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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 2, February 2011 HESCHL'S GYRUS AUDITORY CORTEX SLICE REGISTRATION USING ECHO STATE NEURAL NETWORK (ESNN) 1 2 R.Rajeswari, Dr.Anthony Irudhayaraj Research Scholar, Dean, Information Technology, Department of Computer Science Arupadai Veedu Institute of Technology Mother Theresa Women’s University, Paiyanoor-603104, India. Kodaikanal, India. E-mail: <email@example.com>, Email:firstname.lastname@example.org Abstract—This paper presents Herschel’s gyrus analysis. A fundamental problem in medical auditory cortex slice registration using Echo state image analysis is the integration of information from neural network (ESNN). Training the network is done multiple images of the same subject, acquired using with translation and rotational values of the selective the same or different imaging modalities and possibly points (feature points) from two images at a time at different time points. One essential aspect thereof (source and target images). The input layer is given with is image registration, i.e., recovering the geometric coordinates of the selective points of the source image between corresponding points in multiple images of and in the output layer; the labeling is the translation the same scene. While various more or less and rotational values of the selective points of the target automated approaches for image registration have image. ESNN is an estimation network which estimates the required registration information from the selective been proposed in the field of medical imaging and points of target and source image. The output of ESNN image analysis, one strategy in particular, namely is compared with radial basis function (RBF). maximization of mutual information , has been Keywords-Echo state neural network, functional extremely successful at automatically computing the magnetic resonance imaging (fMRI), Heschl's gyrus, registration of 3-D multimodal medical images of auditory cortex various organs from the image content itself. I. INTRODUCTION II. MATERIALS AND METHODS The image registration  aims to find a transformation that aligns images of the same scene A. Neural Network Structures taken at different times, from different viewpoints. It The Echo state neural network is used for has been studied in various contexts due to its learning the images. The number of neurons in the significance in a wide range of areas, including input layer is 4, and the number of neurons in the medical image fusion, remote sensing, and computer output layer is 6. vision. Medical image acquisition systems generate digital images that can be processed by a computer Input layer description and transferred over computer networks. Digital Node 1 = x coordinate of point in image 2(target imaging allows extracting objective, quantitative image) parameters from the images by image analysis. Medical image analysis exploits the numerical Node 2 = y coordinate of point in image 2(target representation of digital images to develop image image) processing techniques that facilitate computer-aided Node 3 = x coordinate of point in image 1(image interpretation of medical images. The continuing to be registered with target image) advancement of image acquisition technology and the Node 4 = y coordinate of point in image 1(image resulting improvement of radiological image quality to be registered with target image) have led to an increasing clinical need and physician’s demand for quantitative image interpretation in routine practice, imposing new and Output layer description more challenging requirements for medical image Node 1= vertical shift 204 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 2, February 2011 Node 2= upward (1) or downward (2) Column 3= y coordinate of points in target image Node 3=horizontal shift Column 4= x coordinate of points in source image Node 4= left (1) or right (2) Column 5= y coordinate of points in source image Node 5= angle with respect to axis passing Column 6= shift in rows through centre of the image Column 7= Upward or downward translation Node 6= left (1) or right (2) Column 8= shift in columns The hidden layer has been trained with different Column 9 = Horizontal translation number of nodes increasing from 2 neurons. Column 10= Rotation of source pixel coordinate The