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Cellular Automata Based Edge-Detection For Brain Tumor Manoj Diwakar (Department of Computer Science & Engineering), DIT Dehradun, India [email protected] Pawan Kumar Patel (Department of Computer Science & Engineering), IIT Kanpur India [email protected] Kunal Gupta Department of Information technology, HCT, Muscat, Oman [email protected] Abstract— In the area of image processing, several methods of edge detection have been proposed till now like Sobel, Robert, Prewitt, Canny, Marr-Hildreth etc. All these methods are having their own advantages and disadvantages. In this paper a new method has been proposed for edge detection using Cellular Automata. Different rules have been applied for edge detection. The outputs are better in terms of clarity and computation time. Finally, the edge detection has been applied for detecting cancerous cells in brain. Using Cellular Automata rules helps in determining the exact location and size of tumor as edges detected using Cellular Automata are fine, continuous and clear. The results of edge detection are confirmed with graphical examples. Keywords- Edge Detection, Brain Tumor, Cellular Automata I. INTRODUCTION An edge is defined by image pixels. An edge occurs whenever there is an abrupt change in image intensity. Whenever there is a sharp change in the intensity of image pixel, the corresponding pixel would be identified as an edge pixel. The quality of edge identified by edge detection algorithm is limited by the image content. Sometimes a user knows that there should be an edge somewhere in the image but it is not shown in the result. So the parameters of the program are adjusted, trying to get the edge detected. So, developing a generalized edge detection method is a subjective process. Also because of the same reason, it is difficult to compare the performance of two edge detection algorithms. Edge detection refers to the process of identifying and locating sharp discontinuities in an image. The discontinuities appear at the boundaries of objects and edge detection algorithm aims at identifying this boundary. The classical algorithms of edge detection method uses 2D filter and convolve this 2D filter with the image. These filters returns zero values in uniform region and edges are detected in the non-uniform regions. There are large numbers of edge detection operators and each method is sensitive to particular types of edges. There are many ways for performing edge detection. However, the different methods or the operators used for edge detection may be broadly classified into two categories: Gradient: The gradient method detects the edges by looking for the maximum and minimum in the first derivative of the image. Roberts, Prewitt, Sobel works on Gradient method. Laplacian: The Laplacian method searches for zero crossings in the second derivative of the image to find edges. This detector is independent of direction.. The classical edge detection methods have certain advantages and disadvantages listed in table 1.1. TABLE 1.1: SUMMARY OF VARIOUS EDGE DETECTION OPERATORS Operators Advantages Disadvantages Sobel, Robert Simplicity, Better noise suppression Discontinuity in edges, Not accurate result Prewitt Mask simpler as compared to Sobel Discontinuity in edges Laplacian (Zero Crossing) Detection of edges and their orientations, Having fixed characteristics in all directions Noise sensitive Marr- Hildreth Simplicity, Accuracy of Zero crossing locations No edge detection at corners Canny Low error rate, Single edge point response High complexity, Little time consuming compared to others Due to the disadvantages of classical methods, there is need of an efficient method for edge detection. In Cellular Automata, the next generation evolution depends on the number of neighbors and this concept is applicable to edges also. Hence using Cellular Automata for edge detection will provide fine and continuous edges. Brain tumor consists of cancerous cells and these cells have more intensity than non cancerous cells. So these cells can be highlighted by applying edge detection. After identifying these cancerous cells, the surgery procedure requires either complete removal (tumor resection) or removing as much as possible (debulking). In some cases, tumor resection may be the only 53 978-1-4673-6217-7/13/$31.00 c 2013 IEEE
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Page 1: [IEEE 2013 International Conference on Advances in Computing, Communications and Informatics (ICACCI) - Mysore (2013.8.22-2013.8.25)] 2013 International Conference on Advances in Computing,

Cellular Automata Based Edge-Detection For Brain Tumor

Manoj Diwakar (Department of Computer Science &

Engineering), DIT Dehradun, India

[email protected]

Pawan Kumar Patel

(Department of Computer Science & Engineering),

IIT Kanpur India [email protected]

Kunal Gupta

Department of Information technology,

HCT, Muscat, Oman [email protected]

Abstract— In the area of image processing, several methods of edge detection have been proposed till now like Sobel, Robert, Prewitt, Canny, Marr-Hildreth etc. All these methods are having their own advantages and disadvantages. In this paper a new method has been proposed for edge detection using Cellular Automata. Different rules have been applied for edge detection. The outputs are better in terms of clarity and computation time. Finally, the edge detection has been applied for detecting cancerous cells in brain. Using Cellular Automata rules helps in determining the exact location and size of tumor as edges detected using Cellular Automata are fine, continuous and clear. The results of edge detection are confirmed with graphical examples.

