A Fuzzy Image Segmentation using Feedforward Neural Networks with Supervised Learning

Transcription

1 Proceedngs of the Internatonal Conference on Cognton and Recognton Fuzzy Image Segmentaton usng Feedforward Neural Networks wth Supervsed Learnng N. Krshnan 1, C. Nelson Kennedy Babu 2, V.V. Joseph Rajapandan 3 and N. Rchard Devaraj 3 1Professor and Head, CITE, Manonmanam Sundaranar Unversty, Trunelvel, Inda. 2ssstant Professor, Dept. of Computer Scence and Engneerng, Shr Bhagawan Mahaveer Jan College of Engneerng, Bangalore. 3 M. Tech Student, CITE, Manonmanam Sundaranar Unversty, Trunelvel, Inda. Inda. bstract neuro -fuzzy mage segmentat on s proposed n ths paper. The gven mage s clustered by usng Fuzzy-C-Means algorthm whch s an unsupervsed approach. Combnng ths unsupervsed clusterng to a neural network wth unsupervsed learnng wll lead to unrelable segmentaton. Therefore, n the proposed work the labels obtaned from clusterng through the fuzzy-c-means algorthm s used to defne the target of the supervsed feedforward neural network and a fuzzy entropy method s deployed to set a threshold value for mprovng the segmented mage. The proposed algorthm s tested on varous gray-level mages and results good segmentaton. 1. INTRODUCTION Segmentaton subdvdes an mage nto ts consttuent regons or objects. It can also be regarded as a process of groupng pels together that have smlar attrbutes. The level to whch the subdvson s carred depends on the problem beng solved. That s, segmentaton should stop when the objects of nterest n an applcaton have been solated.[1-4] Majorty of the segmentaton algorthms are based on the unsupervsed learnng [5,6] but n ths paper, we propose a system capable to perform segmentaton of mages wth supervsed learnng. The proposed system conssts of four phases. In the frst phase the hstogram values are computed for the gven nput mage. In the second phase, based on the hstogram values clusterng s made by usng Fuzzy-c-Means (FCM). In the thrd phase the mage s segmented by usng a feedforward neural network wth supervsed learnng. In the fnal phase the segmented mage from the neural network s thresholded based on the fuzzy entropy value. The paper s organzed as follows. Secton II contans a survey on pror research that s most closely related to the present work. Papers related to the mage segmentaton, fuzzy clusterng, feedforward neural networks and fuzzy entropy are revewed. In Secton III clusterng usng Fuzzy-c-Means and fuzzy entropy s dscussed. Segmentaton process usng feedforward network s dscussed n Secton IV. Implementaton and the algorthm of the proposed system s presented n Secton V. Results are presented n Secton VI. In secton VII concluson drawn from the proposed work s presented. 2. FUZZY ND NEURL PPROCHES TO IMGE SEGMENTTION There are varety of approaches are avalable for mage segmentaton. In ths the fuzzy and the neural network aspects are enumerated. uto-adaptve Neuro-fuzzy segmentaton by a multlayer perceptron (MLP) network that performs adaptve thresholdng of the gven nput mage [5]. The proposed archtecture s feedforward, but unlke the conventonal MLP the learnng s unsupervsed. The output status of the network s descrbed as a fuzzy set. Fuzzy entropy s used as a measure of the error of the system. n auto adaptve neuro-fuzzy segmentaton and edge detecton archtecture was presented [6]. In that a multlayer perceptron performs mage segmentaton by adaptve thresholdng of the nput mage usng labels automatcally preselected by a fuzzy clusterng technque. The proposed archtecture s feed forward and the learnng s unsupervsed.. 396

2 Proceedngs of the Internatonal Conference on Cognton and Recognton Fuzzy segmentaton s an effectve way of segmentng out objects n pctures contanng both random nose and shadng [7]. Ths s llustrated both on mathematcally created pctures and on some obtaned from medcal magng. Neural networks make t possble to develop specal purpose object detectors that can segment arbtrarly objects n real mages wth a comple dstrbuton n the feature space after tranng wth one or several prevously labeled mages [8]. Segmentaton of medcal mages s very mportant for clncal research and dagnoss, leadng to a requrement for robust automatc methods. report on the combned use of