Accurate Brain Extraction using Active Shape Model and Convolutional
Neural Networks
Nguyen Ho Minh Duya , Nguyen Manh Duya , Mai Thanh Nhat Truongb , Pham The Baoa , Nguyen Thanh
Binha,∗
a Department

arXiv:1802.01268v1 [] 5 Feb 2018

b Department

of Mathematics and Computer Science, Ho Chi Minh City University of Science, Ho Chi Minh City, Viet Nam
of Electrical, Electronic and Control Engineering, Hankyong National University, Anseong, Gyeonggi, Republic
of Korea

Abstract
Brain extraction or skull stripping is a fundamental procedure in most of neuroimaging processing systems.
The performance of this procedure has had a critical impact on the success of neuroimaging analysis. After
several years of research and development, brain extraction still remains a challenging problem. Brain
morphology and intensity characteristics are variable and complex, usually because of the variability in
conditions of image data acquisition, or abnormalities in data such as tumor regions. These difficulties
prevent brain extraction methods from producing acceptable results. In this paper, we propose an effective
method for skull stripping in Magnetic Resonance Imaging (MRI) scans named ASM-CNN. Our system is a
combination of Active Shape Model (ASM) and Convolutional Neural Network (CNN), taking full advantage
of these two methods to achieve remarkable results. Instead of working with 3D structures, we process 2D
image sequences in sagittal plane. First, we divide images into different groups such that, in each group,
the shapes and structures of brain boundaries have similar appearances. This allows developing precise
algorithms for each group in order to produce high performance segmentation results. Second, a modified
version of ASM is used to detect the brain boundary in images by utilizing prior knowledge of each group.
Finally, CNN and the post-processing methods such as Conditional Random Field, Gaussian Process and
some special rules are applied to refine segmentation contour produced by ASM. We compared ASM-CNN
with the latest version of five state-of-the-art, publicly available methods, namely BET, BSE, 3DSS, ROBEX
and BEAST. The evaluation was carried out by using three public datasets IBSR, LPBA and OASIS. The
experimental results show that the proposed method outperforms five states-of-the-art algorithms, surpassing
all the other methods by a significant margin in all experiments.
Keywords: skull stripping, brain extraction, convolutional neural network, active shape model, conditional
random field, gaussian process

∗ Corresponding

author
Email address: ngtbinh@hcmus.edu.vn (Nguyen Thanh Binh)

Preprint submitted to arXiv

1. Introduction
Whole brain segmentation is the problem of extracting brain regions from volumetric data, such as
Magnetic Resonance Imaging (MRI) or Computed Tomography (CT) scans. The results of this process is
segmentation map indicating brain regions after removing non-brain tissue such as eyes, fat, bone, marrow,
and dura. Brain extraction is the first step in most neuroimaging analysis systems which usually consists
of brain tissue classification and volumetric measurement [1], template construction [2], and cortical and
sub-cortical surface analysis [3]. Early preprocessing steps such as bias field correction can also benefit from
brain extraction [4]. Therefore, there is a need for high performance brain extraction methods that can
produce accurate segmentation results.
Automatic skull stripping is a solution to replace manual brain delineation for the purpose of reducing
processing time and preventing any kind of human bias in the results. This is especially true in large scale
studies, where thousands of images with different characteristics and significant anatomical variations are
examined. Most skull stripping methods are optimized and validated for MRI T1-weighted images, since
high resolution T1-weighted structural images are prevalent in clinical studies [5]. Furthermore, T1-weighted
images provide excellent contrast between different brain tissues, making it the leading imaging standard
for volumetric measurements [6]. However, segmentation on T1-weighted data is generally a daunting task
due to the complex nature of the images (ill-defined boundaries, low contrast) and the lack of standard in
image intensity. Several methods have been proposed in the recent years. However, these methods show
good performance only on certain datasets, they produce low quality results when the acquisition conditions
or study populations change [5].
Existing brain extraction methods can be divided into four categories, namely edge-based, templatebased, label fusion with atlas-based and non-local patch based [6]. Edge-based methods focus on detecting
edges between brain and non-brain regions by considering differences in appearance of these structures.
There are several techniques have been employed such as watershed [7], level set [8], histogram analysis [9],
morphological filtering [10], region growing [11], edge detection [12], graph cuts [13], and convolutional neural
networks [14]. Although these methods have proven its effectiveness and achieved comparable results, their
performance tend to be less accurate when working with pathology, different sites, scanners, and imaging
acquisition protocols.
Template-based methods register the subject to a template via affine transform [15] or deformable models
[16] to create an initial estimate for the brain mask. After that, the boundary of brain mask is segmented
again by a classifier, which helps increase the accuracy of final result. Templates can involve one or more
distinctive atlases. Template-based methods are robust, stable in different conditions and highly accurate.
Label fusion with atlas-based techniques, such as Multi-Atlas Propagation and Segmentation (MAPS)
[17], Advanced Normalization Tools (ANTs) [18], and Pincram [19], implement registration of multiple atlases
to a target subject by using deformable models. After being registered to the target space, the brain masks in
all atlases are combined together by using Simultaneous Truth And Performance Level Estimation (STAPLE)
2

[20] or joint label fusion. Because the main operations of these approaches are registration process, their
performance depends on the accuracy of registration and quality of brain mask in each atlas. In addition,
the variability representation in brain anatomy usually requires large number of atlases, hence these methods
usually are time-consuming and computationally intensive.
The last category is non-local patch based methods. At first, these methods transform atlases to subject
space by using affine registration in order to estimate the initial brain mask of the subject. Then, a neighborhood searching process for each small patch, which is around the initial estimates of brain boundary, is
performed. Patches are derived from the registered atlases and located within the neighborhood of target
patch. Then the patches are associated together and similarity weights are computed to generate the final
brain mask. Several methods such as Brain Extraction using non-local Segmentation Technique (BEAST)
[21], Multi-cONtrast brain STRipping (MONSTR) [6] are inspired by this ideas and achieved remarkable performance in aspects of both accuracy and robustness. However, one difficulty of this approach is pinpointing
optimal setting for parameters such as number of atlases or window size. Additionally, in researches related
to disease study, the brain regions in MRI scans usually contain lesion tissues. Therefore, atlases from T1weighted images may not be optimal for detecting brain boundaries since intensity values of structures such
as hemorrhages, tumors, or lesions may be similar to that of non-brain tissues. To overcome this problem,
non-local based methods use different MR acquisition protocols to obtain complementary information. As a
result, it is a complex task and requires more processing time.
In this research, we present a novel approach for brain extraction in T1-weighted MRI data. Our system
is a combination of Active Shape Model (ASM) [22] and Convolutional Neural Network (CNN) [23], hence the
name ASM-CNN. Unlike existing methods, our approach consider brain extraction problem as a segmentation
task for 2D image sequences in sagittal plane instead of working with 3D structure. This approach has several
benefits. First, it allows developing specific algorithms when dealing with images which have different
brain boundary silhouettes. Along image sequences, the shape of brain boundaries and brain sizes vary
significantly. Especially for sagittal slices located at the beginning and ending parts of 3D MRI volumes,
the brain regions are small and the boundaries are very complex. Based on prior knowledge about brain
structures, we developed specific rules representing the relationships between brain tissues. These rules
was applied directly to control the segmentation process effectively. Second, images in sagittal plane are
symmetry across two hemispheres. By utilizing this property, we are able to predict general shape of brain
mask based on the positions of slices. This property also enables us to establish more extensive and accurate
rules for segmentation.
ASM-CNN comprises three main stages: dividing images into groups, applying ASM to detect the brain
boundaries, and finally using CNN also post-processing methods based on Conditional Random Field (CRF),
Gaussian Process (GP) and special rules to refine segmentation contour. In the first stage, all images in
sagittal plane are divided into three groups, namely group I, II, and III. The number of groups was decided
according to our analysis on boundaries of brain masks. The divide of images is performed by a Support

