Feature Selection for Target Detection in SAR Images

Transcription

1 Feature Selecton for Detecton n SAR Images Br Bhanu, Yngqang Ln and Shqn Wang Center for Research n Intellgent Systems Unversty of Calforna, Rversde, CA 95, USA Abstract A genetc algorthm (GA) approach s presented to select a set of features to dscrmnate the targets from the natural clutter false alarms n SAR mages. Four stages of an automatc target detecton system are developed: the rough target detecton, feature extracton from the potental target regons, GA based feature selecton and the fnal Bayesan classfcaton. Expermental results show that the GA selected a good subset of features that gave smlar performance to usng all the features. Key words: Feature selecton, genetc algorthm, ATR system, target detecton.. Introducton Automatc detecton of potental targets n SAR magery s an mportant problem. A CFAR (constant false alarm rate) detector s commonly used to prescreen the mage to localze the possble targets. Generally, targets correspond to brght spots caused by strong radar return from natural or man-made objects. Parts of the magery that are not selected are rejected from further computaton. In the next stage of processng, regons of nterest are further examned to dstngush man-made objects from natural clutter. Fnally, a classfer such as a Bayesan classfer, a template matcher or a modelbased recognzer s used to reject man-made clutter. The goal of feature selecton s to fnd the subset of features whch produces the best detecton/recognton accuracy and requres the least computatonal effort. Feature selecton s mportant to target detecton and recognton systems manly for two reasons: Frst, usng more features can ncrease system complexty, yet t may not always lead to hgher detecton/recognton accuracy. Sometmes, many features are avalable to a detecton/recognton system. However, these features are not ndependent and may be correlated. A bad feature may greatly degrade the performance of the system. Thus, selectng a subset of good features s mportant. Second, usng fewer features can reduce the computatonal cost, whch s mportant for real-tme applcatons. Also t may lead to better classfcaton accuracy due to the fnte sample sze effect. Genetc algorthms (GAs) are wdely used n mage processng, pattern recognton and computer vson. They are used to generate structural elements n mathematcal morphology, to select good parameters for object detecton and recognton, to generate mage flters for target recognton, to select tranng data for neural networks, etc. GAs are also used to automatcally determne the relatve mportance of many dfferent features and to select a good subset of features avalable to the system The focus of ths paper s to select a mnmal set of features to dstngush targets from natural clutter. The approach s based on a closed loop system nvolvng GA based feature selecton and a Bayesan classfer. GA uses an approprate ftness functon that combnes the number of features to be used and the error rate of the classfer. The results are presented usng real SAR mages. The expermental results show that the subset of features selected by GA can greatly reduce the computatonal cost whle at the same tme the detecton accuracy s mantaned. Secton presents the related research and the contrbuton of ths paper. Secton 3 descrbes the approach, the prescreener used to detect potental target regons, the features for target dscrmnaton, feature evaluaton crtera and the applcaton of GAs to feature selecton. Expermental results are presented n Secton 4 and Secton 5 provdes the concluson of the paper.. Related Research Chakla and Q [] consder the mportance of the doman n elmnatng nosy features for feature selecton. They present an approach to desgnng a mult-objectve ftness functon for the genetc algorthm. The results show that the proposed ftness functon can perform more satsfactorly than the tradtonal one. Emmanoulds et al. [] dscuss the use of multcrtera genetc algorthms for feature selecton. The algorthm s shown to yeld a dverse populaton of alternatve feature subsets wth varous accuracy and complexty trade-off. It s appled to select features for performng classfcaton wth fuzzy models and s evaluated on real-world data sets. Estevez et al. [3] propose a genetc algorthm for selectng features for neural network classfers. Ther algorthm s based on a

