Second International Conference on Computer Research and Development
AN IMPROVED METHOD OF SEGMENTATION USING FUZZY-NEURO LOGIC S.Sathish Kumar1, M.Moorthi2, M.Madhu3, Dr.R.Amutha4 1, 2, 3 Research Scholar, Sri Chandrasekhardendra Saraswathi Viswa Mahavidyalaya University, Kanchipuram, India. 4. Professor and Head of the Department Sri Venkateswara college of Engineering, Chennai, India.
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Abstract—Image segmentation is an important process to extract information from complex medical images. Segmentation has wide application in medical field. The main objective of image segmentation is to partition an image into mutually exclusive and exhausted regions such that each region of interest is spatially contiguous and the pixels within the region are homogeneous with respect to a predefined criterion. Widely used homogeneity criteria include values of intensity, texture, color, range, surface normal and surface curvatures. During the past, many researchers in the field of medical imaging and soft computing have made significant survey in the field of image segmentation. This paper aims to develop an improved method of segmentation using FuzzyNeuro logic to detect various tissues like white matter, gray matter; cerebral spinal fluid and tumor for a given magnetic resonance image data set. Generally magnetic resonance images always contain a significant amount of noise caused by operator performance, equipment, and the environment, which can lead to serious inaccuracies. So segmentation of such medical images is a challenging problem in the field of image analysis. Several diagnostics are based on proper segmentation of the digitized image. Segmentation of medical images is needed for applications involving estimation of the boundary of an object, classification of tissue abnormalities, shape analysis, contour detection. In particular Fuzzy-Neuro logic segmentation algorithm is used to provide satisfactory results compared to K-means, Fuzzy C-Means, Neural Network and Fuzzy logic.
II.
A. K-Means K-means is one of the simplest unsupervised learning algorithms that solve the well known clustering problem. The procedure follows a simple and easy way to classify a given data set through a certain number of clusters. Step1: Choose K Initial Centers Z1(1), Z2(2), which are arbitrary. Step2: At the Kth Iterative Step, distribute the sample {X} among the K Cluster Domain ,using the relation X € Sj(k) if || X- zj(k) || < || X-z i(k) ||, Where sj(k) is the set of samples whose cluster center is zj(k). Step3: From the result of step 2, calculate the new clusters zj(k+1), where j=1,2------k zj(k+1)=1/nj ∑ x ,X € Sj(k) Where nj is the number of samples in sj(k) and the cluster centers are sequentially updated. Step4: If zj(k+1)= zj(k) ,then the algorithm is said to have converged and the procedure is terminated ,otherwise go to step 2. The major disadvantage of K- means algorithm is that it contains several misclassified data points after segmentation of brain image [2].
Keywords- Fuzzy-Neuro logic, segmentation, K-means, Fuzzy CMeans, Neural Network, Fuzzy logic.
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B.
Fuzzy C- Means The fuzzy c-means clustering takes more time to perform the classification distinct of tissue types. Fuzzy C-means Clustering (FCM) is a clustering technique which is employs fuzzy partitioning such that a data point can belong to all groups with different membership grades between 0 and 1.FCM is an iterative algorithm. The aim of FCM is to find cluster centers (centroids) that minimize a dissimilarity function. The algorithm is defined by the following steps[3]. Step1. Randomly initialize the membership matrix U according to
INTRODUCTION
Image segmentation may be defined as a technique, which partitions a given image into a finite number of nonoverlapping regions with respect to some characteristics, such as gray value distribution, texture distribution, etc. Segmentation of medical images is required for many medical diagnoses like radiation treatment, planning volume visualization of regions of interest (ROI) defining boundary of brain tumor and intra cerebral brain hemorrhage, etc. Many approaches are based on fuzzy logic, K means and Neural Networks (NN). 978-0-7695-4043-6/10 $26.00 © 2010 IEEE DOI 10.1109/ICCRD.2010.155
EXISITNG METHODS
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c
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ij
1, j 1,..., n .
