Changyuan Xing College of Computer Engineering, Yangtze Normal University, Chongqing , China

Transcription

1 ev. Téc. Ing. Unv. Zula. ol. 39, Nº 6, 6-4, 06 do:0.3/ A Feature Extracton Algorthm of Affne Invarant based on egon Partton Changyuan Xng College of Computer Engneerng, Yangtze Normal Unversty, Chongqng 40800, Chna Fabo Chen* College of Lfe Scences, Yangtze Normal Unversty, Chongqng40800, Chna *Correspondng author(e-mal: chenfabo963@6.com) Yuehan L College of Chemstry and Chemcal Engneerng, Yangtze Normal Unversty, Chongqng40800, Chna Abstract Extractng features s one of the core ssues n pattern recognton, n whch affne nvarant s mportant method to recognze object under complex envronment. To solve the ssues of the error ncreasng and the low effcency for affne nvarant extracton algorthms, a mproved feature extracton algorthm based on regon partton s proposed. Frst, the algorthm gets the centrod and optmalvertex of the bnarzed object mage. Then, a new partton strategy of the affne regon s appled. Fnally, the affne nvarant vecter wll be obtaned by the area rato of the affne regon. Experments on Columba Unversty s Fsh Database show that the nvarant extracted by the proposed algorthm satsfes affne transformaton propertes. Compared wth three popular affne nvarant extracton algorthms, the proposed algorthm can acheve a better performance. The extracted nvarant has a well ablty to dstngush objects. Key words:feature extracton, Affne nvarant,egon partton.. INTODUCTION The extracton of geometrc nvarant features s the key research of pattern recognton. Geometrc features are the basc characterstcs of an object mage, such as the dstrbuton of gray level and texture. Accordng to these features, we can obtan the geometrc nvarant structure of the object represented as constant functon forms n some transform. Wth geometrc nvarants we can dentfy dfferent objects and dstngush the dfferent stuatons of the same object. By usng the pont, the length of lne and area rato, the regon based nvarant wll be constructed. Then, the feature matchng algorthms usually apply dstance measurement to estmate the relatonshp between two mages. The pont feature can be the lne ntersecton ponts (Lu and An, 0), local curvature dscontnuty ponts, curve nflecton ponts (Kogan lver, 05), wavelet transform local extremum and corner ponts (Serej et al., 05). The segmentaton lne or object contour of the mage are the lne feature. A genetc algorthm was proposed to automatc detect edge based on Gaussan transform (Fu et al., 03). andom felds was used to obtan the gray-scale nvarant contour (en et al.,005). A contour matchng method based on B- splnes was publshed for two dmensonal affne nvarant (Wang and Teoh, 007). The regonal feature s the hgh contrast regon wthn the closed boundares (Guo et al., 04). The centrod of the regon s an affne nvarant, and t s not senstve to random nose or gray level change. Tuytelaars and Gool (000) proposed a local affne nvarant regon algorthm based on the densty of mage for wde baselne stereo matchng. Sun et al. (0) analyzed the exstng affne regon detector and the gradent drecton hstogram.sad and Atr (0) used the edge ponts and edge drecton vector to obtan the nvarant descrptors. In the use of multple mage sensors for a certan object, wth dfferent perspectve and poston, we wll get a dfferent number of mages. It wll ncrease the dffculty to extract nvarants. In practce, under the affne transformaton, the affne geometrc nvarant s used as the characterstc values of the mage. The mage does not change the content under the affne transform, just change the coordnates. Therefore, the affne transformaton can effectvely smulate the relatonshp between multple mages of the same object under dfferent angles and dstances. Affne geometrc nvarant can be used n wde applcaton range (Bn and Hao, 0). Yang and Cohen (999) presented a set of local absolute affne nvarants derved from the convex hull of the scattered feature ponts extracted from the mage. The method dealng wth recognton the affne transformed bnary objects s presented (Horáček et al., 008). It dvded an object nto affne nvarant parts and 6

