Comparative analysis of several digital methods to ...scielo.unam.mx/pdf//hbio/v20n2/v20n2a7.pdf · Comparative analysis of several digital methods to recognize diatoms Análisis

158 Álvarez-BorregoJ.andS.Solorza

Hidrobiológica

Hidrobiológica2010,20(2):158-170

Comparative analysis of several digital methods to recognize diatoms

Análisis comparativo de varios métodos digitales para el reconocimiento de diatomeas

JosuéÁlvarez-Borrego1andSeleneSolorza2

1CentrodeInvestigaciónCientíficaydeEducaciónSuperiordeEnsenada,DivisióndeFísicaAplicada,DepartamentodeÓptica,CarreteraEnsenada-Tijuana,No.3918,FraccionamientoZonaPlayitas,Ensenada,B.C.,22860México

2FacultaddeCiencias,UABC,Ensenada,B.C.,México.Km.103CarreteraTijuana-Ensenada,Ensenada,B.C.,22860e-mail:[email protected]

Álvarez-Borrego,J.andS.Solorza.2010Comparativeanalysisofseveraldigitalmethodstorecognizediatoms.Hidrobiológica20(2):158-170.

ABSTRACTIn this paper, severalmethodsarepresentedand compared in order to choose the best digital algorithm to recognizethediatomsspecies.Adigitalsystemof invariantcorrelationtopositionandrotationisconstructed.Basedinabinaryringmaskanaveragesignature filter foraselected image isproduced in fourdifferentwaysandcomparedwithvari-ancespectrummodifiedmethodologyusing fourdifferentways too. It isconclusive that thebestmethodology for thiscase is presented in the first method when the binary mask with a nonlinear filter is used without high frequenciesenhancedinthevariancespectrumoftheinputimageusinganaveragefilterof10inputrotatedimages.Moreovertheconfidencelevelforthiscasewas100%.Thesecondbestcasewasfortheaveragefilterf18,withthesameconfidencelevel,butwherethedifferenceintimeismorethanoneminute.Oneoftheadvantagesofthesekindsofmethodologiesis thatanentireprocesscanbe repeated in thesamewaywithoutmistakesand thediatoms imagesarekeptsave ina hard disk of the computer, so everybody can see again the diatom information of some special localization of theocean.

Key words:Automaticidentificationofdiatoms,imageprocessing,invariantcorrelation,patternrecognition.

RESUMENEn este artículo, se presentan y se comparan varios métodos para escoger el mejor algoritmo digital para reconocerespecies de diatomeas. Se propone un sistema digital de correlación invariante a posición y rotación el cual estábasado en una mascarilla binaria con cuatro diferentes caminos a seguir que produce una firma promedio para unacierta imagen seleccionada. Estos cuatro diferentes modos de correlación se comparan con una nueva metodologíade espectro de varianza modificada que también utiliza cuatro maneras distintas de correlación. Es concluyenteque los mejores resultados corresponden al método que utiliza la máscara binaria con una firma promedio de 10imágenes rotadas y el uso de un filtro no lineal y sin realce del contenido de frecuencias del espectro de varianciadelaimagendeentrada.Elniveldeconfianzaparaestecasofuede100%.Elsegundomejorcaso,conelmismonivelde confianza, fue para el filtro promedio de 18 imágenes rotadas, siendo la diferencia en tiempo de cómputo de másde un minuto. Una de las ventajas de esta clase de metodologías es que un proceso completo puede ser repetidode la misma manera y sin errores y además las imágenes de diatomeas pueden ser guardadas en un disco duro de