Keywords- Edge Detection, Brain Tumor, Cellular Automata

I. INTRODUCTION An edge is defined by image pixels. An edge occurs

whenever there is an abrupt change in image intensity. Whenever there is a sharp change in the intensity of image pixel, the corresponding pixel would be identified as an edge pixel. The quality of edge identified by edge detection algorithm is limited by the image content. Sometimes a user knows that there should be an edge somewhere in the image but it is not shown in the result. So the parameters of the program are adjusted, trying to get the edge detected. So, developing a generalized edge detection method is a subjective process. Also because of the same reason, it is difficult to compare the performance of two edge detection algorithms.

Edge detection refers to the process of identifying and locating sharp discontinuities in an image. The discontinuities appear at the boundaries of objects and edge detection algorithm aims at identifying this boundary. The classical algorithms of edge detection method uses 2D filter and convolve this 2D filter with the image. These filters returns zero values in uniform region and edges are detected in the non-uniform regions. There are large numbers of edge detection operators and each method is sensitive to particular types of edges.

There are many ways for performing edge detection. However, the different methods or the operators used for edge detection may be broadly classified into two categories:

• Gradient: The gradient method detects the edges by looking for the maximum and minimum in the first derivative of the image. Roberts, Prewitt, Sobel works on Gradient method.

• Laplacian: The Laplacian method searches for zero crossings in the second derivative of the image to find edges. This detector is independent of direction..

The classical edge detection methods have certain advantages and disadvantages listed in table 1.1.

TABLE 1.1: SUMMARY OF VARIOUS EDGE DETECTION OPERATORS

Operators Advantages Disadvantages

Sobel, Robert Simplicity, Better noise suppression

Discontinuity in edges, Not accurate result

Prewitt Mask simpler as compared to Sobel

Discontinuity in edges

Laplacian (Zero Crossing)

Detection of edges and their orientations, Having fixed characteristics in all directions

Noise sensitive

Marr- Hildreth Simplicity, Accuracy of Zero crossing locations

No edge detectionat corners

Canny Low error rate, Single edge point response

High complexity, Little time consuming compared to others

Due to the disadvantages of classical methods, there is need of an efficient method for edge detection. In Cellular Automata, the next generation evolution depends on the number of neighbors and this concept is applicable to edges also. Hence using Cellular Automata for edge detection will provide fine and continuous edges.

Brain tumor consists of cancerous cells and these cells have more intensity than non cancerous cells. So these cells can be highlighted by applying edge detection. After identifying these cancerous cells, the surgery procedure requires either complete removal (tumor resection) or removing as much as possible (debulking). In some cases, tumor resection may be the only

53978-1-4673-6217-7/13/$31.00 c©2013 IEEE

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treatment method. Hence using edge detection will help in getting the exact location and size. This detection will help in surgery and also determining the treatment plan if surgery is not required.

II. RELATED WORK Edge detection remains to be the most researched topic for

many decades. Numerous methods have been proposed till now. Each method or algorithm consists of both advantages and disadvantages. Due to the benefit of edge detection in applications such as image recognition, morphing, enhancement, restoration, registration, compression, retrieval, image hiding etc., this field remains to be the most researched field by the researchers [1]. Various methods like statistical methods, difference methods and curve fitting methods have been developed for analyzing variation in image intensities. The early days of works on edge detection were done by Sobel and Roberts and their detection methods were based on simple intensity gradient operators. Later on, advanced techniques were developed by considering factors like noise (eg. in blurred images) and the nature of edges themselves like Marr Hildreth and Canny etc.

