Comparative Studies on Feature Extraction Methods for Multispectral Remote Sensing Image Classification

Transcription

1 Comparatve Studes on Feature Extraton Methods for Multspetral Remote Sensng Image Classfaton Yanqn an and Png Guo Department of Computer Sene Beng Normal Unversty Beng, 00875, Chna Abstrat Feature extraton of multspetral remote sensng mage s an mportant task before lassfyng the mage. When land areas are lustered nto groups of smlar land over, one of the most mportant thngs s to extrat the key features of a gven mage. Usually multspetral remote sensng mages have many bands, and there may have been muh redundany nformaton and t beomes dffult to extrat the key features of the mage. herefore, t s neessary to study methods regardng how to extrat the man features of the mage effetvely. In ths paper, fve methods are omparatvely studed to redue the mult-bands nto lower dmensons n order to extrat the most avalable features. hese methods nlude the Euld dstane measurement (EDM), the dsrete measurement rtera funton (DMCF), the mnmum dfferentated entropy (MDE), the probablty dstane rteron (PDC), and the prnple omponent analyss (PCA) method. he advantage and dsadvantage of eah method are evaluated by the lassfaton results. Keywords: Multspetral Remote Sensng Image, Dmenson Reduton Methods, Feature Extraton. Introduton he number of Earth observaton satelltes that are n operatons s rsng every year. hese satelltes arry a dverse spetrum of radar and optal sensor aptal of arung mageres whh are appled n many felds suh as generatng lassfaton maps. Before the lassfaton, feature extraton s an mportant proessng proedure. Wth extrated features, a lassfer s bult to reognze the nterested obets n remote sensng mage. here are two knds of lassfaton: supervsed and unsupervsed. In general, when we have lttle knowledge about gven mage, we have to adopt unsupervsed lassfaton tehnques. Among the unsupervsed methods, the fnte mxture model analyss has many advantages [][] and t attrats many researhers nterest n mage segmentaton as well as other applatons [3][]; whereas n ths paper we adopt a fnte mxture model as a lassfer. When buldng a lassfer, we assume that the data n the feature spae as a mxture of Gaussan probablty densty dstrbuton, and the fnte mxture model s used to luster the extrated features. he expetaton-maxmzaton (EM) algorthm Mhael R. Lyu Department of Computer Sene & Engneerng he Chnese Unversty of Hong Kong Shatn, Hong Kong, Chna lyu@se.uhk.edu.hk an be used to estmate the model parameters, and fnal Bayes deson s appled to lassfy these data n the feature spae [5]. Gray value s an mportant haraterst for the analyss of varous types of remote sensng mages. It s beleved that the gray value plays an mportant role n the vsual systems for reognton and nterpretaton of gven data. Furthermore, texture analyss s an mportant researh feld n remote sensng mage proessng, as the texture desrbes the attrbuton between a pxel and the other pxels around t [6]. exture feature extraton must be onsdered based on a small regon, not a sngle pxel. However, texture analyss method has shortomngs, suh as the edge between dfferent lasses may be norretly lassfed. herefore, gray value s adopted as the features of the mage n ths paper. here exst a number of dmenson reduton methods n the lterature; here we nvestgate fve dmenson reduton methods [7]. hese methods are the Euld dstane measurement (EDM), the dsrete measurement rtera funton (DMCF), the mnmum dfferentated entropy method (MDE), the probablty dstane rteron (PDC), and the prnple omponent analyss (PCA). We redue the dmensons for the purpose that the feature nformaton may not be redundant and the onvergent speed of estmatng the parameters of lassfers may be aelerated. Classfaton auray s used to assess these methods. Dmenson reduton methods In ths paper, we fous on omparatve studyng the fve methods to redue the dmensons. hese dmenson reduton methods are desrbed n the followng paragraphs. Although we an fnd the theoret desrpton of the frst four methods n the referene [7], few researhers have appled these theores to real applatons. When the frst four methods are appled to analyze the multspetral remote sensng mage, we suppose that the orgnal mage has D bands, and the bands redued nto d dmensons after data dmenson reduton. We an defne the orgnal feature data vetor as y, the transformed data vetor as x, where y = [ y ], y, L, yd, x = [ x ], x, L, xd, and the transformaton formula s:

2 x=w y. () W s the ombnaton of the d dmenson egenvetors of a spetral matrx, where the egenvetors are orrespondng to the frst d maxmum egenvalues, and W s a D d dmenson matrx.. EDM method In the method of EDM, W s the ombnaton of the d dmenson egenvetors of matrx Sw Sb. S b s the dsrete measurement matrx among dfferent lasses and S w s the dsrete measurement matrx n the same lass [7]: S = PE ( y )( y ) () w = ( )( ) S = P b = where s the number of all the lasses, s the average vetor of the th lass, s the average vetor of all the vetor data and P s the pror probablty funton of the orrespondng th lass. E s the expetaton between the vetor data and the average vetor of the th lass. How to ompute the transformaton matrx W s llustrated wth followng numeral example. For example, there are two lasses, whh have the same pror probablty. he orrespondng mean vetors are: = [, 3, ], [ ] =,,. he orrespondng ovarane matres are: = = 0 0 0, he mean vetor s = ( + ) = [ 0,,0], the dsrete measurement matrx among dfferent lasses S b and the dsrete measurement matrx n the same lass S w omputed respetvely as follows: (3) S = ( )( ) b = = = ( )( ) ( ) Sw = S w = ( +) 3 0 = here s only one egenvalue of Sw Sb, so W=w. hen Sw Sbw= λw, or Sw ( )( ) w= λw. In ths equaton, ( ) w s a sale value, so W = w= S ( ) ( ) w =, 5, 8.. DMCF method For the DMCF method, W s the egenvetor system of the matrx. For the sum matrx between every two lasses, s desrbed as the followng equaton: ( ) = + = = M, are the ovarane of the th and th lasses, and the ovarane an be desrbed as l = l {( )( ) } = E y y = 0 ( y )( y ) () - - (5) M ( )( ) = ; and are the mean vetors of the th and th lasses, respetvely.

3 .3 MDE method For the MDE method, s the dfferentated entropy. For two lasses, = V( p, q) + V( q, p) (6) where V( p, q) s the relatve entropy, the defnton of whh an be desrbed as the followng: [ ] V( p, q) = p( y )log p( y ) q( y ) (7) py ( ), qy ( ) are the dstrbuted pror probablty funtons of the two lasses. On the assumpton that, for remote sensng mage, the pror probablty s the gray value when t s read by usng the omputer mahne. And Equaton 6 an be wrtten as ( pq, ) = px ( )log px ( ) qx ( )log qx ( ) (8) + px ( )log qx ( ) + qx ( )log px ( ) For more than two lasses, beomes ( V p p V p p ) = (, ) + (, ). (9) = = where means the summaton of all the two dfferent lasses relatve entropy.. PDC method For the method of PDC, generally W s the ombnaton of the d dmenson egenvetors of the egenvetor system = where, are the ovarane matres of the two lasses, respetvely. Here, system s supposed as the followng hypothess: the mean vetors of every lass are equal. If the mean vetors are not equal and the ovarane matres are equal whh are desrbed as, then the egenvetor system an be desrbed as the followng equaton: ( ) = (0) For more than two lasses, the egenvetor system an be wrtten as = = = ().5 PCA method For the method of PCA, we an refer to the defntons n referene paper [8]. And the transform formula s x=w (y-m); W s the ombnaton of the d dmenson egenvetors of the ovarane of the mage, n whh the orrespondng egenvalues are the maxmal ones. And W s a D d matrx and m s the data mean vetor. From the detaled desrpton of eah dmenson reduton method, we an know that exept the PCA method, all the other methods need to assgn eah pxel to a lass label at frst. However, usually we have lttle pror knowledge about of eah pxel s lass membershp. In order to resolve ths problem, we adopt the random sample method, whh means we an frst assgn eah pxel to a lass randomly. 3 Experments In order to speedup the onvergent rate whle estmatng the parameters, we use the gray hstogram method to ntalze the mean vetors and the ovarane matres. However, f an mage ontans many lasses, the peaks of the hstogram are not dstnt from eah other. It s very dffult to determne whh lasses the peaks n the hstogram should belong to and to fnd proper parameters for ntalzaton before applyng the EM algorthm. In ths ase, only random ntalzaton parameter method an be adopted. How to udge whether the feature extraton methods are good or not? In ths paper, under the same lassfaton rumstane we assess the feature extraton methods by usng the lassfaton auray. For the same testng data, f the lassfaton auray s the hghest, we thnk ths feature extraton method s the best. he fnte mxture model s adopted to analyze the multspetral remote sensng mages and the Expetaton- Maxmzaton (EM) [9] algorthm s used to estmate the parameters. Wth ths teratve EM algorthm, the mxture parameters an be estmated untl the lkelhood funton reahes a loal mnmum value. Redner [] has proved that the EM algorthm was onvergent and assured lkelhood funton ould be lose to a loal mnmum value. Perhaps there are many loal mnmum values for a gven funton. In ths paper, the parameters are adopted when the loal mnmum values reah the smallest one. Wth the pre-assgned lassfaton regon number k, P = x, the posteror probablty an be desrbed as: ( ) P( = x), L P( = k x), we use Bayes deson