Figure 1. Architecture of RBF Neural Network
(1)
i 1
¦ ¦ n j
ci
Step2. Calculate the centroid using
It is a multilayer feed forward network. There exists n number of input neurons and m number of output neurons with hidden layers existing between the input and output layers. The interconnection between the input and hidden layers forms hypothetical connection and between the hidden layer and output layers forms weighted connections. The training algorithm is used for the update of weights in all the interconnection [7]. The important aspect of the RBF Network is the usage of activation function for computing the output, where it uses the Gaussian activation function. The response of such a function is non negative for all values of x. The function is defined as f(x) = exp(-x2)
m
u xj 1 ij n j 1
u ij
m
Step3. Compute dissimilarity between centroids and data points using c
¦ Ji
J (U , c1 , c2 ,..., cc )
i 1
i;
c
n
¦¦ u
m ij
d ij
2
i 1 j 1
Where, uij is between 0 and 1; ci is the centroid of cluster
dij is the Euclidian distance between ith centroid(ci) and jth data point; and m є [1,∞] is a weighting exponent. Stop if its improvement over previous iteration is below a threshold. Step4. Compute a new U using
1
uij
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c k
§ d ij ¨ 1¨ © d kj
· ¸ ¸ ¹
2 /( m 1)
The training algorithm Step 1: Initialize the weights Step 2: While stopping is false do step 3 to step 10 Step 3: For each input do step 4 to step 9 Step 4: Each input unit xi ,i=1----n.Receives input signals to all units in the layer above (hidden unit) Step5: Calculate the radial basis function Step 6: Choose the center for the RBF, the centers are chosen from the set of input vectors. A sufficient number of centers have to be selected in order to ensure adequate sampling of the input vector space Step 7: The output of the unit vi(xi) in the hidden layer and is given as vi(xi) = exp (xji ^ -xji) 2 / σi2 Where xji^ = center of the RBF unit for input variables, σi2 = width of the ith RBF unit , Xji = j th variable of input pattern Step 8: Initialize the weights in the output layers of the network to some random value Step 9: Calculate the output of the network using Ynet= wim vi (xi)+ wo, Where, H= number of hidden layer , Ynet= output value of the mth node in output layer for the nth incoming pattern, Wim = weight between ith RBF unit and mth output node, Wo = biasing term at mth output node Step 10: Calculate error and test the stopping condition.
and go to step 2.
By iteratively updating the cluster centers and the membership grades for each data point, FCM iteratively moves the cluster centers to the "right" location within a data set. FCM does not ensure that it converges to an optimal solution because of cluster centers (centroids) being initialized using U that is randomly initialized as in (1). This problem must be considered to improve the effectiveness of the FCM algorithm. C. Neural Network A Neural Network is used in order to significantly reduce the computation time, and misclassification rate of the system [4-5]. The architecture of RBF Network consists of 3 layers namely, the input, the hidden and the output layers as shown in Fig.1 1
D. Fuzzy Logic Fuzzy set theory provides a host of attractive aggregation connectives for integrating membership values representing uncertain information. The membership function of a fuzzy set in a functional form typically may be a bell-shaped function, triangle-shaped function, trapezoid-shaped function, etc. In fuzzy systems, describing the control rules is usually simpler and easier, often requiring fewer rules, and thus the systems execute faster than conventional systems. Fuzzy systems often achieve tractability, robustness, and overall low cost. The procedure for obtaining the fuzzy output of such a knowledge base can be formulated as follows [1],[6], 1) The firing level of the ith rule is determined by Ai(x0) × Bi(y0). 2) The output of the ith rule is calculated by
Φ
Xi1
Zi1
Xi1
Φ
Zi1
Φ
Xi1 Input layer
Hidden layer
Output layer
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Ci(w) = Ai(x0) × Bi(y0) → Ci(w) for all w € W 3) The overall system output, C, is obtained from the individual rule outputs Ci by C(w) = Agg{C1, . . . , Cn}for all w € W. III.
