USING LEARNING CELLULAR AUTOMATA FOR POST CLASSIFICATION SATELLITE IMAGERY

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1 USING LEARNING CELLULAR AUTOMATA FOR POST CLASSIFICATION SATELLITE IMAGERY B. Moarad a, C.Lucas b, M.Varshosaz a a Facuty of Geodesy and Geomatcs Eng., KN Toos Unversty of Technoogy, Va_Asr Street, Mrdamad Cross, Tehran, Iran, Moarad@aborz.ntu.ac.r, varshosazm@ntu.ac.r b Dept. of Eectrca and Computer scence Engneerng, Unversty of Tehran,Amrabad Cross,Tehran, Iran, Lucas@mp.r KEY WORDS: Ceuar Automata, Expert System, Entropy, Hyper Spectra, Informaton Extracton, Post Cassfcaton, Reabty, Uncertanty ABSTRACT: When cassfyng an mage, there mght be severa pxes havng near among probabty, spectra ange or mahaanobs dstance whch are normay regarded as uncassfed or mscassfed. These pxes so caed chaos pxes exst because of radometrc overap between casses, accuracy of parameters estmated, etc. whch ead to some uncertanty n assgnng a abe to the pxes. To resove such uncertanty, some post cassfcaton agorthms e Maorty, Transton matrx and Probabstc Labe Reaxaton (PLR are tradtonay used. Unfortunatey, these technques are nfexbe so a desred accuracy can not be acheved. Therefore, technques are needed capabe of mprovng themseves automatcay. Learnng Automata have been used to mode boogca earnng systems n computer scence to fnd an optma acton offered by an envronment. In ths researche have used pxes as the ceuar automata and the thematc map as the envronment to desgn a sefmprovng post cassfcaton technque. Each pxe nteracts wth the thematc map n a seres of repettve feedbac cyces. In each cyce, the pxe chooses a cass (an actonhch trggers a response from the thematc map (the envronment; the response can ether be a reward or a penaty. The current and past actons performed by the pxe and ts neghbours defne what the next acton shoud be. In fact, by earnng, the automata (pxes change the cass probabty and choose the optma cass adaptng tsef to the envronment. For earnng, tow crtera for oca and goba optmzaton, the entropy of each pxe and Producer's Accuracy of casses have been used. Tests were carred out usng a subset of AVIRIS magery. The resuts showed an mprovement n the accuracy of test sampes. In addton, the approach was compared wth PLR, the resuts of whch suggested hgh stabty of the agorthm and ustfed ts advantages over the current post cassfcaton technques. 1. INTRUDUCTION There are many technques for hyper spectra mage anayss n order to extract nformaton. Cassfcaton s one of these whch are used frequenty n remote sensng. Maxmum Lehood (ML, Spectra Ange Mapper, Lnear Spectra Unmxng (LSU, fuzzy and bnary encodng are conventona agorthms for mut spectra and hyperspectra mage cassfcaton. These agorthms have ther own accuracy whch shoud be nvestgated. In order to produce thematc map t s necessary to performed post processng agorthms on the resut of cassfcaton. There are many parameters that tend to mae uncertanty n remote sensed data. These parameters arse from sensor system, compexty of the area that s covered by mage, geometrc and atmospherc dstortons (Francscus Johannes, 2000.Furthermore tranng data, sze of sampe data for estmatng of statstc such as mean and standard devaton, statstca mode for computng statstc parameters, radometrc overap and aso cassfcaton agorthms effect on abe cassfed pxes. These parameters cause to decrease accuracy of cassfcaton whch shoud be mproved n post processng stage. There are many conventona technques such as, maorty fter, Tomas s fter, transton matrx, Probabty Labe Reaxaton (PLR mode whch are used to mprove accuracy of cassfcaton resuts. Most of these agorthms are mted and nfexbe or need some bacground for usng. Ther accuracy depends on the nowedge; therefore, technques are needed capabe of mprovng themseves automatcay and compensate the ac of compete nowedge. In ths paper, at frst we express dfferent technques of post processng, then we ntroduce components of earnng automata and ther structures. We foowed by dscussng about ceuar earnng automata and the way of earnng ceuar automata. As ceuar earnng automata s goa orented and try to change ts acton wth respect many parameters such as ts experments, acton of ts neghbours and the response of envronment, t coud be used for dfferent purpose. In ths research ceuar earnng automata s used for post processng of resut of cassfcaton whch performed by maxmum ehood and near spectra unmxng agorthms. At the end the resut of agorthm s compared wth probabty abe reaxaton. 2. CONVENTIONAL POST CLASSIFICATION ALGORITHM 2.1 Maorty Fter Maorty fter s a ogca fter whch reabe centre pxe, f t s not a member of maorty cass; n other word the abe of maorty cass s gven to center pxe.ths agorthm perform n the foowng expresson.