Comparativeanalysisofseveraldigitalmethodstorecognizediatoms 159

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INTRODUCTION

Microscopy is the principal method used to identify and countphytoplankton. Microscopical counts have been used to describephytoplankton communities and their spatial and temporal distri-bution patterns, and have also been used to convert phytoplank-ton numbers to biomass or energy (e. g. in terms of organic car-bon or calories, respectively) (Pech-Pacheco & Álvarez-Borrego,1998). However, microscopical examination entails considerabletime and labor for the processing of a large number of samples(Furuya, 1982); moreover, mistakes are easily made. Methodsenabling the rapid identification and quantification of organismsin a phytoplankton sample are needed. Since 40 years ago, Dr.Silverio Almeida’s group applied for the first time optical systeminorder to identifydiatoms (Almeidaet al.,1972,1978;Cairnset al.,1972;AlmeidaandEu,1976;FujiiandAlmeida,1979a-b;Fujiiet al.,1980).Thesestudiesprovedtheusefulnessofdiffractionpat-terns(Cairnset al.,1982).However,noneofthestudiesanalyzeindetail the problems that are encountered during the recognitionprocess, such as the invariance in the localization of the organ-ismswithin the image, the rotationand thedifferentscaleof theorganisms, the background noise problem generated by bodiesforeign to the organisms that are found in an image (detritus,inorganic particles, etc.), and the morphological variation of thespecies, among others, which in one way or another modify thefrequencies information that form the image, generating errone-ousidentifications.

Circularharmonicfiltershavebeenappliedtoidentifyplank-ton. With this kind of filters the rotation of the organisms in thesample is solved. The advantages of these filters are numerous.First, the correlation plane is invariant to rotation, and secondthere are a great number of theoretical studies that have provedtheir sensitivity to noise (Zavala-Hamz & Álvarez-Borrego, 1997).Thedisadvantageisthattheylosetheirpowerofdiscriminationiftheexpansioncenter, orproper center, isnotpreviously selectedand moreover excessive computer time is used in all the proce-dure.

An optical system invariant to position, rotation and scalewas applied to identify five phytoplankton species of the Cera- tium genus (family Ceratiidae) (Pech-Pacheco & Álvarez-Bor-rego,1998).To recognize theorganisms, theyused the frequencycontent of the images like start point (Zavala-Hamz et al., 1996;Pech-Pacheco et al., 1999). Pech-Pacheco et al., (1999) could toidentify Ceratium furca Lemmermann images with detritus, air-

bubblesandwith fragmentsof variousspecieswitha confidencelevelof90%.

Small fragmentsof12speciesoffossildiatomswere identi-fiedwithaninvariantdigitalsystemtoposition,rotationandscaleand a numerical simulation was performed in order to correlatediatomfossilsspecieswithphase-onlyfilters(Villalobos-Floreset al.,2001).Eachfragmentedimagewascomparedwithitsoriginalimageandother fragments inorder to find theminimuminforma-tionrequiredfortheidentificationofthespecies.

Diatomsareoneofthebasicsourcesfortheformationofor-ganic matter in the ocean, and actively participate in sedimenta-tion,notonlyduringrecentperiodsoftimebutthroughtheremotepast.Thepresenceofdiatomvalves inmarinepaleoenvironmentshas been used for the study of climatic changes as well as geo-morphological process (Hajós, 1976; Koizumi & Tanimura, 1985).One of the most important features for the recognition of diatomspecies as paleoenvironment and paleoclimatic indicators is thehigh correlation between the groups of diatoms and their eco-physiologicalbehaviour, thispermit toassociatethespecieswithdiversegeologicalandhydrodynamicfeatures.

The identification of diatom fossils requires the analysis ofa great number of valves per sample. Generally, to obtain rela-tive abundances and diversity indexes, diatom counts must gofrom 400 to 107 structures per gram (Esparza-Álvarez, 1995). Theanalysis of these samples requires a great amount of time andexperience and, on the other hand, the samples analyzed fre-quentlycontainmaterialwithdifferentfragmentationdegreesandthis can lead to confusion and loss of information. Therefore, itis necessary the development of new techniques to facilitate thespeciesrecognition.

In this paper, several methods are presented and comparedinorder tochooseanefficientalgorithmaccordingwith the levelof confidence and less computational cost to recognize the dia-tomsspecies(Figs.1-21).

