Brain Tumor Extraction from T1- Weighted MRI using Co-clustering and Level Set Methods

S.Satheesh, Dr.K.V.S.V.R Prasad & Dr.K.Jitender Reddy
International Journal of Image Processing (IJIP), Volume (7): Issue (2): 2013 219
Brain Tumor Extraction from T1- Weighted MRI using
Co-clustering and Level Set Methods
S.Satheesh satheesh.s17@gmail.com
Dept. of ECE,
G. Narayanamma Institute of Technology and Science,
Hyderabad, India.
Dr.K.V.S.V.R Prasad kvsvr@yahoo.com
Dept. of ECE,
D.M.S.S.V.H. College of Engineering,
Machilipatnam, India.
Dr.K.Jitender Reddy kjitenderreddymdrd@gmail.com
Dept. of Radiology and Imaging Sciences,
Apollo Health City,
Hyderabad, India.
Abstract
The aim of the paper is to propose effective technique for tumor extraction from T1-weighted
magnetic resonance brain images with combination of co-clustering and level set methods. The
co-clustering is the effective region based segmentation technique for the brain tumor extraction
but have a drawback at the boundary of tumors. While, the level set without re-initialization which
is good edge based segmentation technique but have some drawbacks in providing initial
contour. Therefore, in this paper the region based co-clustering and edge-based level set method
are combined through initially extracting tumor using co-clustering and then providing the initial
contour to level set method, which help in cancelling the drawbacks of co-clustering and level set
method. The data set of five patients, where one slice is selected from each data set is used to
analyze the performance of the proposed method. The quality metrics analysis of the proposed
method is proved much better as compared to level set without re-initialization method.
Keywords: Magnetic Resonance Imaging, Tumor Extraction, Co-clustering Method, Level Set
Method.
1. INTRODUCTION
Brain tumor is considered to be one of the significant diseases which require a controlled and
timely diagnosis and treatment. It alarms an emergence of improved medical imaging techniques
to be developed for treating the disease [1]. These technological innovations lead to early
pathological diagnosis, their follow-ups, planning and guidance for surgeries along with
quantitative analysis of the images. Among all imaging techniques, Magnetic Resonance Imaging
(MRI) plays a vital role due to its ability in generating multi planar, good contrast, spatial
resolution with anatomical details and capability to create 3D images for analyzing anatomy of
brain in more in depth way in order to identify pathologies.
In brain tumor analysis, segmentation of abnormal tissues, anatomical structures and pathologies
from MRI in particular, plays a predominant role. The results from this segmentation are the
foundation for further analysis. It is necessary to change the segmentation methods depending on
the hard and soft tissues and image modalities. In addition to, segmentation of MR brain images
is a daunting task because they generally involve a large amount of data. While undergoing MRI