a neural network (a multlayer perceptron, MLP) and actve contour model ( snake ) to segment structures n magnetc resonance (MR) mages s presented [9]. The concept of supervsed learnng n mult-layer perceptrons based on the technque of gradent descent was ntroduced [10]. novel mage segmentaton algorthm derved under fuzzy entropy framework was presented [11]. The fuzzy entropy functon s computed based on fuzzy regon wdth and the Shannon s functon of the mage. The defnton of Shannon s entropy n the contet of nformaton theory s crtcally eamned and some of ts applcatons to mage processng problems are revewed. new defnton of classcal entropy based on the eponental behavour of nformaton -gan s proposed along wth ts justfcaton [12]. new defnton of classcal entropy based on the eponental behavor of nformaton-gan s proposed along wth ts justfcaton [13]. The concept s then etended to gray tone mage for defnng ts global, local and condtonal entropy. 3. FUZZY CLUSTERING ND FUZZY ENTROPY 3.1 Fuzzy-c-means Fuzzy-C-Means (FCM) s the popular method of classfcaton. In FCM n-dmensonal Eucldean spaces are used to determne the geometrc closeness of data ponts by assgnng them to varous clusters or classes and then determnng the dstance between the clusters. FCM s an unsupervsed fuzzy clusterng algorthm. Unsupervsed clusterng s motvated by the need to fnd nterestng patterns or groupngs n a gven set of data. Clusterng refers to dentfyng the number of subclasses of c clusters n a data unverse X comprsed of n data samples, and parttonng X nto c clusters where ( 2 c < n). If c = 1 t denotes the rejecton of the hypothess that there are clusters n the data. If c = n consttutes the trval case where each sample s n a cluster by tself [14]. The fuzzy c-means algorthm s gven below Step 1: rbtrarly choose the ntal class centers z of the gray levels wth 1 c, where c s the total number of classes. Step 2: Compute the square Eucldean dstance measure between the gray levels g and the class center z for all classes as follows: d for 2 2, = g z (1) 1 n, c 1. Step 3: Calculate the membershp matr U gven as u, and = c = 1 2 1/ [ ( ) ] ( m 1 1/ d ), 2 1/ [ ( ) ] ( m 1 1/ d, ) 1, = 0,, for g z (2) If =, u, (3) Otherwse. Step 4: Update the class centers as 1 ( u ) n m z = n m = 1, ( u ) = h 1, g h (4) 397

3 Step 5: Check = ma Fuzzy Image Segmentaton usng Feedforward Neural Networks wth Supervsed Learnng ( t+ 1) t [ U U ]. (5) If >, then go to Step3 otherwse, Stop. The ntal value m, called the fuzzfcaton parameter, s set to be two, and t wll allevate the nose effect when computng the class centers. If the value of m s larger the senstvty of the nose wll be more. 3.2 Fuzzy Entropy The defnton of Shannon s entropy n the contet of nformaton theory s crtcally eamned and some of ts applcatons to mage processng problems [12,13]. noton of entropy n the fuzzy set was frst ntroduced by de Luca and Termn [6]. The entropy was defned to be a functonal on the fuzzy subsets of a set satsfyng a lst of aoms epressng reasonable propertes of a measure of fuzzness. The entropy ntroduced by de Luca and Termn was based on Shannon s functon ( ) = ln ( 1 ) ln(1 ),0 1 H (6) Several fuzzy entropy measures are avalable one among them s the logarthmc entropy [6]. Regardng the orgnal Shannon functon replacng µ ( ) wth p (), the probablty of occurrence of ; 1 H ( ) = µ ) nln [ ( ) ( ) ( ) ( ) ] ( ) µ lnµ + (1 µ )(1 ln 2 (7) By applyng the above Equaton (7) fuzzy entropy value s calculated and for each and every pel value n the segmented output mage from the neural network the entropy value s compared and the correspondng assgnments are made to mprove the clarty of the segmented mage. 4. SEGMENTTION USING NEURL NETWORK In ths work the network archtecture preferred s a feedforward neural network. The layers n the network are nput, hdden and output layer. ll the layers n the network wll have equal amount of the neurons. ll the neurons n the nput layer are connected to the hdden layer neurons and all the neurons n the hdden layer are connected to output layer neurons. There wll not be any drect connecton between neurons n the nput layer and the neurons n the out put layer. Ecept to the nput layer for all the other layers prevous layers gve the nputs [15]. In feedforward neural networks every node n layer L receves nput s from every node n the precedng layer L-1 and projects outputs to every node n the followng layer L+1 [15,16] The nput pattern s a 33 block and the target s defned as an error functon based on the labels that are generated usng fuzzy-c-means. Hdden Layer Input Image 33 Block k Input Layer Output Layer Fg. 1: Input mage passed as 33 block to the feedforward neural network 398