MATERIAL AND METHODS

Thediatomsamplesare fromCuencadeSanLázaro inBajaCali-fornia. This is localized to the northwest to Cabo San Lázaro to25o10’Noflatitudeand112o45’Woflongitude.TheCuencahasa deep of about 540 m. These samples were taken in 1996 in anoceanographic ship called El PUMA. For specific details of thecharacteristicsofthesamplesseeEsparza-Álvarez,1999.

computadora de tal manera que cualquier persona pueda tener acceso a la base de datos de alguna localizaciónespecialenelocéano.

Palabras clave: Identificaciónautomáticadediatomeas,procesamientode imágenes, correlación invariante, recono-cimientodepatrones.


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Binary ringmask.Adigitalsystemof invariantcorrelationtoposition and rotation is constructed based in a binary ring maskproducingasignaturefilteroftheselectedimage.

Themaskofaselectedimage,namedI,isbuiltbytakingtherealpartofits2D-Fouriertransform(FT),givenby

yxIFTyxf ,Re, (1)

where yx, represent a pixel of the image. Based on equation(1),weobtainedtheone-variablefunction,

otherwise,0

0,if,1)(

ycfxz x (2)

where( yx cc , )isthecentred-pixelofIandygoesfrom0towideofI,whereIisansquareimage.Next,takingtheverticalaxisasthe

Figs.1-9.Fig.1.Azpeitia nodulifera(Schmidt)FryxelletSims,Fig.2.Azpeitia sp,Fig.3.Coscinodiscus radiatesEhrenberg,Fig.4.Actinocyclus ingensRattray,Fig.5.Actinocyclus ellipticusGrunowinvanHeurck,Fig.6.Actinpcyclus ellipticusvar.moronensis(DebyexRattray)Kolbe,Fig.7.Asteromphalus imbricatusWallich,Fig.8.Pseudotriceratium cinnamomeum(Greville)Grunow,Fig.9.Stephanodiscussp.Figs.4-6,8-9withscalebarof10mm.Figs.1-2,7withscalebarof20mm.Fig.3withscalebarof25mm.


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rotation axis, the graph of Z is rotated 360° to obtain concentriccylindersofheightone,differentwidthsandcentered in ( yx cc , ).Finally, mapping those cylinders in two dimensions we built thebinaryringmaskassociatedtoimageI.

The objective is identifying a specific target (diatom to rec-ognize) no matter the angle of rotation presented on the verti-

cal-axis. Inorder tohave invariancetopositionwedid thebinarymask from the frequency content of the image. So, the mask isapplied in the Fourier plane for sampling the frequencies patternof the object; Figure 22 shows two examples. In the figure 22(a)wehave the targetor the image tobe recognized.The frequencycontent (Fourier domain) is obtained for each image (Fig. 22(b)).

Figs.10-21.Fig.10.Actinoptychus undulates(Bailey)Ralf,Fig.11.Actinoptychus bipunctatusLohman,Fig.12.Actinoptychus splendens(Shad-bolt)RalfexPritchard,Fig.13.Thalassiosira kozloviiMakarova,Fig.14.Thalassiosira oestruppivar.1,Fig.15.Thalassiosira oestruppivar.2,Fig.16.Thalassiosira domifacta(Hendey)Jouse,Fig.17.Diploneis bombusCleve-EulerinBackmanetCleve-Euler,Fig.18.Denticulopsis praedimorphaBarronexAkiba,Fig.19.Nitzchia praereinholdiiSchrader,Fig.20.Nitzschia reinholdiiKanayaemendBarronetBaldauf,Fig.21.Bogorovia praepaleacea(Schrader)Jouse.Figs.14-15withscalebarof5mm.Figs.12-13,16-18,20withscalebarof10mm.Figs.10-11,19withscalebarof15mm.Fig.21withscalebarof20mm.


