Rice Kernel Shape Description Using an Improved Fourier Descriptor

Transcription

1 Rce Kernel Shape Descrpton Usng an Improved Fourer Descrptor Hua Gao, Yaqn Wang, Guangme Zhang, Pngu Ge, Yong Lang To cte ths verson: Hua Gao, Yaqn Wang, Guangme Zhang, Pngu Ge, Yong Lang. Rce Kernel Shape Descrpton Usng an Improved Fourer Descrptor. Daolang L; Yngy Chen. 5th Computer and Computng Technologes n Agrculture (CCTA), Oct 0, Beng, Chna. Sprnger, IFIP Advances n Informaton and Communcaton Technology, AICT-368 (Part I), pp.04-4, 0, Computer and Computng Technologes n Agrculture V. <0.007/ _4>. <hal > HAL Id: hal Submtted on 4 Aug 06 HAL s a mult-dscplnary open access archve for the depost and dssemnaton of scentfc research documents, whether they are publshed or not. The documents may come from teachng and research nsttutons n France or abroad, or from publc or prvate research centers. L archve ouverte plurdscplnare HAL, est destnée au dépôt et à la dffuson de documents scentfques de nveau recherche, publés ou non, émanant des établssements d ensegnement et de recherche franças ou étrangers, des laboratores publcs ou prvés. Dstrbuted under a Creatve Commons Attrbuton 4.0 Internatonal Lcense

2 Rce Kernel Shape Descrpton Usng an Improved Fourer Descrptor Hua Gao, Yaqn Wang, Guangme Zhang, Pngu Ge, Yong Lang College of Informaton Scence & Engneerng, Shandong Agrcultural Unversty, o. 6 Dazong Road, Taan, Shandong 708, Chna Abstract: A Fourer descrptor s one of the best methods for descrbng obect boundares, but there are lmtatons n descrbng the boundary of rce kernels usng tradtonal Fourer descrptors. An nnovatve approach was developed to descrbe rce kernel boundares by mprovng a tradtonal Fourer descrptor. Ths radus Fourer descrptor (RFD) uses a radus set for rce kernel mages as ts bass functon, and uses ampltude spectrum of Fourer transform for the radus set as ts descrptor. Ths method only retans the frst 9 components of RFD, whch s smple and the dmenson of the feature vector can be reduced greatly wthout concern for the ntal startng pont on the contour. The method was valdated n terms of area computaton, varety dstance calculaton, shape descrpton, and detecton of broken kernels usng a backpropagaton (BP) neural network for several varetes of rce kernels. The detecton accuracy for whole rce kernels of dfferent samples was 96%-00% and for broken rce kernels was 96.5%. Key words: Image processng, Radus set, Rce kernel shape descrpton, Radus Fourer descrptor Introducton The shape of rce kernels s a basc parameter for qualty assessment and classfcaton of rce [-]. Accordng to GB , the man parameters for rce qualty assessment nclude machnng precson, gran ntegrty, mpurtes, and broken rce rate. These parameters are related to kernel shape drectly or ndrectly. To realze detecton of rce parameters usng machne vson, one of the maor challenges s to fnd a method to effectvely and accurately descrbe rce shape features and dscrmnate whole rce kernels. At present, there are several parameters used to descrbe the kernel shape of agrcultural products [3-4], ncludng area, eccentrc moment, elongaton, nertal center, aspect rato, flakness rato, sphercty, roundness Supported by the Innovaton and Technology Fund of Shandong Agrcultural Unversty of Chna under Grant o Frst author: Hua Gao, 963, Male, Professor. Research nterests: Image processng, Precson agrculture. E-mal: gaoh@sdau.edu.cn. Correspondng author: Yaqn Wang, wyq@sdau.edu.cn