4 Proceedngs of the Internatonal Conference on Cognton and Recognton 4.1 Tranng the Network The objectve of tranng the network s to nculcate the network to learn the patterns and targets. It s an teratve process guded by optmzaton algorthms. Durng tranng the nput patterns are presented as 33 blocks and propagated through the network to produce the output. In ths work the followng steps are carred out to tran the network [15, 16]. Step 1: Present a tranng pattern and propagate t through the network to obtan the outputs. Step 2: Compare the outputs wth the desred values and calculate the error. Step 3: Calculate the dervatves?e /?? j of the error wth respect to the weghts. Step 4: djust the weghts to mnmze the error. Step 5: Repeat untl the error s acceptable small or tme s ehausted. Step 1 s a Feed-forward step or forward propagaton. Step 3 and Step4 are known as reverse pass and t s mplemented usng back propagaton tranng algorthms 4.2 Supervsed Learnng Supervsed learnng requres the parng of each nput vector wth a target vector representng the desred output; together these are called a tranng par. Usually a network s traned over a number of such tra nng pars. n nput vector s appled, the output of the network s calculated and compared to the correspondng target vector, and weghts are changed accordng to an algorthm that tends to mnmze the error. The vectors of the tranng set are appled sequentally, and errors are calculated and weghts adjusted for each vector, untl the error for the entre tranng set s at an acceptably low level [11,15]. 4.3 Forward Propagaton The frst phase s the forward propagaton. The node output values are calculated. We know that, each neuron s a processng element. Each nput s multpled by the weghts before t s appled to summaton block of neuron. The NET value wll be n NET = w (8) 1 The summated NET value wll be large n magntude and t s dffcult to be processed by the neuron. So t s further processed by the actvaton functon F to produce the neuron s output sgnal, OUT. OUT = F(NET) (9) F s a bounded non-decreasng nonlnear functon such as the sgmod functon F() -X = 1/(1 + e ) (10) So the OUT functon can be represented as - NET OUT = (1 / (1 + e ) (11) 4.4 Backpropagaton Back-propagaton s the most commonly used method for tranng multlayer feed-forward networks. The term backpropagaton refers to two dfferent thngs. It descrbes a method to calculate the dervatves of the network tranng error wth respect to the weghts by a clever applcaton of the dervatve chan-rule. It descrbes a tranng algorthm, bascally equvalent to gradent descent optmzaton, for usng those dervatves to adjust the weghts to mnmze the error. s a tranng algorthm, the purpose of back-propagaton s to adjust the network weghts so the network produces the desred output n response to every nput pattern n a predetermned set of tranng patterns. In the proposed system the weghts are updated n batch mode. 399

5 Fuzzy Image Segmentaton usng Feedforward Neural Networks wth Supervsed Learnng The error functon measures the cost of dfferences between the network outputs and the desred values. The sum-of-square error (SSE) defned below s a common choce. SSE ( t p - y p) E (12) = 2 Here p ndees the patterns n the tranng set, ndees the output nodes, and t p and y p are, respectvely, the target and actual network output for the th output node on the pth pattern. The mean-squared-error (MSE) normalzes E SSE for the number E MSE = (1/PN) E SSE (13) of tranng patterns P and network outputs N. dvantages of the SSE and MSE functons nclude easy dfferentablty and the fact that the cost depends only on the magntude of the error. 