PERFORMANCE EVALUATION FOR SCENE MATCHING ALGORITHMS BY SVM
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1 PERFORMACE EVALUAIO FOR SCEE MACHIG ALGORIHMS BY SVM Zhaohu Yang a, b, *, Yngyng Chen a, Shaomng Zhang a a he Research Center of Remote Sensng and Geomatc, ongj Unversty, Shangha , Chna - yzhac@63.com b School of Envronmental Scence and Engneerng, Suzhou Unversty of Scence and echnology, Suzhou 250, Chna - yzhmlan@gmal.com Commsson VII, WG VII/4 KEY WORDS: Scene matchng, Classfcaton, Support vector machne, Performance evaluaton, Measure descrptor, ranng ABSRAC: Scene matchng s the process of locatng a regon of an mage wth the correspondng regon of another mage both mage regons represent the same scene. Although a lot of algorthms have appeared on scene matchng, performance analyss s usually based on smple statstc experment and performed smply and vsually, and lttle attenton has been gven to evaluate performance of dfferent algorthms. In order to choose sutable algorthms and mprove the performances of the algorthms, we present a novel performance evaluaton method for scene matchng algorthms based on support vector machne (SVM), whch can partly show nteract-effect of numerous smlarty measure factors and fnd a dependency lnk between two correlatve mages. he method s descrbed wth a three-step procedure. Frstly we buld samples data set usng smlarty measure descrptors of mage pars. hen decson functon s obtaned through tranng and testng process wth nput of samples data. Fnally, we adopt result of SVM classfcaton to evaluate two classcal algorthms: normalzed cross-correlaton algorthm and Canny-based edge extracton algorthm. he expermental results show that ths method holds the capablty of automatc decson ablty for performance evaluaton and hgh rato of correct predcton.. IRODUCIO Scene matchng refers to the process of locatng a regon n one mage wth the correspondng regon n another mage both mage regons represent the same scene. he two mages are often taken under dfferent tme, dfferent sensor pose geometry, or taken wth dfferent types of sensor (Sjahputera, 2004). he man goal n scene matchng s to assess the degree of smlarty and fnd a dependency lnk between two correlatve mages. ow scene matchng s a wdely used technology n real-tme applcatons such as flght navgaton and mssle gudance. Some classcal algorthms have been developed les n the varety of sensor styles and varety of mage characterstcs. In order to choose sutable algorthms and mprove the performances of the algorthms, some researchers have studed performance evaluaton for matchng algorthms (Mogne, et al., 998; Coutre, et al., 2000), whch s essental for the successful creaton and nterpretaton the crteron of test data of matchng algorthm. However, defnng nter-comparson crtera s a dffcult task, snce each algorthm should take nto account not only the geometrc dstorton between the mages but also radometrc deformatons and nose corrupton and applcatondependent mages characterstcs. herefore, an accurate mathematcal model that s able to ncorporate all smlarty measure descrptors and can predct the outcome of matchng algorthms s not feasble. Currently, most of performance evaluaton methods are based on smple statstc experment, whch cannot deal wth nteract effect of numerous smlarty measure factors. Furthermore, the statstc methods are useful for large-scale tran data set, but they do not seem suted for the problem only wth a few of examples avalable. o overcome above drawback, we ntroduce the support vector machne (SVM) to performance evaluaton for scene matchng algorthms. Frstly we buld a low number of sample data set usng smlarty measure descrptors of pars of reference and sensed mages. hen decson functon s traned through tranng and testng wth nput of samples data. Fnally, we use SVM classfcaton output to evaluate classcal algorthms. hus we can obtan an objectve performance evaluaton for scene matchng algorthms at same condton wthout any pror knowledge. 