3

Vector Machine (SVM) classifier and a set of rates learned from data, for the purpose of determining position
for each group. In group II and III, images have similar shapes and structures while group I consists of images
which have small brain sizes and complex structures. In the next stage, ASM is applied to group II and
group III to estimate initial contours for brain mask. After that, these contours are refined using CNN
before fed into post-processing based on CRF to obtain the final segmentation. For group I, because the
shapes of brain are complex and the sizes of brain regions are smaller than that in other groups, we take
the segmentation result of the slice in group II which is right next to the beginning position of group I and
use it as an initial brain mask. This brain mask is then fed into CNN for further analysis with specific
rules and GP to produce high quality results. The flowchart of our system is given in Figures 1. The main
contributions of the proposed method are:
1. Our approach is based on processing 2D images, this helps increase accuracy in segmenting small-sized
brain regions while preserving stable performance in overall segmentation.
2. CNN with high-level feature representations is utilized to refine voxels around brain boundaries. In
addition, global spatial information of each voxels is combined with features from CNN by using deep
neural networks. In this way, the proposed method is able to represent global and local features
simultaneously.
3. ASM is applied to different groups. The similarity of brain contours in each group allows ASM to detect
the general properties of boundaries, guaranteeing the geometry attributes of object thus enhancing
the accuracy of segmentation results.
4. Finally, our framework does not depend on any specific MRI format so that it can be applied effectively
in various acquisitions conditions.
The remainder of this paper is organized as follows. In section 2, we introduce several notations, and
present the design and algorithms of our system. In section 3, we report the experimental results, where the
proposed method was applied to three public datasets, namely IBSR, LPBA, OASIS, and compared with
five state-of-the-art brain extraction methods. Section 4 gives further analysis regarding important issues of
the proposed method and discussions for future research. The conclusions of this research are presented in
Section 5.

4

5
Figure 1: Flowchart of proposed brain extraction algorithm.

Figure 2: The illustration of the order of three groups in Sagittal plane.

2. Methodology
In neuroimaging, a three-plane coordinate system is used to describe the standard anatomical position of
human body. These imaging planes are transverse plane, sagittal plane, and coronal plane. Transverse plane
is an X-Z plane and parallel to the ground. Sagittal plane is an Y-Z plane and perpendicular to transverse
plane, separating the left side and the right side. Coronal plane is a Y-X plane and perpendicular to sagittal
plane, separating the front and the back. In our method, we choose to process 2D sagittal slices because
human brains are nearly symmetrical with respect to the mid-sagittal plane. This property enable us predict
the general shapes of brain regions more accurately. In the following subsections, we describe three main
stages of the proposed method for brain extraction.
2.1. Dividing sagittal slices into groups
The first stage of the algorithm is dividing sagittal slices into groups. The rules for division is based on
our analysis on shapes of brain regions. Slices whose brain regions have similar shapes will be put in the
same group. Figure 3 indicates some images in group I. The areas of brains in this group are small compared
to the sizes of images. Figures 4 and 5 illustrate images in group II and III, respectively. Brain sizes in these
groups are relatively large, and in group III, brain regions extend out at the lower left corner of images. Due
to the symmetry of brain, from the first to the last sagittal slice, the assigned groups of slices would be from
group I to group II, then group III, to group II again and then group I. Figure 2 depicts how three groups
are divided in sagittal axis. The main goal of this stage is to group images which have similar brain shapes
for the purpose of maximizing the performance of ASM in the next stage.
Before presenting our method in this stage, we introduce the notations used to describe the algorithms:
• P = {p1 , p2 , ..., pm }: the set of people in each dataset, pi (1 ≤ i ≤ m) is the ith person.
• N = {n1 , n2 , ..., nm }: the set that indicates the numbers of 2D images of a person P where nj (1 ≤
j ≤ m) is the number of 2D images of pj .
6

• Ipj = {Ipj 1 , Ipj 2 , ..., Ipj nj }: the set of images of person pj where Ipj k (1 ≤ k ≤ nj ) is the kth image of
pj .
• G = {G1 , G2 , G3 }: image groups where Gq (1 ≤ q ≤ 3) is the set of images in group q for all people.
• G1ph = {G1ph 1 , G1ph 2 , ..., G1ph a },
G2ph = {G2ph 1 , G2ph 2 , ..., G2ph b },
G3ph = {G3ph 1 , G3ph 2 , ..., G3ph c },
represent the set of images in group I, group II, and group III respectively for person ph where a+b+c =
nh .
• M12 , M23 : the models trained by SVM for classify images between group I and group II, group II and
group III.
• R1 , R2 , R3 , R4 : the rates used for estimating the positions of slices in each group.
In this stage, we train an SVM classifier for the dividing task (Algorithm 1), in which the feature used for
training is the histogram of oriented gradients (HOG) [24] extracted from a sub-rectangle. The sub-rectangle
in Algorithm 1 is illustrated in Figure 6, which indicates the differences between brain shapes in different
groups. Figures 6a and 6b are two adjacent slices from group II and group I, respectively. As shown in
this figure, the brain in 6a has a small tail at the lower left part, while the brain in 6b does not. It is
apparent that the brain shapes are significantly different even though the slices are adjacent. Similarly, 6c
and 6d are two adjacent slices from, respectively, group II and group III. The brain shape in group II is more
convex, while that in group III is concave at the lower right part. We utilize these differences to maximize
the classification performance of SVM. Algorithm 2 is used to divide sagittal slices of any MRI volumes into
groups, using the SVM model produced by Algorithm 1. In the next stage, we use ASM to estimate initial
contours for brain masks of slices in group II and group III. For group I, because the shapes of brain are
complex and the sizes of brain regions are smaller than that in other groups, we need specific algorithms for
this group. The algorithms for brain extraction in group I are detailed in subsection 2.4.

Figure 3: Typical appearances of slices in group I.

7

Algorithm 1: Training classifiers for dividing images to groups
Input : P
Output: M12 , M23 , R1 , R2 , R3 , R4
1

foreach person Pj ∈ P do

2

select k1 , k2 , k3 , k4 such that:

3

A = {Ipj 1 , Ipj 2 , ..., Ipj k1 } ∈ G1pj

4

B = {Ipj k1 +1 , Ipj k1 +2 , ..., Ipj k2 } ∈ G2pj

5

C = {Ipj k2 +1 , Ipj k2 +2 , ..., Ipj k3 } ∈ G3pj

6

D = {Ipj k3 +1 , Ipj k3 +2 , ..., Ipj k4 } ∈ G2pj

7

insert:

8

Gxpj to vector Gx (x ∈ 1, 2, 3)

9

ky /nj to vector Ratey (y ∈ 1, 2, 3, 4)

10

end

11

foreach group Gi ∈ G do

12

select constant k

13

foreach image I ∈ Gi do

14

Rec ← Extract rectangle containing the skull of I using Algorithm5

15

SubRec ← Extract sub rectangle from Rec with k

16

f eature ← Calculate feature for I in SubRec with HOG

17

insert f eature to vector Fi

18

end

19

end

20

M12 ← Create model using SVM algorithm, F1 , F2

21

M23 ← Create model using SVM algorithm, F2 , F3

22

Rid ← mean (Rateid ); id ∈ 1, 2, 3, 4)

23

return M12 , M23 , R1 , R2 , R3 , R4

8

Algorithm 2: Dividing images to three groups
Input : M12 , M23 , R1 , R2 , R3 , R4 , Ipj
Output: G1pj , G2pj , G3pj
1

Ri new ← Ri .nj (i ∈ {1, 2, 3, 4}), nj is the number images of pj

2

for id ← R1, new − 10 to R1, new + 10 do

3

if M12 (Ipj id ) == 0 then

4

insert A = {Ipj 1 , Ipj 2 , ..., Ipj id−1 } to vector G1pj

5

R1, new ← id − 1

6

break

7

end

8

end

9

for id ← R2, new − 10 to R2, new + 10 do

10

if M23 (Ipj id ) == 0 then

11

insert B = {Ipj R1,new +1 , Ipj R1,new +2 , ..., Ipj id−1 } to vector G2pj

12

R2, new ← id − 1

13

break

14

end

15

end

16

for id ← R3, new − 10 to R3, new + 10 do

17

if M23 (Ipj id ) == 1 then

18

insert C = {Ipj R2,new +1 , Ipj R1,new +2 , ..., Ipj id−1 } to vector G3pj

19

R3, new ← id − 1

20

break

21

end

22

end

23

for id ← R4, new − 10 to R4, new + 10 do

24

if M12 (Ipj id ) == 1 then

25

insert D = {Ipj R3,new +1 , Ipj R1,new +2 , ..., Ipj id−1 } to vector G2pj

26

R4, new ← id − 1

27

insert E = {Ipj R4,new +1 , Ipj R1,new +2 , ..., Ipj nj } to vector G1pj

28

break

29

end

30

end

31

return G1pj , G2pj , G3pj

9

Figure 4: Typical appearances of slices in group II.

