Signal Processing for Remote Sensing - Chapter 2

2 Statistical Pattern Recognition and Signal Processing in Remote Sensing Chi Hau Chen CONTENTS 2.1 Introduction......................................................................................................................... 23 2.2 Introduction to Statistical Pattern Recognition in Remote Sensing............................ 24 2.3 Using Self-Organizing Maps and Radial Basis Function Networks for Pixel Classification ....................................................................................................... 26 2.4 Introduction to Statistical Signal Processing in Remote Sensing................................ 26 2.5 Conclusions.......................................................................................................................... 28 References ..................................................................................................................................... 28 2.1 Introduction Basically, statistical pattern recognition deals with the correct classification of a pattern into one of several available pattern classes. Basic topics in statistical pattern recognition include: preprocessing, feature extraction and selection, parametric or non-parametric probability density, decision-making processes, performance evaluation, post-processing as needed, supervised and unsupervised learning, or training, and cluster analysis. The large amount of data available makes remote-sensing data uniquely suitable for statistical pattern recognition. Signal processing is needed not only to reduce the undesired noises and interferences but also to extract desired information from the data as well as to perform the preprocessing task for pattern recognition. Remote-sensing data considered include those from multispectral, hyperspectral, radar, optical, and infrared sensors. Statistical signal-processing methods, as used in remote sensing, include transform methods such as principal component analysis (PCA), independent component analysis (ICA), factor analysis, and the methods using high-order statistics. This chapter is presented as a brief overview of the statistical pattern recognition and statistical signal processing in remote sensing. The views and comments presented, however, are largely those of this author. The chapter introduces the pattern recognition and signal-processing topics dealt in this book. The readers are highly recommended to refer the book by Landgrebe [1] for remote-sensing pattern classification issues and the article by Duin and Tax [2] for a survey on statistical pattern recognition. ß 2007 by Taylor & Francis Group, LLC. Although there are many applications of statistical pattern recognition, its theory has been developed only during the last half century. A list of some major theoretical developments includes the following: . Formulation of pattern recognition as a Bayes decision theory problem [3] . Nearest neighbor decision rules (NNDRs) and density estimation [4] . Use of Parzen density estimate in nonparametric pattern recognition [5] . Leave-one-out method of error estimation [6] . Use of statistical distance measures and error bounds in feature evaluation [7] . Hidden Markov models as one way to deal with contextual information [8] . Minimization of the perceptron criterion function [9] . Fisher linear discriminant and multicategory generlizations [10] . Link between backpropagation trained neural networks and the Bayes dis-criminant [11] . Cover’s theorem on the separability of patterns [12] . Unsupervised learning by decomposition of mixture densities [13] . K-mean algorithm [14] . Self-organizing map (SOM) [15] . Statistical learning theory and VC dimension [16,17] . Support vector machine for pattern recognition [17] . Combining classifiers [18] . Nonlinear mapping [19] . Effect of finite sample size (e.g., [13]) In the above discussion, the role of artificial neural networks on statistical classification and clustering has been taken into account. The above list is clearly not complete and is quite subjective. However, these developments clearly have a significant impact on information processing in remote sensing. We now examine briefly the performance measures in statistical pattern recognition. . Error probability. This is most popular as the Bayes decision rule is optimum for minimum error probability. It is noted that an average classification accuracy was proposed by Wilkinson [20] for remote sensing. . Ratio of interclass distance to within-class distance. This is most popular for discrim-inant analysis that seeks to maximize such a ratio. . Mean square error. This is most popular mainly in error correction learning and in neural networks. . ROC (receiver operating characteristics) curve, which is a plot of the probability of correct decision versus the probability of false alarm, with other parameters given. Other measures, like error-reject tradeoff, are often used in character recognition. 