3 and Fourer descrptors. Whle for shape-based pattern recognton technque, moment nvarant [5] and Fourer descrptor [6-8] are two maor mage recognton methods. Epermental tests ndcated that coordnate sequences for obect contours based on a Fourer descrptor had the best shape recognton ablty. Kauppen and Sepanen compared auto regressve and Fourer based descrptors n D shape classfcaton [6]. We et al. revewed on shape representaton technques and ther applcatons n mage retreval [9]. Zhang and Lu classfed and revewed some mportant shape representaton and descrpton technques [0]. However, tradtonal descrptors use Fourer transforms of a seres of coordnate pars for a shape boundary. Accordng to the propertes of the Fourer transform, a tradtonal Fourer descrptor s related to boundary scale, drecton, and startng poston of the curve, resultng n many lmtatons n descrbng rce shape boundares. Accordng to the perodcty of Fourer transform, when the orgnal functon of a Fourer transform shfts, the phase spectrum of Fourer transform wll change, but the ampltude spectrum of Fourer transform wll not change. In ths paper, the ampltude of Fourer transform coeffcent for a boundary radus set s used as a descrptor to descrbe rce kernel shape. Ths descrptor s named as Radus Fourer Descrptor (RFD). The rotaton of rce kernel, correspondng to the shft of radus set, affects phase spectrum only, but does not affect ampltude spectrum. Therefore, t s rotaton nvarant to descrbe rce kernel shape usng the RFD. Materals and methods. Image Acquston Several varetes of whole rce kernels and broken ones, ncludng Dongbe long gran rce, Mehe rce, and Tha asmne rce were taken as epermental obects. The orgnal rce kernel mages were acqured on a fed mage collecton bench n ths research. The surface of the mage collecton bench was covered wth black cloth. A lghtng chamber comprsng a metal cylnder of 60 cm n dameter and 60 cm n heght contaned four 0-W ordnary fluorescent lamps nstalled symmetrcally. The nternal wall of the chamber was panted whte to yeld equal dffuse reflecton. The test camera (Canon A580), fed wth a homemade arm wth adustable poston and heght, had a resoluton of and was placed at the center of the chamber, 50 cm above the bench. Part of the orgnal rce kernel mages were shown n Fg.. To determne the boundary of every rce kernel, several preprocessng steps ncludng mage flterng, bnarzaton and segmentaton [] were carred out. Fg. was the segmentaton result of Fg. a. Based on the segmentaton result, the boundary of every rce kernel was obtaned. Fg. 3 was the boundary mage of fve touched kernels on the top-left corner of Fg..

4 Fg. Rce kernel mages: (a) Dongbe long gran rce; (b) Mehe rce; (c) Tha asmne rce. Fg. The segmentaton result of Fg. a. Fg. 3 The boundary of the fve touched kernels on the top-left corner of Fg... Fourer Descrptor Poston nformaton for boundary ponts s vtal n defnng mage boundares, whereas gray nformaton can be neglected n ths study. A normalzed boundary s a closed curve, so the boundary can be regarded as a curve y=f() consstng of a set of ponts n the regular y Cartesan coordnate system. A large amount of data s needed to totally descrbe such a curve n the spatal doman, resultng n complcated feature etracton. Thus, a boundary can be descrbed n the frequency doman usng a Fourer transform n a method known as a Fourer descrptor [8]. Tradtonal Fourer descrptor s related to boundary scale, drecton, and start pont poston of curve, whch result n many lmtatons for descrbng rce boundary wth tradtonal Fourer descrptor. The ampltude of Fourer transform coeffcent for a boundary radus set s used as a descrptor to descrbe rce kernel shape. Ths method can descrbe rce kernel shape accurately, and t s rotaton nvarant. Wthout concern for the start pont of boundary when calculatng, the method s smple to process and has a small amount of data.