Figure 5: Typical appearances of slices in group III.

Figure 6: Sub-rectangles and differences between brain shapes in different groups.

10

2.2. Active shape model with optimal feature
Recently, ASM has been applied successfully in several researches related to medical imaging [25, 26, 27].
In our system, we utilize the similarity of brain shapes of images in the same group by applying ASM with
specific model to each group, producing rough segmentations of brain regions which will be refined later.
For enhacing the modeling capacity of the gray-level variations around the border of the object, we use a
modified version of ASM called Active Shape Model with optimal feature (ASM-OF) [22]. In particular, the
optimal displacements for landmarks in original ASM is replaced by using a nonlinear kNN-classifier instead
of the linear Mahalanobis distance [28]. We denote some annotations, which are used in section below for
describing how ASM-OF is applied to segment each brain image in each group .
• s: the number of training images.
• n: the number of landmark points used to represent each image.
• ns : the number of new positions evaluated during searching.
• k: the number of points in profile located either inside and outside of the landmark point.
• lmax : the number of resolution levels for appearance model.
• ngrid : size of ngrid × ngrid of points, which are sampled in training process.
• nmax : the number of iterations per resolution level.
• kN N : number of neighbors used in k-NN classifier during searching and feature selection.
• fv : part of variance to be explained by the shape model, determining number of modes.
This stage comprises three subroutines. First, the ASM-OF create a shape model from landmarks in the
training set. Second, a k-nearest neighbor classifier (k-NN, [29]) is constructed using a gray-level appearance
model. Finally, the shape model and k-NN classifier are combined to produce preliminary estimations of
brain masks. The detail of each subroutine is described below.
2.2.1. Shape Model
A brain image in s images is represented by vector xi by stacking n landmark ((x1 , y1 ), . . . (xn , yn )) as
xi = (x1 , y1 , . . . , xn , yn )T with i ∈ [1, s]

(1)

Principal component analysis (PCA) is used to calculate the mean shape xs and covariance matrix C, the
eigenvectors φm (m = 1, . . . , t) correspond to the first t largest eigenvalues of the covariance matrix, and φm
is the respective variances λm as
s

xs =

s

1X
1 X
xi , C =
(xi − xs )(xi − xs )T
s i=1
s − 1 i=1
11

(2)

where φm and λm is calculated by singular value decomposition. When brain shape in the training set can
be approximated by
xs ≈ xs + Φs bs

(3)

where Φs = (φ1 . . . φt ) is the first t eigenvectors, and bs is a set of shape parameters which is calculated as
bs = ΦTs (xi − xs )

(4)

In experiment, bs is usually bounded by
−q

p
p
λi ≤ bs ≤q λi (i = 1, ..., t)

(5)

where q varies in the interval [2, 3]. The value t eigenvalues to retain is chosen so as to explain a certain
proportion fv of the variance in the training shapes, usually ranging from 90% to 99.5%. The desired number
of modes is given by the smallest t such that
t
X

λ i ≥ fv

i=1

2n
X

λi

(6)

i=1

2.2.2. Gray-level appearance model with optimal features
The gray-level appearance model that describes the typical image structure around each landmark is
obtained by applying k-NN instead from pixel profiles, sampled by using linear interpolation around each
landmark, perpendicular to the contour. From each training image and for each landmark a square grid of
ngrid × ngrid points is defined where ngrid is an odd integer and the landmark point at the center of the
grid. In our experiments, ngrid is set to 5 hence a feature vector has 60 elements which are calculated at 25
points. The output of feature vector is 1 if point is inside the objects or 0 if outside. The k-NN classifier with
weight to each vote is exp(−d2 ), where d is the Euclidean distance to each neighbor in the feature space.
For selecting the best feature, MannWhitney algorithm is used [30].
Given an input image, each position along the profile is calculated yielding 60 feature images and processing again to create the optimal feature. These features are then fed into k-NN classifier to determine
the probability of being inside the object for this pixel. Then we determine the point gi in the set of point
of the profile g such that the object function f (g) is minimized
f (g) =

−1
X

gi +

+k
X

(1 − gi )

(7)

i=0

i=−k

where gi is oriented from the outside to the inside of the object, runs from −k, to +k.
2.2.3. Evolution of the models
After both shape model and k-NN classifiers are constructed from training images, ASM-OF can be
applied to segment object by performing the procedures listed below.
• Step 1. Initialize the shape model with xs using (2).
12

• Step 2. For each landmark, put it at 2ns + 1 new locations, evaluate the equation (7) with the k-NN
classifier to find and move it to a new position denoted is xN ew .
• Step 3. Fit the shape model by calculating bsNew using (4) as (8), and limiting the values of bsNew using
(5).
bsN ew = ΦT
s (xN ew − xs )

(8)

where xN ew = (x1N ew , x2N ew , . . . , xnN ew )
• Step 4. Update the shape landmarks using (3) as
xsN ew ≈ xs + Φs bsNew
• Step 5. Iterate steps 2 and 4 up to predefined nmax times
Because ASM-OF is only able to capture the general shapes of brain region so the derived boundaries are
very smooth. Therefore, in the next stage, we apply convolutional neural networks to refine the preliminary
estimations from ASM-OF for the purpose of localizing accurate brain boundaries.
2.3. Convolutional neural networks
Convolutional neural networks (CNNs) are developed from multi-layer perceptrons, which allow exploiting
spatial information by using localized convolutional kernels. The main advantage of CNNs is the ability to
learn complex, nonlinear and high-dimensional mappings from large data. This attribute makes CNNs
achieve remarkable successes in 2D medical image analysis [31, 32]. The typical structure of CNN consists of
several pairs of convolutional, sub-sampling layers and multi-layer perceptron. The convolutional layers take
input as receptive fields in the previous layer and calculate features while spatial information is preserved.
Denote hlj is the j-th feature map of the l-th layer and hl−1
n (n = 1, . . . , N ) is the m-th feature map of the
(l − 1)-th layer, the feature map hlj is computed by equation:
hlj = σ(

N
X

l
Wjn
∗ hl−1
+ bl )
n

(9)

n=1
l
where Wjn
is the convolutional kernel associated with n-th feature map of the previous layer; bl is the bias

at the l th layer; and σ is the non-linear activation function.
The main operation of sub-sampling is pooling over local neighborhood to reduce the resolution of feature
maps. Max-pooling layers are special cases of sub-sampling in which non-max suppression and down-sample
the resolution of the feature maps are performed. The multi-layer perceptron with fully connected layers
is usually followed several convolutional layers and sub-sampling layers. The final layer of the multi-layer
perceptron are values, which are the posterior probability for each class with softmax function.
In our approach, a CNN is used as a classifier to refine the brain contour produced by ASM-OF. Unlike
the recent approach using CNNs, our method focuses on pixels located around boundaries of the preliminary
13

brain masks produced by ASM-OF in the previous stage, instead of processing for all pixels in image. In
addition, we also exploit the global spatial information [33] and combine it with feature maps learned from
a CNN as a input for multi-layer perceptrons. The details of construction for our CNN are described below.
2.3.1. Input and output space
Denotes that N is the number of slices of an MRI volume, I1 = {I11 , ..., I1p }, I2 = {I21 , ..., I2q }, I3 =
{I31 , ..., I3r } are the sets of images in group I, II, III, respectively where p+q+r = N , M2 = {M21 , ..., M2q }, M3 =
{M31 , ..., M3r } are the sets of brain masks produced by ASM for group II and III. For each image in group II
and III, position of pixels around the boundary of Mi (i ∈ {2, 3}) with distance 5 pixels are detected by using
algorithm 4 (Figure 7). These position then are extracted information based on Ij (j ∈ {2, 3}). With images
in I1 , all pixels within the rectangle, which contains the skull, are used as features. The aim of employing a
CNN is to classify pixels into brain and non-brain classes.
We extract two types of features for describing each pixel. The first type is local features, which are
three adjacent image slices with size 11 × 11 centered around each pixel. The second type of features is
global features, which are combining position (x, y) of each pixel and index z of image where pixel belongs in
(1 ≤ z ≤ N ). Figure 8 illustrate the feature extraction step and combine two features in network structure.
In the training process, the total of number brain and non-brain samples are approximately 4000000,
9000000 and 18000000 for IBSR, LPBA and OASIS dataset, respectively. The different in number samples
between dataset is mainly caused by the number of subjects in each dataset.