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Whenequations1and2areapplied to the frequencypattern thebinarymaskiscalculated(Fig.22(c)).Afterthis,thefrequencyim-ageismultipliedelementbyelementbythebinarymaskobtainingtheimageshowedinfigure22(d).Forhavingabettervisualizationintheimagesalogwasappliedinfigures22(b)and22(d).Finally,themodulusoftheFouriertransformforeachringissummedandthen assigned to the corresponding ring index to obtain the sig-natureoftheimage.Becausethesignatureoftheimagedependsuponthenumberofringsinthemask,andthemaskchangeswiththetarget,thelengthofthesignaturealsochange.

Figure23showstheprocedureof thedigitalcorrelationsys-teminvarianttopositionandrotation.Inthismethod,thefirststep

selectsthetarget. Instep2,therealvalueoftheFTofthetargetis obtained. The binary mask of concentric rings is built (step 3).Theimagesrotatedaregiven(step4).Aparabolicmaskisapplied(Pech Pacheco et al., 2003) or not, depending of the decision ifwewanttoenhancethehighfrequenciesinthefilterornot(step5).Next,themodulusoftheFTofeachimageisobtained(step6).Whenthebinarymaskisappliedtoeach|FT|obtainedinstep6thesignatureofeach image rotated isobtained (step7)andanaver-agefilterofthetargetiscalculatedbyaliasing(step8). Figures24and 25 show two examples for step 8 of the procedure consider-ingtheenhancementofthehighfrequenciesinthefilterornot.Infigure24awecanseethesignaturewhentheparabolicmaskwas

Figure22.Tworingmaskexamples.a)thediatomimage,b)theabsolutevalueofitsfrequencycontent,c)thebinarymask,d)thebinarymaskappliedtob).


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notappliedfortheaveragesignaturefilterofActinocyclus ingensRattray (specieA, Figs.1-21)and figure24bshowsacomparisonofthesignaturesofA. ingensandPseudotriceratium cinanomeum (Greville)Grunow(specieM,Figs.1-21).Figure25showsthesigna-turefilters,withthesamediatoms,whentheparabolicmaskwasapplied.

For making the average signature filter of a given target,a complete rotation of 360 deg is performed to it with a rotationangle of deg; hence we generate 360/ images. Then, thesignaturesofthoseimagesareobtainedtoaveragethemtobuildthe average filter of the target, with = 20 deg, thus the av-erage filter is constructed with 18 images. Here we choose thenumber of images in the filter making this work more flexible(Figs.24-25).

Todiscriminatebetween images,aproblemimage (PI) isse-lected(step9inFig.23);itcouldbeanyimagedifferentorsimilartothetarget.Then,thesignatureoftheproblemimageisobtainedfollowingthesteps10,11,5,6and12showninFig.23.

Then,instep13thesignatureofthePIiscomparedwiththeaverage filter f to recognize or not the target using a linear cor-relation,CL(inthiscaseaphase-onlycorrelation),thatis

C PI F PI f FT FT PI eLf, 1 1 (3)

where meanscorrelation, 1i and f is thephaseof theFourier transform of the linear filter; or we can use a non-linearcorrelation between them, CNL, of the form (Guerrero-Moreno &Álvarez-Borrego,2009).

Figure23.Binarymaskmethodologywithitsdifferentvariants.


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The second method used in this comparison was describedby Álvarez-Borrego and Castro-Longoria, (2003). News modifica-tions to this algorithm are presented in figure 26. The variancespectrum (square of the module of the frequency pattern of theimage) is obtained (step 3) from the target (diatom to be recog-nized) (step 1) and from the problem image (step 2) in order tohave invariance toposition.Aparabolicmask isappliedornot toeach variance spectrum depending of the decision if we want toenhance thehigh frequencies (step4). Instep5,apolarmappingis obtained in order to have the invariance to rotation and againthe Fourier transform is applied in order to have the frequencypatternofthetargetandtheproblemimage(step6).Instep7wedecide if we want a linear or a non-linear correlation betweenthem. If the correlation value is significant, hence, the target is

C PI f PI f

FT FT PI e FT f eNL

k i k iPI f

,

| | | ( )|1 (4)

with PI being the phase of the Fourier transform of the PI and10 k isthenon-linearityfactor.Inthiswork 1.0k .