5 If Fourer transformaton s performed usng y=f() drectly, the transform result wll depend on the specfc coordnates of and y, whch cannot satsfy shft and rotaton nvarablty requrements []. Thus, the RFD was ntroduced to satsfy these requrements. Defnton : Suppose that a closed mage boundary s a set B consstng of M boundary ponts and b (, y ) s any pont on the boundary. The center pont of the boundary, p o ( o, y o ), can then be defned as: o M M /, o /,,. () M y y M b y B 0 0 Defnton : As shown n Fg. 4, radal lnes were constructed from p o to obect mage boundary wth equal angle nterval of л/. Let b (, y ) be the ntersecton pont of the radal lnes and the obect boundary, where =0,,,,. The radus descrptor of the obect can then be defned as radus set R=[r 0,r, r ], where: r y y. () o o Fg. 4 Dagram showng calculaton of the radus descrptor R. Because of the rgdty characterstc of rce kernel, t s mpossble to produce deep hole on the fracture surface of rce kernel after breakng. Therefore, radal lnes from the mass center ntersect a rce boundary only once ether for ntact grans or for broken ones. Defnton 3: The dscrete Fourer transform for R s descrbed by the equaton: F ( u) r u r ep[ ] 0 (3)

6 F r ( u) R ( u) I ( u) (4) Where ^=. R(u) s the real part of Fr(u), and I(u) s the magnary part of Fr(u). And F r (u) s defned as the RFD of the obect boundary. Accordng to the process of FFT algorthm, the value of s to the power of n (n s an nteger). It s usually not necessary to represent rce kernel shape wth very hgh precson n practcal applcatons, so the value of s not necessary to be too bg (the bgger the value of, the more accurate the descrpton). Epermental test ndcated that 3 or 64 of can epress the detal of rce kernel shape accurately. The value of s set to 3 n ths research. Accordng to the perodcty of Fourer transform, when the orgnal functon of a Fourer transform shfts, the phase spectrum of Fourer transform wll change, but not the ampltude spectrum. Therefore, the ampltude spectrum of RFD s rotaton nvarant..3 RFD Calculaton The frst step n RFD calculaton s to fnd the boundary center pont p o and then the ntersecton pont b (, y ) of the radal lnes and the boundary, wth / as the nterval angle. Because of the dscreteness of dgtal mages, many radal lnes mght not ntersect wth the boundary so the coordnates of a vrtual ntersecton pont coordnates must be obtaned by nterpolaton. The specfc algorthm proposed n ths paper s as follows. () Rce mage boundary: The orgnal rce mage was processed va flterng, segmentaton and bnarzaton to obtan a bnary mage. Then the 8-neghbour boundary of the rce kernel was obtaned usng a morphologcal method: Where A s the bnary mage, B A ( AE) (5) 0 E s a structural eroson element, and 0 operator - stands for the subtracton operaton, and stands for the eroson operaton. () Coordnates of the boundary center p o : For any pont on the boundary as the startng pont, each pont was traversed along the boundary from the start untl the pont was reached agan. The average of all traverse ponts was calculated usng Eq. () to yeld the coordnates of p o ( o, y o ). (3) Smlar crcle radus: () Fnd the frst boundary pont b 0 along the straght lne y= o from p o ( o, y o ) and traverse every pont b (, y ) on the boundary to calculate the angle φ : 0 0

7 arccos o o o y y (6) () Confrm an ntersecton pont for the radus and boundary, b (=0,,, ). If φ =*/, pont b s an ntersecton pont for a smlar crcle radus and the boundary. If φ <*/, fnd the net pont b +. If φ >*/, the coordnates of b can be calculated accordng to: / / (7) / / y y y () Obtan R by calculatng r accordng to Eq. (). (4) Fourer transform for R: Accordng to Eq. (3), all calculatons requre multplcatons and ( ) addtons so the computatonal workload ncreases greatly wth. To mprove the computatonal effcency, a fast Fourer transform (FFT) was used for practcal applcaton: 0,,0 0, 0,0 ) ( (0) r r r r w w w w F F (8) Where u u e w,. The computatonal complety can be reduced to log () when usng FFT for = n, otherwse zero should be added..4 RFD Intercept The Fourer transform s a reversble lnear ntegral transform (Eqs. (3) and (4)). Therefore, the radus descrptor r can be restored by the Fourer descrptor F r (u). If all the coeffcents of the Fourer transform were chosen as the boundary descrpton feature, the dmenson of the feature vector would be too hgh and the computatonal workload would be ecessve, even though no contour nformaton would be lost.

