FRACTAL CHARACTERIZATION OF WHEAT CROP BASED ON DIGITAL IMAGES CAPTURED IN THE VISIBLE SPECTRUM

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1 FRACTAL CHARACTERIZATION OF WHEAT CROP BASED ON DIGITAL IMAGES CAPTURED IN THE VISIBLE SPECTRUM Florin SALA, Mrius BOLDEA, Iosif GERGEN Bnt University of Agriulturl Sienes nd Veterinry Mediine, Regele Mihi I l României, Timisor, Cle Ardului 119, , Timisor, Romni, Phone: , Fx: , Emils: florin_sl@us-tm.ro, mrius_olde@us-tm.ro, igergen@yhoo.om Astrt AgroLife Sientifi Journl - Volume 3, Numer 1, 2014 ISSN ; ISSN CD-ROM ; ISSN ONLINE ; ISSN-L Corresponding uthor emil: florin_sl@us-tm.ro Frtl nlysis ws used s n instrument for the hrteriztion of winter whet rop in different vegettion stges. The digitl imges ptured in the visile spetrum were nlyzed with the soft HrFA nd ImgeJ, nd the dt otined filitted the frtl hrteriztion of the whet rop. The frtl dimension (FD) vries in reltion with the growth stges nlyzed, etween 1.896± ±0.017 (with HrFA) nd 1.898± ±0.064 (with ImgeJ), with orreltion R 2 = for FD. The highest vlues of the frtl dimension were reorded in the stge of physiologil mturity of plnts. Prtiulr vlues of the frtl prmeters (frtl spetrum FS, frtl dimension - FD) re speifi for eh vegettion stge nd n represent stle elements for hrterizing the whet rop development. Keywords: frtl nlysis, frtl dimension, frtl spetrum, imge proessing, Tritium estivum L. INTRODUCTION The vegetl over of the erth is hrterized y wide dynmis in spe nd time, depending on vrious ftors, mong whih the limte nd nthropi tions ply key role, (Vitousek et l., 1997; Krl nd Trenerth, 2003). Reserh on the sptil nd temporl development of nturl vegettion (grssy or woody) nd of griulturl rops is of gret interest, nd the methods of investigtion hve developed, diversified nd re interorrelted in order to filitte their prmeteriztion nd quntifition for vrious purposes, with sientifi nd prtil pplitions. In this diretion, frtl nlysis oupies speil ple, (Wlker nd Kenkel, 1998; Li, 2000; Aldos et l., 2005). Frtl theory gives qulittive nd quntittive desription of the irregulrity inherent to ny rel ojet or phenomenon, in reltion to the presene of omplexity in vrile dimensionl sles. If the lssi sttisti theory desries irregulrities of limited numer of prmeters in popultion with the other stle prmeters, frtl nlysis rings quntittive mesure in the se of strutures of unlimited omplexity, 133 inluding the hnging of the sle to whih the nlysis is mde. As mtter of ft, tht is how ll iologil strutures re, esily identifile s pproximte frtls (Mndelrot, 1983; Zmeškl et l., 2001). Eghll nd Power (1995) used frtl method to nlyse nd hrterize temporl vriility for verge yield in the United Stte of different rops with wide rnge of yield levels nd found with this method tht rops were signifintly different in terms of temporl vriility. Eghll nd Vrfel (1997) oserved different vriility for rops under the influene of environmentl ftors nd the mngement prties. They onluded in their reserh tht temporl vriility ws muh more dominnt thn sptil vriility. Temporl vriility my gretly influene how sptil vriility is expressed in given field. Florin et l. (2009) studied the whet yield vrition ross spe nd time. They sid tht is serious need to further question how temporl vrition of rop yield impts one s ility to mnge sptil vrition. With greter depth of temporl rop yield dt this is promising perspetive from whih to identify

optiml sptil mngement strtegies. Numerous other studies hve used frtl methods for the study of lnd omplexes (spontneous grssy or woody vegettion, ultivted res, urn res et.

The im of the present reserh ws to nlyze digitl imges ptured in the visile spetrum of whet rop, in different growth stges, for otining frtl hrteriztion of the rop.

The vegettive mss of the rop displys wide dynmis in spe nd time, given y the individul morphology, y plnt density nd the morphologi speifiity of eh growth stge.