2 ev. Téc. Ing. Unv. Zula. ol. 39, Nº 6, 6-4, 06 uses modfed radal vector for the descrpton of parts. Yuan and L (0) proposed a recognton method for palm ven based on affne geometrc propertes. Convex hull based features are affne nvarant attrbutes. They are used for solated oman numerals recognton n paper (Das et al., 00). Zhang et al. (05) proposed a scale nvarant and approxmate affne transformaton nvarant feature pont detecton algorthm based on the Gabor flter decomposton and phase congruency. The dffculty of constructng geometrc nvarant s how to use the mage gray dstrbuton to delneate the stable regon. Yang s algorthm needs to calculate and select the connectons between the convex hull vertces, when the dstance of two adjacent convex hull vertex s near, t wll result n unstable nvarant feature value (such as very large or very small egenvalues) due to pxel nterpolaton dfferences. Ths paper presents a new mproved feature extracton algorthm of affne nvarant based on area rato. We frstly extract the centrod and optmalvertex(whch s one of the convex hull vertexes of the object mage). Secondly, wth the affne nvarent propertes, a new affne regon partton strategy s determned. The affne nvarant vecter wll be obtaned by the area rato of affne regon fnally. Experments show that the proposed algorthm achves a better performance to other three affne nvarant extracton algorthms, and the extracted nvarant has a well ablty to dstngush objects. The rest of the paper s organzed as follows. In Secton, some propertes of affne transformaton are brefly ntroduced. In Secton 3, the specfc steps of the algorthm are ntroduced. We present expermental results n Secton 4. Fnally, we conclude the study.. POPETIES OF AFFINE TANSFOMATION Theoretcally, the affne transformaton of the mage s the pxel coordnates transform, the content of mage wll not be changed, nclude collnear ponts, coplanar ponts and parallel lne. Generally speakng, the dfference between the mages of the same object s from dfferent samplng and nterpolaton methods. Ths paper focuses on the affne nvarant extracton of two-dmensonal (D) planar mages. An affne transformaton T = {[A],b} n D space between pont par x andx a s gven by x a a a x b, y a a a y b t s a combnaton of three specal mappngs, such as a translaton, a scalng, a rotaton. It s a lnear transformaton f b = 0. If the rank of [A] s full,.e., det{[a]} 0, then the affne transform maps D objects to D objects. We dscuss that the transformaton matrx [A] has full rank. Affne transformaton has some propertes, the followng are wdely used n affne nvarant. ) The area a of the mage of an object after affne transformaton s equal to the product of ts orgnal area a tmes the determnant of the transformaton matrx,.e., a det A a. ) Parallel lnes map onto parallel lnes, ntersectng lnes map nto ntersectng lnes wth the pont of ntersecton of two lnes mappng nto the pont of ntersecton of ther mages. 3) Any three noncollnear ponts have noncollnear mages. 4) Any convex set has a convex mage. Let P and P be two dfferent convex polygons. P and P aretransformedpolygons under an affne transformaton T respectvely. Mathematcally, a relatve nvarant s represented by () f, f, () P P P P f and f are the rato of two area formed by the pxels n the same mage. From the property ), we can deduce that f f. Under the transformaton T, the nvarant f does not change at all, t s an absolute nvarant (Yang and Cohen, 999). 3. POPOSED ALGOITHM Convex hull s the smallest convex polygon contanng all the mage pxels of the object. It s unque for the same mage, and t has the propertes of local controllablty (when feature ponts are ether added to or subtracted from the orgnal mage, the convex hull s locally affected). When all the vertexes of the convex hull of the object are known, the affne nvarant vector can be constructed by applyng the absolute nvarant f. The key process s to fnd an approprate partton strategy of convex hull. In ths paper, we proposed a new partton strategy for the affne convex hull. 7