Figure 7: Preliminary brain boundary produced by ASM (green) and surrounding pixels that will be classified by CNN (red).

2.3.2. CNN architecture
Figure 8 illustrates our network structure. It includes three convolutional layers followed by four fully
connected layers, including the final two node layer for output. The size of convolutional layers is 3 × 3 and
max pooling uses 2 × 2 kernel. We configures the depths of the first, second and third convolutional layers
to 13, 26 and 39, respectively. The ReLU activation function is applied to the outputs of the convolutional
layer.
f (x) = max(0, x)

14

(10)

Three vectors from three slices of images obtained from convolutional layers are concatenated with the
normalize coordinates to form a new vector. Then this vector is fed into the fully connected layers. The
depths of four fully connected layers are 574, 300, 50, and 2, respectively. The final layer has the size of two,
indicating the probability of the input pixel belonging to the brain or non-brain class.
2.3.3. Training and Optimization
The aim of CNN is to minimize the cost function:
n
1X
η
L(w) =
l(z, f (x, w)) + ||w||2 ,
n i=1
2

(11)

for a labeled training set (xi , zi ), i ∈ (1, n) and weights including convolutional kernel weights and bias
weight (w1 , . . . wL ) with a loss function l . The loss function l is defined as:
l(z, f (x, w)) = −

N
M
1 XX
Bm,n log(pm,n )
N n=1 m=1

(12)

where N is the number of training images in the batch, M is the number of classes, pm,n is the probability
of the n the example being classified into the m-th class. If the n-th example is classified into the m-th class,
Bm,n equals 1, otherwise Bm,n equals 0.
In equation (11), L2 regularization is used to penalize the size of w with η = 0.005 is the coefficient of
regularization. The weights wt+1 at step t + 1 are updated by applied Adam algorithm [34]:
mt+1

= β1 mt + (1 − β1 )∇L(wt )

(13)

vt+1

= β2 vt + (1 − β2 )∇L(wt )2
mt+1
=
1 − β1t+1
vt+1
=
1 − β2t+1
αm̂t+1
= wt − p
v̂t+1 + 

(14)

m̂t+1
v̂ t+1
wt+1

(15)
(16)
(17)

where t is the iteration index, α = 1e − 04, β1 = 0.9, β2 = 0.999 and  = 1e − 08, m0 = 0, v0 = 0.
The weights in each layer at convolutional layer and are initialized from a normal distribution of N (0, 0.1)
while weights in multi-layer perceptron layer are created from normal distribution of N (0, β) with
β=

1
nhidden

(18)

where nhidden is the number of hidden layers of previous layer.
The CNN is trained by using mini-batch stochastic gradient descent with batch size of 128. For preventing
over-fitting, we use dropout layer after each layer in fully connected layer with rate 0.5.
2.4. Special Rules for Group I
The brain regions in group I are small and have a lot of noise, there would be cases where CNNs produce
two regions as segmentation results but it is difficult to automatically determine which area is the brain
region. In this paper, we utilized Gaussian Process [35] to overcome this situation.
15

16
Figure 8: Feature extraction step and our deep neural network structure.

Gaussian Process is used to to learn a line that changes center positions of the brain image from the
beginning to the end. Based on this line we can predict the center of the cerebral images in region I. Then
the closest area closest to the center of gravity is selected for processing. This line is learned based on the
Gaussian Process, because it is able to learn complex functions by adjusting the kernel functions.
Figure 9 illustrates the Gaussian Process training results with the IBSR dataset [36]. The blue lines
illustrate the change of the cerebral ventricles for each object from start to end position. The training set of
IBSR consists of 12 people hence there are 12 blue lines. It is worth noting that the positions of starting and
ending slice in MRI volumes are not constants. For example, scans of patient ID 1 start at slice 25 and end
at slice 200, scans of patient ID 2 start at slice 20, end at slice 220. Therefore, we normalized the starting
and ending slices to [1, 100]. The red line illustrates the result of the Gaussian Process.
Figure 10 illustrates the predicted results of the Gaussian Process. The red line illustrates the Gaussian
Process’s initial prediction for a new subject. After adjusting this prediction, we obtain the blue line which
is the final result of the Gaussian Process. The brown line is the ground truth. The adjustment from initial
prediction to final result is based on two factors:
• Because of the image acquisition condition, the image of a subject can be shifted, however, the rate
of change of the center of the image along the slices remains unchanged. Therefore, it is possible to
correctly predict the center of brain regions by translating the initial prediction by a value α.
• The value α is estimated based on a basis that, for each subject, we used a combination of ASM-OF,
CNN, and CRF to find the positions of region II and III based on the proposed algorithm. Then we
consider the center of all the images in region II and III. By compare the deviation with the result of
the Gaussian Process and taking the mean value, we obtain the desired value of α.

Figure 9: Illustration for training process of Gaussian process in IBSR dataset.

17

Figure 10: Prediction results of Gaussian process in IBSR dataset.

After the translation and obtaining the blue line, for each slice in region I, we calculate the distance
between each connected component in the slice and the predicted value of the Gaussian Process, finally we
select the region with the shortest distance. The algorithm 3 describes in detail how images in group I are
processed. The list of sub algorithms in the algorithm 3 including CheckCenter 6, CheckArea 7,ConvertRange
5 and CheckDistance 8 are presented in Appendices and CRF is presented in section 3.

3. Post-processing
Because the main procedures are pixel-wise approaches, the segmentation maps are considerably noisy,
decreasing overall accuracy of the brain extraction process significantly. To overcome this problem, we utilize
a post-processing technique based on conditional random field (CRF) for validating the extraction results
from ASM-OF and CNN, as well as finally refining the segmentation maps. Originally CRF was designed
for text segmenting and labeling [37], however there were several success in applying CRF to vision-based
applications [38, 39, 40], especially medical imaging [41, 42, 43]. In this research, we use fully connected CRF
as the main framework for post-processing because of its capability in producing highly refined segmentation
results.
Let I be an image of size N and x be a segmentation map of I, the Gibbs energy of x is given by
E(x) =

X

ϕu (xi ) +

i

X

ϕp (xi , xj )

(19)

i<j

where xi , xj is the label assigned to pixel i, j, respectively. In our system, the properties of segmentation
maps are x ∈ LN , L ∈ {0, 1} which are respective to “brain” (label 1) and “non-brain” (label 0) regions. The
unary potential is given by ϕu (xi ) = − log P (xi ), where P (xi ) is the probability of pixel i getting classified
as “brain”. This probability is acquired from the output of the main procedure.
18

Algorithm 3: Process Images in Group I
Input : Cb → Cm , Cq+1 → Ce : CNN Result Images of Group 01
Fm+1 , Fq : 2 Final Segmentation Images in Group II
GP M : Gaussian Process Model
Output: Final Images in Group 0I Fb → Fm , Fq+1 → Fe
1

Image1 = Fm+1

2

Image2 = F q

3

α = 0.4

4

β = 1.75

5

for i ∈ [m, m − 1, ..., b + 1, b] do

6

Ci ← Denoise in Ci

7

Ci = CheckCenter(Ci , Image1 )

8

Ci = CheckArea(Ci , α)

9

iGP M = ConvertRange(b, e, 1, 100, i)

10

di ← GP M (iGP M )

11

Ci = CheckDistance(Ci , di , β)

12

Fi ← CRF (Ci )

13

Image1 = Fi

14

end

15

for j ∈ [q + 1, q + 2, ..., e − 1, e] do

16

Cj ← Denoise in Cj

17

Cj = CheckCenter(Cj , Image2 )

18

Cj = CheckArea(Cj , α)

19

jGP M = ConvertRange(b, e, 1, 100, j)

20

dj ← GP M (jGP M )

21

Cj = CheckDistance(Cj , dj , β)

22

Fj ← CRF (Cj )

23

Image2 = Fj

24

end

25

return Fb → Fm , Fq+1 → Fe

19

The pairwise potential ϕp (xi , xj ) is given by
ϕp (xi , xj ) = µ(xi , xj )

K
X

wm km (fi , fj )

(20)

m=1

where µ(xi , xj ) follows Potts model, which is

 1
µ(xi , xj ) =
 0

xi 6= xj

(21)

otherwise

The weights are denoted as wm and km (fi , fj ) is the Gaussian kernel depends on feature vectors fi and fj .
Similarly to [39], we employ appearance kernel and smoothness kernel, which are respectively defined as
!
|Ii − Ij |2
|pi − pj |2
−
(22)
k1 (fi , fj ) = exp −
2σα2
2σβ2


|pi − pj |2
k2 (fi , fj ) = exp −
(23)
2σγ2
where pi , pj are positions, Ii , Ij are intensity values of pixel i, j. The sigmas (σα , σβ , σγ ) are used to control
the degrees of Gaussian kernels.
The most probable segmentation map x∗ is calculated by
x∗ = arg min E(x)

(24)

x∈LN

Because finding the exact minimization is infeasible, the CRF distribution is approximated by a mean-field
approximation. The detailed algorithm is presented in [39]. Besides performing mean-field approximation,
we need to determine the values of parameters of the model. In our system, we hard-coded the values of w2
and σγ because their effects to segmentation accuracy were insignificant. The other parameters (w1 , σα and
σβ ) were determined by random search with cross validation.
Figures 11 and 12 illustrate all processing stages of the proposed brain extraction system.

