International Conference on Communication and Signal Processing, April 6-8, 2017, India
Integrated Spatial Fuzzy Clustering with Variational Level Set Method for MRI Brain Image Segmentation P Sudharshan Duth, Vipuldas C A and Saikrishnan V P Abstract—Advancements in medical imaging technologies have raised many effective analytical procedures. The promptness in the acquisition and resolution enhancements of the imaging modalities have given a lot more information to the physicians in a less intrusive way about their patients. Active contours are used to the path, segment and make images of an atomic structure matching. To do like that molding functions, that are resulting in the image data and proceeding information about size, shape, and location of this structure are considered. A part of active contour family is invoked from the level set method. The major hindrances of the level setting methods are the loading of controlling constraints and time complexity. The proposed method follows Spatial Kernel Fuzzy C-Means (SKFCM) and Variational Level Set Method (VLSM) to avoid all these imperfections. SKFCM is related to standard Fuzzy C-Means algorithm which makes uses of Gaussian RBF kernel function as a distance metric that incorporates spatial information. The VLSM uses the energy function to govern and scale down the exact processing time that will address the time complexity. The proposed system is a hybrid of both SKFCM and VLSM combined approach. Index Terms—Fuzzy C-Means, Spatial Fuzzy C-Means, Kernal Fuzzy C-Means, Spatial Kernel Fuzzy C-Means, Level Set Method, Variational Level Set Method
Segmentation is the essential part in restorative picture preparing. Image Segmentation is the method by part the pictures into equivalent amounts of called pixels. Image Segmentation can be finished in light of watching sets of pixels whereby pixels speaking to a district can be recognized by some homogeneity criteria like shading, surface or power in order to find and distinguish borders in a picture. Segmentation of medicinal pictures is unpredictable because of a few reasons, for example, attributes of imaging methodology, the geometry of life systems, incomplete volume impact, the nearness of items and clamor. Utilizations of segmentation in restorative picture handling are to recognize tumors and different pathologies. Through segmentation, different procedures like edge analysis, power location and inconsistency distinguishing proof are done. These procedures permit a doctor's assignment of diagnosing the phase of the tumor to be considerably less demanding. The rest of the paper is mentioned as below. The literature survey and the background are described in section II and III respectively. Section IV discuss about the results. II. LITERATURE SURVEY
I. INTRODUCTION
T
erapeutic imaging has encountered headway in the earlier decade. The procedure of therapeutic imaging includes portrayal of the body's inside organs, which helps in restorative examination and other medicinal resolutions. There are numerous methods for therapeutic imaging at present-day like X-RAY, CT's and MRI. The information delivered through these techniques are connected in various ranges of restorative investigation like molecular imaging, nanotechnology and so on.
P Sudharshan Duth is associated with the Department of Computer Science, Amrita School of Arts and Sciences, Amrita Vishwa Vidhyapeetham, Mysore Campus, Amrita University, Karnataka, India. (Email:
[email protected]). Vipuldas C A is with the Department of Computer Science, Amrita School of Arts and Sciences, Amrita Vishwa Vidhyapeetham, Mysore Campus, Amrita University, Karnataka, India. (E-mail:
[email protected]). Saikrishnan V P is with the Department of Computer Science, Amrita School of Arts and Sciences, Amrita Vishwa Vidhyapeetham, Mysore Campus, Amrita University, Karnataka, India. (E-mail:
[email protected]).
In the Literature survey that we have done, we found that many researchers experimented on segmentation methods. Chan and Vese [1] proposes a method to detect an object using active contour model with the help of image using curve evolution and level set methods. And also they found that this approach can help to find boundaries of objects that are not securely defined by the gradient. Also, they reduce the enthalpy which is presented on a specific scenario of “minimal partition problem”. During formulation of the level which is set the “mean curve flow “turn into a problem on the active contour that results the boundary stop. For that, they applied numerical algorithm with a finite difference. While doing experiments on images it is founded that some sample classical snake methods based on gradient are not applicable. Pham and Prince [2] proposes an algorithm for Fuzzy segmentation on Magnetic Resonance (MR) image that having shading artefacts. This proposed algorithm is a continuation of 2-D adaptive Fuzzy c-mean with three-dimensional images.