3 ev. Téc. Ing. Unv. Zula. ol. 39, Nº 6, 6-4, Overvew of The Algorthm In our algorthm, a color D mage I(x) of an object (e.g. a fsh mage) s regarded as the nput. Then, the followng four steps are to process I(x). Fnally, the algorthm outputs the vector of affne nvarant for the object. Step : Preprocess the mage I(x). The background nose s removed and I(x) s bnarzed to I bw (x). Step : Calculate the convex hull CHI of I bw (x), and choose an optmal vertex of CH I. Step 3: Partton I bw (x) accordng to the centrod and the optmal vertex. Step 4: Construct the affne nvarant vector based on the rato of parttoned affne area. The processng flow s llustrated n Fg.. Input color D mage I(x) Preprocess the mage I(x) to I bw (x) Calculate the convex hull CH I of I bw (x) and choose an optmal vertex of CH I Partton I bw (x) accordng to the centrod and the optmal vertex Construct the affne nvarant vecter based on the rato of parttoned area Output feature Fgure. The processng flow of the proposed algorthm. 3.. Image Preprocessng Due to the complcated envronmental factors (such as background, llumnaton and mutual overlap), the mage acqured from the sensor needs to be preprocessed before the feature extracton. Image segmentaton s the process of segmentng the dgtal mage nto a set of sub regons (pxels). The purpose of segmentaton s to smplfy, or change representaton of the mage, makng t easer to understand and analyze. Although many varous mage segmentaton algorthms have been proposed (nclude K-based clusterng algorthm, hstogram method, edge operator detecton method, regon growth, level set method, energy mnmzaton method, smulated annealng method, etc.), there s no unform soluton to mage segmentaton. To solve the segmentaton problem, ths technology s usually combned wth the knowledge of related felds. We used Columba Unversty s typcal database-fsh Database for testng n the experment. The mages of Fsh Database are gray segmented mages (the background s whte). In order to extract the centrod and the convex hull of a fsh, we need to bnary processng. In ths paper, we use Otsu s algorthm to reduce a gray level mage to a bnary mage. Otsu s algorthm assumes that the mage contans two classes of pxels followng bmodal hstogram (foreground pxels and background pxels), t then calculates the optmum threshold t separatng the two classes. In Otsu s method we exhaustvely search for the threshold that mnmzes the ntra-class varance (the varance wthn the class), defned as a weghted sum of varances of the two classes ( t) ( t) ( t) ( t) ( t), (3) and weghts, are the probabltes of the two classes separated by a threshold t and, are varances of these two classes. Otsu shows that mnmzng the ntra-class varance s the same as maxmzng nter-class varance 8