Other edge detection methods include differentiation based edge detection using logarithmic image processing (LIP) models, contrast-based methods, relaxation labeling techniques and anisotropic diffusion. In fact, these methods can be combined to achieve better performance. For instance, the second directional derivative edge detector proposed by Haralick et al. [2] is a hybrid of the differentiation method and the statistical hypothesis testing method, which leads to better performance in a noisy environment.

Also much work has been carried out using Cellular Automata for edge detection. For instance, Shohei Sato et al. [3] proposed an improved method for designing the CA based edge detector. Different rules Cellular Automata provide different accuracy. For instance in the work carried out by Fasel Qadir et al. [4], they studied the linear rules of cellular automata for edge detection and based on their study, they classified the rules into no edge detection rules, strong edge detection rules and weak edge detection rules. Finally, they showed the comparison of their classification by applying different rules on standard images. They classified 512 rules in 3 groups.

Implementations of imaging techniques in field of medicines have been an area of wide interest. One of the applications of image processing is the detection of cancerous cells. For instance, C.C. Leung et al. [5] detected the boundary of brain tumor using generalized Fuzzy Operator. Marcel Prastawa et al. [6] described a framework for automatic brain tumor segmentation from MRI images. In contrast with many other tumor segmentation methods that rely on the intensity enhancement, the method proposed does not required contrast enhanced image channels. In the work presented by Anam Mustaqeem et al. [7], an efficient algorithm was proposed for tumor detection based on segmentation and morphological

operators. In the work presented by S. Murugavalli et al. [8], an improved implementation of brain tumor detection using segmentation based on Neuro fuzzy technique had been proposed. For classification of MRI images, Kailash D.Kharat et al. [9] presented two Neural Network techniques. Based on cloud model cellular automata, Zhang Ke et al. [10] presented a new improved edge detection algorithm of images. The cloud model Cellular Automata uses direction information and edge order information as important information and finally when Cellular Automata generations are evolved, edges are detected. T.Logeswari et al. [11] presented a clustering based approach using a Self Organizing Map (SOM) algorithm for medical image segmentation. V.J.Nagalkar et al. [12] used the CT scan technique for the monitoring the images of brain part which were damaged. Tuhin Utsab Paul et al. [13] proposed a fully automated two step segmentation process of brain MRI images. Parwinder Kaur Dhillon [14] proposed a robust edge detection method based Cellular Automata (CA). In the proposed approach to the edge detection the edge pixels were strengthened and the non-edge pixels were weakened. P. Tamije Selvy et al. [15] analyzed various clustering techniques for identifying cancerous regions in MR images. Khan M. Iftekharuddin et al. [16] investigated the advantages of combining two novel texture features along with intensity in magnetic resonance (MR) images for brain tumor detection. Mona Choubey et al. [17] proposed an algorithm based on segmentation concept and runs effectively with all image formats. Khadijeh Mirzaei et al. [18] proposed a new method for eliminating noise and for detecting image edges through the use of fuzzy cellular automata. The algorithm based on the proposed method was used for edge detection in Gray level images and for noise elimination in images containing salt and pepper noise. Sudipta Roy et al. [19] proposed a fully automatic algorithm to detect brain tumors by using symmetry analysis is proposed. Here the tumor was detected and then the tumor was segmented and finally the area of the tumor was calculated.

Now, there are various disadvantages like discontinuity in edges detected, not detecting proper edges or showing edges at false place, containing extra pixels resulting in thick edges, no edge detection in noisy images etc. Due to various disadvantages, Cellular automata is an effective method and performs greatly with complex images. The proposed method using Cellular Automata is compared with classical methods and it would be shown that CA based method performs better than the classical operators.

III. CELLULAR AUTOMATA The cellular automata (CA) remain to be the most

researched topic among researchers. It is used in many physical applications. The Cellular automata have applications in various fields like biological models, image processing, language recognition, simulation, computer architecture, cryptography etc. For example, a typical application of Cellular Automata is in the generation of pseudo random numbers.