8 Such hgh precson s usually not necessary n practcal applcatons. Therefore, selectve ntercepton for the Fourer transform coeffcent s essental. F r (u) s a sequence of frequency ponts and has conugate symmetry wth yqust frequency n=/+ as ts center. Therefore, only half of the F r (u) ponts (/) are requred for spectral analyss. Because the power of Fourer spectrum manly focuses on the low-frequency components, the fundamental shape of rce kernel can be descrbed wth small amount of low-frequency components. Eperments have been done to test how many components should be reserved to restore the rce kernel shape. Fg.5 shows the restoraton of rce kernel shape wth dfferent number of components, such as 3, 5, 7, and 9 components. Test result ndcated that the frst 9 components of RDF could restore the contours of obect almost wthout dstorton [3]. Therefore, only the frst 9 components of RFD (that s the frst 9 low-frequency coeffcents of DFT) are requred for rce shape descrpton. Fg. 5 Dagram showng restoraton of the rce shape wth dfferent number of Fourer lowfrequency components: (a) orgnal mage; (b) restoraton wth 3 components; (c) restoraton wth 5 components; (d) restoraton wth 7 components; and (e) restoraton wth 9 components. 3 Results and Analyss Accordng to the physcal meanng of Fourer transform, each component of the descrptor represents a specfc meanng of rce shape. That s, F r (0) ncludes the scale nformaton, F r () ncludes the crcularty nformaton, F r () ncludes the length nformaton, F r (3) ncludes the trangularty nformaton, F r (4) ncludes the rectangularty nformaton, F r (5) ncludes the pentagon nformaton, F r (6) ncludes the heagon nformaton, and so on. Each knd of nformaton can be used to perform shape calculaton and recognton for dfferent knd of applcatons. For eample, F r (0) could calculate area appromately, and the frst 9 components could detect rce varety and broken rce kernel. Especally, wth the development of neural network, relable classfcaton and recognton can be fnshed only through approprate dscplne wthout regard for the meanng of components of Fourer descrptor. To verfy the usablty of the RFD, eperments were carred out on some whole rce kernels and broken ones of Chna Dongbe long gran rce, Mehe rce and Tha

9 asmne rce. Results for kernel area, varety dstance computaton, and rce varety and broken kernel detecton usng RFD are dscussed n the followng sectons. 3. Computaton of Kernel Area Accordng to the characterstc of Fourer transform, the frst coeffcent of Fourer transform reflects the scale nformaton of mage. If we take the rce kernel mage as a smlar crcle, we can use r a =F r (0)/ representng rce kernel radus appromately. Therefore, we can use the formula S=kr a to appromately epress the area of the enclosed regon, where k s an adustment coeffcent that can be set to dfferent values for dfferent obects accordng to eperence. Table lsts the kernel area results for sample rce kernels. The actual area was obtaned usng a pel statstcal method. The unt of measurement would be sze nstead of pels n practcal applcatons. Table Calculaton result of rce kernel area Sample umber Average area (pels) Calculated Actual Error STDEV Broken kernels (8.7%) Whole kernels of Dongbe long gran rce (4.46%) Whole kernels of Mehe rce (3.36%) Whole kernels of Tha asmne rce (4.64%) 3. Shape Smlarty. The bass functon of the Fourer transform s a set of orthogonal normalzaton functons. Its transform coeffcent s determned by the nner product of the nput functon (mage) and ts bass functon and s a measure of the smlarty of the nput and bass functons. Therefore, the dstance for RFD spectral vectors can be used to measure the smlarty of two contours. To compare rce kernels of dfferent sze and resoluton, a normalzaton procedure should be appled to F r (u) accordng to: F F ( u) r rs ( u) (9) ra The normalzed RFD s scale nvarance and s only assocated wth the contour shape and s not related to the sze of the rce kernel. Therefore, the dstance between the normalzed Fourer spectrum vectors for two contours can be used as varety dstance for rce varety and broken kernel classfcaton and dfferentaton. For easy classfcaton, the Eucldean dstance ( k, l ) s used to descrbe the contour smlarty for rce kernels k and l :