4 ev. Téc. Ing. Unv. Zula. ol. 39, Nº 6, 6-4, 06 ( t b ) ( t ) ( t ) ( t )[ ( t ) ( t )]. (4) The Otsu algorthm wll frstly compute hstogram and probabltes of each ntensty level, and set up ntal (0) and (0). Then, step through all possble thresholds t = maxmum ntensty, update and to compute () t. Fnally, t desres threshold corresponds to the maxmum () t. b Usng the threshold t, our algorthm bnares the fsh grayscale mage I(x) nto the mage I bw (x). For convenence, we let the expresson of black color (background) be zero, and whte color be one. The example fsh mage s shown n Fg.. I bw x 0,, x I x I t t b (5) (a) Fgure. The bnarzaton example of a grayscale fsh. (a) The grayscale mage of the fsh. (b) The fsh mage after the bnarzaton (The background s black) Convex Hull Calculaton and The Optmal ertex Chosen Two dfferent ponts can determne a straght lne, and the centrod O and the convex hull vertexes of mage I bw (x) can be regard as nherent ponts wth the affne transformaton propertes. The affne transformaton propertes ) and 3) show that the lne L through the centrod O and the th vertex of convex hull stll satfes the affne nvarance propertes, t wll dvde mage nto two closed regons. After affne transformaton T, the straght lne L can fnd the correspondng lne L. The ponts reletve postons n Fg.3(a) wll not change n Fg.3(b). The regon of the mage after affne transformaton s correspondng to ts orgnal regon. We can deduce that det A and det A. (b) The lne L dvdes the mage nto two closed regons and, we call t the frst tme regon partton for the object mage. The centrod O of the object can easly fnd, but how can we confrm the pont P opt n Fgure 3(a)? L O O L P opt P opt (a) (b) Fgure 3. The partton regon example of mage before and after the affne transformaton. (a) The parttoned mage before the affne transformaton. (b) The parttoned mage after the affne transformaton. 9

5 ev. Téc. Ing. Unv. Zula. ol. 39, Nº 6, 6-4, 06 P 5 P 4 P 3 P P Fgure 4. The convex hull CH I of a fsh mage ( P s vertex of CH I ). The pont P opt s the optmal vertex of convex hull of object mage. After we fnd the convex hull CH I (see Fg.4), we can use the followng steps to solve P opt. Frstly, we calculate each lne L whch passes through O( x 0, y 0 )and the th pont P ( xp, y P ) n CH I, the slope a of L s defned as a, xp x0 0 yp y 0 a, otherwse. xp x 0 Secondly, letdbe the sum of the dstances from each whte pxel dot s defned as Da ( ) ( y y ) a ( x x ) (6) Pd j ( xpd, y Pd ) n I bw (x) to L, whch n Pd j 0 Pd j 0, (7) j0 a where n s total number of whte pxel dots n I bw (x). Let A = {a }, for each a, we calculate the value D(a ). Lastly, let a arg mn{ D( a )}. Therefore, we can select the optmal lne L opt (wth the slope a) and confrm aa the optmal pont P opt n L opt (n Fgure 4, the P 3 s the optmal pont) Image Partton Strategy Wth the advancement n networkng and multmeda technologes enables the dstrbuton and sharng of multmeda content wdely. In the meantme, pracy becomes ncreasngly rampant as the customers can easly duplcate and redstrbute the receved multmeda content to a large audence. Insurng the copyrghted multmeda content s approprately used has become ncreasngly crtcal. In Fg.3(a), the lne L dvdes the mage nto two closed regons and, we call t the frst tme regon partton for the object mage. Let O be the centrod of regons and respectvely, the lne L passes throutgh O. Huang et al. (03) has proved that O, O are collnear. The second tme regon partton starts from the lne L and L whch dvde reman mage nto four closed regons (see Fg. 5(a)). Let the centrod of these four closed regons be O, O 3, O 4 5. When we connect 6 the centrod O wth the other four centrods O, O 3, O 4 5, the whole mage wll be dvded nto eght 6 closed regons (see Fgure 5(b)). j j L O3 L O O O O O6 O4 O O5 O Popt L Popt L (a) (b) Fgure 5. The partton strategy of mage area of the proposed algorthm. (a) The second tme regon partton of the mage. (b) The thrd tme regon partton of the mage. 0