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The initial study of Cellular Automata was done by by J. Von Neumann and Stan Ulam. Von Neumann studied that Cellular automata is universal and applies to nature also. The cellular automata devised by Neumann consist of 29 states and were capable of doing all calculations. However, Von Neumann rules were never implemented on a computer due to the complexity factor. Von Neumann's study divided the Cellular automata research in 2 parts. In the first part it was shown that a centralized CA machine can perform any calculations and in the second part, it was shown that the designing of centralized CA machine is a complex task for simulation. The study of Cellular automata by Neumann only showed theoretical concept. So the researchers tried to build a practical centralized CA for simulation. Taking this concept in mind, Conway and Wolfram contribution was significant. During the seventies, Wolfram proposed his famous game of life example in which a cell would be alive in next generation only after meeting some conditions. Also during eighties, Wolfram studied the one dimensional Cellular Automata in detail and showed that 1D CA also comes with great complex behavior in coming generations.

Cell is the basic component of Cellular Automata and all calculations or operations depend on the state of cells. A cell is just like a memory element and is able to store only one state at a time. It consists of a regular grid of cells and each cell can exist in one of the two states i.e. either “On” or “Off”. The grid can be in any finite number of dimensions. Each cell consists of neighbors and sometimes the cell in consideration may also be included in neighbor. The neighborhood is defined by distance. Distance is positive number specifying the distance of neighbors from cell. Initially, all cells are in state 0 and in coming generations, the state of cells would be changed to 1 only after meeting certain conditions specified by rule numbers. For example, the rule might state that the cell would be "On" in the next generation if exactly two of the cells in the neighborhood are "On" in the current generation; otherwise the cell is "Off" in the next generation. Generally, same rule would be applied to cell but different rules can also be applied to different cells leading to a hybrid model of Cellular Automata.

The cells are arranged in a lattice form. The cells exist in one of the finite state. The state of a cell in next generation depends on the rule applied. The requirement of these rules is to define the state of the cells for the next generation. These rules are defined depending on the number of neighbors in consideration. The state in next generation depends on the state in current generation. Using a particular rule, the states are updated synchronously. For a m-state CA, each cell can take any of the values between 0 and (m 1). Then for 2-state CA the value of state of each cell can be either 0 or 1. In general, this relationship can be expressed as:

Si(t+1) = f(Si(t) + Sneigh(i)(t)) ………….. (1)

where Si denotes the state of the ith cell, t denotes the number of generations that have evolved, Sneigh(i) denotes the

set of neighbors (according to the chosen neighborhood) of the ith cell.

Figure 1.1: Generalized model of Cellular Automata

As shown in the figure 1.1, Cellular Automata changes their state continuously, according to a rule that specifies the new state of each cell based on the old states and its neighbors gives the global change of CA. After each iteration, next state is calculated according to some rules. These rules are different in 1D and 2D cellular automata. The types of cellular automata are defined by their dimension. They can be 1D, 2D, 3D etc.

1D Cellular Automata was initially studied by Wolfram. Rules defined for 1D are called Wolfram rules. There are 256 Wolfram rules numbered from 0 to 255. For 2D Cellular Automata, the models available are Moore neighborhood model (dependency on 9 neighbors), Von Neumann model (dependency on 5 neighbors), Extended Moore Neighborhood model (dependency on 25 neighbors) etc. Moore neighborhood model has been used in this algorithm i.e. the evolution of next generation of a cell depends on its 8 neighbor’s cell and the cell itself. So there can be 29=512 patterns. Each of the patterns produces either 0 or 1 input. So there are 2512 rules available.

IV. PROPOSED ALGORITHM Edge detection can be done by applying 1D or 2D rules. 2D

Cellular Automata have been used in this algorithm. The steps involved in edge detection are shown by flowchart in figure 1.2.

Figure 1.2: Steps of proposed algorithm

Setting Cellular Automata Map

Conversion to binary image

Count number of neighbors

Apply edge detection rules

Transition Function

Current State

Next State

Neighborhood State

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A. Conversion to binary image

The algorithm used here works with binary images, so the first step is to convert gray image to binary image. A binary image is a logical array of 0’s (black) and 1’s (white). For obtaining corresponding binary image of a gray scale image, toolbox function im2bw is used. It scales the entire range of the pixels intensities in the range [0 1]. Now for this conversion, various methods are available. Thresholding concept has been used here. The threshold concept works by choosing a threshold value, T, automatically and then extract (or separate) object from background.

