Research Article Plant Leaf Recognition through Local Discriminative Tangent Space Alignment

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1 Electrcal and Computer Engneerng Volume 2016, Artcle ID , 5 pages Research Artcle Plant Leaf Recognton through Local Dscrmnatve Tangent Space Algnment Chuanle Zhang, 1 Shanwen Zhang, 2 and Wedong Fang 3 1 School of Scence and Informaton Engneerng, Tanjn Unversty of Scence and Technology, Tanjn , Chna 2 Department of Electroncs and Informaton Engneerng, Xjng Unversty, X an , Chna 3 Key Laboratory of Specalty Fber Optcs and Optcal Access Networks, Shangha Unversty, Shangha , Chna Correspondence should be addressed to Shanwen Zhang; wjdw716@163.com Receved 5 December 2015; Accepted 15 February 2016 Academc Edtor: Hu Cheng Copyrght 2016 Chuanle Zhang et al. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. Manfold learnng based dmensonalty reducton algorthms have been payed much attenton n plant leaf recognton as the algorthms can select a subset of effectve and effcent dscrmnatve features n the leaf mages. In ths paper, a dmensonalty reducton method based on local dscrmnatve tangent space algnment (LDTSA) s ntroduced for plant leaf recognton based on leaf mages. The proposed method can embrace part optmzaton and whole algnment and encapsulate the geometrc and dscrmnatve nformaton nto a local patch. The experments on two plant leaf databases, ICL and Swedsh plant leaf datasets, demonstrate the effectveness and feasblty of the proposed method. 1. Introducton Plant recognton based on leaf mages plays an mportant role n agrcultural nformatzaton, ecologcal protecton, and automatc plant recognton system. One of the most mportant steps n the mage based plant recognton s to valdly extract classfyng features. Currently, the commonly employed classfyng features for plant recognton based on leaf mage could be categorzed nto color, shape, and texture features [1 3]. Plant leaf classfcaton s a challengng problem due to ts hgh dmensonalty data, complexty, and rregular shape of plant leaf mages [4 6]. Tradtonal dmensonalty reducton methods typcally have a smaller data space from lnear combnatons of the orgnal data. The most common example s prncpal component analyss (PCA), whch seeks a low-dmensonal lnear subspace spanned by the egenvectors whch correspond to the largest egenvalues of the covarance matrx of all the samples. However, for plant leaf mages, the assumpton of global lnearty s a severe constrant because the leaf mages are qute senstve to seasonalty, locaton, and llumnaton condtons. Thus, t s not reasonable to beleve that the leaf mage data could be lnearly separable from each other. Manfold learnng has been utlzed n many applcatons such as pattern recognton, vsualzaton, and classfcaton tasks. In the last ten years, many manfold learnng nonlnear algorthms have been ntroduced wth an assumpton that the processed data les on or close to some low-dmensonal manfolds whch are embedded n a hgh-dmensonal unorganzedeucldeanspace.inthesemanfoldlearnngalgorthms, the most representatve ones are sometrc feature mappng (ISOMAP) n [7], locally lnear embeddng (LLE) n [8], Laplacan egenmaps (LE) n [9], Hessan-based locally lnear embeddng (HLLE) n [10], maxmum varance unfoldng (MVU) n [11], local tangent space algnment (LTSA) n [12], local splne embeddng (LSE) n [13], and local dscrmnatve tangent space algnment (LDTSA) n [14]. One of the most mportant advantages of manfold learnng [7 14] compared wth conventonal methods s how the data are treated mathematcally. Manfold learnng methods allow the data to be related nonlnearly, whch leads to the fact that manfold learnng methods can much more accurately capture the proper structures among the data, thus allowng for accurate recognton. For every manfold learnng algorthm, t tres to preserve a dfferent geometrcal property of the underlyng manfold. Local methods such as LLE, HLLE, LE, LTSA,