2 If (n > n && n > n t for a = then x ε ω (1 x = centre pxe, n & n = the number of adacent pxes beong to cass and nt = threshod Usuay a movng 3*3 wndow s used and threshod 5 apped for ths purpose, the effect of ths agorthm s to smooth the cassfed mage by weedng out soated pxes that were ntay gven abes that were dssmar abes assgned to the surroundng pxes. (Mather, Thomas Fter concepts of probabty, compatbty coeffcent, neghborhood functon, and updatng rue (Rchards Probabtes: Probabtes for each pxe descrbe the chance that the pxe beongs to each of the possbe casses. In the nta stage, a set of probabtes coud be computed from pxe based and subpxe cassfers. These agorthms performed by spectra data aone, maxmum ehood and near spectra Unmxng are among these agorthms. In ths research for LSU cassfcaton the fracton of each endemember s consder as nta stage. p ( = 1 = 1 ω 0 p ( 1 ω (3 Thomas (Thomas,1980ntroduce a method based on proxmty functon whch s descrbed as foows: p (ω = probabtes of pxe beongs to cass q q f = 5 f x d2 Є ω then q =2 ese q =0 (2 5 f x 5 Є ω then q 5 =2 ese q 5 =1 (=2,4,6,8 (=1,2,3, Compatbty Coeffcent: A compatbty coeffcent descrbes the context of the neghbour and how compatbe t s to have pxe m cassfed as ω and neghbourng pxe n cassfed as ω.t s defnd as q = weght of th pxe q5= center pxe ω = th cass d52=dstance between th and center pxe. As shown n fgure1 ths agorthm uses drect adacent for ts cacuaton. Le the maorty fter, Tomas fter remove soated pxes and reabe consderng drect neghbours. It mght aso reaocate a prevousy uncassfed pxe that had been paced n the reect cass by the cassfcaton agorthm. (mather, Transton Matrces Fgure1: drect neghbor pxes Transton Probabty Matrces s an agorthm whch uses tempora nformaton and expresses the expectaton that cover types w change durng a partcuar perod of tme (Francscus Johannes, 2000 Knowedge about the dependency of crops to seasons and ther mutua sequences s vauabe for defnng the condtona probabty as P(cass ω at tme t 2 / cass ω at tme t 1. The statstca concept of marcov chans s cosey reated to ths subect, as t descrbes the dependences between a state at t 2 and the prevous states (t 1,t 0,t -1, ths agorthm concern to agrcuture area. 2.4 Probabty Labe Reaxaton N r = og K K (4 N N = 1 = 1 N = the frequency of occurrence of cass ω ω was neghbours at pxe and ; Neghbourhood Functon: A neghborhood functon s a functon of the abe probabtes of the neghborng pxes, compatbty coeffcents, and neghborhood weghts. It s defned as: q N b Nc = d r = 1 = 1 p N b = the number of neghbors consdered for pxe d =the weght factor of neghbors N c = number of casses T=number of teraton Updatng Rue: A neghborhood functon aows the neghborhoods to nfuence the possbe cassfcaton of the center pxe and update the probabtes, by mutpyng the abe probabtes by the neghborhood functon. These new vaues are dvded by ther sum n order to the new set of abe probabtes sums to be one. (5 Probabstc abe reaxaton s a postcassfcaton context agorthm whch begns by assumng that a cassfcaton based on spectra data aone has been carred out. Ths agorthm was ntroduced by hurres n 1985.Ths method s based on the ey

3 [ 1 + q ] [ 1 q ] (t+ 1 p p = (6 p + = 1 P (ω = the probabty of pxe beongs to cass ω of the t-th teraton q (ω = neghborhood functon of pxe beongs to cass ω of the t-th teraton; Therefore reaxaton s an teratve technque whch probabtes of neghbourng pxes are used teratvey to update the probabtes for a gven pxe based on a reaton between the pxe abes specfed by compatbty coeffcent. Ths approach s computatonay ntensve and robust to mage nose (zur Erangung, Fxed Structure Learnng Automata Fxed structure automata exhbt transton and output matrces whch are tme nvarant. A={α,β,F,G,φ} s a fxed structure automata whch α = {α 1,..., α r } s the set of r actons offered by the envronment that the earnng automata must choose from, β = {0, 1} s the set of nputs from the envronment, φ s set of nner state of automata, F s set of updatng nner state automata based on exst state automata and penaty and reward of envronment, G s choosng acton functon based on new state of automata 3.2 Varabe Learnng Automata Varabe structure automata exhbt transton and output matrces whch are change wth tme, a varabe earnng automata can be formay defned as a quadrupe (Oommen1, 2003: 3. LEARNING ATOMATA AND ENVIRONMENT The goa of many ntegent probem-sovng systems s to be abe to mae decsons wthout a compete nowedge of the consequences of the varous choces avaabe. In order for a system to perform we under condtons of uncertanty, t has to be abe to acqure some nowedge about