The threshold function of binary image t(a, b) is defined as: x, if f(a,b) > T

t(a,b) = y, if f(a,b) T

Pixels labeled ‘x’ correspond to object and pixels labeled ‘y’ correspond to background. Usually, x=1 (white) and y=0 (black) by convention. When constant T is applied over an entire image, the above equation is referred to as Global thresholding. In this algorithm, global thresholding concept using Otsu’s method has been used. Toolbox function graythresh computes Otsu’s threshold. The syntax is:

[T, SM] = graythresh(f)

where f is input image, T is resulting threshold, normalized to range [0 1] and SM is separability measure. The image is segmented using function im2bw. This step is important because here the object is separated from background and so this conversion needs to be more accurate. For this reason, many different techniques were applied and it was concluded that Otsu’s method provided much better results.

B. Setting Cellular Automata Map

The next step is to define a rule i.e. for certain number of neighbors whether a cell will die, born or keep is state. For the example above, it can be assumed that all cells having 2 neighbors or less will die of loneliness, and those cells with 8 neighbors or more will die of over population. Only the cells with 5 neighbors will be born, and furthermore the cells with 3, 4, 6 and 7 neighbors keep its previous state. Here the central cell has also been taken in consideration. So the minimum number of neighbors can be 0 and maximum number of neighbors can be 9. The next step is to set up the cellular automata map which where the edge detector operation will be performed. This can be directly done by separating each pixel of the original image into one cell. The rule 124 defined for the algorithm can be stated as:

a) If a cell has less than 2 neighbors, it dies - loneliness b) If a cell has more than 8 neighbors, it dies – over

population c) If a cell has either 3, 4,6 or 7 alive neighbors, it goes

on living -- happiness d) If a cell has exactly 5 neighbors, it comes alive --

reproduction.

C. Count number of neighbors

After conversion into binary image, all cells have either black or white color. Black represents alive cells and white represents dead cells. The next step is to calculate the number of neighbors. The neighborhood matrix is calculated by considering 3 X 3 matrix at a time and then sum the values in 3 X 3 matrix. In this way, neighborhood matrix is created.

D. Apply Edge Detection Rules

The last step is to apply the edge detection rule. Different rules have been used in this algorithm. After applying the rule, the cells having 3, 4, 5, 6 and 7 will be alive in next generation. Other cells become dead in next generation and hence edge gets detected.

V. RESULTS For comparison, following 4 images have been taken in

account:

• Lena.bmp • Peppers_gray.bmp

For edge detection using Cellular Automata, rule 124 have been applied as it provides strong edge detection. Rule 124 states that “Only the cells with 3, 4, 5, 6 and 7 neighbors will be alive in next generation”. For comparison, the following classical edge detection methods have been taken in account:

• Sobel • Prewitt • Robert • Canny • Marr-Hildreth

Figure 1.3 shows the output of Lena image after applying various edge detection methods. Figure 1.3(a) to figure 1.3(g) shows the result after applying Sobel, Robert, Prewitt, Canny, Marr- Hildreth and Cellular Automata respectively. Sobel operator provides thick edges that provide clarity. At the same time, it is not able to detect the left vertical lines. Robert’s operator result is similar to Sobel with similar problem. Prewitt and Canny does not provide continuous edges. Marr-Hildreth method is also not able to detect left vertical line.

Figure 1.3(a): Original Image Figure 1.3(b): Sobel Operator

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Figure 1.3(c): Robert Operator Figure 1.3(d): Prewitt Operator

Figure 1.3(e): Canny Figure 1.3(f): Marr-Hildreth

Figure 1.3(g): Cellular Automata Rule 124

Figure 1.3: Lena Image

The graph in Figure 1.4 compares the time taken by all methods. Canny edge detection method is the most time consuming method. Time taken by Cellular Automata edge detection method is not least but as compared to other methods with respect to clarity, time taken is less.

0

0.5

1

1.5

2

Com

puta

tion

Tim

e (in

se

cond

s)

Figure 1.4: Computation time for Lena image

Figure 1.5(a) shows the original gray scale pepper image. Figure 1.5(b) to figure 1.5(g) shows the result after applying Sobel, Robert, Prewitt, Canny, Marr- Hildreth and Cellular Automata respectively.