4 ( ) * = arg max P x to lassfy x nto luster *. hs proedure s alled Bayesan probablst lassfaton. he unsupervsed lassfaton method s adopted beause we an get better results n the ase where there s a lak of pror knowledge about remote sensng mages. he testng remote sensng mages are from the database of platform Landsat-5, whh was launhed on Marh n 98 by USA, and the remote sensor was themat mapper (M). For the 6th band the resoluton s 0 meters, and for other bands, the resoluton s 30 meters. All the data are M mages of Beng, Chna n 996 and all the data an be lassfed at least two lasses nludng water and other geographal obets. hen the orgnal remote sensng data have 7 bands, and for better and easy lusterng, only 3 bands are used after proessng features. Fgure. Comparson of dfferent methods In ths paper fve smple multspetral remote sensng mages are adopted as the testng data, the orgnal remote sensng mages are shown n Fgure, and the lassfaton auraes an be seen n able. Fgure and Fgure 3 are the graph dsplay of the auraes of all the feature extraton methods nvestgated n ths work. Fgure 3. Comparson of dfferent data sets able. Classfaton auraes Methods EDM DMCF MDE PDC PCA Data 9.7% 9.0% 9.7% 9.3% 93.80% Data 98.3% 98.37% 99.9% 96.83% 95.8% Data3 97.3% 9.5% 90.68% 97.3% 96.0% Data 99.33% 9.5% 95.3% 99.33% 97.% Data % 9.6% 96.8% 96.89% 96.% able. Rank of the feature extraton methods Fgure. he orgnal remote sensng mages Methods EDM DMCF MDE PDC PCA Data 5 3 Data 3 5 Data3 5 3 Data 5 3 Data5 5 3 Average

5 From fgure, we an know that: For all of the dmenson reduton methods, the lassfaton auraes are hgher than 90% regardless of data set, whh valdate the effetveness of nvestgated methods. From the results we an fnd that the features of Data are obvously better extrated when usng the EDM, DMCF, MDE, PDC and PCA methods. In other words, for the same feature extraton methods, the effetveness s data dependent. In the experments, usng the Data and Data an get hgher lassfaton auray than other data set. By analyzng Fgure 3, able and able, we an get followng ponts: For Data, the features extrated wth the EDM method are sutable to luster, and the lassfaton auray s 9.7%; For Data, the MDE method s the best and the lassfaton auray s as hgh as 99.9%; For Data3, the EDM or PDC method are the same n feature extraton and the lassfaton auray an reah to 97.3%. For Data, the lassfaton auray s 99.33% based on the EDM or PDC method. Fnally for Data5, 96.89% lassfaton auray s obtaned based on EDM or PDC feature extraton method. In summary, the EDM and PDC methods are better than the other dmenson reduton methods for all data sets used n ths paper. For the same testng mage, wth the EDM and PDC methods, espeally wth the EDM method, we an get better features for lassfaton. When extratng the features of multspetral remote sensng mages, the EDM and PDC methods should be hosen frstly. In pratal applatons, f obtaned remote sensng mage has a smlar data struture to that of Data3, Data or Data5, when extratng the key features of the mage, t s suggested that the EDM or PDC method should be onsdered frstly. If the data struture s smlar to that of Data, frst of all we should hoose the EDM method. But f the data struture s smlar to that of Data, the MDE method s the best one for the purpose of extratng the key features. Conlusons In ths paper, fve feature extraton methods are omparatvely studed. he results may be dfferent wth dfferent data sets, but as a whole the EDM and PDC methods are better whle extratng the key features of the multspetral remote sensng mages. Oasonally, MDE s also a better method to extrat the key features, and the DMCF and PCA methods are the worst ones among all of the fve feature extraton methods. herefore, when lassfyng the remote sensng mages, we suggest that the EDM or PDC method should be used to extrat the features n order to obtan hgher lassfaton auray. Aknowledgement he researh work desrbed n ths paper was fully supported by a grant from the Natonal Natural Sene Foundaton of Chna (Proet No ) and a grant from the Researh Grants Counl of the Hong Kong Speal Admnstratve Regon, Chna (Proet No. CUHK8/03E). Referenes [] A. P. Dempster, N. M. Lard, D. B. Rubn, Maxmum-lkelhood from nomplete data va the EM algorthm, J. Royal Statst. Soety (B), Vol. 39, No., pp. -38, 997. [] R. A. Redner, H. F. Walker, Mxture denstes, maxmum lkelhood and the EM algorthm, SIAM Revew, Vol. 6, No., pp , 98. [3] P. Santago, H. D. Gage, Statstal models of partal volume effet, IEEE rans. Image Proessng, Vol., No., pp , 995. [] S. Sanay-Gopal,. J. Hebert, Bayesan pxel lassfaton usng spatally varant fnte mxtures and the generalzed EM algorthm, IEEE rans. Image Proessng, Vol. 7, No. 7, pp. 0-08, 998. [5] P. Guo, H. Lu, A Study on Bayesan Probablst Image Automat Segmentaton, Ata Opta Sna, Vol., No., pp , 00. [6] B. anunath, exture Features for Browsng and Retreval of Image Data, IEEE ransaton on Pattern Analyss and Mahne Intellgene, Vol. 8, pp , 996. [7] Z. Ban, X. Zhang, Pattern Reognton, snghua Unversty Press, Beng, 00. [8] S. Lee, H. C. Km, D. Km, and YoungSk Cho, Fae Retreval Usng st- and nd-order PCA Mxture Model, Leture Notes n Computer Sene, Vol. 668, pp , 003. [9] E. M. Mohamed, P.W. Robert, D. Rdder, V. Atalay, exture Segmentaton Usng the Mxtures of Prnpal Component Analyzers, Leture Notes n Computer Sene, Vol. 869, pp , 003.