6 ev. Téc. Ing. Unv. Zula. ol. 39, Nº 6, 6-4, 06 These eght regons can fnd the correspondng regons after the affne transformaton T. Ths partton strategy avods creatng the mnma parttoned area, and reduces the nfluence of the pxel accumulaton error, t also mproves the recognton ablty of the nvarant vector feature Affne Invarants Constructon In the upper subsecton, the mage s dvded nto eght closed regons, let each of these regon be ={,...,8}. Accordng to the propertes of the affne transformaton, after T. We can deduce that det can fnd the correspondng regon, A, (8) and det A,thenthe absolute nvarant f could be wrten as A det A f f. (9) det So the absolute affne nvarant vector F { f, f,..., f8} ofi bw (x) s obtaned. For hgh dmensonal nvarant vector of the mage, we can partton the I bw (x) to 6 and 3 closed subregons. Due to lmted space, n ths paper, the propertes of eght dmensonal nvarant vector are analyzed. 4.EXPEIMENTAL ESULTS In ths secton, we present varous experments to evaluate the effcency of the proposed algorthm. We use Columba Unversty s typcal database-fsh Database for testng n the experment. The mages of Fsh Database are gray segmented mages (the background s whte). Frstly, we check the ablty of the proposed algorthm n extractng the affne nvarant vector of the mage on the example fsh sets. Secondly, we compare tme consumpton wth ECAC (Huang et al., 03), S (Chen et al., 007) and MSA (Wang et al., 03) algorthms. Fnally, we analyze the tme complexty of the proposed method. The process s mplemented wth MATLAB 04, and all experments are performed on a Desktop runnng Wndows XP wthintel Pentum 3.0GHz Dual-Core CPU and GB memory. fsh_ fsh fsh fsh 3 fsh 4 fsh_ fsh fsh fsh 3 fsh 4 fsh_3 fsh_3_ fsh_3_ fsh_3_3 fsh_3_4 fsh_4 fsh_4_ fsh_4_ fsh_4_3 fsh_4_4 Fgure 6. Four type fshs and the mages n dfferent perspectve. 4.. Affne nvarance analyss Four type fsh were selected from Fsh Database, and each type ncludes fve mages (one front-vew mage and other four dfferent perspectve mages, see Fgure 6). We frst extract the affne nvarant vectors from each type fsh mages by our algorthm, and the feature vectors are plotted as curves accordng to class. Each vector curve belongs to same class s represented as dfferent lne and symbolc (seefgure7). Through the analyss of the curves, we can conclude:

7 ev. Téc. Ing. Unv. Zula. ol. 39, Nº 6, 6-4, 06 ) For the same type of fsh, the trend of the fve vector curves extracted from the dfferent perspectve s bascally the same. ) For the dfferent types of fsh, the extracted feature vector curves are totally dfferent. 3) The affne nvarant feature of the proposed algorthm has a well ablty to dstngush and dentfy, and satsfy the propertes of the affne transformaton. (a) (b) (c) (d) Fgure 7. The nvarant feature curves of fsh mages n dfferent perspectves. (a) The nvarant feature curves of fsh_. (b) The nvarant feature curves of fsh_. (c) The nvarant feature curves of fsh_3. (d) The nvarant feature curves of fsh_4. The features extracted from multple mages of the same type s concdent. The slght dfferences of egenvalues are manly caused by nterpolaton errors and the quantzaton errors n preprocess. 4.. The comparson of tme consumpton Dfferent algorthms are used one by one to extract affne nvarant n Fsh Database, and compared the tme consumpton wth our proposed algorthm. After analyzng the runnng tme of all four steps n our algorthm, we know that the Steps, 3, and 4 can be completed n O(n) tme. Snce we calculate convex hull of the object mage n Step, the proposed algorthm runs n O(nlogn) tme, where n s the number of total pxels of the mage I bw (x). The tme complexty of ECAC and S algorthms s O(n ), and MSA s O(n logn). Table. The average computaton tme of compared algorthms. The unt s second. Image sze Algorthm MSA ECAC S GIA Proposed 00* * * * * *