5. IMPLEMENTTION ND THE PROPOSED LGORITHM In the frst phase, for the nput mage f(,y) hstogram values are calculated. Ths hstogram values are used for clusterng. The second phase of the project s clusterng usng fuzzy c-means algorthm (FCM). In clusterng frst arbtrarly choose the ntal class centers z of the gray levels wth 1 c, where c s the total number of classes. Then we have to compute the square Eucldean dstance measure between the gray levels g and the class center z for all classes and we have to calculate the membershp matr gven as U after that the class centers value has to be updated. Then delta ( ) value has to be verfed f t s greater than the specfed value, once agan we have to fnd the membershp matr, f t s lesser stop the process. Through ths clusterng approach the gven data set s clustered and labels are generated and then we have to assgn labels for each pel. Based on ths an error functon wll be generated. Ths error functon s used as a target for the neural network. In the error functon s defned by assgn values for each and every pel based on the labels that are generated. In the thrd phase, the mage s segmented by usng the neural network. The proposed network archtecture s a feedforward network wth supervsed learnng, so the nput and the target has to be specfed to the neural network. In ths 33 block s passed as nput. The target value s the error functon. Input, hdden and output layers wll have nne neurons. Frst a feed forward network wll be constructed and the weghts W and V are ntalzed. Weght W s the weght between the nput and hdden layer neurons. Weght V s the weght between hdden and output layer neurons. Then a pattern s passed nto the network and that pattern wll be propagated forward. We have to summate the node values to calculate the node output by applyng the equatons (8) and (11). Then the node output value s compared wth the target value f the error value s less or equal to the specfed tolerant level then the nput pattern s correct for the specfed target. If the error value s hgher than the specfed value the output value has to be back propagated. In the backpropagaton the correspondng changes are made n the weght wth respect to the nput, hdden and output layer and the weghts are updated and once agan the same pattern s passed to the network and the node output value wll be compared wth the target values. Ths s an teratve process untl the error converges to the specfed value. In ths work the value specfed for convergence s For error calculaton mean square error s used (MSE). The segmented output mage from the neural network s mproved by applyng fuzzy entropy. In ths the hstogram value for the segmented mage s computed. The mamum value and the total summaton of the hstogram values are computer to obtan a probablty matr. We are computng ths because n the orgnal Shannon s functon replacng the µ ( ) wth p (), where p () s the probablty f occurrence of. From ths we can obtan the probablty matr. Usng ths n the Equaton (7) we can compute the entropy. The actual value n the pel s compared wth the entropy value and the correspondng label wll be assgned for each pel. Then the resultant wll be the thresholded output mage. 5.1 Proposed lgorthm Step 1: Input an Image f(,y) Step 2: Calculate the hstogram value h for the mage f(,y) Step 3: Cluster the mage by the hstogram value 3.1 pply FCM to generate labels 3.2 Defne the Error Functon 400

6 Proceedngs of the Internatonal Conference on Cognton and Recognton Step 4: Construct a Feedforward network and ntalze the weghts W and V. 4.1 Pass a 33 block of the gven mage as nput to the neural network 4.2 Calculate OUT (NET) n forward propagaton 4.3 Calculate Mean Square Error (MSE) 4.4 If MSE value s mnmum Go To Step pply Backpropagaton to change the weghts. 4.6 Repeat Step 4 untl all the pels n the mage are covered 4.7 STORE ths block n the segmented mage Step 5: Calculate the threshold value for the segmented mage by fuzzy entropy by usng equaton (7) Step 6: STORE the Thresholded-segmented mage n OUTPUT. Step 7: End. 6. EXPERIMENTL RESULTS In ths project so many gray level mages are tested. For a sample the results obtaned for two mages are dscussed. Frst let us consder the spne mage.