To compute the correlation, the average filter and the sig-nature of the problem image vectors need to have the samelength. Because of the use of different ring masks this not hap-pensalways, hence zerosareadding to the shorter length vectortomatch the lengthofboth vectors. If themaximumvalueof themagnitude for the correlation (step 14) is significant, hence, theproblem image contains the target, otherwise has an image dif-ferenttothetarget.

Figure24a-b.a)AveragefilterforspecieAwithoutthehighfrequen-cyenhanced,b)ComparisonoftheaveragefilterforspecieAandMwithoutthehighfrequencyenhanced.

Figure25a-b.a)AveragefilterforspecieAwiththehighfrequencyenhanced,b)Comparisonof theaveragefilter forspecieAandMwiththehighfrequencyenhanced.


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ganismintheproblemimage.Eachwaydoesadifferentalgorithmwithdifferentcomputertimeintheprocess.

RESULTS

The algorithms were programming in Matlab 7.1 in a MacBookPro3,1 with a Intel Core 2 Duo processor of 2.4 GHz, memory of2GB667MHzDDR2SDRAM,L2Cacheof4MBand800MHzofBusSpeed.

Table 1 and 2 give us a review of the results when we didthecorrelationofall the21species (Figs.1-21), eachoneversusallof themand its360 rotated images.First, inTable1,wehave

recognizedintheproblemimage(step8),otherwisehasanimagedifferenttothetarget.

Figures 27 and 28 show two examples when the variancespectrum methodology is applied to Actinocyclus ingens (specieA,Figs.1-21)andPseudotriceratium cinanomeum (specieM,Figs.1-21). The spectrum variance with high frequencies enhanced islog visualized in figures 27a and 28a, respectively, for these twospecies and the spectrum variance without high frequencies en-hanced is logvisualized in figures27dand28d, respectively.Theoutputcorrelationsinlogvisualizedareshowninfigures27b,27c,27e,27f,28b,28c,28eand28f.Theselastfiguresmentionedshowthedifferentwayscanbetakeninordertorecognizeornotanor-

Table1.Binaryringmask:Diatomsconfidencelevel(greaterorequalthan)foranaveragesignaturefiltercomputedof

Linearfilter Non-linearFilter

withouthighfrequenciesenhanced

withhighfrequenciesenhanced



species f10 f18 f10 f18 f10 f18 f10 f18

A 100%1. 100%1. 100%1. 100%1. 100% 100% 100% 100%B 100%1. 100%1. 100%1. 100%1. 100% 100% 100% 100%C 100%1. 100%1. 195.4% 195.4% 100% 100% 100% 100%D 100%1. 100%1. 100%1. 100%1. 100% 100% 100% 100%E 195.4% 195.4% 100%1. 100%1. 100% 100% 100% 100%F 100%1. 100%1. 100%1. 100%1. 100% 100% 100% 100%G 100%1. 100%1. 195.4% 195.4% 100% 100% 100% 100%H 100%1. 100%1. 100%1. 100%1. 100% 100% 100% 100%I 100%1. 100%1. 100%1. 100%1. 100% 100% 100% 100%J 100%1. 100%1. 100%1. 100%1. 100% 100% 100% 100%K 100%1. 100%1. 100%1. 100%1. 100% 100% 100% 100%L 100%1. 100%1. 100%1. 100%1. 100% 100% 100% 100%M 195.4% 195.4% 195.4% 195.4% 100% 100% 100% 100%N 100%1. 100%1. 100%1. 100%1. 100% 100% 100% 100%O 100%1. 100%1. 100%1. 100%1. 100% 100% 100% 100%P 100%1. 100%1. 100%1. 100%1. 100% 100% 100% 100%Q 100%1. 100%1. 100%1. 100%1. 100% 100% 100% 100%R 100% 1. 100%1. 100%1. 100%1. 100% 100% 100% 100%S 100%1. 100%1. 100%1. 100%

without C100% 100% 100% 100%

T 100%1. 100%1. 100%1. 100%1. 100% 100% 100% 100%

U 100%1. 100%1. 168.3% 168.3% 100% 100% 100% 100%Time per correlation(secs)