2. SUPPOR VECOR MACHIE Support vector machne (SVM) les n strong connecton to the statstcal learnng theory, t mplements the structural rsk mnmzaton for solvng two class classfcaton problems (Vapnk, 998). SVM transforms the nput nto a hghdmensonal space usng a nonlnear mappng. o overcome the ncreased computatonal complexty and over-fttng problems caused by the transformaton, SVM constructs a maxmum margn hyper-plane and support vectors. he maxmum margn hyper-plane s set as far away as possble between classes, and the support vectors are the nstances that are closest to the maxmum margn hyper-plane. Gven a tranng set of nstance-label pars n each nput x R and the output label y { } y, x = R, wth, the support * Correspondng author 503
2 he Internatonal Archves of the Photogrammetry, Remote Sensng and Spatal Informaton Scences. Vol. XXXVII. Part B7. Bejng 2008 vector method ams at buldng a decson functon for classfcaton as follow. () α ϕ ϕ 2 = yx ( ) = sgn y ( x), ( x) + b α = postve real constants b = real constant ϕ = nonlnear mappng, = nner product 0 Y b 0 = Y ZZ c I α r (7) + z ϕ( x ) y,, ϕ( x ) y = L [ ] Y = y,, L y r = [, L,] α = [ α, L, α ] Usng the kernel functon K( x nstead of the nner, xj) product, the low-dmensonal nput could be mapped nto the hgh-dmensonal space and Eq.() could be replaced as follow. yx ( ) = sgn αykxx (, ) + b = the classfer s constructed as (2) y = w ϕ( x) + b =,2, L (3) When the tranng set s not separable, the SVM algorthm tres to mnmze w under the condton of separatng the data wth a mnmum number of errors. hs s mproved by slack varableζ and penalty parameter c. hus SVM requres the soluton of the followng optmzaton problem: mn ww+ c ζ wb,, ζ 2 = subject to : y = w ϕ( x) + b ζ =,2, L ζ 0 In least squares support vector machnes (LS-SVM), least squares verson s related to the cost functon (Suykens and Vandewalle, 2000). he optmzaton problem s modfed nto c 2 mn τ( w, ζ) = w w+ ζ 2 2 = subject to : y w ϕ( x) + b = ζ =,2, L the correspondng Lagrangan s Lwb (,, ζ, α) = τ( w, ζ) α{ y wϕ( x) + b + ζ} = (4) (5) (6) the optmalty condton leads to the set of lnear equaton as 3. CLASSIC SCEE MACHIG ALGORIHMS Classc scene matchng methods can be dvded nto two major groups (Brown, 992; Ztova and Flusser, 2003): area-based algorthms that used mages pxel ntensty values drectly (Barnea and Slverman, 972) and feature-based algorthms that use obvous features such as edges and ponts (Wong, 980; erefa and Harada, 200). Recently, scene matchng methods usng smultaneously both area-based and feature-based approaches have started to appear. Area-based algorthms have good capablty of representng the mage s ntensty character under the low dstorton and low greyscale dfference condton. However, they are just a type of smple smlarty measurement and are weak-robust to nose or great dstorton. On the other hand, feature-based algorthms, whch match features represent nformaton on global level, are typcally appled when the local structural nformaton s more sgnfcant than the ntensty nformaton. hs property makes feature-based methods sutable for stuatons when great llumnaton and dstorton changes are expected or mult-sensor mage analyss s needed. Here, we choose two classcal algorthms as research targets of performance evaluaton. One s the normalzed cross-correlaton algorthm (CC) whch s representatve of the area-based methods. CC algorthm computes the measure of smlarty for wndow pars of mages and searches ts maxmum as matchng locaton. Despte hgh computatonal complexty, ths method s stll often n use, partcularly thanks to ts easy hardware mplementaton, whch makes t sutable for real-tme applcatons. Another s Canny-based edge extracton algorthm (CEE) whch belongs to feature-based algorthms. he method elmnates background edges n mages by makng smooth flter frstly. hen usng Canny edge detector, only salent edges are extracted by adjustng the threshold to mnmze the weak edges. Fnally, the couple of bnary edge mages are matched and the parwse correspondence between reference mage and sensed mage s obtaned usng ther spatal edge relatons of features. 