American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 © Global Society of Scientific Research and Researchers http://asrjetsjournal.org/ Comparison from Accuracy Time between Artificial Neural Networks (ANN) of Matlab & Iterative Resolution with Gauss Seidal to Detect the Lesion Kaouther El Kourda*, A. Naoulb, A. MAlkic aPhysics Department, E.P.S.T.A School of Algiers, Algeria, B.P:62-R.P:07000-Biskra-Algeria b,c Electronic of engineering, Biskra university, Algeria aEmail: kaouther_youcef@yahoo.fr bEmail: naoualatia@yahoo.com cEmail: malkin010455@yahoo.fr Abstract In this paper we propose an iterative method (Gauss seidal technique (GS)) to detect the lesion than compared with Matlab program for neuronal network (ANN technique), where we can see clearly the high level of detection for the both methods, but for accuracy time our propose with G S present an excellent time in front of ANN technique, The program used is Matlab. Keywords: ANN; SOR; Relaxation; Iterative. 1. Introduction In numerical linear algebra, the Gauss–Seidel method, known as the Liebmann method [1]. It is an iterative method used to solve a linear system of equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel [1]. Though it can be applied to any matrix with non-zero elements on the diagonals, convergence is only guaranteed if the matrix is either diagonally dominant, or symmetric and positive definite. It was only mentioned in a private letter from Gauss to his student Gerling in 1823[1]. A publication was not delivered before 1874 by Seidel [1]. ------------------------------------------------------------------------ * Corresponding author. E-mail address: kaouther_youcef@yahoo.fr 53 http://asrjetsjournal.org/ mailto:naoualatia@yahoo.com American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2015) Volume 14, No 2, pp 53-64 Mathematical models for information processing in computer vision could reviews all aspects of image processing, pattern recognition, geometric optics, and artificial intelligence that are important to solving computer vision problems. Also provides an introduction to digital image acquisition and display, hardware, and techniques. Discusses special computer architectures for computer vision, new neural network applications, edge detection strategies, and segmentation. For example the iterative methods used for solving large linear systems were based on relaxation of the coordinates. Beginning with a given approximate solution, these methods modify the components of the approximation, one or a few at a time and in a certain order, until convergence is reached [2]. From SPM logiciel come our idea to apply the numerical analysis in processing of image [3]. In this paper we use Gauss seidal technique to detect the position of disease medical images which obtained from hospital of Algiers-Algeria with format of "DICOM". We have problem of cost computation & accuracy of that we thought for another method which was iterative approach (Gauss Seidal (G.S)) for linear resolution . the results obtained excellent if compared with ANN technique . This paper is organized as follow. Section II, presents the principle of Gauss seidal method than some principle of ANN method. Section III describes the proposed model. Experimental results are shown in section IV. Finally section V concludes the paper. For more details of this paper by used neuronal networks, Gauss seidal & their mathematic capabilities to detect the lesion in processing of image, we pass to the following title of "back ground". 2. Background The next subtitle We are going to present some theory of numerical analysis method with GS technique than the Networks method with ANN. 2.1 Gauss Seidal method The description of Gauss Seidal method used for given a square system of n linear equations as the following [4][5][6][7][8][9][10][11]: bXA =* (1) Where             =               =           = n n nnnn n b b b b x x x X aaa aaa A . ; . .; ... ........ ... 2 1 2 1 21 11211 Then A can be decomposed into a diagonal component D, and the remainder R: 54 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2015) Volume 14, No 2, pp 53-64 ULA += (2) Where           =           = 0...00 ..00 ...0 ; ... ........ ... 2 112 21 11211 n n nnnn n a aa U aaa aaa L The solution is then obtained iteratively via )( )(1)1( kk RXbDX −= −+ (3) The element-based formula is thus: njiaab a xxx k ij ij ij k jij iji ii k i ,...2,1,;)(1 )()1()1( =−−= ∑∑ > + < + (4) Note that the computation of xi(k+1) requires each element in x(k) except itself. Unlike the Gauss–Seidel method, we can't overwrite xi(k) with xi(k+1), as that value will be needed by the rest of the computation. The minimum amount of storage is two vectors of size n. a. Convergence The convergence properties of the Gauss–Seidel method are dependent on the matrix A. Namely, the procedure is known to converge if either [2]: • A is symmetric positive-definite • A is strictly or irreducibly diagonally dominant. The Gauss–Seidel method sometimes converges even if these conditions are not satisfied. 