2 Input SAR Image CFAR Detector Potental Regons Feature Extractor Results Classfer Best Feature Subset Extracted Features Feature Selecton Feedback Fg.. System dagram for feature selecton. nchng method to fnd and mantan multple optma. They also ntroduce a new mutaton operator to speed up the convergence of the genetc algorthm. Rhee and Lee [0] present an unsupervsed feature selecton method usng a fuzzy-genetc approach. The method mnmzes a feature evaluaton ndex whch ncorporates a weghted dstance used to rank the mportance of the ndvdual features. Matsu et al. [6] use genetc algorthm to select the optmal combnaton of features to mprove the performance of tssue classfcaton neural networks and apply ther method to problems of bran MRI segmentaton to classfy gray matter/whte matter regons. In ths paper, we use genetc algorthm to select a good subset of features used for target detecton n SAR mages. The target detecton task nvolves the selecton of a subset of features to dscrmnate SAR mages contanng targets from those contanng clutter. Our method s a novel combnaton of genetc algorthm based optmzaton of a crteron functon that nvolves classfcaton error and the number of features that are used for the dscrmnaton of targets from natural clutter n SAR mages. The crteron functon s optmzed n closed-loop wth a Bayesan classfer. As compared to ths work, the feature selecton presented n [5, 8] for target vs. natural clutter dscrmnaton s not optmal but ad hoc. 3. Techncal Approach The purpose of the genetc algorthm (GA) based feature selecton approach presented n ths paper s to select a set of features to dscrmnate the targets from the natural clutter false alarms n SAR mages. The approach ncludes four stages: rough target detecton, feature extracton from the potental target regons, feature selecton based on the tranng data and the fnal dscrmnaton. The frst two stages are based on the Lncoln Lab ATR system [5, 7, 8]. In the feature selecton stage, we use GAs to select a best feature subset, defned as a partcular set of features whch s the best n dscrmnatng the target from the natural clutter false alarm. The dagram for feature selecton s gven n Fg CFAR Detector A two-parameter CFAR detector s used as a prescreener to dentfy potental targets n the mage on the bass of radar ampltude. A guard area around a potental target pxel s used for the estmaton of clutter statstcs. The ampltude of the test pxel s compared wth the mean and standard devaton of the clutter accordng to the followng rule: X ˆ t u c > K CFAR target, otherwse clutter () σˆ c where X t s the ampltude of the test pxel, û c s the estmated mean of the clutter ampltude, σˆ c s the estmated standard devaton of the clutter ampltude, and K CFAR s a constant threshold value that defnes the false-alarm rate. Only those test pxels whose ampltude s much hgher than that of the surroundng pxels are declared to be targets. The hgher we set the threshold value of K CFAR, the more a test pxel must stand out from ts background for t to be declared as a target. Because a sngle target can produce multple CFAR detectons, the detected pxels are grouped together f they are wthn a target-szed neghborhood. The CFAR detecton threshold n the prescreener s set relatvely low to obtan a hgh ntal probablty of detecton for the target data. It s the responsblty of the dscrmnator to capture and reject those escapng clutter false alarms from the prescreen stage. An example SAR mage and correspondng detecton results are shown n Fg Feature Extractor Frst, we use a target-sze rectangular template to determne the poston and orentaton of the detected target [4]. The algorthm sldes and rotates the template untl the energy wthn the template s maxmzed. Then we extract a set of features from the target-szed

3 template or the regon of nterest. By usng ths set of features [], we try to dscrmnate the targets from the natural clutter. s usually exhbt much larger standard devaton than the natural clutter, as llustrated by Fg The standard-devaton feature The standard devaton of the data wthn the template s a statstcal measurement of the fluctuaton of the pxel ntenstes. If we use P ( r, a) to represent the radar ntensty n power from range r and azmuth a, the standard devaton can be calculated as follows: where (a) Example SAR mage. (b) Detecton result. Fg.. SAR mage and CFAR detecton result. σ = S S N N 0log0 (, ) r, a regon S = [0 log0 P( r, a)] r, a regon and N s the number of ponts n the regon. S = P r a () (a) A typcal natural clutter mage wth standard devaton (b) A typcal target mage wth standard devaton Fg. 3. Example of the standard devaton feature The fractal dmenson feature The fractal dmenson of the pxels n the regon