4. SIMILARIY MEASURE DESCRIPORS In order to evaluate performance of scene matchng algorthms, we should extract measure descrptors (also called features or parameters) from reference and sensed mage nformaton. Once the measure descrptors have been acheved, they must be coded as a descrpton vector whch acts as the nput of SVM. In our method, the measure descrptors can be classfed n two groups: gray-based descrptors and edge-based descrptors. he former are drectly obtaned from mage ntensty and assess statstcal characterstcs, and the latter are ganed from edge 504
3 he Internatonal Archves of the Photogrammetry, Remote Sensng and Spatal Informaton Scences. Vol. XXXVII. Part B7. Bejng 2008 nformaton of mage and descrbe the unque structure features. hese two level descrptors actually represent mage s nformaton from fne to coarse scale, and they are supplementary from each other. here are lots of methods to gan the edge nformaton, such as the edge detecton algorthm, the local mage gradents, etc. In ths paper, we adopt Canny (Canny, 986) operator to extract the edge nformaton due to ts excellent capablty of accurate localzaton and responses to a sngle edge. Here, we totally extract two gray-based descrptors (mean varance of mage and mage entropy) and two edge-based descrptors (edge densty and geometrc nvarants). 4. Varance of mage he varance of mage s the average squared devaton of all pxels from the sample mean. he varance of mage, var, s computed usng the equaton Canny(I) = total number of edge ponts M = mage sze 4.4 Geometrc nvarants Another descrptor computed from extracted edges wll be used: the geometrc nvarants. A famly of seven nvarants wth respect to planar transformatons s frstly obtaned by Hu (Hu, 962). hose nvarants are nvarants to rotaton, scalng and translaton, whch can be regarded as nonlnear combnatons of complex geometrc moments: c + + p q pq x + y) ( x y) f ( x, y) = ( dxdy (2) x, y = coordnates of the mage f ( xy, ) = magnary unt p+q = order of c pq M var = [(, I j) E] M = = 0 j 0 2 (8) Here we use modfed nvarants (Flusser, 2000), whch have the followng forms: M = mage sze I(,j) = ntensty n poston of (,j) of reference mage E = average of reference mage ntensty. 4.2 Image entropy Image entropy s a quantty whch s used to character the certan qualty of an mage. Low entropy mages lack of detal nformaton and hgh entropy mages have a great deal of contrast nformaton. Consequently hgh entropy mages can show the more detal nformaton of mage. Image entropy s calculated wth follow formula = c = c c = re c20c2 4 = m c20c = re( c30c2) 6 = m( c30c2 2 7 = c22 8 = re( c3c2) = m( c3c2) 0 = re( c40c2 4 = m( c40c2) ( ) ( ) 5. SVM CLASSIFICAIO 5. Samples data set constructon ) ) (3) H M f = pj log pj = j= M p f (, j)/ f (, j) j = = j= p j = probablty of dfference ntensty of (,j) f(,j) = gray value of pxel (,j) n reference mage 4.3 Edge densty (9) (0) Edge densty can show the concentraton of features n orgnal mage. We use edge densty ED as descrptor, whch s computed from bnary Canny-edge mage by Canny( I) ED = M () he sample data set s obtaned by combnaton of SPO 5 panchromatc mages, EM+ band 8 panchromatc mages and SAR mages. SPO 5 mage patches regard as reference mages, and EM mage patches and SAR mage patches smulate as sensed mages. In ths way, each type of sensed mage and correspondng reference mage compose a par of sample mages. We process the scene matchng between each par of sample mage usng CC algorthm and CEE algorthm respectvely. Accordng to the matchng locaton offset, we classfy two labels as rght matchng class (less than three pxels offset) and wrong matchng class (great than three pxels offset) for each algorthm. hat s tradtonal two-class problems n SVM classfcaton. We select some pars of sample mages for each algorthm respectvely and buld a characterzaton of each par of sample mages usng above measure descrptors. By computng varance of mage, mage entropy, edge densty and geometrc nvarants drectly from sample mages, we can code descrpton feature vectors whch wll be fed to the learnng engne of SVM. Each feature vector has 4 components totally and normalzed before tranng. 505