target values corresponding to x, y values of with respect to corresponding target pixel coordinate image 1 and image2 are calculated as follows Column 11= Clock wise or counterclockwise TS=size (Directions, 1) rotation for i=1:TS-1%1 I=Directions(i,:); F=Directions(i+1,:); Table 1 Rotation of source coordinates from X=F(1,1)-I(1,1); Target image coordinates Y=F(1,2)-I(1,2); 1 if X==0 & Y==1 D(i)=1; elseif X==0 & Y==1 D(i)=2; elseif X==-1 & Y==0 D(i)=3; 2 elseif X==1 & Y==0 D(i)=4; elseif X==-1 & Y==-1 D(i)=5; elseif X==1 & Y==1 D(i)=6; elseif X==-1 & Y==1 3 D(i)=7; elseif X==1 & Y==-1 D(i)=8; end end 4 Table 1 shows the direction of rotation among pixel coordinates of source and target image. The size of the image considered is 63 rows by 63 columns. The term ‘T’ refers to target image and ‘S’ refers to source image. Curved arrow to the right is the clockwise direction and the curved arrow to the left is the counter clockwise direction. Table 1 shows the 5 possible rotation of the pixel of source image to different location in target image. Table 2 presents 10 sample pixel coordinates that is used for training the network. For testing the network, the same sample points with another 10 points (total 20 points) are presented. The description of Table is as follows. Column 1 = pattern number Column 2= x coordinate of points in target image Table 2 Patterns used for training and testing ESNN Input pattern Target pattern Target(actual) Source(distorted) Translation (pixel) Rotation (degrees) 205 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 2, February 2011 Pattern x y x y Vertical Upward(1) Horizontal Left(1) Angle Direction number shift Downward(2) shift Right(2) rotated CW(2) / CCW(1) 1 3 14 1 17 2 1 1 2 3.05 2 2 5 41 3 42 2 1 1 2 0.59 1 3 22 47 19 48 3 1 1 2 5.4 1 4 34 47 32 48 2 1 1 2 7.59 2 5 38 18 36 18 2 1 0 0 7.25 1 6 28 6 27 7 1 1 1 2 2.56 2 7 48 14 47 15 1 1 1 2 0.2 2 8 49 45 48 45 1 1 0 0 1.68 1 9 36 62 35 62 1 1 0 0 1.88 1 10 13 57 12 58 1 1 1 2 0.33 1 B ECHO STATE NEURAL NETWORK in the overall architecture that have not yet been fully (ESNN) studied. An Artificial Neural Network (ANN) is an The echo state condition is defined in terms of the abstract stimulation of a real nervous system that spectral radius (the largest among the absolute values contains a collection of neuron units, communicating of the eigenvalues of a matrix, denoted by (|| || ) of the with each other via axon connections. Artificial reservoir’s weight matrix (|| W || < 1). This condition neural networks are computing elements which are states that the dynamics of the ESNN is uniquely based on the structure and function of the biological controlled by the input, and the effect of the initial neurons. These networks have nodes or neurons states vanishes. The current design of ESNN which are described by difference or differential parameters relies on the selection of spectral radius. equations. There are many possible weight matrices with the same spectral radius, and unfortunately they do not Dynamic computational models require the ability perform at the same level of mean square error to store and access the time history of their inputs and (MSE) for functional approximation. outputs. The most common dynamic neural architecture is the Time-Delay Neural Network (TDNN) that couples delay lines with a nonlinear static architecture where all the parameters (weights) are adapted with the back propagation algorithm. Recurrent Neural Networks (RNNs) implement a different type of embedding that is largely unexplored. RNNs are perhaps the most biologically plausible of the Artificial Neural Network (ANN) models. One of the main practical problems with RNNs is the difficulty to adapt the system weights. Various algorithms, such as back propagation through time and real-time recurrent learning, have been proposed to train RNNs; these algorithms suffer from computational complexity, resulting in slow training, complex performance surfaces, the possibility of instability, and the decay of gradients through the topology and time. The problem of decaying gradients has been addressed with special processing elements (PEs). ESNN possesses a highly Figure 1 Echo State Network (ESNN) interconnected and recurrent topology of nonlinear PEs that constitutes a reservoir of rich dynamics and contains information about the history