(fg.2) The sze of the spne mage s The mage s clustered nto three classes e) c=3 and the fuzzfcaton parameter value s consdered as 2. Based on ths the mage s clustered and labels are generated. In the neural network segmentaton process the learnng parameterη s a constant. The segmented mage obtaned from the neural network s gven n the Fg. 3 and the segmented mage after thresholdng s n Fg CONCLUSION Fg. 2: Input Image Fg. 3: Segmented Image by Neural Network Fg. 4: Segmented Image after thresholdng Image segmentaton s an mportant preprocessng stage encountered n most automated mage understandng process. The proposed system s a blend of fuzzy logc and neural networks, that makes a system to comprehend the nformaton n an easer manner and enable the system wth the good learnng capablty. The heart of the proposed system s a feedforward neural networks that performs the adaptve segmentaton, whch s bologcally nspred. In ths work an mage s segmented by deployng a fuzzy clusterng approach and feedforward neural networks wth the supervsed learnng. The labels are generated based on the fuzzy clusterng. In ths work the cluster value s fed as 3 and the fuzzfcaton parameter m as 2. Error functon s defned based on the labels. The network archtecture desgned s 3-layer network archtecture wth nput, hdden and output layer. The sngle hdden layer feedforward neural network s traned wth the backpropagaton algorthm. The weght updaton s done n batch mode. In the segmented mage obtaned from the neural network a small amount of overlappng of gray levels s notced. To rectfy ths segmented mage s thresholded based on the fuzzy entropy [6,12,13]. fter threshold the clarty of the mage s mproved. The nose level s low n the fnal segmented mage. The system provded good results for varous mages. In most of the cases the neural network wth unsupervsed learnng s proposed for mage segmentaton [5,6,17]. In unsupervsed approach t s not possble for predctng the convergence because of the self-learnng. But n the case of the supervsed learnng, the network s traned based on the value obtaned. So the proposed system s a relable one when comparng to other approaches. 401

7 Fuzzy Image Segmentaton usng Feedforward Neural Networks wth Supervsed Learnng REFERENCES [1] Gonzalez, R.C., and Woods R.E, (2003) Dgtal Image Processng, Pearson Educaton, 2nd Edton. [2] Efford, N, (2002), Dgtal Image Processng a practcal ntroducton usng JV, Pearson Educaton. [3] Umbaugh, S.E, (1998), Computer Vson and Image Processng, Prentce-Hall Internatonal., Inc. [4] Weeks,.R,. (2003), Fundamentals of Electronc Image Processng PHI. [5] Boskovtz, V., and Guterman, H., (1996), Neuro-Fuzzy for daptve Multlevel Image Segmentaton, IEEE, p [6] Boskovtz, V., and Guterman, H., (prl 2002), n daptve Neuro Fuzzy System for utomatc Image Segmentaton and Edge Detecton IEEE Transacton on Fuzzy Systems Vol 10 No.2. [7] Carvalho, B.M., Gau, J.C., Herman, G.T., and Kong, Y., (1999), lgorthms for Fuzzy Segmentaton, Pattern nalyss & pplcatons, Spnger-Verlag. [8] Lttmann, E., and Rtter, V.H., (January 1997), daptve Color Segmentaton Comparson of Neural nd Statstcal Methods, IEEE Transactons on Neural Networks, Vol -8, No.1. [9] Mddleton, I., Damper, R.I., (2004), Segmentaton of Magnetc Resonance Images Usng Combnaton Of Neural Networks nd ctve Contour Models, ELSEVIER, Medcal Engneerng & Physcs 26, [10] Redmller, M., (1994), dvanced Supervsed Learnng n Mult-layer Perceptrons From Backpropagaton to daptve Learnng lgorthms, specal ssue on Neura l Networks (5). [11] L, X.Q., Zhao Z.W., Cheng H.D., Huang C.M., Harrs R.W., (1994), Fuzzy Logc pproach To Image Segmentaton, IEEE [12] Pal, N.R., and Pal, S.K., (July1989), Object -Background Segmentaton Usng New Defntons of Entropy, IEE Proceedngs, vol.136. [13] Pal, N.R., and Pal, S.K., (1991), Entropy: New Defnton and ts pplcatons, IEEE Transactons On Systems nd Cybernetcs, Vol.21, No 5. [14] Ross, T.J., (1997), Fuzzy Logc wth Engneerng pplcatons, McGraw-Hll Internatonal Edtons. [15] Reed, R.D., (1998), Neural Smthng Supervsed Learnng n Feedforwad rtfcal Neural Networks, Bradford Book, MIT Press Cambrdge, Massachusetts. [16] Wasserman, P.D., (1989), Neural Computng Theory and Practce, Van Nostrand Renhold, New York. [17] Hall, L.O., Bensad, M., Clarke, L.P., Velthuzen, R.P., Slbger, M.S., and Bezdek, J.C., (1992), Comparson of Neural Network and Fuzzy Clusterng Technques n segmentng Magnetc Resonance Images of the Bran IEEE Transactons on Neural Networks, Vol. 3, N