4. Experiments
4.1. Methods for comparison and dataset
In this paper, we consider comparing our proposed system with five well-known methods, namely Brain
Extraction Tool (BET) [44], Brain Surface Extractor (BSE) [45], 3DSkullStrip (3DSS) [46], ROBEX [15],
and Brain Extraction based on nonlocal Segmentation Technique (BEAST) [21]. The implementations of all
algorithms are optimized to work with T1-weighted data. BET is specifically designed for brain extraction
tasks. This method utilizes deformable models based on locally adaptive forces to produce brain mask
results. In the first stage, the center of the head is estimated. Then, the deformable model with a spherical
mesh is applied to fit brain boundaries around this position. BET is very fast and simple but requires manual
parameter settings to produce good results. In the experiment, we used BET 2.0, the latest version with
several improvements.
20

Figure 11: Processing steps for group I.

The next method for comparison is BSE. This method comprises several procedures: anisotropic diffusion
filtering, edge detection, and morphological operators. Anisotropic diffusion filtering is used to reduce noise
in images while preserving edge boundaries. Marr-Hildreth edge detection is employed to identify the border
of the brain regions. Finally, morphological operators such as erosion and dilation is applied to ensure that
the result is correct. Although BSE can provide high level of accuracy for whole-brain segmentations, fine
parameter tuning is usually required for method to work effectively in specific studies. In this study, we used
BSE in BrainSuite15c package, which was released in January 2016.
3DSS is a modification of BET, included in the AFNI package [46]. It uses the spherical surface expansion

Figure 12: Processing steps for group II and group III.

21

paradigm, with several modifications to avoid the eyes and ventricles regions, reducing misclassification.
Furthermore, not only points inside the surface, but also points located outside are combined together in
order to support the evolution of the mesh. In our experiment, we used 3DSS in the AFNI package released
on January 2016.
[15] proposed a method called ROBEX. This approach is a combination of a discriminative and a generative model. The random forest classifier is used as a discriminative model to detect voxels located on the
brain boundary. The generative model is based on a point distribution model to make sure the shape of the
mask is reasonable. In the first stage, ROBEX registers the subject to a template via affine transform. The
signal intensities are then normalized and applied bias correction before being fed into the discriminative
model. ROBEX is able to work effectively across multiple datasets without requiring any parameter tunning.
However, ROBEX uses an adult template as the standard for training the discriminative model, and the
target subject is supposed to be aligned. This limits the flexibility of ROBEX in working with different
conditions such as imaging modalities and young populations. For evaluating the performance of ROBEX,
we used the ROBEX version 1.2 released in November 2013.
The last method used for comparison is BEAST. The ideas of this technique is based on non-local patch
matching using multiple atlases. The sum of squared differences metric is used to determine suitable patches.
For optimization, input data and prior atlasyes library need to be normalized in terms of space and intensity.
An important characteristics of BEAST is that atlases library needs to be representative of the given data
and therefore user is able to add custom priors to the library. When sets of library are selected appropriately,
the method can achieve state-of-the-art performance for several data sets even when the data are related to
disease such as Alzheimers Disease Neuroimaging Initiative [47].
Three publicly available datasets were used for evaluation. In each dataset, the samples were randomly
divided into training and testing groups. The first dataset is Internet Brain Segmentation Repository (IBSR)
[36]. This dataset comprises T1-weighted scans (0.94 × 1.5 × 0.94 mm) of 20 healthy subjects (10 males and
10 females) whose ages vary from 24 to 34. The scans were provided along with manual segmentation
performed by experts. Two different scanners were used to acquire the scans. The first scanner, 1.5 Tesla
Siemens Magnetom MR System, was used to acquire scans from 4 males and 6 females with a Fast Low
Angle SHot (FLASH) pulse sequence and the following parameters: T R/T E = 40/8 ms, flip angle 50◦ , slice
thickness 3.1 mm, in-plane resolution 1 × 1 mm. The scans from the remaining subjects were acquired from a
1.5 Tesla General Electric Signa MR system with a 3D-CAPRY pulse sequence and the following parameters:
T R/T E = 50/9 ms, flip angle 50◦ , slice thickness 3.0 mm, in-plane resolution 1 × 1 mm. Owing to severe
striation artifacts existed in some scans, it is challenging to segment on this dataset.
The second dataset is LONI Probabilistic Brain Atlas (LPBA40) [48] which were acquired from healthy
volunteers. It contains 40 T1-weighted scans (0.86 × 1.5 × 0.86 mm) of 20 males and 20 females with the
average age is 29.2. The scans were acquired with a 3D spoiled gradient echo sequence on a GE 1.5T system
with TR: 10.0-12.5 ms; TE range 4.22-4.5 ms; flip angle 20◦ . Coronal slices were acquired 1.5 mm apart

22

with in-plane resolution of 0.86 mm (38 subjects) or 0.78 mm (2 subjects).
The third dataset was obtained from The Open Access Series of Imaging Studies (OASIS) project [49].
It is a cross-sectional and longitudinal collection of 416 subjects aged from 18 to 96. The data were acquired
by using T Siemens scanner with a MP-RAGE sequence, T R/T E/T I/T D = 9.7 ms/4.0 ms/20 ms/200 ms,
flip angle 10◦ . Sagittal slices were acquired 1.5 mm apart with in-plane resolution of 1 mm. We only used 77
T1-weighted scans (1 × 1 × 1 mm) acquired from 55 females and 22 males aged 51.64 ± 24.67 years to make
our results comparable to [15]. Differently from IBSR and LPBA40, 20 out of 77 subjects were clinically
diagnosed with very mild to moderate Alzheimers disease. Even though the brain masks are not created
manually but by a customized method based on registration to an atlas, the results from this method were
carefully checked by experts before releasing. This dataset is worthwhile by virtue of including scans from
a very diverse subjects with a expansive age range in addition to diseased brains. On account of this, it is
sufficient to use this dataset in order to prove the effectiveness and robustness of our approach.
In this research, 6 out of 20 subjects in IBSR dataset were used for training and the 14 remained subjects
were for evaluating. Similarly, 12/28 is the number of training/testing subjects in LPBA40 dataset and
22/55 is the ratio for OASIS dataset.
4.2. Setup
The proposed method was implemented in MATLAB and Python. Applying ASM-OF as well as extracting features for CNN were done using MATLAB. The deep neural networks used for training and testing
process was implemented in Python because of its various supported deep learning libraries e.g. TensorFlow.
In these experiments, we used the same deep neural network structure for all three datasets, as shown
in Figure 8. In the training process, the values of all weights of networks were randomly generated from
a normal distribution with mean 0 and standard deviation 0.1. To overcome overfitting problem, we also
added dropout layers with the rate 0.5 after each layer in deep neural network. The ReLU function was
selected as an activation function in our experiments. The processing time of the training phase varies
depending on the size of dataset. It took approximately 3.2 hours for IBSR, 6.4 hours for LPBA40, and 12.8
hours for OASIS to complete the training phase. This process was performed on a workstation with Intel(R)
Core(TM) i7-6700K CPU running at 4.00Ghz and an NVIDIA GeForce GTX 980 GPU. The average time
for processing one single MRI volume in testing phase is roughly 4 minutes.
4.3. Evaluation Metrics
We evaluated the performance of our brain extraction method by comparing the segmentation results
with the ground truth in each dataset. Among several popular metrics used for measuring the distance or
similarity between two images, we used the Dice coefficient, the Jaccard index and the Average Haussdorff
Distance (AHD). Furthermore, sensitivity and specificity scores were also calculated.
Aforementioned metrics can be derived from the four basic cardinalities of the confusion matrix, which
are true positives (TP), false positives (FP), true negatives (TN), and false negatives(FN). TP are voxels
23

correctly classified as brain tissue while TN consisted of voxels precisely predicted as non-brain tissue. FN
are brain tissue voxels in the ground truth but misclassified by the methods. In contrast, FP are incorrectly
identified brain tissue voxels.
The Dice coefficient is commonly used to measure repeatability in order to compare directly machinegenerated and ground truth segmentation. It is possibly the most-used measure for validating medical
segmentations. The Dice coefficient is calculated by
D=