of input and output patterns. The outputs of this internal PEs (echo states) are fed to a memory less but adaptive readout ALGORITHM network (generally linear) that produces the network output. The interesting property of ESNN is that only the memory less readout is trained, whereas the 1.Read data recurrent topology has fixed connection weights. This 2.Separate into inputs (datain) and target outputs reduces the complexity of RNN training to simple (dataout) linear regression while preserving a recurrent 3.Initialize number of reservoirs topology, but obviously places important constraints 206 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 2, February 2011 4.Initialize (Input to hidden layer, output to hidden Here, all fi’s are hyperbolic tangent layer, hidden to hidden layer) 5.Initialize state vector e x − e− x functions . The output from the readout • Calculate next state= tanh (input matrix * e x + e− x Input vector + hidden matrix * state +output matrix * target output) network is computed according to • Assign next state to present state and repeat step 5 and step 6 y(n + 1) = fout(Woutx(n + 1)), . (4) • Find pseudo inverse for the state matrix and multiply with targets where The recurrent network is a reservoir of highly interconnected dynamical components, states of which are called echo states. The memory less linear f out = ( f1out , f2out ,...., f Lout ) are the output unit’s readout is trained to produce the output. nonlinear functions. Generally, the readout is linear Consider the recurrent discrete-time neural network so fout is identity . The flowcharts for training and given in Figure 1 with M input units, N internal PEs, testing ESNN are given in Figure 2 and Figure 3 and L output units. The value of the input unit at time n is u(n) = [u1(n), u2(n), . . . , uM(n)]T , III IMAGE REGISTRATION Characteristic points in image 1 (Source) and The internal units are x(n) = [x1(n), x2(n), . . . , image 2 (Target) are defined. Characteristic points xN(n)]T (1) are important points through maximum alignment , and can be done. By this, unnecessary points choosing Output units are y(n) = [y1(n), y2(n), . . . , yL (n)]T can be avoided and hence the ESNN can learn with (2). less number of patterns. During training, the x, y The connection weights are given coordinates of the characteristic points of image 1 • in an (N x M) weight matrix W back = Wijback and image 2 are input in the input layer and the horizontal, vertical shifts along with angle are given for connections between the input and the in the output layer of ESNN. internal PEs, Implementation steps: Training • in an N × N matrix W = W in in ij for Step 1: Identify characteristic points in image 1 and image 2. connections between the internal PEs Step 2: Calculate translation and rotation angle. Step 3: Generate training patterns with the • in an L × N matrix W out = Wijout for information obtained in step 1 and step 2. Step 4: Train ESNN with training patterns. connections from PEs to the output units and Testing • in an N × L matrix W back = Wijback for the Step 5: Present the same set of characteristic points and obtain values in the output layer. Find connections that project back from the output to the error between obtained and actual values. the internal PEs. The activation of the internal PEs (echo state) is updated according to x(n + 1) = f(Win u(n + 1) + Wx(n) +Wbacky(n)), (3) where f = ( f1, f2, . . . , fN) are the internal PEs’ activation functions. 207 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 2, February 2011 Read a Pattern (I) and its Target (T) Read a Pattern (I) and its Target (T) value value Decide the number of reservoirs Decide the number of reservoirs Decide the number of sides in the input layer = length of pattern Decide the number of sides in the input Decide the number of sides in the output layer = layer = length of pattern number of target values Initialize random weights between input and Calculate F=Ih*I hidden layer (Ih) hidden and output layer (Ho) and Reservoir (R), State matrix (S) Calculate F=Ih*I TH = Ho * T TH = Ho * T TT = R*S TT = R*S S = tan h(F+TT+TH) S = tan h(F+TT+TH) a = Pseudo inverse (S) Wout = a*T Wout = a * T Figure 3 Flow chart for testing the ESNN IV. RESULTS AND DISCUSSIONS Figure 2 Flow chart for Training ESNN The fMRI have been obtained with standard setup