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Due to the potential data size of the 3-D image, they came up with better multigrid based algorithm. And they tested on MR data and its found that 2-D adaptive Fuzzy c-mean gives less error rate as compared to the normal Fuzzy C-Mean algorithm. Khoo et al., [3] examine about the limitation of Radio Therapy planning and its solution for that problem by using the MRI-based efficient tool. It is used in image segmentation and registration techniques to make an effective prediction in the brain. It has found that this tool is efficient in terms of cost and performance. Zijdenbos and Dawant [4] presents a segmentation techniques on Magnetic Resonance (MR) image of the brain with emphasis on the white matter a review of methods and techniques that have suggested on Magnetic Resonance (MR) brain images segmentation with special emphasis on the White Matter Lesions segmentation. They experimented on the objects affecting MR images like noise, shading artefact. And these factors examined and proposed methods to correct for these factors affecting on MR images. And they presented generic segmentation algorithms and categorised by using region-based, edge-based, and classification algorithms. Sawant et al., [5] refers to the previous work on supervised as well as unsupervised pattern recognition technique on MR images. And due to the acquisition artefacts, it can reduce the efficiency. So they proposed interslice intensity variation approach to increase the performance of neural network back propagation for image segmentation. It has different methods, the first one is the selected point of the image fits a surface directly and another one is intermediate classification operation used to fits the surface. The two approaches showing better results in terms of quality and accuracy.
spatial information and uses Gaussian RBF kernel function. It produces good results as it uses numerous benefits of different methods. 1) SKFCM Algorithm The functioning of the SKFCM algorithm is based on the following steps: 1) Allocates the selected image pixels into dataset “X” and set the value of centres Ɛ, m 2) Membership values uij are calculated against each pixel centres such as
(1 K ( x j , vi ))
“ uij
c
1
¦ (1 K ( x , v )) j
( m 1) 1
” ( m 1)
k
k 1
wij are calculated,
3) New membership value
“ wij
uij p sij q c
¦u
p kj
skj
” q
k 1
s
“ ij
¦
kNK ( x j )
uik
”
Here NK ( x j ) denotes a square window cantered in the spatial domain x j 4) Objective function J has determined by
“J
c
N
2¦¦ wijm (1 K ( x j , vi )) ” i 1 j 1
5) Compute new centre values vi
III. BACKGROUND
n
A. Spatial Kernel FCM (SKFCM Clustering and segmentation are very adjacent terms in image processing. Clustering techniques separate pixels having the same characteristics. The separation is based on parameters like spatial information and distance metrics. During the segmentation process, the outcome of clustering is mapped to the Spatial Domain as different regions. Here data is divided into clusters based on some resemblance measures like distance, connectivity, intensity during clustering. Fuzzy cmeans is well-known clustering method where based on membership function data points are arranged. The traditional FCM is not fit for revealing non-Euclidean structure, because of spatial information does not utilise by the algorithm. spatial information is used to develop the segmentation results, Spatial FCM (SFCM) was introduced which is more efficient towards noises and outliers but only removes noise partially. A kernel parameter, using all data points in the collection is resolute in Kernel FCM (KFCM). The Euclidean distance of FCM is replaced with kernel-induced distance. KFCM with spatial constraints (SKFCM), it provides better and in addition faster segmentation result than FCM and SFCM alone. SKFCM is based on standard FCM algorithm, which combines
vi
¦w j 1 n
m ij
xj
¦w
m ij
j 1
6) The threshold of termination condition is evaluated {J (i ) J (i 1)} Ɛ , where in which the termination criterion is represented by Ɛ. If the condition is satisfies stop the procedure , else go to step2 B. Level Set Method (LSM) Level set method (LSM) act as a conceptual framework as well as a tool for numerical analysis on surface and shapes of an object in an image. Without Eulerian approach level set method can perform numerical analysis on curves and surfaces on a Cartesian grid. Also another advantage is that it can follow the object shapes. During the segmentation of 2-D images the level set method denotes zero for the closed curves this is called level set function. . Level set equation can be represented as follow.
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wT V I wt
b'I
In this equation
(1)
I
represents gradient of
I
and 'I represents the Laplacian of I . The artificial viscosity is represented as b'I and distance of curvature is represented by k. By using these level set equation we can obtain an equation as follow.
wT V I wt
bk | 'I |
Fig. 1. variational level set advancement of (a)” μ=0.02” and (b) “μ=0.01” for 200 iterations
(2)
C. Variational Level Set Method The Variational Level Set” Methodology (VLSM) concentrates in holding the amount set perform to be closed to a signeddistance perform, this eradicates re-initialisation method. Now segmenting image, the active curve will change in the direction of the borders of an entity. This is ready through energy from outside that moves the 0th level curvatures to margins of respective region. Here little parameters are compelled to be thought of during this Variational Level Set technique, inorder for inducing the outcome as correct as possible. Quality deviance of Gaussian distribution has these aspects, internal energies constraint, constraints of Weighted Length Term along with constraint of Weighted Space Term. Everyone plays a significant part within the progression of Level Set technique. Cautious choice of those values of the parameters are required to keep up the steadiness of development Level Set equivalence. The interior energy is the constraint that reins the outcome of castigating the deviance φ from the allotted role of distance. There is a vary in the period step τ and therefore the constant μ should satisfy τμτμ < 0.2 so as to conserve stablility in Level Set development. On behalf of τμ < 0.2, minor μ takes lengthier period to phase the image with an equivalent range of iterations. Fig. 1(b) displays the ultimate development of Level Set bend outlying from borderline of object with the same number of iteration comparing with respect to Fig. 1(a). The constraint of Prejudiced Space Term, α can be progressive or destructive, accountable for comparative point of the preliminary contour to the article of interest. The positive ‘α’ is used for shrinking inwardly and negative ‘α’ is contour to inflate outward. The standard deviation value can make the change in outcome of the real contour value. The value of boundary pointer is related to Gaussian distribution of the collected image. The Gaussian method value is totally based on the value of Standard Deviance. It always shows about the bell shaped distribution, which is denoted as normal distribution. The properties of Gaussian and Standard Deviation value reflects the width as well as shape of the bell. The small pointers is related to slight bell and showing tall peak. The large value in Standard Deviance shows a extensive bell in addition to short uttermost changes.