2T P
2T P + F P + F N

(25)

The values of this coefficient is in the interval [0, 1] where the maximum value indicates that two segmentation
map are identical.
The Jaccard index is another widely used similarity measure and closely related to the Dice coefficient.
The relationship of two metrics is represented by
2J
1+J

(26)

TP
TP + FP + FN

(27)

D=
hence
J=

Sensitivity and specificity are similar to each other. Sensitivity is essentially how good a prediction is at
true positive. Analogously, specificity is a measure of how accurate a prediction is against false positives.
However, it is not common to use these two measures for evaluation of medical image segmentation because
of their sensibility to segments size. These metrics are defined as follows:

TP
TP + FN
TN
Spec =
TN + FP

Sens =

(28)
(29)

Differently from other metrics, the AHD is a spatial distance based metrics measuring dissimilarity
between two segmentations, where one is the predicted result needs to be evaluated and the other is respective
ground truth. These metrics are usually used when the overall accuracy, for instance the contour of the
segmentation, of the result is of importance. Because the normal Haussdorff distance is sensitive to outliers,
it is recommended to use the AHD which is known to be more stable. The AHD between two segmentation
map X and Y is defined by
AHD(X, Y ) = max(d(X, Y ), d(Y, X))

(30)

where d(X, Y ) is the directed average distance given by
d(X, Y ) =

1 X
min kx − yk
y∈Y
N
x∈X

24

(31)

5. Results
5.1. Qualitative evaluation
The segmentation results of all method including our proposed in a sagittal plane for IBSR, LPBA and
OASIS are illustrated in Figure 13 - 15 respectively. Each figure includes 6 typical testing scans from all
three groups (2 scans for each group). Although ASM-CNN approaches the sagittal plane, it also works well
and gives correct segmentation in two other planes, which are transverse and coronal plane. Figure 16 shows
the comparison between our approach and other methods on each dataset for these two planes.
For the BET, it generally gives good results for almost testing samples. Missing the cerebellum in its
segmentation is the crucial problem of this method. Even for scans in group III which are brains in a big
size with not so complex structure, BET sometime provides false segmented result (see Figure 13 and Figure
15). This issue appears in IBSR and mostly in OASIS dataset which can be clearly seen in coronal plane in
Figure 16. For the LPBA samples it seems to be improved and gets better performance. However, comparing
with other methods, it happens more frequent on BET. Moreover, Figure 16 shows that BET often leaves
out the lateral ventricles of its segmented result along with BSE and 3DSS. Although fails in group II and
III, this method can produce acceptable segmentations on images in group I (see Figure 15).
BSE seems to have the same performance with BET method which also fails at cerebellum segmentation
and does not include the ventricles. Different from other methods, sustainability is the main disadvantage
of BSE. It can gives excellent results in LPBA dataset but very poor in IBSR and OASIS. This can be
seen clearly in II scans in the same group III and same dataset in Figure 13. BSE works well in the first
scan although the dura matter and the cranium is oversegmented. However, for the second scan which has
higher contrast in the same group III, this method completely fails to produce correctly result. One of the
reasons for unstable segmentation is because we employed the default parameters. Hence carefully tuning
the parameters is necessary when using BSE. Besides, Figure 13 also shows that this method sometime gives
good segmentation for images in group I.
The extracted results obtained by 3DSS, which is a modified version of BET, are slightly better than BET
and BSE. 3DSS produces great segmentation in LPBA and its performance decreases in IBSR and OASIS.
Unlike BET, segmentation by 3DSS can avoid the eyes (see the second scan in Figure 13) and reduce leakage
into the skull although there are some minor oversegmentation at temporal lobe of cerebral hemisphere (see
the first scan in Figure 14). The same with BSE, this method leaves the ventricles out in its segmentation.
However, the results are extremely sharp at the boundary which sometimes loss the interhemispheric tissue
in the segmentation (see Figure 16). Furthermore, the extracted brains in group I by 3DSS are also not good
as those from BSE.
Both BEAST and ROBEX all have the higher performance than the aboved methods. They produce
precise segmentations of cerebellum which BET and BSE often fails at. Besides, the ventricles, which are
usually left out in 3DSS or BSE, are included in the segmentations. However, BEAST gives results sharp as
those from 3DSS causing to decrease the accuracy. Moreover, the main problem of ROBEX is that it gives
25

oversmoothed results, leading to inclusion of dura and gray matter loss [6] (see the second scan in Figure
16). Generally, both can provide accurate extracted brains but ROBEX seems to be slightly better than
BEAST. Unfortunately, they both work bad for small size brains in group I, even worse than the aboved
methods.
Finally, ASM-CNN provides extremely accurate segmentations in all three datasets. The results obtained
by our proposed are the same with those by ROBEX with smoothed boundaries. However we can still keep
the gray and dura matter in our extracted brains in most of cases in which they are usually left out by
ROBEX (see the second scans in Figure 16). Although there are some minor leakage into the skull in ASMCNN, it happens least than ROBEX and BEAST with smaller oversegmentation. The critical impact of our
method is that it can work precisely for the small size brains in group I where other methods usually fail at.
We observe in scans from this group in Figure 13 - 15 that our extractions are identical to the groundtruth
even for the tiny size brains (see two last scans in Figure 13). However the final result still has a few false
negatives and false positive in some cases because of the complex structure in this group. In spite of some
minor incorrect segmentation, ASM-CNN still has a better performance than others with higher accuracy.
5.2. Quantitative evaluation
We use five evaluation metrics which are Dice coefficient, Jaccard index, average Haussdorff distance,
sensitivity and specificity to compare our method with others. For the sake of easy comparison, we evaluate all
methods in 2D (sagittal plane) and 3D form for each dataset. Table 1 - 3 displays the average and standard
deviations (SD) of the metrics for IBSR, LPBA and OASIS dataset on 2D plane respectively. Similarly,
Table 4 - 6 shows the accuracy of the results executed on 3D structure. The results of different metrics from
evaluated methods on three datasets are depicted by box plots in Figure from 17 to 22 respectively.
Because our approach is working with 2D scans, we formulated the result on 3D structure of other
algorithms as 2D images sequences in sagittal plane for the reliable evaluating. Base on the result, all
methods prone to getting higher scores on the LPBA dataset in which BSE has significant changes when
working on this dataset such as the average of Dice coefficient of this method greatly increases about 9%
(85% to 94.27%) for the LPBA scans. BEAST has the highest mean of Specificity with small SD for three
datasets although there is no big difference between six methods at this evaluation metric. Surpassing all
other algorithms, ASM-CNN gets the best performance with the highest average of Dice overlap (with 0.55
- 1.63% higher than the second), Jaccard index (0.8 - 2.45 % higher) and AHD on three datasets and the
best Sensitivity on LPBA and OASIS while ROBEX produces the highest on IBSR. Besides, BSE also
achieve the same AHD score on LPBA like ASM-CNN but its SD is higher than us (0.32 compared with
0.19). Furthermore, ASM-CNN not only has outstanding mean of evaluation metric scores but also gets the
smallest SD values in Dice coefficient, Jaccard index and Sensitivity which can show the consistency of our
method.
Although process with 2D plane, we still create 3D results by combining sequences of scans to make ASMCNN more comparable with other algorithms. There is a increase at the accuracy of five remain methods
26