some artifacts will occur due to the patient’s movements. Leading to the soft tissue boundaries
which also can not be well defined.
When we deal with brain tumors, various other problems also arise making their segmentation
more difficult. There are large number of types of tumors having a variety of shapes and sizes.
These may be located at any place in the brain with various intensities. Sometimes, some of them
will deform the surrounding structures that alter the intensities around the tumor. With the
existence of different MR acquisition protocols different information is provided on the brain
highlighting the region of the tumor.
Several segmentation methods such as thresholding, watershed, level set, zero crossing and
region-based segmentation are used for tumor segmentation. In these methods, some methods
are region based and they have a main disadvantage at the boundary of tumors. They suffer from
misclassification of pixels and hence, it is hard to have a crisp region of tumor. Some of the
methods are edge based and are suffer from initialization problems. But the medical images have
both of two properties that are required to be overcome to get effective brain tumor extraction.
Looking at the advantages of boundary based and region based methods, the third class of tumor
segmentation methods was designed , which is the combination of region and boundary based
techniques.
The first approach of this type was presented by Zhu and Yang [2].In their study they used
thresholding and morphological operations. Law et al.,[3] proposed another method by integrating
FCM clustering with the conventional snake. Chen et al.,[4] presented a new hybrid framework by
integrating Gibbs model, marching cubes and parametric deformable models. Ho et al.,[5]
presented a method to segment brain tumors by combining level set and fuzzy clustering. Taheri
et al.,[6] combined threshold based method and level set to segment the brain tumor.
It is observed that co-clustering [7, 8], which is the region based segmentation method, is the
effective clustering technique for the brain tumor extraction [9]. The level set without re-
initialization [10], which is edge-based technique, is also efficient for the tumor extraction from MR
brain images. Hence, in this paper both co-clustering region based technique is integrated with
level set [10] edge based technique for taking advantages of both techniques while reducing their
drawbacks to acquire effective tumor extraction of MR brain image. For this hybrid approach
firstly tumor is extracted using co-clustering and then given this as the initial contour to level set.
The experimental analysis of the proposed method is proved much better when compared with
level set without re-initialization.
The overall structure of the research paper is demonstrated as follows; the second section
provides the overview of co-clustering method. Third section illustrates level set without
re-initialization overview. Fourth section describes the proposed technique steps, which is
combining the co-clustering and level set methods. Fifth section illustrates regarding collected
results with the evaluation of performance based on chosen evaluation metrics. Sixth section
summarizes the proposed methodology of the research problem and gives future
recommendations.
2. CO-CLUSTERING
The clustering is a collection of similar gray levels in the image, where gray levels are divided into
diverse segments. On the other hand, co-clustering is partitioning of rows and columns
simultaneously for an image [7, 8]. This kind of algorithm is significant in finding k-cluster of MR
brain images. The T1-weighted MR brain images are skull stripped using [9] before applying to
co-clustering algorithm.
The algorithm of co-clustering is summarized as follows:
Input: Skull stripped T1-weighted MR brain image of size i ൈ j (Ii, j) and Number of clusters (k)
Output: Segmented MR brain image with k clusters

1. Form I୬ ൌ Dଵ
షభ
మ
ൈ I ൈ Dଶ
షభ
మ
where Dଵሺi, iሻ ൌ ∑ I୧,୨୨ and Dଶሺj, jሻ ൌ ∑ I୧,୨୧
2. Compute L ൌ ‫ڿ‬logଶ k‫ۀ‬ singular vectors of I୬
3. Apply singular value decomposition (SVD) technique on I୬ to obtain
ሾU S Vሿ ൌ SVDሺI୬ሻ
where U and V represent the left and right eigenvector of 2
nd
to (L+1)
th
eigen values.
U ൌ ሾuଶ, uଷ, … . , uLାଵ and V ൌ ሾvଶ, vଷ, … . , vLାଵ]
4. Form the matrix Z ൌ ቎
Dଵ
షభ
మ
ൈ U
Dଶ
షభ
మ
ൈ V
቏
5. The k-means algorithm is applied on the L -dimensional data Z to obtain the k number of
clusters.
6. Find out the mean of the centers and their indices from the obtained clusters.
7. Extract the segmented portion by indexing the obtained L-dimensional data with
respective to original image.
8. Apply morphological region filling operator to refine the tumor region.
Co-clustering is found taking advantage from the duality between the columns and rows, in order
to deal with the high dimensional data influentially. There is a limitation of over segmentation,
associated with co-clustering based image segmentation. Thus, in order to overcome the issue of
over segmentation, integration of edge based segmentation will give better results.
3. LEVEL SET WITHOUT RE-INITIALIZATION
Osher and Sethian [11] initially introduced level set methods for capturing moving fronts. The
level set method is the effective way to demonstrate active contour, which helps in MR brain
tumor segmentation. Recently, several research works have been done on the geometric active
contours [12-16], where active contours applied through level set method to address the broad
range of image segmentation problems in image processing and computer vision.
Active contours employed through level set methods can be formulated as zero level set of a time
dependent function ߶ that varies according to the equation (1).
డథ
డ௧
൅ ‫|߶׏|ܨ‬ ൌ 0 (1)
Equation (1) is known as level set equation. Here, ‫ܨ‬ is called speed function depending on image
data and level set function ߶. While implementing the level set method, it is compulsory to keep
the evolving level set function close to a signed distance function in order to sustain stable curve
evolution. Yet, the process of re-initialization makes the total computation expensive. It also
causes numerical error in the location of the zero level set.
In this paper, we have used a level set evolution method which is based on energy penalty term
without re-initialization introduced by Li Chunming et al., [10].
Let ‫ܫ‬ be an image, and ݃ be the edge indicator function defined by equation (2).
݃ ൌ
ଵ
ଵା|ఇீ഑‫כ‬ூ|మ (2)