0.125491 0.125604 0.126209 0.126366 0.126203 0.126360 0.126732 0.127040

Time for 158,760 correlations*

5hrs 32' 3" = 19,923"

5hrs 32' 21" = 19,941"

5hrs 33' 57" = 20,037"

5hrs 34' 22" = 20,062"

5hrs 33' 56" = 20,036"

5hrs 34' 21" = 20,061"

5hrs 35' 20" = 20,120"

5hrs 36' 09" = 20,169"

*Correlationsforthe7560differentimages.


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Table2.Spectrumfilter:Diatomsconfidencelevel(greaterorequalthan)foranaveragesignaturefiltercomputedof

Linearfilter Non-linearfilter





species f10 f18 f10 f18 f10 f18 f10 f18

A 100%1. 100%1. 100%1. 100%1. 100%1. 100%1. 195.4% 195.4%B 100%1. 100%1. 100%1. 100%1. 100%1. 100%1. 195.4% 195.4%C 100%1. 100%1. 100%1. 100%1. 100%1. 100%1. 100%1. 100%1.D 195.4% 195.4% 100%1. 100%1. 100%

without A100%

without A68.3%

without K, N68.3%

without NE 100%1. 100%1. 100%1. 100%1. 195.4% 195.4% 68.3%

without D68.3%

without DF 100%1. 100%1. 100%1. 100%1. 100%1. 100%1. 95.4%

without E95.4%

without EG 100%1. 100%1. 100%1. 100%1. 100%1. 100%1. 168.3% 168.3%H 100%1. 100%1. 100%

without U100%

without U100%

without U100%

without U168.3% 95.4%

without PI 100%1. 100%1. 100%1. 100%1. 100%1. 100%1. 68.3%

without S95.4%

without NJ 100%1. 100%1. 195.4% 195.4% 100%1. 100%1. 68.3%

without O168.3%

K 100%1. 100%1. 195.4% 195.4% 100%1. 100%1. 68.3% without A, R

95.4% without J

L 100%1. 100%1. 100%1. 100%1. 100%1. 100%1. 168.3% 95.4% without O

M 100%1. 100%1. 100%1. 100%1. 195.4% 195.4% 95.4% without S

95.4% without S

N 168.3% 168.3% 195.4% 195.4% 100%1. 100%1. 95.4% without R

68.3% without R

O 100%1. 100%1. 100%1. 100%1. 100% without K

100% without K

168.3% 95.4% without B

P 195.4% 168.3% 100%1. 100%1. 168.3% 95.4% without D

195.4% 168.3%

Q 100%1. 100%1. 195.4% 195.4% 195.4% 100%1. 95.4%without B, C

95.4% without B, C

R 100%1. 100%1. 195.4% 195.4% 100%1. 100%1. 68.3% without L, T

68.3% without L, T

S 100%1. 100%1. 195.4% 195.4% 100%1. 100%1. 95.4% without J, R

95.4% without J, R

T 100%1. 100%1. 1.95.4% 195.4% 100% without L

100%withoutL

68.3%withoutA

95.4%withoutA,Q

U 100%1. 100%1. 168.3% 168.3% 100% without H

100% without H

168.3% 195.4%

Time per correlation(secs)

2.472871 2.473563 2.475428 2.475491 2.576688 2.587540 2.593965 2.601341

Time for 158,760 correlations*

4d 13hrs 03' 13" = 392593"

4d 13hrs 05' 03" = 392703"

4d 13hrs 09' 59" = 392999"

4d 13hrs 10' 09" = 393009"

4d 17hrs 37' 55"= 409075"

4d 18hrs 06' 38"= 410798"

4d 18hrs 23' 38"= 411818"

4d 18hrs 43' 09"= 412989"

*Correlationsforthe7560differentimages.