10 m ( k, l ) Frsk ( ) Frsl ( ) (0) Where m s the number of components of the Fourer descrptor. The smaller the ( k, l ), the smaller the dfference between two rce kernels and the greater ther smlarty. If ( k, l ) =0, the two kernels are dentcal. Data on shape smlarty for dfferent rce samples are lsted n Table. Table Shape smlarty for rce kernels Comparson umber Average smlarty Varance Whole Dongbe long gran rce kernels Whole Mehe rce kernels Whole Tha asmne rce kernels Whole Dongbe long gran rce and Mehe rce kernels Whole Dongbe long gran rce and Tha asmne rce kernels Whole Tha asmne rce and Mehe rce kernels Broken kernels Whole and broken kernels * Whole and broken kernels ** otes: *The comparson sample s the mture of whole and broken kernels. **The comparson sample s a group of whole kernels and a group of broken kernels, whch means that each whole kernel s compared wth every broken kernel and each ndvdual n the group of broken kernels s compared wth every ndvdual n the group of whole kernels. We can see from table that there are sgnfcant dfferences n smlarty among dfferent varetes of rce kernels as well as between whole rce kernels and broken rce kernels. Therefore, they can be classfed and recognzed n theory. We have used artfcal neural network to recognze rce kernels wth hgh effcency. 3.3 Recognton of Rce Kernels Usng an Artfcal eural etwork A BP neural network was used as the classfer. The network structure has three layers: an nput layer, a hdden layer, and an output layer. There are nne nodes n the nput layer, correspondng to the frst nne RFD components. There are two nodes n the output layer, consderng network epansblty. Suppose that an output of 00 denotes a standard rce kernel and an output of denotes a broken kernel. Epermental tests revealed that there can be four hdden nodes, Tansg can be used for the actvaton functon, and the YPROP algorthm can be used to deal wth the problem of low convergence speed.

11 A sample of 00 rce kernels (50 whole and 50 broken) was used to tran the network and then to determne the network weght value. Another sample of 800 rce kernels (600 whole and 00 broken) were used as test samples for classfcaton. The test results are presented n Table 3. Table 3 Detecton of broken rce usng a BP neural network Sample umber umber detected Accuracy (%) Whole Dongbe long gran rce kernels Whole Mehe rce kernels Whole Tha asmne rce kernels Broken rce kernels Conclusons In ths research we developed an mproved Fourer descrptor, a radus Fourer descrptor. Epermental test ndcated that ths RFD ncludes almost all the shape nformaton of rce kernel. It s evdent that we can calculate rce kernel area and dfferentate rce varety and broken kernels usng RFD. As a result, only usng the frst 9 RFD components we can reproduce rce contours wthout dstorton and retan almost all of the feature nformaton. Wthout concern for the ntal startng pont on the contour, ths method s smple and the dmenson of the feature vector can be reduced greatly. Takng Chna Dongbe long gran rce, Mehe rce, and Tha asmne rce as eamples, area of rce kernels and varety dstance between dfferent rce samples were calculated and a backpropagaton neural network was tested for detecton of broken rce kernels. The detecton accuracy for whole rce kernels of dfferent samples was 96%-00% and for broken rce kernels was 96.5%. Combned wth backpropagaton neural network, we can classfy rce varety accurately. Moreover, the RFD has the followng advantages for descrbng the contours of rce kernels:. Unqueness: the Fourer transform s a one-to-one mappng and one descrptor set corresponds to one boundary contour mage.. Shft nvarance: The transform coeffcent of the RFD reles only on the boundary shape and s not related to the mage poston. 3. Rotaton nvarance: Image rotaton only changes the phase spectrum of descrptor and the power spectrum does not change. 4. Scale nvarance: The descrptor s scale-nvarant after normalzaton. 5. Precse descrpton: An mage boundary can be totally restored usng the RFD, whch s mpossble usng other boundary descrpton methods. 6. Low dmensonalty of the feature vector: Fewer components are requred to descrbe the boundary and the Eucldean dstance s used for easy classfcaton. The RFD provdes a means to analyze the shape of rce kernels n the frequency doman. It also provdes a reference scheme for shape analyss of other agrcultural products. For eample, t has practcal sgnfcance for qualty assessment,

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