4 he Internatonal Archves of the Photogrammetry, Remote Sensng and Spatal Informaton Scences. Vol. XXXVII. Part B7. Bejng ranng By selectng a subset of samples as a tranng set and the complementary subset as the test set we can buld an automatc SVM classfcaton system, whch can label par of mages accordng to ts lkelhood of belongng to rght matchng class or not. hat s to say, we construct decson functon usng nput of feature vectors and output of class labels from samples. he radal bass functon (RBF) kernel n Eq. (4) wll be used n classfcaton, whch outperforms the lnear and polynomal kernel. And whole tranng set s traned by two best parameters whch are optmzed after cross valdaton and an exhaustve grd search. After tranng, a decson functon of classfcaton model s bult. hus we can test the tranng result usng complementary test set. K x x = x x > (4) 2 (, j) exp( γ j ), γ Performance evaluaton by classfcaton Analyss for performance evaluaton s performed at the last step. Wth the nput of descrpton feature vectors based on mages nformaton, we can obtan the output label (rght matchng class and wrong matchng class) by SVM classfcaton and predct whether the algorthm can make good matchng performance or not. From output of classfcaton, we can judge how well a partcular matchng algorthm perform wth respect to a certan scene and, by comparson, how well they perform wth respect to one another. 6. EXPERIMEAL RESULS A sequence of experments was performed to verfy our method descrbed n ths paper. Frstly, we selected SPO 5 panchromatc mages wth 2.5 m resoluton, EM+ band 8 panchromatc mages wth 5 m resoluton and SAR mages wth 0 m resoluton as orgnal test data. In order to undertake scene matchng, all types of above mages were resampled to 0 m resoluton. hen we cut 00 patch samples ( pxels sze) from SPO mages. he patch samples, whch regarded as reference mages, represented typcal scenes (brdge, lake, rver, buldng, road, etc). In addton, we also cut 00 patch samples (80 80 pxels sze) from EM and SAR mages respectvely whch located n the range of correspondng reference mages and regarded as sensed mages. hus each SPO reference mage and correspondng EM sensed mage composed a par of sample mages. And each SPO reference mage and correspondng SAR sensed mage composed another par of sample mages (Fg. ). As a result, we collected 00 pars of SPO-EM mages and 00 pars of SPO-SAR mages totally. Fgure. Pars of sample mages We computed smlarty measure descrptors from pars of samples and coded feature vectors as nput of SVM system. At the same tme, we obtaned matchng result usng CC algorthm and CEE algorthm, whch labelled as output of tranng data set. We use 60% of samples n tranng and complementary 40% n testng. hat s to say, 40 samples n each group can be tested and evaluated after SVM classfcaton. Here, confuson matrx was used to perform the analyss of overall system performances. he results of SPO-EM par mode usng CC algorthm are shown n able, each column corresponds to the reference class, each row corresponds to output class decded by the SVM classfcaton and each cell n the table gves the number of rght matchng class (RM Class) and wrong matchng class (WM Class). We see that user s total accuracy s detected at 87.5%. Smlarly, we can gan 82.5% total accuracy n SPO-SAR par mode usng CC algorthm (abel 2), 85% total accuracy n SPO-EM par mode usng CEE algorthm (abel 3) and 80% total accuracy n SPO-SAR par mode usng CEE algorthm (abel 4) respectvely. CC algorthm Result of SVM RM class 29 2 classfcaton WM class 3 6 able. Confuson matrx analyss of SPO-EM par mode usng CC algorthm CC algorthm Result of SVM RM class 7 4 classfcaton WM class 3 6 able 2. Confuson matrx analyss of SPO-SAR par mode usng CC algorthm CEE algorthm Result of SVM RM class 29 classfcaton WM class 5 5 able 3. Confuson matrx analyss of SPO-EM par mode usng CEE algorthm CEE algorthm Result of SVM RM class 24 4 classfcaton WM class able 4. Confuson matrx analyss of SPO-SAR par mode usng CEE algorthm