of nterest provdes nformaton about the spatal dstrbuton of the brghtest scatterers of the detected object. It complements the standard-devaton feature, whch depends only on the ntenstes of the scatterers, not on ther spatal locatons. The frst step n applyng the fractal-dmenson concept to a radar mage s to select an approprately szed regon of nterest, and then convert the pxel values n the regon of nterest to bnary. One method of performng ths converson s to select the N brghtest pxels n the regon of nterest and convert ther values to, whle convertng the rest of pxel values to 0. Based on these N brghtest pxels, we approxmate the fractal dmenson by usng the followng formula: logm logm logm logm dm= = log log log where M represents the mnmum number of -pxelby--pxel boxes that cover all N brghtest pxels n the regon of nterest (Ths number s obvously equal to N) and M represents the mnmum number of -pxel-by- -pxel boxes requred to cover all N brghtest pxels. The brght pxels for a natural clutter tend to be wdely separated, thus produce a low value for the fractal dmenson, whle the brght pxels for the target tend to be closely bunched, thus we expect a hgh value for the fractal dmenson, whch s llustrated by Fg. 4. Fg. 4. (a) shows a natural clutter mage chp. In Fg. 4. (b), the 50 brghtest pxels from ths natural clutter are relatvely solated, and 46 -pxel boxes are needed to cover them, whch results n a low fractal dmenson of 0.9. Fg. 4. (c) shows a target mage chp. In Fg. 4. (d), the 50 brghtest pxels from the target mage are tghtly clustered, and -pxel boxes are needed to (3) 3

4 cover them, whch results n a hgh fractal dmenson of.. (a) Natural clutter mage. (b) 50 brghtest pxels n (a). (c) mage. (d) 50 brghtest pxels n (c). Fg. 4. Example of the fractal dmenson feature. (a) The left-hand sde fgures represent the target mages and rght-hand fgures represent ther correspondng morphologcal blobs Weghted-Rank Fll Rato Feature Ths textual feature measures the percentage of the total energy contaned n the brghtest scatterers of a detected object. We defne the weghted-rank fll rato as follows: η = k brghtest all pxels P ( r, a ) pxels P ( r, a ) (4) Ths feature attempts to explot the fact that power returns from most targets tend to be concentrated n a few brght scatters, whereas power returns form natural-clutter false alarm tend to be more dffuse. Fg. 5 shows the fll rato we get from typcal examples of target and clutter mages. (b) The left-hand sde fgures represent the clutter mages and rght-hand fgures represent ther correspondng morphologcal blobs. Fg. 6. Examples of the sze feature for (a) targets and (b) clutter. (a) A typcal natural clutter mage and the fll rato s 0.3. (b) A typcal target mage and the fll rato s Fg. 5. An llustraton of the fll rato feature Sze-related feature The three sze-related features utlze only the bnary mage created by the morphologcal operatons.. The mass feature s computed by countng the number of pxels n the morphologcal blob.. The dameter s the length of the dagonal of the smallest rectangle that encloses the blob. 3. The square-normalzed rotatonal nerta s the second mechancal moment of the blob around ts center of mass, normalzed by the nerta of an equal mass square. 4

5 In our experments, we found the sze features are not effectve n scenaros where the targets are partally occluded or hdden. After the prescreener stage, the sze and the shape of the detected morphologcal blob can be arbtrary. For the clutter, there s also no ground to assert that the resultng morphologcal blob wll exhbt a certan amount of coherence. The expermental results n Fg. 6 show the arbtrarness of the morphologcal blobs for the targets as well as the clutter The contrast-based features The CFAR statstc s computed for each pxel n the targetshaped blob to create a CFAR mage. Then the three features can be derved as follows:. The maxmum CFAR feature s the maxmum value n the CFAR mage contaned wth the target-szed blob.. The mean CFAR feature s the average of the CFAR mage taken over the target-shaped blob. 3. The percent brght CFAR feature s the percentage of pxels wthn the target-szed blob that exceed a certan CFAR value. (a) A typcal natural clutter mage and the three CFAR features are 0.3,.37 and 0.004, respectvely. (b) A typcal target mage and the three CFAR features are 55.69, 5.53 and 0.5, respectvely. Fg. 7. Examples of the CFAR features. We can see from Fg. 7 that the CFAR feature values for the target are much larger than those for the natural clutter