2 2 Electrcal and Computer Engneerng and LSE try to preserve the neghborhood structure n the data, whle global methods lke ISOMAP am to preserve the metrcs at all scales. Thanks to ther nonlnear nature, geometrc ntuton, and computatonal feasblty, these nonlnear methods have promsng results on some artfcal and real-world datasets. In [15] a framework, whch s called patch algnment, was proposed and t conssts of two stages: part optmzaton and whole algnment. In ths paper, we take an alternatve vew of the framework to ntroduce an effcent method based on local dscrmnatve tangent space algnment (LDTSA) for plant leaf recognton. Compared wth current plant leaf recognton methods, the proposed one can avod the small sample sze problem, preserves the dscrmnatve capablty, and detects the ntrnsc structure from the plantleafmagedata. The paper s organzed as follows: Secton 2 brefly descrbes the dmensonalty reducton algorthm based on local dscrmnatve tangent space algnment and ts procedures. Experments on plant leaf database are offered n Secton 3 and the paper s ended wth some conclusons n Secton Local Dscrmnatve Tangent Space Algnment Algorthm Suppose n orgnal labeled data ponts X = [x 1,...,x n ], ncludng all the samples x R m, = 1,2,...,n. The objectve of a dmensonalty reducton algorthm s to compute the correspondng low-dmensonal representatons of XY=[y 1,...,y n ], y R d, = 1,2,...,n,whered m. For the lnear dmensonalty reducton, t s necessary to fnd projecton matrx A, suchthaty = A T X.For the nonlnear dmensonalty reducton, t s usually dffcult to provde an explct mappng to transform data from a hgh-dmensonal space to a low-dmensonal subspace. For classfcaton task, n part optmzaton stage we always hope to project the hgh-dmensonal data nto a low-dmensonal feature space, n whch the projecton s characterzed by wthn-class compactness and between-class separablty [15]. Assume that there s an nteracton force between any parwse ponts n the ambent space; the mutual force can be dstngushed as wthn-class attracton or between-class repulson between any parwse ponts from the same or dfferent class, respectvely (see Fgure 1) [16]. In the reduced subspace, n order to acheve wthn-class attracton for data pont y, the followng objectve functon s defned as arg mn k 1 y y j 2, (1) where k 1 s the number of the nearest neghbors wth respect to x from data ponts n the same class as x. A attracts B N(X ) (a) A repulses B N(X ) Fgure 1: An ntutve demonstraton of wthn-class attracton and between-class repulson between parwse ponts, where the crcle denotes k nearest neghbors N(X ) of X ; (a) A and B belong to the same class; (b) A and B belong to dfferent classes. In order to acheve between-class separablty purpose for the data pont y, the followng objectve functon s defned as arg max k 2 p 1 (b) y 2 y p. (2) LTSA uses tangent coordnates to ndcate the local geometry. Assume that there s an affne projecton matrx, whch projects tangent coordnates to the low-dmensonal coordnates n a local patch whch contans neghbors from both the same and dfferent classes. To obtan the optmal tangent coordnates, we have the followng objectve functon on each patch: arg mn Y R k+1 T Θ 2, (3) where R k+1 =I k+1 e k+1 e T k+1 /(k+1)denotes the centralzaton matrx; e k+1 = [1,...,1] T R k+1 ; I k+1 s (k + 1) (k + 1) dentty matrx; and Θ R dλ(k+1) s the tangent coordnates correspondng to an orthonormal bass matrx of the tangent space. Snce the patch formed by the local neghborhood can be consdered approxmately lnear, we wrte the part dscrmnator by usng the lnear manpulaton as follows: k ( y j 1 argmn α k 2 p 1 y y j 2 y 2 y p +β Y R k+1 T Θ 2 ), where α and β are scalng factors to unfy dfferent data ponts of the wthn-class dstance and the between-class dstance and they are selected based on experments. Then objectve functon (4) can be rewrtten by patch algnment: argmn Y l [tr (Y L w1 Y T )+βtr (Y L w2 Y T ) αtr (Y L b Y T )], (4) (5)