5 he Internatonal Archves of the Photogrammetry, Remote Sensng and Spatal Informaton Scences. Vol. XXXVII. Part B7. Bejng 2008 In order to valdate the correctness of SVM classfcaton system output, another experment was performed. 50 pars of SPO-EM patches and 50 pars of SPO-SAR patches were selected randomly and fed nto the traned SVM system. he results of classfcaton are shown n able 5 and able 6. gan the better classfcaton accuracy. Fnally, further tests wth addtonal data bases would be nterestng n order to valdate the applcablty of the method to other types of algorthms and sensors. REFERECES CC algorthm Result of classfcaton SPO-EM par mode 45 5 SPO-SAR par mode able 5. Performance of CC algorthm CEE algorthm Result of classfcaton SPO-EM par mode 43 7 SPO-SAR par mode 39 able 6. Performance of CEE algorthm he results of the experment allow us to draw the followng general concluson: () When the reference mage and sensed mage have smlar ntensty and texture nformaton, CC and CEE algorthms both work and seem to have equal matchng probablty. (2) When the ntensty s very dfferent, the CC algorthm gves bad results. On the contrary, CEE algorthm gans good results. 7. COCLUSIO In the paper, we present a novelty objectve performance evaluaton approach for scene matchng, whch automatcally trans and tests data va SVM. hs approach has no a pror knowledge, and only a set of tran examples for the learnng step s needed, whch s very mportant for choosng the scene matchng algorthms and mprovng the performance of algorthms. Another aspect of ths research whch should be mproved s the set of measure descrptors (features) used for the SVM classfcaton. We should select more sutable measure descrptors whch can optmze computatonal effcency and Barnea, D. I., Slverman, H. F.,972. A class of algorthm for fast dgtal regstraton. IEEE rans. Comput., 2, pp Brown, L. G.,992. A survey of mage regstraton technques. ACM Computng Surveys, 24(4), pp Canny, J. F.,986. A computatonal approach to edge detecton. IEEE rans. Pattern Analyss and Machne Intellgence, 8, pp Coutre, S. C., Evens, M. W., Armato, S. G.,2000. Performance evaluaton of mage regstraton. Proceedngs of the 22nd Annual Internatonal Conference of the IEEE, pp Flusser, J.,2000. On the ndependence of rotaton moment nvarants. Pattern Recognton, 33 (9), pp Hu, M.K.,962. Vsual pattern recognton by moment nvarants. IEEE ransactons on Informaton heory, 8 (2), pp Mogne, J. L., Xa, W., Chalermwat, P., et al.,998. Frst evaluaton of automatc mage regstraton methods. Geoscence and Remote Sensng Symposum Proceedngs, pp Sjahputera, O.,2004. Object Regstraton n Scene Matchng based on Spatal Relatonshps. ProQuest Informaton and Learnng Company, USA. Suykens, J. A. K., and Vandewalle, J.,2000. Recurrent least squares support vector machnes. IEEE ransactons on Crcuts and Systems-I, 47(7), pp erefa, D. A., and Harada, K.,200. A complement to the 8- pont algorthm n matchng uncalbrated mage sequences of a scene. Machne Graphcs and Vson, 0(), pp Vapnk, V.,998. Statstcal learnng theory. John Wley, ew York. Wong, R. Y.,980. Intensty sgnal processng of mages for optcal to radar scene matchng. IEEE rans. On Acoustcs, Speech, and Sgnal Processng, 28(2), pp Ztova, B., Flusser, J.,2003. Image regstraton methods: a survey. Image and Vson Computng, (2), pp
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