false alarm The count feature The count feature s very smple; t counts the number of pxels that exceeded the threshold T and normalze ths value by the total possble number of pxels n a target blob. The threshold T s set to the quantty correspondng to the 98th percentle of the surroundng clutter. The Fg. 8 shows the count feature values obtaned from a par of typcal target and clutter mages. We can see from Fg. 8 that the count feature value for the target s much larger than that for the nature clutter false alarm. Ths makes sense because the ntensty values of the pxels belongng to the target stand out from the surroundng clutter, whle the natural clutter false alarms do not have ths property. (a) A typcal natural clutter mage and the count feature value s Feature Evaluaton and selecton Addng more features does not necessarly mprove dscrmnaton performance. An mportant goal s to choose the best set of features from the dscrmnaton features gven n secton 3. above. Before we do the feature selecton, t s approprate to gve a set of feature evaluaton crtera, whch measure the dscmnaton capablty of each feature or the combnaton of several features. Dvergence: Dvergence s bascally a form of the Kulback-Lebler dstance measure between densty functons. If we assume that the target as well as the natural clutter feature vectors follow the Gaussan dstrbutons respectvely, that s, N ( u, Σ ) and N ( u, Σ ), the dvergence can be computed as follows: d = trace { Σ Σ +Σ Σ I } + T ( u u ) ( Σ +Σ )( u u ) (5) Scatter Matrces: One major drawback of the dvergence d s that t s not easly computed, unless the Gaussan assumpton s employed. For SAR magery, the Gaussan assumpton tself s n queston. So we consder a smpler crteron that s based upon the nformaton related to the way feature vector samples are scattered n the l-dmensonal feature space. At the begnnng, we defne two knds of scatter matrces, that s, wthn-class scatter matrx and between-class scatter matrx. Wthn-class scatter matrx S w = M = P S (b) A typcal target mage and the count feature value s 0.6. Fg. 8. The llustraton of the count feature., where S s the covarance 5

6 matrx for class ω and P s the a pror probablty of class ω. S ω matrx measures how feature vector samples are scattered wthn each class. Between-class scatter matrx s defned as M S b P follows: = ( u )( u ) = T u 0 u 0, where 0 u s the global mean vector and u s the mean for each class, =,, M. The between-class scatter matrx measures how the feature vector samples are scattered between dfferent classes. Based on the dfferent combnatons of these two scatter matrces, a set of class separablty crtera can be derved. We choose to use one of them that can be defned as Sb follows: J =. If the feature vector samples wthn each S w class are scattered compactly and dfferent classes are far away from one other, we expect that J value would be hgh. Ths also mples that the features we choose have large dscrmnaton capablty. Feature vector evaluaton usng a classfer: Another method for feature evaluaton depends on the specfc classfer. The task of feature selecton s to select or determne a set of features, that when fed nto the classfer, wll let the classfer acheve the best performance. So t makes sense to relate the feature selecton procedure to the partcular classfer used. Durng the tranng tme, we have all the features extracted from the tranng data. What we can do s to select a subset of these features and feed them nto the classfer and see the classfcaton result. Then the goodness of each feature subset s ndcated by ther classfcaton error rate GAs for Feature selecton The genetc algorthm s an optmzaton procedure that operates n bnary search spaces (the search space conssts of bnary strngs). A pont n the search space s represented by a fnte sequence of 0's and 's, called a chromosome. The algorthm manpulates a fnte set of chromosomes, the populaton, n a manner resemblng the mechansm of natural evoluton. Each chromosome s evaluated to determne ts ftness, whch determnes how lkely the chromosome s to survve and breed nto the next generaton. The probablty of survval s proportonal to the chromosome s ftness value. Those chromosomes whch have hgher ftness values are gven more chances to "reproduce" by the processes of crossover and mutaton. The functon of crossover s to mate two parental chromosomes to produce a par of offsprng chromosomes. In partcular, f a chromosome s represented by a bnary strng, crossover can be mplemented by randomly choosng a pont, called the crossover