where G஢ is the Gaussian kernel with standard deviation ߪ.
The external energy for a function ߶ሺ‫,ݔ‬ ‫ݕ‬ሻ is defined as
ࣟ௚,ఒ,௩ሺ߶ሻ ൌ ߣࣦ௚ሺ߶ሻ ൅ ‫ࣛݒ‬௚ሺ߶ሻ (3)
where ߣ ൐ 0 and ‫ݒ‬ are constants.
The terms ࣦ௚ሺ߶ሻ and ࣛ௚ሺ߶ሻ can be defined as
ࣦ௚ሺ߶ሻ ൌ
Ω∫ ݃ߜሺ߶ሻ|‫ݔ݀|߶׏‬ ݀‫ݕ‬ (4)
ࣛ௚ሺ߶ሻ ൌ
Ω∫ ݃‫ܪ‬ሺെ߶ሻ݀‫ݔ‬ ݀‫ݕ‬ (5)
where ߜ is the univariate Dirac function, and H is the Heaviside function.
The total energy function is defined as
ࣟሺ߶ሻ ൌ ߤ࣪ሺ߶ሻ ൅ ࣟ௚,ఒ,௩ሺ߶ሻ (6)
Here, the total energy function contains both an internal energy term and an external energy
term. The internal energy term ࣪ሺ߶ሻ penalizes the deviation of the level set function from a
signed distance function and the external energy term ࣟ௚,ఒ,௩ሺ߶ሻ drives to motion of the zero level
set to the required image features like object boundaries.
The evolution equation of the level set function is defined as
డథ
డ௧
ൌ ߤ ቂ∆߶ െ ݀݅‫ݒ‬ ቀ
‫׏‬థ
|‫׏‬థ|
ቁቃ ൅ ߣߜሺ߶ሻ݀݅‫ݒ‬ ቀ݃
‫׏‬థ
|‫׏‬థ|
ቁ ൅ ‫ߜ݃ݒ‬ሺ߶ሻ (7)
4. PROPOSED METHODOLOGY
The hybrid approach is being proposed to acquire the best possible methodology for effective
tumor extraction results. The proposed algorithm can be summarized as follows:
Step 1: The first step of the combined methodology is to read the T1-weighted MR brain image.
Step 2: Apply morphological operations [9] on T1-weighted MR brain image to remove non brain
data (skull, fat, skin, muscle).
Step 3: After removing the non brain region from the T1-weighted MR brain image, use co-
clustering algorithm, in order to extract the tumor region [9].
Step 4: The tumor region obtained in the step 3, is to be defined as initial contour for level set
method.
Step 5: Use the initial contour, which is defined in the step 4 of the methodology in order to obtain
final tumor contour, by level set without re-initialization [10], which is defined in equation (7).
In order to understand the proposed methodology more clearly diagrammatic illustration is
provided in Figure 1. It can be observed that after doing initial segmentation of tumor through
co-clustering, there is a need to refine the segmentation by the level set without re-initialization.
Thus, after applying both the methods in this proposed methodology, evaluation of the
segmentation is done systematically.