Figure 1.5(a): Original Image Figure 1.5(b): Sobel

Figure 1.5(c): Robert Figure 1.5(d): Prewitt

Figure 1.5(e): Canny Figure 1.5(f): Marr-Hildreth

Figure 1.5(g): Cellular Automata Rule 124

Figure 1.5: Pepper image

Figure 1.6 shows the computation time taken for pepper image.

For this image also, the edges detected using Cellular Automata are fine and continuous. Also, the time taken is less as compared to Sobel, Prewitt and Canny edge detection methods.

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0123456

mpu

tati

on T

ime

(in s

econ

ds)

Figure 1.6: Computation time for Pepper image using different methods

VI. APPLYING EDGE DETECTION IN BRAIN TUMOR DETECTION

Now after getting an efficient method of edge detection, there is need to apply to some application. In this paper, the algorithm has been applied for detecting edges of tumor. The method of edge detection cannot be applied directly. Figure 1.7 shows the result after applying edge detection directly.

Figure 1.7: Applying edge detection to MRI scan of brain

As it can be seen from above figure, no conclusion can be drawn. So, in order to detect tumor properly, a number steps have to be applied before [20]. After applying all the steps, the final highlighted region obtained is shown in Figure 1.8.

Figure 1.8: Highlighted region of tumor

Now, the classical methods will be applied to the above result. The result obtained is shown in Figure 1.9. Figure 1.9(a) to Figure 1.9(f) shows the result after applying Sobel, Robert, Prewitt, Canny, Marr-Hildreth and Cellular Automata.

Figure 1.9(a): Sobel Figure 1.9(b): Robert

Figure 1.9(c): Prewitt Figure 1.9(d): Canny

Figure 1.9(e): Marr-Hildreth Figure 1.9(f): Cellular Automata Rule 124

Figure 1.9: Result after applying Classical Edge Detection methods and Cellular Automata Rule 124

As it can be seen from above figure, Sobel Operator does not provide exact size as it shows extra pixels. Robert Operator does not provide clear and continuous output. Prewitt Operator also shows extra pixels. Canny edge detection takes more time and no continuous edges are shown. Marr-Hildreth also shows slightly extra pixels. But the output obtained by using Cellular Automata provides clear, fine and continuous edges. Also, no extra pixels are detected. Further, by studying the computation time taken by various methods, it can be concluded that Cellular Automata results are much satisfactory. The computing time for edge detection of tumor is shown in figure 1.10.

00.10.20.30.40.5

Com

puta

tion

Tim

e(in

sec

onds

)

Figure 1.10: Computation Time for detecting edges of tumor

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VII. CONCLUSION For edge detection there are various classical methods but

in this algorithm edge detection using 2D Cellular Automata concept was used because the detection of edges depends on neighborhood pixels. The Cellular Automata rule number 124 provides strong and continuous edge detection. Finally the edge detection was applied to brain tumor detection. Getting accurate size and location helps in surgical approaches in brain tumor treatment which includes tumor resection (complete removal) or debulking (removing as much as possible). The algorithm was applied on numerous images and the results obtained were very good and efficient.

REFERENCES [1] Djemel Ziou, Salvatore Tabbone, “Edge Detection Techniques - An

Overview”, International Journal of Pattern Recognition and Image Analysis, 1998.

[2] Haralick, Robert M., Digital step edges from Zero crossing of Second Directional Derivatives, Pattern Analysis and Machine Intelligence, IEEE Transactions, PAMI 6 , Issue: 1, Page(s): 58- 68, Jan. 1984.

[3] Shohei Sato and Hitoshi Kanoh, “Evolutionary Design of Edge Detector Using Rule -Changing Cellular Automata”, Nature and Biologically Inspired Computing (NaBIC), Second World Congress, Page(s): 60- 65, 15-17 Dec. 2010.

[4] Fasel Qadir, Khan K. A, “Investigations of Cellular Automata Linear Rules for Edge Detection”, I. J. Computer Network and Information Security, Vol. 3, Pages 47-53, 2012.