2 optiml sptil mngement strtegies. Numerous other studies hve used frtl methods for the study of lnd omplexes (spontneous grssy or woody vegettion, ultivted res, urn res et.) sed on stellite imges or terrestril imges (Eghll et l., 1997; Green et l., 2004; Hot nd Novotný, 2006; Linres et l., 2006; Zhu et l., 2006; Ehsni et l., 2008). The im of the present reserh ws to nlyze digitl imges ptured in the visile spetrum of whet rop, in different growth stges, for otining frtl hrteriztion of the rop. distriution ngles in three-dimensionl pln. The vegettive mss of the rop displys wide dynmis in spe nd time, given y the individul morphology, y plnt density nd the morphologi speifiity of eh growth stge. Digitl imges of whet rop, Ingenio ultivr, ptured 1.5 m high, underwent nlysis for frtl hrteriztion of the respetive rop in vrious growth stges, s shown in Figure 1. MATERIALS AND METHODS The reserh foused on ssessing the fetures nd otining frtl hrteriztion of whet rop in different growth stges, sed on digitl imges ptured in the visile spetrum. Biologi mteril. The iologi mteril ws represented y speies Tritium estivum L. ssp. vulgre, Ingenio ultivr, in uniform rop ondition. The ssessment ws mde in three growth stges: vegettive growth, ooting nd full mturity. Cpture of digitl imges. Digitl imges were ptured with Nikon D300 mer, 12 MP, DX formt, 24 mm fol lens, from height of 1.5 m. Four digitl imges were tken for eh growth stge, for the purpose of work uniformity. Imge proessing nd frtl nlysis. Box- Counting is the most importnt pproximte lultion method for ssessing the frtl dimension (Husdorff). The Box-Counting method ws used for evluting the frtl properties of the whet rop in different stges. For this, the softwre used ws HrFA lite v5.5.30, whih ws developed t the Institute of Physil nd Applied Chemistry, Tehnil University of Brno in the Czeh Repuli. The softwre inludes proedure lled Box- Counting, whih filittes the evlution of the frtl dimension (Buhní ek et l., 2000; Nežádl et l., 2001). RESULTS AND DISCUSSIONS The nopy of whet rop in whet rop is very omplex, due to its onstitutive elements: plnts, stems, leves, spikes with different 134 Stge 1 - vegettive growth stge Stge 2 - ooting stge Stge 3 - physiologil mturity stge Figure 1. Originl imges of whet rop in different stges of vegettion, Ingenio ultivr HrFA softwre nlyses lk & white imges. The Box-Counting method utilizes the overing frtl pttern with rster of oxes (squres) nd then evlutes how mny oxes, or of the rster re needed to over frtl ompletely (Kuík, 2005), where: - numer of lk squres; - numer of white squres; - numer of lk&vhite squres; - numer of lk nd lk&white squres; - numer of white nd lk&white squres.

These spets re importnt, euse for different vlues of Msk Intensity on sle from 0 to 255 pixels (lk & white), different vlues of the frtl prmeters re otined for the sme imge.

The slopes of the liner funtions (1), (2), (3):, (1), (2), (3) give D BW, D BBW nd D WBW the frtl dimensions.

This proedure ws used for nlyzing ll digitl imges for the three growth stges of the whet rop under reserh.

Bsed on the nlysis of the B&W histogrm of the imges ptured, for every imge we otined totl numer of 12212224 pixels, with intensity vrition speifi for eh growth stge nlyzed, s shown in Figures 2-4.

vlue for every imge nd the frtl spetr were otined, Figures 2-4, where: - inry imge for frtl nlysis, - histogrm distriution of pixels in B&W imge, - frtl spetr.

3 These spets re importnt, euse for different vlues of Msk Intensity on sle from 0 to 255 pixels (lk & white), different vlues of the frtl prmeters re otined for the sme imge. Repeting this mesurement with different sizes of oxes r = 1/ will result in logrithmil funtion of ox size r nd numer of oxes N(r) needed to ompletely over frtl. The slopes of the liner funtions (1), (2), (3):, (1), (2), (3) give D BW, D BBW nd D WBW the frtl dimensions. D BW hrterizes the properties of order of the frtl pttern, D BBW hrterizes the frtl pttern on the white kground nd D WBW hrterizes the frtl pttern on the lk kground. This proedure ws used for nlyzing ll digitl imges for the three growth stges of the whet rop under reserh. The ox ounting dimension ws omputed over lk nd white representtion of the imge re (4288 x 2848 pixels). Bsed on the nlysis of the B&W histogrm of the imges ptured, for every imge we otined totl numer of pixels, with intensity vrition speifi for eh growth stge nlyzed, s shown in Figures 2-4. Tking into ount the 0 to 255 vrition intervl for Msk Intensity nd onsequently the rnge of thresholding onditions (frtl nlysis intervl), frtl dimension nlysis ws mde on the intervl minim vlue - mxim vlue for every imge nd the frtl spetr were otined, Figures 2-4, where: - inry imge for frtl nlysis, - histogrm distriution of pixels in B&W imge, - frtl spetr. From the nlysis of frtl spetr nd of histogrm distriutions, the thresholding intervls were estlished for eh digitl imge. For these prtiulr ses in the entire frtl spetrum, Tle 1 presents the thresholding funtions nd the orreltion vlues (R) orresponding to the growth stges under nlysis, while Figure 5 shows the regression funtions. 135 Figure 2. Frtl spetr for stge 1 of whet rop Figure 3. Frtl spetr for stge 2 of whet rop The frtl dimensions otined on the nlyzed intervl, when oth tegories of oxes re tken into onsidertion (fully overed nd prtilly overed), re: for stge 1; for stge 2 nd for stge 3.