Fig . 2. The evolution of variational level set with various standard deviation. Edge indicator is on the left side and complete level set curve on the right of image.
“Variational Level Set Method” in Medical Image Segmentation “Different sorts of medical pictures, for example, “X-RAY image, MRI (Magnetic Resonance Imaging)” picture and ultrasound picture have the variational level set strategy tried. Fig. 3 depicts the process of the Level Set contour on different images of bone. The Level Set curvature has slowly moved towards the borders of the bone area. The first rectangle contour filled the borders leg bone at 850 repetitions. At each Level Set, contour is of bounded bones shape. “Variational Level Set Method(VLSM)” can handle the various piercing turns of the brains, and is on the way to change the level of border of brain. 1) Algorithm The computational steps are given below, 1. v1 and v2 are “class centroid values” of “Distance function ” and. Also Set B with zeros. 2. Calculate Level set functions and using (20) 3. Compute v1 and v2 with (21) 4. Compute B with the equation (22) 5. External force is Calculate using (25) 6. External force is added using (25) 7. LBM can be used to resolve convection diffusion using equation (3). 8. On each grid point Accumulate values using equation (6) that creates at each point with an updated database. 9. Check the contour. 10. “ O “ value is increased if segmentation is incomplete. And go to step 5
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IV. EXPERIMENTAL RESULTS The enactment of the suggested SKFCM is evaluates in this section. The image of brain MRI is taken for trial and it is in 3 bands such as: T1-weighted, proton density (pd)-weighted and T2-weighted. The Brain Web image is used to obtain the brain image. In the proposed work we have taken the transversal bit map, the slice fatness is with 1 mm slice thickness in addition to 217 x 181 pixels size. We used the 3x3 square brain image pixels with similar weighting exponent m=2.0. MatlabR R2013a Used to implement and simulated all the algorithms.
many kinds of noise. Thus for image segmentation it is appropriate to use variational level set method. The below Table I shows the achieved CPU time in seconds for the proposed method with other existing methods which proves reduction in time complexity.
Fig. 5. (a) “Segmentation outcomes of CV method” (b) “Segmentation outcome of Balla et al.,” (c) “Segmentation results of proposed method.”
ACKNOWLEDGMENT
Fig. 3. Initial segmentation using SKFCM
We are thankful to our guide and the faculties of Computer Science Department, (Amrita Vishwa Vidyapeetham, Mysuru Campus) who helped me in guiding at various stages of the work. REFERENCES [1] [2] [3]
[4] [5]
Fig. 4. Final segmentation using proposed method
[6]
Fig. 3 shows the initial segmentation results using SKFCM method. Fig. 4 indicates the result of final segmentation of suggested technique. In summary, suggested technique gives a good segmentation result. Since, SKFCM incorporate spatial information and uses kernel metric, it shows less liable to
[7]
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Chan, T. F., & Vese, L. A. (2001). Active contours without edges. IEEE Transactions on image processing, 10(2), 266-277. Pham, D. L., & Prince, J. L. (1999). Adaptive fuzzy segmentation of magnetic resonance images. IEEE transactions on medical imaging, 18(9), 737-752. Khoo, V. S., Dearnaley, D. P., Finnigan, D. J., Padhani, A., Tanner, S. F., & Leach, M. O. (1997). Magnetic resonance imaging (MRI): considerations and applications in radiotherapy treatment planning. Radiotherapy and Oncology, 42(1), 1-15. Zijdenbos, A. P., & Dawant, B. M. (1993). Brain segmentation and white matter lesion detection in MR images. Critical reviews in biomedical engineering, 22(5-6), 401-465. Dawant, B. M., Zijdenbos, A. P., & Margolin, R. A. (1993). Correction of intensity variations in MR images for computer-aided tissue classification. IEEE transactions on medical imaging, 12(4), 770-781. C. S. Vijayashree, Rani, N. S., and Vasudev, T., “An unsupervised classification technique for detection of flipped orientations in document images”, International Journal of Electrical and Computer Engineering, vol. 6, pp. 2140-2149, 2016. M., D. Dhanya, “Text Line Segmentation of Curved Document Images”, International Journal of Engineering Research and Applications, vol. 4, pp. 32-36, 2014.