the consequences of dfferent choces. Ths acquston of the reevant nowedge can be expressed as a earnng probem. Learnng Automata s a mode of computer earnng whch has been used to mode boogca earnng systems and to fnd the optma acton whch s offered by a random envronment. Learnng automata has found appcatons n system that process ncompete nowedge about the envronment n whch they operate. These appcatons ncudes parameter optmzaton, statstca decson mang, teephone routng, pattern recognton, game payng, natura anguage processng, modeng boogca earnng systems, and obect parttonng(oommen1, The earnng oop nvoves two enttes: the envronment and earnng automata; the actua process of earnng s represented as a set of nteractons between the envronment and the earnng automata the earnng automata s mted to choosng ony one of actons at any gven tme from a set of actons{α 1,..., α r } whch are offered by the envronment. Once the earnng automata decde on an acton a, ths acton w serve as nput to the envronment. The envronment w then respond to the nput by ether gvng a reward, or a penaty, based on the penaty probabty c assocated wth α. Ths response serves as the nput to the automata. Based upon the response from the envronment and the current nformaton accumuated so far, the earnng automata decde on ts next acton and the process repeats. The ntenton s that the earnng automata graduay converge toward an utmate goa. α(n {c 1,c 2,c 3, c n } Random Envronment Learnng Automata β(n Fgure2: Interacton between envronment and automata A= {α, P, b, T} (7, α = {α 1,..., α r } s the set of r actons offered by the envronment that the LA must choose from. P = [p 1 (n,..., p r (n] s the acton probabty vector p represents the probabty of choosng acton α at the nth tme nstant. β = {0, 1} s the set of nputs from the envronment 0 represents a reward and 1 a penaty. T: P β P s the updatng scheme. and defnes the method of updatng the acton probabtes on recevng an nput from the envronment. If(β=1&& α s chosen then P (n+1=p (n+α[1- P (n] If(β=1&& α s chosen then P (n+1=(1-ap (n If(β=0&& α s chosen then P (n+1=(1-bp (n If(β=0&& α s chosen then P (n+1=b/(r-1+(1-bp (n (8 Accordng to equaton 8 f a and b be equa the earnng agorthm w be nown as near reward penaty. If b<<a the earnng agorthm w nown as near reward epson penaty and f b=0 the earnng agorthm w be a near reward nacton. 4. LEARNING CELLULAR ATOMATA Learnng ceuar automata A and ts envronment E are defned as foows (Fe Qan 2001., A = {U,X, Y, Q,N, ξ, F,O, T} (9 E = {Y,C, r} (10 U = {u, = 1, 2,..., n} s the ceuar space. X = {x, 0 < } s the set of nputs Y = {y, 0 < } s the set of outputs N = {n1,, n N } s the st of neghborhood reatons. Q = {q, 0 < } s the set of nterna states. ξ : U Ω,Ω U s the neghborhood state confguraton functon

4 F : Q X r Q s the stochastc state transton functon O : Q Y s the stochastc output functon Q(t + 1 = T(Q s the renforcement scheme. C = {c, 0 < } s the penaty probabty dstrbuton. r = {r, 0 < }s the renforcement sgna. 5. USING CELLULAR LEARNING ATOMATA FOR POSTCLASSIFICATOIN In order to use ceuar earnng automata for mprovng cassfcaton accuracy, a ceuar earnng wth 8 neghbour structures s consdered, and the foowng steps whch ncude choosng an acton by automata, compute penaty probabty by envronment, updatng neghbour functons and updatng nner state are consdered Acton: Acton α s choosng one of two casses whch have more probabty; at nta state t choose randomy by automata Penaty probabty: penaty probabty c s assocated wth acton α whch s chosen by envronment. The envronment consders two crtera for evauatng acton automata: pxe entropy for oca optmzaton and omsson error for goba optmzaton of each cass. Once the automata choose an acton that ead to ncrease the entropy of pxe, envronment gves t penaty. After each teraton f the omsson error decreased the envronment w gve reward to the automata s acton. Amount of reward and penaty s compute as foows: Computng nner state of automata: n ths stage, at frst the oca probabtes of pxes based on two stage of percpence memory of neghbour pxe whch refers to penaty probabty are computed. Then, an updatng probabty roe whch depends on oca probabtes, nta nner state and neghbor functon was ntroduced. After that, nner state of automata s computed by probabty roe. The agorthm executes the steps mentoned aready and contnues unt reach to a best stuaton; the best stuaton s a state pxes have ess entropy wth the casses havng ess omsson error. 