FIGURE 1: Diagrammatic Illustration of the Proposed Methodology.
5. RESULTS AND DISCUSSION
5.1 Data Sets
Data sets were collected from the Department of Radiology and Imaging Science, Apollo Health
City, Hyderabad, India and Lucid Diagnostics, Hyderabad, India. These data sets have been
acquired on 1.5T Philips achieva apparatus and 1.5T G.E apparatus using an axial T1-weighted
sequence with contrast agent. The proposed method was verified on MR brain image data sets of
five patients named as Patient 1 to patient 5 where one slice was selected from the data set of
each patient to analyze the performance of the proposed method.
5.2 Evaluation Metrics
The evaluation metrics for analyzing the proposed methodology includes:
Similarity Index (SI): SI is the measurement, which provides true-segmented region relative to
the total segmented region.
ܵ‫ܫ‬ ൌ
ଶ்௉
ଶ்௉ାி௉ାிே
ൈ 100% (8)
where TP is the number of pixels detected correctly, FP is the number of pixels detected falsely
as tumor and FN is the number of pixels detected falsely as non-tumor.
Correct Detection Ratio (CDR): The CDR value indicates the degree of trueness of the actual
tumor.
‫ܴܦܥ‬ ൌ
்௉
்௉ାிே
ൈ 100% (9)
Total Segmentation Error (TSE): It is the sum of Under Segmentation Error (USE) and Over
Segmentation Error (OSE).
ܶܵ‫ܧ‬ ൌ ܷܵ‫ܧ‬ ൅ ܱܵ‫ܧ‬ (10)
where ܷܵ‫ܧ‬ ൌ
ி௉
்௉ାிே
ൈ 100% and ܱܵ‫ܧ‬ ൌ
ிே
்௉ାிே
ൈ 100%
T1-Weighted MR Brain Image
Initial Segmentation of Tumor by
Co-clustering
Refine Segmentation by Level
Set Method
Segmentation Evaluation
Skull Removal

5.3 Discussion
In this paper, we have evaluated the tumor extraction results based on the suitable evaluation
metrics like SI, CDR and TSE, and analyzed the outcomes of the proposed methodology quality
metrics values with the level set method [10]. The extracted results of proposed methodology of
the tumor are demonstrated in Figure 2 for the slice 95 of patient 2. It is observed that close
proximity to the manually segmented images by the experts and are better than level set method.
The quantitative results attained by the proposed method in comparison with level set method are
provided in Table 1.
(a) (b) (c)
(d) (e) (f)
Figure 2: Tumor extraction result of patient 2 of slice 95 (a) One axial slice of the selected tumor class (b)
Initial contour for proposed method (c) Final contour of proposed method (d) Final extracted tumor by the
proposed method (e) Extracted tumor by the level set without re-initialization (f) Manually segmented tumor.
Patient Slice No. Method SI (%) CDR (%) TSE (%)
1
101
Level Set 85.246 100 34.615
Proposed Method 88.954 96.795 24.038
2 95
Level Set 91.12 100 19.491
Proposed Method 96.305 98.488 07.5577
3 167
Level Set 80 100 50
Proposed Method 87.826 91.818 25.455
4 120
Level Set 83.119 100 40.618
Proposed Method 93.268 98.284 14.188
5 83
Level Set 81.569 100 45.192
Proposed Method 90.942 97.5 19.423
Table 1: Comparison of evaluation metrics obtained using the proposed method and level set method.
It is observed from the Table 1 that the SI of the proposed methodology varies from 87.826% to
96.305% but for level set method it is 80% to 91.12%. The CDR ranges from 91.818% to

98.488% for the proposed method. But for the level set method for all the five images CDR is
100% which is due to under segmentation. The TSE ranges from 07.5577% to 25.455% for the
proposed method and for level set method it is 19.491% to 50%, which confirms good results of
the proposed methodology as compared to level set without re-initialization.
6. CONCLUSION
The proposed tumor extraction method was tested on five abnormal brain slices of different
patients ranges from patient 1 to patient 5 and the performance was evaluated based on the SI ,
CDR and TSE evaluation metrics. It is observed that combining level set without re-initialization
with the co-clustering technique in the proposed methodology reduces the segmentation error
and provided much better quality metrics values as compared to the level set without
re-initialization. In the future research, the effect of the prior information on the object boundary
extraction with the level set method such as shape and size can be further analyze. Moreover,
the performance of the image segmentation method can be evaluated with other quality metrics
along with SI, CDR and TSE to analyze the results more efficiently.
Acknowledgement
We wish to express our sincere thanks to Dept. of Radiology & Imaging Sciences, Apollo Health
City, Hyderabad, India and Lucid Diagnostics, Hyderabad, India for providing us with different MR
Image datasets.
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Brain Tumor Extraction from T1- Weighted MRI using Co-clustering and Level Set Methods

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