Input Image
Pre-processing
PROPOSED METHOD
The new algorithm is proposed to overcome the above said drawbacks Step 1: Read the given image, and convert it into a matrix form where each pixel value is in the range from 0-255. Step 2: Apply median filtering to remove noise. Step 3: Create fuzzy interference system. Step 4: Decide the number and type of Membership functions for the input image by tuning the membership functions. The following fuzzy rules are used in the proposed algorithm for clustering. 1) If the mean value is low and the standard deviation value is low then it is not an edge pixel. 2) If the mean value is medium and the standard deviation value is low then it is an edge pixel. 3) If the mean value is high and the standard deviation value is low then it is not an edge pixel. 4) If the mean value is low and the standard deviation value is high then it is not an edge pixel. 5) If the mean value is medium and the standard deviation value is high then it is not an edge pixel. 6) If the mean value is high and the standard deviation value is high then it is not an edge pixel. Step 5: Apply Fuzzification using the rules developed above on the corresponding pixel values of the input image which gives a fuzzy set represented by a membership function. Check the rules using rule viewer and surface viewer Step 6: Choose the cluster centers and extract the features Step 7: Clustering is done based on similarity measures Step 8: Update the membership function and cluster centers Step 9: Calculate the cost function and update the weights Step 10: Test the stopping condition and convert the column form to matrix form and display the segmented image. In Fig.2, first the input image is preprocessed using median filter to remove noise and then the membership functions are defined for the filtered image and clusters are formed using fuzziness .Then neighborhood attraction is considered to exist between neighboring pixels. This is considered as a feature for extraction. During clustering, each pixel attempts to attract its neighboring pixels toward its own cluster. This neighborhood attraction depends on two factors; the pixel intensities or feature attraction, and the spatial position of the neighbors or distance attraction, which also depends on the neighborhood structure. Consideration of these neighboring pixels greatly restrains the influence of noise.
Membership functions and Cluster centers
FL
Feature extraction
ANN
Similarity Measures
Update Membership functions and Cluster centers
Cost functions
Figure 2. Flow Diagram
Finally, the parameters referring to the degree of feature extraction are determined using RBF neural network model. Thus, the above mentioned algorithm is used to segment the white matter, gray matter, cerebral spinal fluid (CSF) and tumor for a given MRI data set. IV.
RESULTS
The following shows the input MRI image for segmentation
Figure 3. Input Image
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Thus it is seen that the misclassification rate in classifying the white , gray and CSf are highly reduced in the proposed method as compared to the previous algorithms.
The following are the segmented outputs of the given MRI image using the various methods such as K-means, Fuzzy C-means, Fuzzy Logic and Fuzzy-Neuro logic.
TABLE I.
COMPARISONS OF VARIOUS ALGORITHMS Misclassification Rate
Name of Algorithms
K-Means Fuzzy C Means RBF Neural Network
Figure 4. K Means
Fuzzy Logic Fuzzy – Neuro Logic
WHITE MATTER
GRAY MATTER
CSF
73.68
30.10
73.68
29.60
30.50
29.60
43.51
28.28
43.51
41.86
51.33
41.80
4.411
21.012
4.41
V.
Figure 5. Fuzzy C Means
CONCLUSION
In this paper, the proposed method of Fuzzy – Neuro logic, segments the different regions of the given MRI brain image data. It is seen that the misclassification rate is less using the FNL method as compared with the other previous methods. Future work will focus on developing an algorithm for reducing the misclassification rate (MR) in clustering the gray matter, where the MR is 21.012. More comprehensive comparison of FNL and the generalization of the ANN model will be addressed.