in this type of evaluation with a great improvement at standard deviation. Among the other algorithms,
BEAST has major changes in its accuracy for several evaluated metrics on three datasets. For instance, it
approximately gains more 3.47 - 5.1% on Dice, Jaccard and Sensitivity metrics. Furthermore, BEAST still
provides the highest Specificity which is almost 100% for all dataset. Meanwhile, ROBEX continually obtains
the best scores in Sensitivity metric on IBSE and LPBA. Despite not our main approach, the 3D results
produced by ASM-CNN are remarkable which can be competitive with others. It preserves the impressive
performance which gets the best on 3 dataset at Dice coefficient, Jaccard index, AHD and on OASIS at
Sensitivity.
The boxplots in Figure 17 and 20 shows that BSE has a big interquartile range (IQR) on IBSR which
means the results given from it are more disperse and have larger variance than other algorithms. However
this method has the best performance on LPBA (Figure 18, Figure 21) which gives extremely accurate results
and better than others although it has a terrible outlier (about 72% at Dice overlap for 2D evaluation).
Indeed, this issue was mentioned above that BSE can provide very accurate segmentations but also may give
atrocious results which is based on tuning employed parameters. By contrast, ASM-CNN shows its durable
and unaffected by datasets that outperforms than others with high accuracy and small IQR as well as SD
on three datasets especially on OASIS (Figure 19, Figure 22). Unfortunately, its Specificity is worse than
several methods. However it can be improved by employment a suitable post-processing method to mitigate
several false positive in the segmentations.

27

Figure 13: Comparison between ASM-CNN with other methods on IBSR dataset.

28

Figure 14: Comparison between ASM-CNN with other methods on LPBA dataset.

29

Figure 15: Comparison between ASM-CNN with other methods on OASIS dataset.

30

Figure 16: Result image on transverse and coronal plane for IBSR, LPBA, OASIS dataset.

31

Figure 17: 2D Box plots of Dice coefficient, Jaccard index, Average Hausdorff distance, Sensitivity and Specificity for IBSR
dataset.

Figure 18: 2D Box plots of Dice coefficient, Jaccard index, Average Hausdorff distance, Sensitivity and Specificity for LPBA
dataset.

32

Figure 19: 2D Box plots of Dice coefficient, Jaccard index, Average Hausdorff distance, Sensitivity and Specificity for OASIS
dataset.

Figure 20: 3D Box plots of Dice coefficient, Jaccard index, Average Hausdorff distance, Sensitivity and Specificity for IBSR
dataset.

33

Figure 21: 3D Box plots of Dice coefficient, Jaccard index, Average Hausdorff distance, Sensitivity and Specificity for LPBA
dataset.

Figure 22: 3D Box plots of Dice coefficient, Jaccard index, Average Hausdorff distance, Sensitivity and Specificity for OASIS
dataset.

34

Method

Dice

Jaccard

Average Hausdorff

Sensitivity

Specificity

BET

87.99 ± 10.49

79.68 ± 12.27

1.16 ± 0.55

80.76 ± 12.25

99.53 ± 0.43

BSE

85.23 ± 16.56

77.17 ± 20.61

0.85 ± 0.41

78.90 ± 21.63

99.36 ± 0.8

3DSS

91.42 ± 13.31

85.99 ± 14.9

0.72 ± 0.22

88.21 ± 15.55

99.1 ± 1.04

ROBEX

94.32 ± 8.13

90.02 ± 10.37

0.61 ± 0.24

95.22 ± 9.43

98.38 ± 1.57

BEAST

90.00 ± 16.51

84.46 ± 17.97

0.61 ± 0.15

84.63 ± 18.02

99.93 ± 0.1

ASM-CNN

94.89 ± 6.33

90.82 ± 9.15

0.57 ± 0.15

93.24 ± 8.53

99.36 ± 0.72

Table 1: 2D Results of different methods in IBSR dataset.

Method

Dice

Jaccard

Average Hausdorff

Sensitivity

Specificity

BET

93.25 ± 8.35

88.17 ± 10.76

0.72 ± 0.28

89.69 ± 10.71

99.34 ± 0.62

BSE

94.37 ± 10.32

90.63 ± 13.51

0.57 ± 0.32

92.41 ± 13.55

99.33 ± 0.66

3DSS

92.47 ± 13.89

87.93 ± 15.27

0.75 ± 0.21

91.46 ± 16.1

98.22 ± 1.6

ROBEX

93.85 ± 12.74

90.12 ± 14.45

0.62 ± 0.17

92.53 ± 14.82

99.08 ± 0.56

BEAST

93.00 ± 13.50

88.83 ± 15.37

0.62 ± 0.16

89.65 ± 15.38

99.67 ± 0.64

ASM-CNN

95.39 ± 7.02

91.87 ± 10.25

0.57 ± 0.19

94.72 ± 7.01

99.33 ± 1.01

Table 2: 2D Results of different methods in LPBA dataset.

Method

Dice

Jaccard

Average Hausdorff

Sensitivity

Specificity

BET

85.34 ± 13.24

76.17 ± 15.41

1.91 ± 0.77

78.17 ± 15.78

98.9 ± 1.05

BSE

85.53 ± 11.68

76.18 ± 14.48

1.94 ± 0.7

78.45 ± 14.96

98.80 ± 1.34

3DSS

87.30 ± 14.49

79.64 ± 17.25

1.81 ± 0.67

82.91 ± 17.8

98.48 ± 1.36

ROBEX

93.44 ± 8.75

88.59 ± 11.16

1.27 ± 0.27

92.1 ± 10.43

98.44 ± 1.05

BEAST

88.56 ± 14.17

81.49 ± 16.27

1.59 ± 0.37

82.71 ± 16.41

99.26 ± 0.99

ASM-CNN

95.07 ± 5.36

91.04 ± 8.46

1.13 ± 0.42

94.36 ± 7.1

98.53 ± 1.46

Table 3: 2D Results of different methods in OASIS dataset.

35

Method

Dice

Jaccard

Average Hausdorff

Sensitivity

Specificity

BET

89.63 ± 3.86

81.39 ± 6.42

34.99 ± 7.2

82.53 ± 6.09

99.57 ± 0.17

BSE

88.48 ± 9.84

80.50 ± 15.79

32.06 ± 12.88

82.09 ± 17.18

99.42 ± 0.53

3DSS

94.56 ± 2.11

89.75 ± 3.78

24.05 ± 2.2

92.02 ± 5.26

99.18 ± 0.63

ROBEX

96.24 ± 1.28

92.78 ± 2.34

22.72 ± 3.55

97.14 ± 1.63

98.47 ± 1.34

BEAST

94.46 ± 2.27

89.57 ± 4.07

22.27 ± 3.07

89.76 ± 4.2

99.93 ± 0.05

ASM-CNN

96.51 ± 1.03

93.27 ± 1.92

20.63 ± 1.15

95.04 ± 2.92

99.39 ± 0.39

Table 4: 3D Results of different methods in IBSR dataset.

Method

Dice

Jaccard

Average Hausdorff

Sensitivity

Specificity

BET

95.19 ± 1.81

90.87 ± 3.23

26.52 ± 5.1

92.33 ± 3.34

99.40 ± 0.24

BSE

96.19 ± 5.56

93.09 ± 8.96

21.17 ± 8.75

94.66 ± 9.46

99.39 ± 0.32

3DSS

95.85 ± 0.49

92.04 ± 0.91

24.52 ± 2.44

95.90 ± 0.75

98.41 ± 0.60

ROBEX

96.91 ± 0.18

94.00 ± 0.34

21.88 ± 1.07

96.18 ± 0.88

99.13 ± 0.28

BEAST

96.47 ± 0.61

93.20 ± 1.14

21.11 ± 2.08

93.93 ± 1.09

99.72 ± 0.43

ASM-CNN

97.14 ± 0.75

94.46 ± 1.40

20.15 ± 2.19

96.14 ± 1.65

99.33 ± 0.34

Table 5: 3D Results of different methods in LPBA dataset.

Method

Dice

Jaccard

Average Hausdorff

Sensitivity

Specificity

BET

87.99 ± 6.55

79.09 ± 9.72

46.42 ± 10.03

80.73 ± 10.51

98.98 ± 0.82

BSE

88.27 ± 4.88

79.32 ± 7.63

46.16 ± 7.61

81.15 ± 8.84

98.87 ± 1.12

3DSS

90.26 ± 7.15

82.93 ± 10.99

40.54 ± 10.54

85.39 ± 12.37

98.57 ± 1.02

ROBEX

95.64 ± 0.86

91.66 ± 1.57

30.31 ± 1.97

94.36 ± 2.55

98.49 ± 0.79

BEAST

92.72 ± 1.47

86.45 ± 2.52

35.65 ± 2.71

87.59 ± 3.03

99.33 ± 0.82

ASM-CNN

96.50 ± 0.91

93.25 ± 1.68

26.17 ± 2.28

95.82 ± 1.93

98.58 ± 0.65

Table 6: 3D Results of different methods in OASIS dataset.