After proessing the digitl imges with the softwre ImgeJ on the three growth stges of the whet rop, eqution (13), the results show inrese in the verge vlue of the frtl dimension (FD) together with the

(13) where: FD = frtl dimension F = oxes ontining foreground pixels = Box size/imge dimension The highest vlue of the frtl dimension ws reorded t physiologil mturity of the whet rop, s shown in Tle 2.

Funtions for lulting the frtl dimensions D BW, D BBW nd D WBW nd the vlues of the orreltion oeffiients prtiulrized for the thresholding ondition Growth stge Equtions Eqution numer (4) Correltion (R)

4 After proessing the digitl imges with the softwre ImgeJ on the three growth stges of the whet rop, eqution (13), the results show inrese in the verge vlue of the frtl dimension (FD) together with the morphologil nd physiologil hnges in plnts rought out y different phenophses, similrly with the vlues determined with HrFA. (13) where: FD = frtl dimension F = oxes ontining foreground pixels = Box size/imge dimension The highest vlue of the frtl dimension ws reorded t physiologil mturity of the whet rop, s shown in Tle 2. Anov sttistil nlysis indites reliility of the results otined y frtl nlysis of whet rop, Ingenio ultivr (F>F rit, p<0.01), Tle 3. Figure 4. Frtl spetr for stge 3 of whet rop Tle 1. Funtions for lulting the frtl dimensions D BW, D BBW nd D WBW nd the vlues of the orreltion oeffiients prtiulrized for the thresholding ondition Growth stge Equtions Eqution numer (4) Correltion (R) Stge 1 (5) (6) (7) Stge 2 (8) (9) (10) Stge 3 (11) (12) The orreltion oeffiients resulting from the formuls: lultion of the frtl dimension (FD) with two pplitions, HrFA nd ImgeJ, hve vlues of , whih lso hs high sfety results. nd Frtl dimension vlues otined (FD) re etween 1-2 nd topologil spet of whet rop n e onsidered, s frtl properties, etween segment nd squre fter generl 136 for segment (vlue 1) for squre (vlue 2).

CONCLUSIONS The results otined through this study filitted the prmeteriztion nd frtl hrteriztion of the whet rop, Ingenio ultivr, sed on digitl imges ptured in different growth stges.

The vlues of the verge frtl dimension vried depending on the growth stge nlyzed.

Frtl dimension n e ssoited with other whet rop prmeters in order to provide more informtion out the growth stge. ACKNOWLEDGEMENTS Figure 5.

5 CONCLUSIONS The results otined through this study filitted the prmeteriztion nd frtl hrteriztion of the whet rop, Ingenio ultivr, sed on digitl imges ptured in different growth stges. The frtl spetrum (FS) hs prtiulr distriutions nd offers informtion tht is speifi for eh growth stge of the whet rop under nlysis. The vlues of the verge frtl dimension vried depending on the growth stge nlyzed. One prtiulrity oserved through the present study ws tht the frtl dimension inresed s the whet rop developed from one growth stge to nother. Frtl dimension n e ssoited with other whet rop prmeters in order to provide more informtion out the growth stge. ACKNOWLEDGEMENTS Figure 5. Regression lines for frtl dimension nlysis (, nd ) using Box-Counting on whet rop, Ingenio ultivr; softwre HrFA lite ( - stge 1; - stge 2; - stge 3) Tle 2. Frtl dimension (FD) in the three growth stges on whet, Ingenio ultivr Growth stge Frtl dimension (FD) HrFA ImgeJ Stge ± ±0.105 Stge ± ±0.042 Stge ± ±0.064 The uthors would like to express their thnks to the leders nd stff of the Didti nd Experimentl Sttion of Bnt University of Agriulturl Sienes nd Veterinry Mediine "Regele Mihi I l României" of Timisor, Romni for filitting the setup of the experimentl field for this reserh. We lso ppreite the efforts of the tem tht developed HrF, omplex nd very urte pplition for frtl nlysis, with multiple uses. For the purpose of the present reserh, the version used ws HrFA lite In ddition, we ppreite the effort of the designer nd developers of ImgeJ pplition nd of the plug-ins tht ompleted the se pplition, espe-illy FrL, whih ws used in the present study. Tle 3. ANOVA: Single Ftor nlysis Soure of Vrition SS df MS F P-vlue F rit Between Groups E Within Groups Totl Alf = 0.05 REFERENCES Aldos C.L., Pueyo Y., Nvs D., Cezudo B., Buhní ek M., Nežádl M., Zmeškl O., Numeri Gonzlez A., Freemn D.C., Frtl nlysis of Clultion of Frtl Dimension. 3 rd Predition plnt sptil ptterns: monitoring tool for vegettion trnsition shifts. Biodiversity nd Conservtion 14: Coferene, Fulty of Tehnology Zlin, BUT Brno, Otoer 2-3, p DOI /s , p