6. EVALUATION AND EXPERIMENT RESULTS In order to evauate the agorthm of post processng, a subset mage (Fgure 3 whch s a porton of the Arborne Vsbe/Infrared Imagng Spectrometer (AVIRIS of hyperspectra data s used. Ths mage was taen over an agrcutura area of Caforna, USA n Ths data has 220 spectra bands about 10 nm apart n the spectra regon from 0.4 to 2.45 µm wth a spata resouton of 20 m. The subset mage s 145 by 145 pxes and ts correspondng ground truth map s shown n Fgure 4.the mage area has 12 casses. C = a*c 1 +b*c 2 (11 C2 =omsson error 0<a,b<1, a+b=1 C 1 n p(ω= ω x = p(ω = ω x og 1 = 2 (12 Fgure 3. AVIRIS mage The amount of C maps to 0 and 1 as foows: If (C 0. 5 then β=1 ese β=0 ( Neghbour functon between automata: n order to compute the nner state of automata t shoud compute neghbour functon between automata. We use equaton 5 n whch way that the C affects on neghbour functon between automata. Fgure 4. Grand truth of area wth 12 casses At frst some nosy bands were put away. In order to separate nose, and to extract orgna sgna from mage bands the mnmum nose fracton transform was performed. Based on egenvaue of components we chose components whch had hgh varance; therefore the orgna mage dmenson was reduced. We used 46 components whch contan hgh percent of

5 orgna mage content nformaton. These features are used for cassfcaton. In order to compute cassfcaton parameters and endemember seecton the tranng sampe wth proper schema were ntroduced; aso test sampe for computng overa accuracy and cassfcaton assessment were pced. At the end, the mage was cassfed by ML (fgure 5 and LSU agorthms. The resuts of cassfcaton were sequence, rue mages and fracton mages whch used for post cassfcaton. that the CLA taes more tme as compared wth PLR and we shoud contro t by the number of teratons. 7. CONCLOSION The agorthm deveoped s so fexbe that can change abe pxes to reach an agreement between neghbour pxes and decrease chaos n envronment of mage cassfed. Therefore ceuar automata have good potenta for deang wth probems whch need to fnd the best choce unt transtng from chaos envronment to order envronment. REFERENCES References from Boos: Mather, pau M Computer processng of remotey-sensed mages, ohn wey& sons,pp Rchards, A. John,1993. Remote sensng dgta mage anayss, Thrd edton, Sprnger- Verag Bern Hedeberg, Prnted n Germany, pp Fgure 5. Maxmum ehood cassfcaton We mpemented two agorthms of ceuar earnng automata and probabty abe reaxaton. These two agorthms were used for post cassfcaton of the resut of MLC and LSU cassfcaton whch foowng resuts (tabe 1 for test sampes were obtaned. Cassfcaton Agorthm ML LSU Post processng Wthout post PLR CA Wthout post PLR CA agorthm process process Overa accuracy Tabe 1. The resut of post processng agorthm Notcng to the resut, t coud be reased that the accuracy of mages was ncreased, and the ceuar earnng automata adapted tsef better to the envronment as compared of probabty reaxaton agorthm. Another nterestng resut s that the resut of CLA for two cassfcaton agorthms s cose together. Therefore t coud be sad that the CLA coud overcome the resut of poor cassfcaton such as MLC n Hyperspectra mages. And aso CLA coud be used for transt fracton mages computed by LSU to mage cassfed and t s usefu for accuracy assessment of sub pxe cassfer. Another advantage of LA s that the CLA compensates the poor resut of cassfcaton agorthm and t sn t so senstve to nta probabty (state but PLR s too senstve to the nta probabty. In addton the resut of CLA agorthm s amost ndependent from nta probabtes and wth respect to two parameters of entropy and omsson error the CLA agorthm tres to optmze these parameters and to reach a goba optmzaton. However n PLR t s possbe to agorthm satsfed n oca optmzaton. The two parameters of a and b n equaton 11 affect to the resuts of post processng and t depends on our bas to oca or goba optmzaton. The prosperous of agorthm depends on schema whch desgns envronment so actve n whch way, response actuay to the acton of automata and compute penaty and reward n a rea way. One of the dsadvantage whch experments showed was References from webstes: Francscus Johannes Mara van der We, Assessment and vsuasaton of uncertanty n remote sensng and cover cassfcatons Facutet Rumtee Wetenschappen Unverstet Utrecht Netherands Fe Qan,Yue Zhao Hronor Hrata, Learnng Ceuar Automata for Functon Optmzaton Probems T.IEE Japan, Vo. 121-C, No.1. Oommen1,B. John and T. Dae Roberts,2003 contnuous earnng automata soutons to the capacty assgnment probem, Schoo of Computer Scence Careton Unversty Ottawa; zur Erangung des Grades, A New Informaton Fuson Method for Land-Use Cassfcaton Usng Hgh Resouton Satete Imagery An Appcaton n Landau, Germany Dssertaton archmed.un-manz.de/pub/2000/0004/dss.pdf