pont, at whch two chromosomes exchange ther parts to create two new chromosome. Mutaton randomly perturbs the bts of a sngle parent to create a chld. Ths procedure can ncrease the varablty of the populaton. A mutaton can be created by flppng at random one or more bts n the chromosome. In ths work, there are 0 features as descrbed earler. Each feature s represented as a bt n the genetc algorthm. There are 04 possble combnaton of these features. Applyng GA for feature selecton: We use GA to seek the smallest (or the least costly) subset of features for whch the classfer s performance does not detero-rate below a certan specfed level [9, ]. The basc system framework s shown n the Fg.. When the error of a classfer s used to measure the performance, a subset of features s defned as feasble f the classfer's error rate s below the so-called feasblty threshold. We search for the smallest subset of features among all feasble subsets. Durng the search, each subset can be coded as a d-element bt strng (d s the ntal number of features). The th element of the bt strng assumes 0 f the th feature s excluded from the subset and f t s present n the subset. We use the followng penalty functon []: exp(( e t) / m) p( e) = exp() (6) where e s the error rate, t s the feasblty threshold and m s called the tolerance margn. Ths penalty functon can be seen Fg 9, where t = 0. and m = We can see from Fg. 9, f e < t, p(e) s negatve and as e approaches zero, p(e) slowly approaches ts mnmal value. Note also that p(t) = 0 and p(t + m) =. For greater values of the error rate, ths penalty functon quckly rses toward nfnty. We modfy the penalty functon n equaton (6) by addng the number of features n the evaluated subset to produce the score J: J = γ number_ of _ features+ ( γ ) p( e) (7) where γ s the weght between [0, ] that we gve to the number of features. The last thng we need to do s to desgn a ftness functon used to evaluate the ftness of each chromosome c. Snce n our case, we look for the mnmum of the score, we defne the ftness functon as f c ) = J( c ) ( (8) 6

7 p(e) t=0. t+m=0.5 e Fg. 9. The penalty functon. 4. Expermental Results All the SAR mages used n these experments are downloaded from a webste of the MIT Lncoln Lab ame.htm. From these SAR mages, 40 target chps (contanng target) and 40 clutter chps (contanng clutter) are generated. Some of the target and clutter chps are used as tranng data n our experments and the rest are used as testng data. The GA selects a good subset of features from the 0 features descrbed prevously to classfy an mage chp nto ether a target or clutter. Based on the data we have, we use the CFAR detector n the prescreener stage to detect the potental target regons. Snce we know the ground truth, we know whch one s the real target and whch one s the clutter false alarm among the potental target regons detected. Ths allows us to construct a set of tranng data (tranng target data and tranng natural clutter false alarm data) for the feature selecton. Then we extract a set of 0 features from each potental target regon and do the feature selecton. Fnally n the testng stage we use the selected features to dscrmnate the targets from the natural clutter false alarm Fg. 0 shows the feature extracton nterface. On the left-hand sde of the nterface, we can choose any combnaton of the features and the number of the tranng samples. The plot n the mddle of rght-hand sde vsualzes the target samples as well as the natural clutter false alarm samples n the feature space. At the bottom, we gve a set of feature evaluaton values by usng the dvergence, scatter matrx and the Bayesan Classfer. We can also use the nterface to browse through the target tranng mages and the natural clutter ranng mages. If we are nterested n a partcular tranng mage, by clckng on that mage, we can get the values of the features we extract from that mage. Fg. 0. The feature extracton nterface. 7