6 Eghll B., Power J.F., Frtl desription of temporl yield vriility of 10 rops in the United Sttes, Agronomy Journl, 87, p Eghll B., Vrvel G.E., Frtl Anlysis of Temporl Yield Vriility of Crop Sequenes: Implitions for Site-Speifi Mngement". Agronomy Journl, No. 6, Vol. 89, p Eghll B., Herget G.W., Lesoing G.W., Ferguson R.B., Frtl nlysis of sptil nd temporl vriility. Geoderm, Vol. 88 (3-4), p Ehsni R., Krimi D., Lee K.H., Frtl Anlysis of Yield Mps. Trnstions of the ASABE, 51(5), p Florin M.J., MBrtney A.B., Wheln B.M., Quntifition nd omprison of whet yield vrition ross spe nd time. Europen Journl of Agronomy, 30, p Green T.R., Erskine R.H., Mrtinez A., Murphy M.R., Ajuj L.R., Sls D.J., Rmirez J.A., Sptil Crop Yield nd Soil Wter Content: Mesurement, Sling nd Topogrphi Anlyses, Hydrologil roesses. Speil Issue: Sle nd Sling in Hydrology, vol. 18 (8), p Hot V., Novotný F., Surfe Defets Evlution y Frtl Geometry nd Sttistil Anlysis, HrFA - Hrmoni nd Frtl Imge Anlysis. e-journl, p Krl T.R., Trenerth K.E., Modern Glol Climte Chnge, Siene, Vol. 302, (5651) DOI: /siene , p Kuík L., Frtl Anlysis of Apple Flesh Struture HrFA - Hrmoni nd Frtl Imge Anlysis. e-journl, p Li B.L., Frtl geometry pplitions in desription nd nlysis of pth ptterns nd pth dynmis. Eologil Modelling 132, p Linres J.C., Esten F.J., Viñegl B., Crreir J.A., A Computtionl Anlysis of Multi-temporl Vegettion Chnges Using the Frtl Dimension Spetrum, HrFA - Hrmoni nd Frtl Imge Anlysis. e-journl, p Mndelrot B.B., Frtl Geometry of Nture. W.H. Freemn nd Co., New York. Nežádl M., Zmeškl O., Buhní ek M., The Box- Counting: Critil Study. 4 th Predition Conferene, Institute of Informtion Tehnologies, Fulty of Tehnology, Toms Bt University in Zlin, Otoer 25-26, p. 18. Vitousek P.M., Mooney H.A., Luheno J., Melillo J.M., Humn Domintion of Erth's Eosystems. Siene 25 July, Vol. 277, No. 5325, DOI: /siene , p Wlker D.J., Kenkel N.C., Frtl nlysis of sptio-temporl dynmis in orel forest lndspe. Astrt Botni 22, p Zmeškl O., Veselý M., Nežádl M., Buhní ek M., Frtl Anlysis of Imge Strutures, HrFA - Hrmoni nd Frtl Imge Anlysis, e-journl, p Zhu X., Nilnhl P., Zuo W., Yng X., Frtl nlysis pplied to sptil struture of hin's vegettion. Chinese Geogrphil Siene, Vol. 16, No. 1, Siene Press, Beijing, Chin, p ***HrFA , Hrmoni nd Frtl Imge Anlyser, Softwre for Determintion of Frtl Dimension, /imgesi. ***ImgeJ 1.47t, Imge Proessing nd Anlysis in Jv, Wyne Rsnd developer, Ntionl Institute of Helt, USA. 138

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