. (11) with respect to
ϕ
, we have the gradient descent flow as follows:
where
with
 2.3 The LGDF model
The local Gaussian distribution fitting (LGDF) model has been recently proposed by Li Wang et. al
[14]
for segmenting images with inhomogeneous intensity. The image domain can be partitioned into two regions corresponding to the foreground object and background. These two regions can be represented as the regions outside and inside the zero level set of function
ϕ
. The energy as in terms of
ϕ
,
u_{i}
and
σ_{i}
^{2}
can be expressed
where M
_{1}
(
ϕ
(
x
))=
H
(
ϕ
(
x
)) and M
_{2}
(
ϕ
(
x
))=1
H
(
ϕ
(
x
)). Thus the energy
E^{LGDF}
can be rewritten as
where
H
(
ϕ
(
x
)) is Heaviside function as defined in Eq. (3).
For more accurate computation involving the level set function and its evolution, we need to regularize the level set function by penalizing its deviation from a signed distance function
[18]
, the energy function which is defined in Eq. (9). The level set method needs to regularize the zero level set by penalizing its length to drive a smooth contour during evolution as defined in Eq. (10). Therefore, the entire energy function as follows
where
ν
and
μ
are positive weighting constants. The minimization of the energy function is in Eq. (17) with respect to
ϕ
where
δ
(
ϕ
) is Dirac function as defined in Eq. (6). The new imagebased terms (
e
_{1}
,
e
_{2}
) are independent of the scale of local intensity caused by inhomogeneous intensity.
Therefore, the new local intensity means
μ_{i}
(
x
) and variances
σ_{i}
(
x
)
^{2}
can define as
3. EXPERIMENTAL RESULTS
We have taken the MR images which contained the corpus callosum and normal hippocampus from Haeundae Paik Hospital, Korea with the scanner type of 3.0T and subject age is 29 years old man. However, to illustrate the segmenting process in the real implementation, we performed our experiments in this study following the three LSBAC models such as; the LIF, the LBF, and the LGDF model dealing with MR brain images. To compare the efficient performance of these models, we firstly show the segmentation the target with satisfied results. The based on the results, we could choose the suitable model for medical image segmentation.
Fig. 1
shows the segmentation results obtained by using the LIF, LBF, and LGDF methods respectively. In this case, the initial contours are located at the same position in the image. The test image is a corpus callosum in an MR brain image. As we can see
Fig. 1
LIF model which is failed to segment the corpus callosum as shown in
Fig.1
(a). The LBF model can segment the Corpus Callosum but the contour is not smooth as shown in
Fig. 1
(b). With the LGDF model, the segmented result is satisfied since it exactly segment the corpus callosum.
The segmented results of Corpus Callosum on MR brain images by (a) LIF, (b) LBF, and (c) LGDF method. An initial curve, two curve evolutions and the final result were shown from the left to right column respectively.
Fig. 2
is comparison of the LIF, the LBF, and the LGDF models in segmenting the real hippocampus MR images. The hippocampus in this case is an intensity inhomogeneous image. One can see from this figure, the LIF fails to segment the image with some parts invisible as shown in
Fig. 2
(a). With the LBF model, even though the segmentation result as in Fig. (b) is better than that by the LIF model, it also detect an unexpected region. In
Fig. 2
(c) shows the accurate result when using the LGDF model.
The segmented results on the hippocampus MR images by (a) LIF, (b) LBF, and (c) LGDF method. An initial curve, two curve evolutions and the final result have shown from the left to right column respectively.
4. CONCLUSION
This paper has presented the level set based on the LIF, the LBF, and LGDF model for general classification of imagery whose regions of interest cannot be distinguished according to their respective pixel intensity distributions. While a number of active contour models were proposed to solve the image segmentation problem but only a few models have been proposed to solve the MR brain image segmentation problem due to the efficiency of methods and also the difficulty on MR brain image itself which cause many algorithms failed to segment hippocampus or corpus callosum. Therefore, this study has presented the performance validation of some recent level setbased active contour methods when dealing with intensity inhomogeneous images. The LGDF model has given the best result visualization for the subcortical image segmentation.
BIO
Bouasone Vongphachanh
He has been a graduate student at the Department of Computer Engineering of Inje University, Korea and he has joined the Medical Image Technology Laboratory (MITL). He has received his B.S. degree from the Department of Mathematics, Souphanouvong University, Laos in 2010 and M.S. degree of the Department of Computer Engineering of Inje University, Korea in 2014. Now he is working at Tang Dee Electronics Co. Ltd. and cooperated with KOICA for establishing the electronic medical record system and healthcare networks for hospital in Luang Prabang, Laos. His main research interests are image segmentation and image visualization.
HeungKook Choi
He has gone the undergraduate studying and graduate studying in computer science and engineering at the Department of Electrical Engineering of Linköping University, Sweden (19841990) and Ph.D. studying in computerized image analysis at the Center for Image Analysis of Uppsala University, Sweden (19901996). He was President of Industry and Academic Cooperation Foundation at Inje University and President of Korea Multimedia Society. Currently he is President of Gimhae Biomedical Center. His interesting research fields are in computer graphics, virtual reality, and medical image processing and analysis.
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