8 Table. GA feature selecton tranng and testng results. Tranng Data Testng Data Number of errors Feature Error Error selected rate rate number number Number of features number number error error (a) 5 tranng target and clutter chps (b) 0 tranng target and clutter chps. 4 3 (c) 5 tranng target and clutter chps. 9 9 (d) 30 tranng target and clutter chps. Fg.. Confuson matrces of GA for varous tranng and testng experments. 3 3 (a) 5 tranng target and clutter chps (b) 0 tranng target and clutter chps. 4 3 (c) 5 tranng target and clutter chps (d) 30 tranng target and clutter chps. Fg.. Confuson matrces for varous tranng and testng experments usng all 0 features. The feature extracton nterface s used to conduct a set of experments to evaluate the dscrmnaton power of the features. If the features are uncorrelated, we can select the l best features ndvdually and form a l-dmensonal feature vector features. Ths s called scalar feature selecton. But n realty, there are always some correlatons between dfferent features. So we consder the classfcaton accuracy of feature vectors. For our GA feature selecton framework, we adopt a Bayesan Classfer to classfy the tranng data and the resultng error rate s used as the feedback nto the 8

9 feature selecton algorthm. We fx the parameters of the GA algorthm: crossover rate 0.6, mutaton rate 0. and the sze of the populaton 00. γ s set to 0.5 n equaton (7). A seres of four experments was conducted to test the effectveness of the GA feature selecton. In the frst experment, 5 target and 5 clutter chps are used n tranng and the rest are used n testng; n the second experment, 0 target and 0 clutter chps are used n tranng and the rest are used n testng; n the thrd experment, 5 target and 5 clutter chps are used n tranng and the rest are used n testng; n the fourth experment, 30 target and 30 clutter chps are used n tranng and the rest are used n testng. The expermental results are reported n Table and confuson matrces are shown n Fg.. In order to further evaluate the features selected by GA, another four experments were performed, where all the 0 features are used to dstngush the target chps from the clutter chps. Smlar to the experments reported above, the number of tranng target chps and clutter chps are 5, 0, 5 and 30, respectvely. Fg. shows the confuson matrces that resulted from these four experments. From Fg. and Fg., t s easy to see that the performance of the features selected by GA s smlar to that of usng all the 0 features. So GA s capable of selectng a good subset of features from all the features avalable. However, by usng fewer features, a lot of computaton s saved. 5. Conclusons In ths paper, we ntroduced the GA feature selecton algorthm nto a specfc applcaton doman to dscrmnate the targets from the natural clutter false alarm n SAR mages. Rough target detecton, feature extracton, GA feature selecton and fnal dscrmnaton are successfully mplemented and good results are obtaned. Our expermental results show that the GA selected a good subset of features that gave smlar performance to usng all the features. In the future, we plan to extend ths approach to addtonal features and more complex background clutter. Acknowledgment: Ths work was supported n part by grant F C-440. The contents and nformaton do not necessarly reflect the poston or polcy of U.S. government. References [] N. Chakla and Y. Q, Feature Selecton Usng the Doman Relatonshp wth Genetc Algorthms, Knowledge and Informaton Systems, vol., (no. 3), Sprnger-Verlag, pp , Aug [] C. Emmanoulds, A. Hunter, J. MacIntyre, and C. Cox, Multple-Crtera Genetc Algorthms for Feature Selecton n Neuro-Fuzzy Modelng, Proc. Int. Jont Conf. on Neural Networks, vol. 6, pp , Pscataway, NJ, USA, 999. [3] P.A. Estevez and R.E. Caballero, A Nchng Genetc Algorthm for Selectng Features for Neural Classfers, Proc. 8th Int. Conf. on Artfcal Neural Networks, vol., pp. 3-36, Sprnger-Verlag London, 998. [4] S.D. Halversen, Calculatng the Orentaton of a Rectangular n SAR magery, Proc. IEEE Natonal Aerospace and Electroncs Conf., pp , May 99. [5] D.E. Krethen, S.D. Halversen, and G.J. Owrka, Dscrmnatng s from, Lncoln Laboratory Journal, vol. 6, no., pp. 5 5, Sprng 993. [6] K. Matsu, Y. Suganam, and Y. Kosug, Feature Selecton by Genetc Algorthm for MRI Segmentaton, Systems and Computers n Japan, vol. 30, (no. 7), pp , Scrpta techncal, June [7] L.M. Novak, M.C. Burl, and W.W. Irvng, Optmal Polarmetrc Processng for Enhanced Detecton, IEEE Trans. Aerosp. Electron. Syst. 9, pp , 993. [8] L.M. Novak, G.J. Owrka, and C.M. Netshen, Performance of a Hgh-Resoluton Polarmetrc SAR Automatc Recognton System, Lncoln Laboratory Journal, vol. 6, no., pp. 4, Sprng 993. [9] W.F. Punch and E.D. Goodman, Further Research on Feature Selecton and Classfcaton Usng Genetc Algorthms, Proc. 5th Int. Conf. on Genetc Algorthms, pp , 993. [0] F.C. Rhee and Y.J. Lee, Unsupervsed Feature Selecton Usng a Fuzzy-Genetc Algorthm, Proc. IEEE Int. Fuzzy Systems Conf., vol. 3, pp , Pscataway, NJ, 999. [] W. Sedleck and J. Sklansky, A Note on Genetc Algorthms for Large-Scale Feature Selecton, Pattern Recognton Letters, vol. 0, pp , November