3 Electrcal and Computer Engneerng 3 where k 1 L w1 = [ (ω ) j ω T ], [ ω dag (ω )] L w2 =R k1 +1 V V T, k 2 L b = [ (ω ) j ω T ], [ ω dag (ω )] (6) (a) (b) where V denotes the matrx of d rght sngular vectors of k 1 X R k+1 correspondng to ts d largest values; and ω=[ 1,...,1 k 2, β,..., β] T s a coeffcent vector. In (5), the frst two parts only nvolve the data ponts belongng to wthn-class neghbors and they share the same selecton matrx S w. The thrd part concerns the betweenclass neghbors and uses selecton matrx S b. Then(5)canbereformedtothefollowng: argmn Y l 1 [tr (Y L S w L w (Y L S w ) T )+αtr (Y L S b ) T ] = arg mn Y tr (Y L LY T L ), where S w and S b are selecton matrx and L w =L w1 +βl w2, L= l =1 (7) (S w L w S T w +αs bl b S T b ). (8) In summary, the man procedure of the proposed algorthm for the plant leaf mage classfcaton task can be descrbed as follows. Step 1. Select representatve labeled plant leaf mage samples to whch the followng dmensonalty reducton wll be done. Step 2. For each pont x, fnd ts wthn-class neghborhood set N w (x ) wth k 1 elements and between-class neghborhood set N w (x ) wth k 2 elements. Step 3. Generate two vectors X w =[x 1,...,x k1 ] and X b = [x 1,...,x k2 ], wth ther elements from N w (x ) and N w (x ), respectvely. Step 4. Construct L w1 wth k 1 wthn-class neghbors, then centralze the neghbors and compute the top-d egenvector from the autocorrecton matrx, and then construct L w2 and record the selecton matrx S w. Step 5. Construct L b wth k 2 between-class neghbors, and record the selecton matrx S b. (c) Fgure 2: Typcal leaves of the leaf database ICL. Step 6. Generate global L wth patch algnment through respectve selecton matrx. Step 7. Perform egendecomposton on XLX T and the egenvectors form projecton matrx U. Step 8. Fnal reduced dmensonalty results are Y L =U T X. 3. Experment Results 3.1. Experment Results on ICL Dataset. ICL leaf database has plant leaf mages of 220 speces and mage number of each class s unequal [17]. In order to verfy the effectveness of the proposed method n ths paper, we construct one leaf magesubsetfromtheiclleafdataset,whchhas15speces wth11samplesperspeces,andallclassesarecarefullychosen so that the shapes could be dstngushed easly by human eyes or the shapes are smlar but stll can be dentfed [16]. Some typcal example mages are demonstrated n Fgures 2(a), 2(b), and 2(c). Preprocessng s performed to crop all leaf mages from two databases. The llumnatons keep the same condton and the backgrounds are whte, and the sze of each cropped leaf mage n experments s pxels, wth gray level of 256 gray levels per pxel n preprocessng step, as demonstrated n Fgure 2(c) of one speces. Then, every mage s represented n a 4096-dmensonal vector n the mage space. By prereducng by PCA, 98 percent mage energy s kept and all prncpal components are selected correspondng to the nonzero egenvalues for eachmethod.the1-nnclassfersemployedtoclassfyleaf mages for ts smplcty. The dstance measure s Eucldean dstance. The leaf mage dataset s randomly separated nto two subsets: one part s for tranng (szes are 30, 45, 60, 75, 105, and 120) and the other s for testng purpose. The tranng sets are used to obtan the low-dmensonal subspace wth a projecton matrx. The testng sets are utlzed to test the fnal

4 4 Electrcal and Computer Engneerng Table 1: Average classfcaton rates (%) and standard devatons ICL plant leaf database. Tran samples LSDA LLTSA LDTSA ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 3.78 Table 2: Average classfcaton rates (%) and standard devatons Swedsh plant leaf database. Tran samples LSDA LLTSA LDTSA ± ± ± ± ± ± ± ± ± 2.73 classfcaton accuracy. Each tme the test s repeated 20 tmes and the accuracy rate s calculated each tme, as follows: Num (R) Accuracy = 100%, (9) Num (T) where Num(R) s the rght sample number detected and Num(T) s the total sample number tested. Table 1 shows the average classfcaton