2.2 History of Neural Networks In 1943 McCullough and Pitt [12][13], Modeling the Neuron for Parallel Distributed Processing. In 1969, Minsky and Papert [12], publish limits on the ability of a perceptron to generalize.1970’s and 1980’s are ANN renaissance. In 1986 Rumelhart, Hinton & Williams[12] present back propagation. In 1989, Tsividis[13] is a Neural Network on a chip. 2.2.1 What is a Neural Network? An artificial neural network (ANN) is an information-processing system that has certain performance characteristics in common with biological neural networks. 55 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2015) Volume 14, No 2, pp 53-64 A method of computing based on the interaction of multiple connected processing elements. Mathematical models for information processing, which based on the biological prototypes and mechanisms of human brain activities. Computational models inspired by the human brain:[12][14][15] • Massively parallel, distributed system, made up of simple processing units (neurons) • Synaptic connection strengths among neurons are used to store the acquired knowledge. • Knowledge is acquired by the network from its environment through a learning process 2.2.2 Properties of Nervous Systems • Parallel, distributed information processing • High degree of connectivity among basic units • Connections are modifiable based on experience • Learning is a constant process, and usually unsupervised 2.2.3 Biological Neuron The basic computational unit in the nervous system is the nerve cell, or neuron. A neuron has:See Fig(1) [12][13][16][17] • Dendrites (inputs) • Cell body dendrites • Axon (output) Figure 1: The schematic model of a biological neuron[2] 2.2.4 Model of an artificial neuron Figure(2) present the inputs and out puts to the neurons Synapses Dendrites Soma Axon Dendrite from other 56 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2015) Volume 14, No 2, pp 53-64 Figure 2: Model of artificial neuron [18] Where • x1, x2, ...., xn are the inputs to the neuron • w1, w2, ...., wn are real-valued parameters called weights • net = w1 x1 + w2 x2 +…+ wn xn is called the weighted sum • f: is called the activation function? • y = f(net) is the output of the neuron 2.2.5 Common Activation Functions a. Identity Function The identity function is given by :[2][19] F(x)= x (5) • Binary step function • Threshold activation function • Step f(x)=1 if x >= Ø, else 0.see fig(3) Figure 3: Identify function f[2][19] b. Binary sigmoid function The sigmoid function is: F(net) = 1/(1+exp(-λ*net)) (6) Step Threshold 57 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2015) Volume 14, No 2, pp 53-64 Figure 4: The schematic model of a biological neuron[12][20] 3. Describes The Proposed Mode We have problem of resolution in accuracy time to detect the tumor, where we have applied many numerical analysis methods. In this paper we propose from (eq(4)) a solution of this problem by using Gauss seidal method & we have compare it with network method with ANN technique (eq(6)) in matlab. At the end of resolution we reach that the both methods have same power of presentation the kind of image but Gauss seidal is the best for reduce the time . 4. Experimental Result 4.1. Algorithm • Read both image with "dicom "format • Choose a sample of image • Applied Gauss Seidal equation • Choose precision "e" than compute the error • If result less than the precision put the result on the pathological image for extract the place of lesion • Compare between ANN & Gauss Seidal methods. Examples: In the following examples we choose in Gauss seidal method the following data: -precision :e=10^-3 - Number of iteration max=200 We propose three examples which we have them from kuba hospital of algiers-algeria in 2015 Example1 We have in fig(5(a,b,c,d,e,f)) normal images & pathological ones & we want to display with two method the place of disease, fig(6.b) present the iterative method with gauss seidal, the fig(6.c) present the network mehod with ANN where we could see here that ANN detect more better than GS but the time of execution is very level in front of GS(see fig(7-(a,b)). 58 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2015) Volume 14, No 2, pp 53-64 a b c d e f Figure 5: Reel (a,c,e) & pathological (b,d,f) images Figure 6: presentation the disease with GS and ANN a. pathological image, b. result with GS, c. result with ANN method Fig.a Pathological image Fig.b.Result with Gauss-seidel Fig.c.Result with Network ANN 59 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2015) Volume 14, No 2, pp 53-64 Elapsed time for GS &ANN Elapsed time with Gauss seidal for number of repitition=200 a Elapsed time with :ANN b Figure 7: elapsed time for GS(a) & ANN(b) For the second & third example we applied the same analysis as the first one but the image s change. See fig(8(b,c)), where here GS detect the lesion better ANN & with accuracy time.see(Fig(9(a,b)) Example2 Figure 8: Presentation of illness for GS & ANN Fig.c.Result with ANN Fig.a Pathological image Fig.b.Result with Gauss-seidel 60 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2015) Volume 14, No 2, pp 53-64 Elapsed time for GS &ANN Gauss seidal a ANN b Figure 9: elapsed time for GS(a) & ANN(b) Example3 For the third example where the both method detect with same level the lesion.