2.2 Introduction to Statistical Pattern Recognition in Remote Sensing Feature extraction and selection is still a basic problem in statistical pattern recognition for any application. Feature measurements constructed from multiple bands of the remote-sensing data as a vector are still most commonly used in remote-sensing pattern ß 2007 by Taylor & Francis Group, LLC. recogni tion. Tran sform me thods are useful to redu ce the redu ndancy in v ector me ments. The dim ensional ity red uction has been a par ticularly impor tant topic in re sensing in view of the hyp erspec tral image data, which normal ly has sever al hun spect ral ba nds. The par ametric classific ation rul es incl ude the Bayes or max imum likeliho od dec rule and discr iminan t analysis . The nonpar ametr ic (or distr ibution free) me thod o sificati on incl udes NN DR and its mod ifications, and the Parze n densit y estim ation. early 1970s, the multivari ate Gau ssian assump tion was mos t popu lar in the mu ltisp data classific ation problem . It was demo nstrated that the emp irical data follow s Gauss ian distri bution reasonabl y well [21]. Ev en with the use of new sensors an expande d appli cation of remote sen sing, the Gaussia n assump tion remai ns to be a appro ximat ion. The traditio nal multiv ariate analy sis still plays a useful role in rem sensing pat tern recog nition [22] and, because of the impor tance of covari ance ma methods to use uns uperv ised samp les to ‘‘enha nce’’ the data statistics have also consid ered. Indeed, for good class ificatio n, data statistics must be caref ully exami ned exampl e is the synth etic aperture radar (SAR) image data. Ch apter 1 of the comp volume I(m age Processin g for Remo te )Sepnresisnegnts a discuss ion on the phy sical and statisti cal charact eristics of the SAR imag e data. Withou t making use of the Gaus sian assum ption, the NNDR is the mo st po nonpar ametr ic cl assificatio n method. It works we ll even with a mod erate size da and promis es an error rate that is upper- bound ed by twice the Bayes error Howeve r, its perform ance is limited in remote-sen sing da ta classifica tion, while ne netw orks–bas ed clas sifiers can reach the perform ance nearly equal to that of the B class ifier. Exten sive stud y has been done in the st atistical pat tern reco gnitio n co m to im prove the perform ance of NN DR. We wou ld like to me ntion the work of Gr et al. [23] here, wh ich introd ukc-enseatrhesurrou nding neighbok-Nr SN( ) decisio n rule with appli cation to remote-sen sing da ta clas sificatio n. Some uniqu e pr oblem areas of statistical pattern reco gnition in remote sens ing are use of co ntextu al informati on and the ‘‘Hugh es phe nomenon .’’ The use of Markov r field mo del for contex tual inform ation is presente d in Chapte r 2 of the co mpanion While the classifica tion per formance generall y im prove s with increase s in the fe dimens ion, the per formance rea ches a peak with out a pr oportion al increase in the t sampl e size, beyon d whic h the perform ance degrad es. This is the so-call ed ‘‘H phenome non.’’ Me thods to reduce this pheno menon are wel l presente d in Ref . [1] Data fusion is important i n remote saesnsdinigfferent sensors, which h ave different strengt h s, are o ften used. The su bject is treated i n Chapter 11 o f the com volume. Thou gh the ap proach is not limited to statistical m ethodol ogy [24], appro aches in combining classifier s in statisti cal patte rn reco gnitio n and neural netw can be quite useful in providin g effective utilizatio ns of informati on from dif fe sensors or sour ces to achiev e the best- availa ble classific ation per formance. Chapt and Ch apter 4 of the co mpanion volume pres ent two appr oaches in statisti cal co of classifiers. The recent development in support vector machine appears to present an ultimate classifier that may provide the best classification performance. Indeed, the design of the classifier is fundamental to the classification performance. There is, however, a basic question: ‘‘Is there a best classifier?’’ [25]. The answer is ‘‘No’’ as, among other reasons, it is evident that the classification process is data-dependent. Theory and practice are often not consistent in pattern recognition. The preprocessing and feature extraction and selec-tionareimportantandcaninfluencethefinalclassification performance.Therearenoclear stepstobetakeninpreprocessing,andtheoptimalfeatureextractionandselectionisstillan unsolvedproblem.Asinglefeaturederivedfromthegeneticalgorithmmayperformbetter thanseveraloriginalfeatures.Thereisalwaysachoicetobemadebetweenusingacomplex ß 2007 by Taylor & Francis Group, LLC. feature set follow ed by a sim ple cl assifier and a simple feature set follow ed by a clas sifier. Ch apter 15 of the comp anion volume deals wi th the clas sificatio n by vecto r mach ine. Among man y ot her publicatio ns on the subje ct, Melgani and Bruzzo pro vide an inform ative co mpariso n of the perform ance of several support vector mach 2. 3 U sing Sel f-Organizi ng Maps a nd Radial Basi s Funct ion N et wo for Pixel Class ification In this sec tion, som e experi mental resu lts a re pres ented to illus trate the impor pre process ing before classif ication. The data set, wh ich is now availa ble at the Geosc ience and Remot e Sensing Society database , consists350of p2ix50el image s. They were acqui red by two imag ing sen sors install ed on a Daedal us 1268 Ai Themat ic Map per (AT M) scann er and a PLC-ban d, fully polarim etric NASA /JPL sens or of an agri cultural area near the village of Feltwell, U.K. The origin al SAR i inclu de nine channel s. Figure 2.1 sho ws the origin al nine channels of image data. The radial basis func tion (RBF) neural network is used for classific ation [27]. Howev pre process ing is perform ed by the SOM that perform s pre clusteri ng. The wei ghts SOM are chosen as center s for RBF ne urons. RBF has five output node s fo r five clas ses on the image data consid ered (SAR and ATM image s in an agricul tural We ights of thne’’ ‘‘most-f reque ntly-fired neu rons, wh en each cl ass was pre sented to SOM, were separ ately take n as the center fonr RtBhFe n5eurons. The wei ghts bet ween the hid den-laye r neurons and the outpu t-layer neurons w comp uted by a pro cedure for a gen eralized radial -basis func tion networks . Pix el catio n usin g SO M alon e (u nsupervi sed) is 62.7% correc t. Pix el class ificatio n u alon e (su pervised) is 89.5% correc t, at best. Pix el classific ation usin g bot h SOM an 95.2% correct. This res ult is bet ter than the rep orted resu lts on the sa me data set [28] at 90.5% correc t or ICA- based features with nearest nei ghbor class ificatio n ru le 86% correct. 2. 4 Introduct ion to St atist ical S ignal P roc essi ng i n Remote Sensin Signal and image process ing is needed in remote -sensing inform ation pro cessing redu ce the noi se and interfere nce with the data, to extract the desire d signal and comp onent, or to derive useful me asureme nts for input to the class ifier. The class if pro blem is, in fact , very cl osely linked to signal and image pr ocessin g [30,31]. Transform methods have been most popular in signal and image processing [32]. Thoug the popular wavelet transform method for remote sensing is treated elsewhere [33], we ha included Chapter 1 in this volume, which presents the popular Hilbert–Huang transform; Chapter 12 of the companion volume, which deals with the use of Hermite transform in multispectral image fusion; and Chapter 10 of this volume, Chapter 7, and Chapter 8 of companion volume, which make use of the methods of ICA. Although there is a constant n for better sensors, the signal-processing algorithm such as the one presented in Chapter 7 this volume demonstrates well the role of Kalman filtering in weak signal detection. Tim series modeling as used in remote sensing is the subject of Chapter 8 of this volume Chapter 9 of the companion volume. Chapter 6 of this volume makes use of the factor ana ß 2007 by Taylor & Francis Group, LLC. th-c-hh th-l-hh th-p-hh FIGURE 2.1 A nine-channel SAR image data set. th-c-hv th-l-hv th-p-hv th-c-vv th-l-vv th-p-vv ß 2007 by Taylor & Francis Group, LLC. ... - tailieumienphi.vn