conditions. The magnetic resonance imaging of a subject was performed with a 1.5-T Siemens Magnetom Vision system using a gradient -echo 208 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 2, February 2011 5 10 10 15 20 20 30 25 30 40 35 40 50 45 60 50 10 20 30 40 50 60 10 20 30 40 50 60 70 Fig.4 Heschl's gyrus, auditory cortex(target) Fig.5 Heschl's gyrus, auditory cortex (10o Overlap rotated)(source) Overlap 10 10 20 20 30 30 40 40 50 50 60 60 10 20 30 40 50 60 Fig.6 First alignment Fig.7 Second alignment Overlap Overlap 10 10 20 20 30 30 40 40 50 50 60 60 10 20 30 40 50 60 10 20 30 40 50 60 Fig.8Third alignment Fig.9 Fourth alignment p 10 10 20 20 30 30 40 40 50 50 60 60 10 20 30 40 50 60 10 20 30 40 50 60 209 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 2, February 2011 Fig.10 Fifth alignment Fig.11 Sixth alignment p 10 10 20 20 30 30 40 40 50 50 60 60 10 20 30 40 50 60 10 20 30 40 50 60 Fig.12 Seventh alignment Fig.13 Sixth alignment Overlap 10 10 20 20 30 30 40 40 50 50 60 60 10 20 30 40 50 60 10 20 30 40 50 60 Fig.14 Eighth alignment Fig.15 Final alignment x 10 4 Error Metric 10 1.52 9 1.5 8 Variational Distance 1.48 7 Bhattacharya Distance Harmonic Mean 1.46 Alignment error 6 1.44 5 1.42 4 3 1.4 2 1.38 1 1.36 0 1.34 1 2 3 4 5 6 7 8 9 10 0 5 10 15 20 25 Iteration Fig.16 Error metric Fig.17 MI for the alignment using ESNN 210 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 2, February 2011 echoplanar (EPI) sequence (TE 76 ms, TR 2.4 s, flip Conference on Computational Intelligence and Multimedia Application, Xi’an, China, September angle 90 , field of view 256 - 256 mm, matrix size 64 2003, pp. 385–390. * 64, 42 slices, slice thickness 3 mm, gap 1 mm), and . R. Gan, J. Wu, A. C. S. Chung, S.C.H. Yu, and W.M. a standard head coil. A checkerboard visual stimulus Wells III, “Multiresolution image registration based on flashing at 8 Hz rate (task condition, 24 s) was Kullback-Leibler distance,” in Proceedings of Medical Image Computing and Computer Assisted Intervention alternated with a sound (control condition, 24 s). In (MICCAI), Saint-Malo, 2004, pp. 599–606. total, 110 samples (3-D volumes) were acquired. . J.P.W. Pluim, J.B.A. Maintz, M.A. Viergever, Mutual- information based registration of medical images: a Figure 4 shows the Heschl's gyrus, auditory survey, IEEE Trans. Med.Imaging 22 (6) (2003) 986– 1004. cortex (target) image slice. This image is rotated . S.Purushothaman, D.Suganthi, fmri segmentation using through 10o clockwise. This is treated as the source echo state neural network, International Journal of image (Figure 5). Figure 6 to Figure 15 shows the Image Processing,vol(2),Issue(1),2008,pp 1‐9 alignment of source with target at each iteration. Figure 16 presents the error metric of variational AUTHORS PROFILE distance, Bhattacharya distance and Harmonic Mean and Figure 17 presents the mutual information for the R.Rajeswari was born in Madurai, 04.01.1967, alignment using ESNN. received her masters degree in Information Technology in 2002 from Bharathidasan University, V. CONCLUSION Tiruchirappalli and Master of Philosophy in This paper describes implementation of ESNN Computer science in 2005 from Alagappa University. for registration of Heschl's gyrus, auditory cortex She is pursuing her PhD degree in Mother Teresa image slice. ESNN take least time to learn the Women’s University, Kodaikanal, India. Her alignment of characteristic points. Doctoral study is on Image registration in medical imaging. Her research interests include Image REFERENCES processing. . Josien P. W. Pluim And J. Michael Fitzpatrick, Image Registration , IEEE Transactions On Medical Imaging, Vol. 22, No. 11, November 2003 A.Anthony Irudhayaraj was born on 15-03-1956. He . G. Khaissidi, M. Karoud, H. Tairi and A. Aarab is currently Professor of Information Technology in ‘Medical Image Registration using Regions Matching AVIT, Paiyanoor. He received his masters degree in with Invariant Geometrical Moments’ ICGST Computer science, Anna university and PhD degree International Journal on Graphics, Vision and Image Processing, GVIP, 08(2): pp 15-20, 2008. from Anna university. . R. Wan, M.L. Li, An overview of medical image registration, in: Proceedings of the Fifth International 211 http://sites.google.com/site/ijcsis/ ISSN 1947-5500
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