Figure 6. Fuzzy Logic
REFERENCES [1] Addallah A.Alshemawy, and Ayman A.Aly,”Edge Detection in digital images using Fuzzy logic technique”, World Academy of science ,engineering and technology 51, pp 178 - 186 , 2009. [2] Cheng Wen Cheng, Jiebouo, Kevin J.Parker,” Image segmentation via Adaptive k-means clustering and knowledge based morphological operation with biomedical application”, IEEE transaction on image processing, Vol.7, No.12, pp 1682 – 1688, 1998. [3] D. Q. Zhang and S. C. Chen, “A novel kernelized fuzzy c-means algorithm with application in medical image segmentation,” Artif. Intell. Med., vol. 32, pp. 37–52, 2004. [4] Hall L.O,Bensaid .A, Clarke .L,” A Comparison of Neural Network and Fuzzy clustering technique in segmenting magnetic resonance images of the brain”, IEEE transaction on Neural network, Vol.3, pp 672 – 682, 1992. [5]Haykins .S, “Neural networks a comprehensive foundation”, Prentice Hall Inc second edition, 1999. [6] S. Shen,W. A. Sandham, M. H. Grant, J. Patterson, and M. F. Dempsey, “Fuzzy clustering based applications to medical image processing,” in Proc. IEEE EMBS 25th Annu. Int. Conf., 2003, pp. 747–750. [7] Shah Shen, William Sandham , “MRI fuzzy segmentation of Brain tissue using Neighborhood Attraction with Neural-Network Optimization”IEEE Transaction on Information Technology in Biomedicine,Vol.4,No.3, pp 459- 467 , Sept 2005.
Figure 7. Fuzzy – Neuro Logic
It can be seen from the table I that the misclassification rate (MR) for white matter, gray matter and CSF is 73.68,30.10 and 73.68 using K-means algorithm, is 29.60, 30.50 and 29.60 using FCM algorithm, is 43.51, 28.28 and 43.51 using RBF Neural Network, is 41.86, 51.33 and 41.80 using Fuzzy logic and 4.411, 21.012 and 4.41 using FuzzyNeuro logic.
Kanchipuram. He completed his B.E degree in Electronics and Communication Engineering in the year 2001 and M.E Applied Electronics in the year 2006 , at Arulmigu
Mr.S.Sathish Kumar is pursuing his Ph.D program at Sri Chandrasekhardendra Saraswathi Viswa Mahavidyalaya University,
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Meenakshi Amman College of Engineering, Kanchipuram, Chennai, India. He has 9 years of teaching experience and he is currently working as Associate Professor in the department of Electronics and Communication Engineering at Prathyusha Institute of Technology and management, Chennai. He has published and presented many papers in National and International Conference in the area of Image processing. His research interests are Image Segmentation, Image Compression and Image detection, speech processing.
Mr.M.Moorthi is pursuing his Ph.D program at Sri Chandrasekhardendra Saraswathi Viswa Mahavidyalaya University, Kanchipuram. He completed his B.E degree at Arulmigu Meenakshi Amman College of Engineering, Kanchipuram, in Electronics and Communication Engineering in the year 2001 and M.E Medical Electronics in the year 2007 at Anna University, Guindy campus, Chennai, India. He has 9 years of teaching experience and he is currently working as Associate Professor in the department of Electronics and Communication Engineering at Prathyusha Institute of Technology and management, Chennai. He has published and presented many papers in National and International Conference in the area of Image processing. His research interests are Image Segmentation, Image Compression and Image detection. Mr.M.Madhu is pursuing his Ph.D program at Sri Chandrasekhardendra Saraswathi Viswa Mahavidyalaya University, Kanchipuram. He completed his B.E degree in Electronics and Communication Engineering in the year 2001 and M.E Applied Electronics in the year 2006, at Arulmigu Meenakshi Amman College of Engineering, Kanchipuram, Chennai, India. He has 7 years of teaching experience and he is currently working as Assistant Professor in the department of Electronics and Communication Engineering at Rajiv Gandhi College of Engineering, Sriperumbudur, Chennai. He has published and presented many papers in National and International Conference in the area of Image processing. His research interests are Image Segmentation, Image Compression and Image detection, speech processing.
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