(fi(10)), but always GS is better in accuracy .see(Fig(11(a,b)) Figure 10: Presentation the disease with GS and ANN Fig.a Pathological image Fig.b.Result with Gauss-seidel Fig.c.Result with ANN 61 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2015) Volume 14, No 2, pp 53-64 a.pathological image, b.result with GS ,c.result with ANN method GS a ANN b Figure 11: Elapsed time for GS(a) & ANN(b) Resume the three examples in table Table 1: Two examples' resuts of many surfaces for Gauss & ANN Time of executio n(s) Gauss Time of executio n(s) ANN kind of detectio n Gauss Kind of Detecti on ANN EX1 450X4 50 0.14s 367,9s less good EX2 450X4 50 0.14s 375,5s good less EX3 350X3 50 0.08s 167.28s good good 62 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2015) Volume 14, No 2, pp 53-64 5. Conclusions In this paper, we apply two linear resolution methods to extract the place of diseases in MR image. Our results indicate that the iterative Gauss Seidal converges to the solution I the same way for the both methods but GS detect in less time in comparison with Networks method with ANN. see table1 As Perspective we propose use Gauss Seidal & ANN network to detect the lesion for multi images. References [1] Black, Noel and Moore, Shirley, "Gauss-Seidel Method", MathWorld. [2] L. M. ADAMS AND H. JORDAN, Is SOR color-blind?, SIAM Journal on Scientificand Statistical Computing, 1985 [3] John Ashburner and all, " SPM12 Manual", Functional Imaging [4] Abraham Berman, Robert J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, 1994, SIAM. ISBN 0-89871-321-8. [5] Golub, Gene H.; Van Loan, Charles F. (1996), Matrix Computations (3rd ed.), Baltimore: Johns Hopkins, ISBN 978-0-8018-5414-9. [6] Black, Noel and Moore, Shirley, "Successive Overrelaxation Method", MathWorld. [7] Yousef Saad, Iterative Methods for Sparse Linear Systems, 1st edition, PWS, 1996. [8] Netlib's copy of "Templates for the Solution of Linear Systems", by Barrett et al. [9] Richard S. Varga 2002 Matrix Iterative Analysis, Second ed. (of 1962 Prentice Hall edition), Springer- Verlag. [10] David M. Young, Jr. Iterative Solution of Large Linear Systems, Academic Press, 1971. (reprinted by Dover, 2003) [11] This article incorporates text from the article Successive_over-relaxation_method_-_SOR on CFD-Wiki that is under the GFDL license. [12] Anand, R., Mehrotra, K., Mohan, C., and Ranka, S. Efficient classification for multiclass problems using modular neural networks.1995 [13] Bengio, Y. Neural networks for speech and sequence 1996 63 http://mathworld.wolfram.com/Gauss-SeidelMethod.html http://en.wikipedia.org/wiki/MathWorld http://en.wikipedia.org/wiki/Special:BookSources/0898713218 http://en.wikipedia.org/wiki/Gene_H._Golub http://en.wikipedia.org/wiki/Charles_F._Van_Loan http://en.wikipedia.org/wiki/International_Standard_Book_Number http://en.wikipedia.org/wiki/Special:BookSources/978-0-8018-5414-9 http://mathworld.wolfram.com/SuccessiveOverrelaxationMethod.html http://en.wikipedia.org/wiki/MathWorld http://en.wikipedia.org/wiki/Yousef_Saad http://www-users.cs.umn.edu/%7Esaad/books.html http://www.netlib.org/utk/papers/templates/node11.html http://en.wikipedia.org/wiki/Richard_S._Varga http://en.wikipedia.org/wiki/David_M._Young,_Jr. http://www.cfd-online.com/Wiki/Successive_over-relaxation_method_-_SOR http://www.cfd-online.com/Wiki/Main_Page http://en.wikipedia.org/wiki/GFDL American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2015) Volume 14, No 2, pp 53-64 [14] International Thompson Computer Press, Boston, MA. [15] Bengio, Y., Le Cun, Y., and Henderson, D. Globally trained handwritten word recognizer using spatial representation, space displacement neural networks and hidden Markov models. In Cowan, J., Tesauro, G., and Alspector,1994 [16] J., editors, Advances in Neural Information Processing Systems 6. [17] Morgan Kaufmann, Cambridge, MA. Bishop, C. Neural networks for pattern recognition. Oxford University Press, Oxford.1995 [18] Burrascano, P. A norm selection criterion for the generalized delta rule. 1991 [19] DARFA Neural Network Study, AFCEA Int’l Press, Fairfax,Va.,1988 [20] J. Hertz, A. Krogh, and R.G. Palmer, Introduction to the “Theory of Neural Computation, Addison- Wesley, Reading, Mass.,1991. 64 2.2.4 Model of an artificial neuron 2.2.5 Common Activation Functions