8 ev. Téc. Ing. Unv. Zula. ol. 39, Nº 6, 6-4, 06 For the same mage, the proposed algorthm s faster than ECAC and S algorthms. Compared wth MSA algorthm, when mage sze ncreases, the proposed algorthm can save much computatonal tme and perform more effectvely. 5.CONCLUSIONS Wth the applcaton background of object recognton and mage processng, affne nvarant descrbes the uncharge feature for an object under the affne transformaton, t can be appled to dfferentate the object from the other, and t can also fnd same object after some transformatons. Ths paper presents a mproved feature extracton algorthm of affne nvarant based on regon partton. The man dea s to dvde the regon nto subregon accordng to the centrod and optmal vertex of convex hull of the object mage.expermental results show that the computatonal tme of our algorthm s better than ECAC and S algorthms, and t can be appled to compute affne nvarant feature n bg-sze mage. Acknowledgements Ths work was supported by Scentfc and Technologcal esearch Program of Chongqng Muncpal Educaton Commsson (Grant No.KJ5008), t was also sponsored by Youth esearch Program of Yangtze Normal Unversty (Grant No. 05XJXM30). EFEENCES Bn L I, Hao Y E. (0) obust Image egstraton Method based on Affne Geometrc Invarant,Journal of Shangha Jaotong Unversty, 46(), pp Chen T, Su Y, Jang Y, et al. (007) Affne Invarant Feature Extracton based on Affne Geometry, Journal of Image and Graphcs, (9), pp Das N, Pramank S, Sarkar, et al. (00) ecognton of Isolated Mult-Orented Handwrtten/Prnted Characters usng a Novel Convex-Hull Based Algnment Technque,Internatonal Journal of Computer Applcatons, (3), pp Fu W, Johnston M, Zhang M.(03) Automatc Constructon of Gaussan based Edge Detectors usng Genetc Programmng, Proc. Conf. on Applcatons of Evolutonary Computaton, pp Guo L, Mng D, Mng Z. (04) Quaternon Moment and Its Invarants for Color Object Classfcaton,Informaton Scences, 73(8), pp Horáček O, Kamencký J, Flusser J. (008) ecognton of Partally Occluded and Deformed Bnary Objects,Pattern ecognton Letters, 9(3), pp Huang B, Zhao X H, Sh G T et al.(03) Extracton Method of a Segment Length aton Affne Geometry,Journal of Jln Unversty (Engneerng and Technology Edton), 43(), pp Kogan I A, Olver P J. (05) Invarants of Objects and Ther Images under Surjectve Maps,Lobachevsk Journal of Mathematcs, 36(3), pp Lu Z, An J, Jng Y. (0) A Smple and obust Feature Pont Matchng Algorthm based on estrcted Spatal Order Constrants for Aeral Image egstraton,ieee Transactons on Geoscence & emote Sensng, 50(), pp en X, Fowlkes C C, Malk J. (005) Scale-nvarant Contour Completon usng Condtonal andom Felds,Proc. Conf. on Computer son,ieee,, pp. 4-. Sad Y, Atr M, Tourk. (0) Human Detecton based on Integral Hstograms of Orented Gradents and SM,Proc. Conf. oncommuncatons, Computng and Control Applcatons (CCCA), pp. -5. Serej N D, Ahmadan A, Kasae S, et al.(05) A obust Keypont Extracton and Matchng Algorthm based on Wavelet Transform and Informaton Theory for Pont-based egstraton n Endoscopc Snus Cavty Data,Sgnal Image & deo Processng, pp. -9. Sun Y D, Yang J, Wu M J, et al. (0) Complementarty Analyss of Affne egon Detectors, Proc. Conf. onsymposum Informaton Scence and Engneerng (ISISE), pp Tuytelaars T, Gool L J. (000) Wde Baselne Stereo Matchng based on Local, Affnely Invarant egons, Proc. Conf. onbrtsh Machne son, pp Wang C Y, Zhang Y. (04) Affne Invarant Feature Extracton Algorthm based on Multscale Auto Convoluton Combnng wth Texture Structure Analyss,Optk, 5(3), pp Wang Y, Teoh E K. (007) D Affne-nvarant Contour Matchng usng B-splne Model,IEEE Transactons on Pattern Analyss and Machne Intellgence, 9(0), pp Yuan W Q, L W. (0) A Palm en Feature Extracton Method based on Affne Invarant, Proc. Conf. on obotcs and Bommetcs, pp

9 ev. Téc. Ing. Unv. Zula. ol. 39, Nº 6, 6-4, 06 Yang Z, Cohen F S.(999) Image egstraton bject ecognton usng Affne Invarants and Convex Hulls,IEEE Transactons on Image Processng, 8(7), pp Zhang Q, Wang Y, Wang L. (05) egstraton of Images wth Affne Geometrc Dstorton based on Maxmally Stable Extremal egons and Phase Congruency,Image & son Computng, 36(C), pp