36

6. Discussion
In this research, we proposed a system for brain extraction using active shape model and convolutional
neural network, hence the name ASM - CNN. The idea behind using ASM is to explore general structures
of brain regions, ensuring the consistency of the shape of the object. However, in medical imaging we
demand high precision boundaries for segmentation problems, while ASM only provides general shapes and
quite smooth. Therefore, we implemented CNN to refine the boundaries produced by ASM. After this step,
results from CNN may still be flawed, especially for small and complext brain regions. To overcome this
challenge, we proposed some pre-processing techniques based on CRF and Gaussian Process as the final
step. CRF with its ability to model the relationships between the pixels being predicted is used to produce
a structured output effectively. Gaussian process is applied to learn a non -linear function indicating the
changing of the cerebral images from the beginning to the end image due to its power in learning complex
functions with a suitable kernel function.
Instead of using whole 3D MRI volume, we decided to approach with 2D scans. This approach allows
us to design special rules, adapted for identifying small and complex brain regions, which are often ignored
by techniques that focus on processing 3D volume. In addition, we choose 2D scans in sagittal plane to
process. Harnessing the symmetry of this plane, we can group brain images into pre-defined groups such
that the images in each group have similar shapes. This property enables ASM to learn shape models and
appearance model properly in place of learning all shapes, which change significantly when throughout the
images.
The proposed method has been compared with five state-of-the-art brain extraction methods. By achieving the highest average of Dice coefficient and Jaccard index with smaller standard deviations, ASM-CNN
surpassed all other methods in all experiments. The proposed method also got remarkable scores in other
metrics, not only in 2D but also in 3D perspective as well. Despite the inferior result in Specificity, it is still
sufficient when it made no significant difference between the top method and ours. ROBEX has shown that
it was better than others with many great segmentations. However, the segmentation contours produced
by ROBEX were not as sharp as the groundtruth, leading to the increase in false positive. It is also the
main weakness of ROBEX when being tested with all three datasets. About BEAST and 3DSS, both methods performed great in general. Their segmentation results were regularly the same as the groundtruth in
some cases and their average scores are approximate with each other. Nevertheless, it seemed that BEAST
produced the more stable results than 3DSS which had fluctuation in its scores. For instance, there are
some cases when 3DSS performed on OASIS dataset, it missed some region of cerebellum, as illustrated in
Figure 15. It is worth noting that BEAST was at top in Specificity with the highest average scores in all
datasets. For BET and BSE, the quality of their segmentations is worse comparing with others but still
acceptable. When dealing with the diversity of brain shapes and contrast in scans, BET and BSE produced
some false segmented regions from cerebellum to brain stem which can be easily seen in Figure 13. Their
results were also unstable, especially when being tested with OASIS dataset. Moreover, it is shown that BSE
37

has not been stable on IBSR with the highest standard deviation. On the other hand, BSE was surprisingly
good on LBPA, albeit there was still one outlier which had an extremely low accuracy. It can be caused by
parameters tuning because BSE is extremely sensitive to these values. For example, when default parameter
values were used in LPBA, this tool has obtained superb results. But it was totally different when BSE was
applied to other dataset like IBSR or OASIS.
It is worth noting that the properties of datasets affected the performance of brain extraction methods.
Due to using two scanner to acquire MR images, IBSR comprises many heterogeneous scans with many
obvious artifacts. Besides, this dataset also has the lowest resolution and most anisotropic voxels. LPBA
has better resolution images with less noise but it is also fairly anisotropic. OASIS does not have lots of
noises and it is isotropic, but it includes some diagnosed Alzheimers disease subjects. Therefore, all methods
performed well on LBPA and got the results which did not have any clearly differences. But for other
datasets such as IBSR and OASIS, ASM-CNN has shown its remarkable performance when comparing with
others, especially in OASIS. It is because the contour refinement by CNN and post-processing by CRF and
Gaussian process have done their duty impressively which produced sharp brain boundaries as groundtruth.
Furthermore, combining with specific rules for particular groups helped our method overcome the small brain
region problems. Our result for this phenomenon is demonstrated in Figure 13. It has to be noted that five
other methods were run with the default parameters values. Hence, all the experimental evaluation can be
reproduced.
In our system, ASM is used to keep the original structures. However, ASM can only work effectively when
the shapes of the objects to be similar to the trained active appearance model. Therefore, the algorithm will
likely produce poor results when processing unusual shapes. Unfortunately in medical imaging, the data are
usually obscured by noise due to limitations of image acquisition systems, or the shapes and distributions of
images are not inlcuded in training data. In such cases, ASM may produce severely imprecise boundaries even
CNN cannot verify or refine. In the future work, we intend to study the techniques based on deep learning
for the purpose of constructing better models for shape and apperance. In addition, with improvements
in the future, such as GPU optimization, we believe that the proposed approach can be applied widely in
clinical applications because of its fine and robust performance.

7. Conclusion
In this article, we proposed a novel method for brain extraction in magnetic resonance images, namely
ASM-CNN. The method was named after its main components: Active Shape Model and Convolutional
Neural Network. Unlike existing approaches, ASM-CNN processes 2D sequences of images instead of 3D
brain structures. For each 2D scan, first we use a improved version of ASM is Active Shape Model with
optimal feature to produce a rough estimate of the brain region, its boundary is then refined by a CNN, which
is constructed and trained with several special rules. Finally, the brain region is post-processed by conditional
random field and Gaussian process. The proposed approach has shown its consistency in performance, it can
38

produce high accuracy segmentations in all cases, even when the brain regions are small and scattered. In
the experiments, our method achieved remarkable Dice coefficients and Jaccard indexes for the whole three
datasets (IBSR, LPBA and OASIS) in 2D scans as well as 3D structures, surpassed the performance of five
other state-of-the-art methods (BET, BSE, 3DSS, BEAST and ROBEX).

Acknowledgment
We would like to thank the National Foundation for Science and Technology Development (NAFOSTED),
University of Science VNU - HCM, and Business Intelligence LAB at University of Economics and Law, Viet
Nam for supporting us throughout this paper.

Appendices

Algorithm 4: M ergeSlice(X, Y, α)
Input : Two binary images X, Y ; Open distance α
Output: Binary image Z created by combining X and Y
1

O ← OpenBoundary(Y, α)

2

Core ← Y \O and Boundary ← X ∩ O

3

Z ← Core ∪ Boundary

4

Apply morphology to fill small holes in Z (if exists)

5

return Z

Algorithm 5: ConvertRange – Convert a value xAB in range [A, B] to range [C, D]
Input : A, B, C, D, xAB
Output: xCD
1

xCD = C + (xAB − A) ∗ (D − C)/(B − A)

2

return xCD

39

Algorithm 6: CheckCenter – Remove components in image X whose center is not in image Y to create
image Z
Input : X, Y
Output: Z
1

Z=X

2

bbox ← the smallest bounding box surrounding all components in Y

3

foreach component ci in Z do

4

centeri ← Coordinates of the center of ci

5

if centeri is not in bbox then
Remove ci out of Z

6
7

end

8

end

9

return Z

Algorithm 7: CheckArea – Remove small components in image X with the coefficient α to create
image Y
Input : X, α
Output: Y
1

Y =X

2

foreach component ci in Y do

3

ai ← Area of ci

4

end

5

amax ← max {ai }

6

athreshold = α ∗ amax

7

foreach component ci in Y do

8

if ai < athreshold then

9

Remove ci out of Y

10

end

11

end

12

return Y

40

Algorithm 8: CheckDistance – Remove components having small distance in image X with the coefficient β to create image Y
Input : X, d, β
Output: Y
1

Y =X

2

foreach component ci in Y do

3

centeri ← Coordinates of the center of ci

4

difi = |d − kcenteri k2 |

5

end

6

difmin ← min {difi }

7

difthreshold = β ∗ difmin

8

foreach component ci in Y do

9

if difi > difthreshold then
Remove ci out of Y

10
11

end

12

end

13

return Y

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