rates and standard devatons of three algorthms n our experments on the selected datasets whch are localty senstve dscrmnant analyss (LSDA), lnear local tangent space algnment (LLTSA),andtheproposedLDTSA.Itcanbeseenthatthe proposed method obtans better accuracy Experment Results on Swedsh Dataset. Swedsh leaf dataset [18] has 1125 mages from 15 dfferent plant speces, wth 75 leaf mages per speces. The preprocess of the leaf mage s the same as ICL dataset [16]. For each method, random subsets wth 20, 40, and 60 mages per speces are selected for tranng, the rest for testng. Such experment wth a specfc number s ndependently performed 20 tmes, and then the best average classfcaton results are recoded. Table 2 shows the maxmal average classfcaton accuracy wth dfferent sze of tranng sets and test sets. It could be found that the proposed method outperforms the other algorthms n all the cases. 4. Conclusons Plant recognton based on leaf mages has been an mportant and dffcult research topc, especally for leaves wth dfferent and complcated shapes. Although there are many exstng algorthms for plant leaf recognton, the recognton rates are stll low due to the complexty of plant leaf. Manfold learnng based dmensonalty reducton algorthms are promsng alternatves to tradtonal plant leaf recognton methods. A dmensonalty reducton method based on local dscrmnatve tangent space algnment (LDTSA) s proposed for plant leaf recognton task n ths paper, and t embraces part optmzaton and whole algnment and encapsulates the geometrc and dscrmnatve nformaton nto a local patch. The experment performed on two plant leaf databases shows the effectvenessandfeasbltyoftheproposedmethodnths paper. Competng Interests The authors declare that there s no conflct of nterests regardng the publcaton of ths paper. Acknowledgments The paper was supported by Tanjn Research Program of Applcaton Foundaton and Advanced Technology 14JCY- BJC42500 and Tanjn Cty Hgh School Scence & Technology Fund Plannng Project It was partly funded by the young academc team constructon projects of the twelve fve ntegrated nvestment plannng n Tanjn Unversty of Scence and Technology and the 2015 key projects of Tanjn Scence and Technology Support Program no. 15ZCZDGX Ths work was also supported by the Natonal Natural Scence Foundaton of Chna under Grant no and the Open Fund of Guangdong Provncal Key Laboratory of Petrochemcal Equpment Fault Dagnoss no. GDUPTKLAB References [1] A. El-ghazal, O. A. Basr, and S. Belkasm, Shape-based mage retreval usng par-wse canddate co-rankng, n Image Analyss and Recognton: 4th Internatonal Conference, ICIAR 2007, Montreal, Canada, August 22 24, Proceedngs,M.S.Kamel anda.c.camplho,eds.,vol.4633oflecture Notes n Computer Scence, pp , Sprnger, Berln, Germany, [2] S. Zhang and Y.-K. Le, Modfed locally lnear dscrmnant embeddng for plant leaf recognton, Neurocomputng,vol.74, no , pp , [3] J. Han and K.-K. Ma, Rotaton-nvarant and scale-nvarant Gabor features for texture mage retreval, Image and Vson Computng,vol.25,no.9,pp ,2007. [4] F. Mokhtaran and S. Abbas, Matchng shapes wth selfntersectons: applcaton to leaf classfcaton, IEEE Transactons on Image Processng,vol.13,no.5,pp ,2004. [5] Y. F. L, Q. S. Zhu, Y. K. Cao, and C. L. Wang, A leaf ven extracton method based on snakes technque, n Proceedngs of IEEE Internatonal Conference on Neural Networks and Bran (ICNN&B 05), pp , Bejng, Chna, October [6] S.-W. Zhang and C.-L. Zhang, Two-dmensonal localty dscrmnant projecton for plant leaf classfcaton, Intellgent Computng Theores and Applcatons Lecture Notes n Computer Scence, vol. 7390, pp , [7] J. B. Tenenbaum, V. de Slva, and J. C. Langford, A global geometrc framework for nonlnear dmensonalty reducton, Scence,vol.290,no.5500,pp ,2000. [8] S. T. Rowes and L. K. Saul, Nonlnear dmensonalty reducton by locally lnear embeddng, Scence, vol.290,no.5500, pp , 2000.

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