[5] Leung, CC; Chen, WF; Kwok, PCK; Chan, FHY, “Brain tumor boundary detection in MR image with generalized fuzzy operator”, International Conference on Image Processing Proceedings, Barcelona, Spain, Volume 2, Pages 1057-1060, 14-17, 2003..

[6] Marcel Prastawa, Elizabeth Bullitt, Sean Ho, “A brain tumor segmentation framework based on outlier detection”, Medical Image Analysis, Volume 8, Pages 275–283, 2004.

[7] Anam Mustaqeem, Ali Javed, Tehseen Fatima, “An Efficient Brain Tumor Detection Algorithm Using Watershed & Thresholding Based Segmentation”, I.J. Image, Graphics and Signal Processing, Volume 10, Pages 34-39, 2012

[8] S. Murugavalli and V. Rajamani, “An Improved Implementation of Brain Tumor Detection Using Segmentation Based on Neuro Fuzzy Technique”, Journal of Computer Science, Volume 3 (11), Pages 841-846, 2007.

[9] Kailash D.Kharat, Pradyumna P.Kulkarni, M.B.Nagori, “Brain Tumor Classification Using Neural Network Based Methods”, International Journal of Computer Science and Informatics, Pages 2231 –5292, Vol-1, Issue-4, 2012.

[10] ZHANG Ke, YUAN Jin-sha, YANG Xue-ming, “Edge Detection of Images based on Cloud Model Cellular Automata”, WSEAS TRANSACTIONS on BIOLOGY and BIOMEDICINE, Issue 5, Volume 4, Pages 67-72, May 2007.

[11] T.Logeswari and M.Karnan, “An Improved Implementation of Brain Tumor Detection Using Segmentation Based on Hierarchical Self Organizing Map”, International Journal of Computer Theory and Engineering, Vol. 2, No. 4, Pages 591-595, August, 2010.

[12] V.J. Nagalkar AND S.S.Asole, “Brain Tumor Detection using Digital Image Processing based on Soft Computing”, Journal of Signal and Image Processing, Volume 3, Issue 3, Pages 102-105, 2012.

[13] Tuhin Utsab Paul and Samir Kumar Bandhyopadhyay, “Segmentation of Brain Tumor from Brain MRI Images”, International Journal of Engineering Research and Applications (IJERA), Vol. 2, Issue 3, Pages 226-231, May-Jun 2012.

[14] Prwinder Kaur Dhillon, “A Novel framework to Image Edge Detection using Cellular Automata”, IJCA Special Issue on Confluence 2012 - The Next Generation Information Technology Summit Confluence (1):1-5, September 2012.

[15] P. Tamije Selvy, V. Palanisamy, T. Purusothaman, “Performance Analysis of Clustering Algorithms in Brain Tumor Detection of MR

Images”, European Journal of Scientific Research, Volume 62, Number 3, Pages 321-330, 2011.

[16] Khan M. Iftekharuddin, Jing Zheng, Mohammad A. Islam, Robert J. Ogg, “Fractal-based brain tumor detection in multimodal MRI”, Applied Mathematics and Computation, Volume 207, Issue 1, Pages 23–41, 1 January 2009.

[17] Mona Choubey, Suyash Agrawal, “A Fully Automatic Approach to Detect Brain Cancer Using Random Walk Algorithm”, International .Journal of Computer Technology & Applications, Volume 3 (1), Pages 265-268, 2012.

[18] Khadijeh Mirzaei, Homayun Motameni and Rasul Enayatifar, “New method for edge detection and de noising via Fuzzy Cellular Automata”, International Journal of Physical Sciences Volume 6 (13), Pages 3175-3180, 4 July, 2011.

[19] Sudipta Roy, Samir K. Bandyopadhyay, “Detection and Quantification of Brain Tumor from MRI of Brain and it’s Symmetric Analysis”, International Journal of Information and Communication Technology Research, Volume 2 No. 6, Pages 477-483, June 2012.

[20] Pratibha Sharma, Manoj Diwakar, Sangam Choudhary “Application of Edge Detection in Brain Tumor Detection”, International Journal of Computer Applications (0975 – 8887) , Volume 58 – No.16, Pages 21-25 November 2012 .

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