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theresultforthelinearandnonlinearfiltersusingthebinaryringmask (Fig. 23), without and with high frequencies enhanced fortwokindsofaveragefilters:f10andf18(Solorza&Álvarez-Borrego,2010).Thesubindexnumberindicatesthenumberofimagesusedintheaveragefilter.InthefirstcolumnoftheTable1wehavethetypeofthespeciesusedaccordingwithFigs.1-21.

We can see in Table 1, when the binary mask methodologyuses the linear filter without high frequencies enhanced in thevariance spectrum, the discrimination was at least of a level ofconfidenceof95.4%forspeciesEandMwhenthefiltersf10

andf18wereused.Fortheotherspeciestheconfidencelevelwas100%.

Usingthe linear filterwithhighfrequenciesenhanced inthevariance spectrum the results are not better. For example usingthefilterf10thediscriminationwasatleastofalevelofconfidenceof95.4% for speciesC,GandMandat leastofa levelof confi-dence of 68.3% for specie U. For the other species the level ofconfidencewasof100%.Whenthefilterf18wasuseda95.4%wasobtainedforspeciesC,GandM.A68.3%oflevelofconfidenceforspeciesUwasobtained.Theresthada100%ofconfidencelevel

intherecognitionofthespeciesexceptthespecieSwhichisnotconsideringthespecieC.

We can see in Table 1 t when we used the linear filter thebestcomputertimewasforthefilterf10withoutandwithhighfre-quenciesenhanced,thefilterf10hadabetterperformanceinbothcases.

Theresultsobtainedwiththenonlinearfilterusingthebinaryring mask (Fig. 23), can be seen in the last four columns. For allthe cases, without or with high frequencies enhanced, the con-fidence level was of 100%. In other words, all the species couldbe recognized without mistakes. The best time computer for thiscaseisforthenonlinearfilterwithouthighfrequenciesenhancedin the variance spectrum being of 0.126203 secs per correlationandusingtheaveragefilterf10.

For thesecondalgorithmandall itsvariants (Fig.26) the re-sultsarepresented inTable2.Again, the first columnshows thespecies to be studied in according with Figs. 1-21. The first fourcolumnsshowtheresultsforthelinearfilterwithoutorwithhigh

Figure26.Spectrumfiltermethodologywithitsdifferentvariants.


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frequencies enhanced of the variance spectrum for the averagefiltersf10andf18.Theworstscenarioforthefilterf10isforthespe-cieNwith68.3%ofconfidencelevelfollowingthespeciesDandPwith95.4%ofconfidencelevel.Theothercasesshoweda100%ofconfidencelevelintherecognitionofthespecies.Forthefilterf18 theworst scenario is for the caseNandP following the caseDwith95.4%ofconfidencelevel.Theothercasesshoweda100%of confidence level in the recognition of the species. When theaverage linear filter, f10, is used with high frequencies enhancedseven cases presented 95.4% of confidence level only: J, K, N,Q, R, S and T. The worst scenarios were the cases H and U. Theother cases showed 100% of confidence level. For the averagelinearfilterf18thesameresultwasfound.

Showing the results of the last four columns of the Table 2weseeabadscenario forbothof thecaseswithoutorwithhigh

frequenciesenhancedandforbothofthefiltersf10andf18.Insev-eral of the cases many of the species could not be recognizedwith this kind of methodology. The worst case was the averagenonlinearfilter,f18,withhighfrequenciesenhancedwith14cases.f10presented12badcases.

However, forall thecases in thisTable2 thecomputer timeisaboutfourdaysandseveralhoursinordertoobtaintheresultsinthisspeciesrecognitionmethodology.

DISCUSSION

In this paper several methods are presented and compared inorder to choose the best digital algorithm to recognize the dia-tomsspecies(Figs.1-21).Wewillchoosethealgorithmwithmorelevelofconfidenceand lesscomputationalcost.Weused f10and

Figure27.Methodologyofthefigure26appliedtospeciesAshowingthedifferentsvariantsintheprocess.


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f18averagefiltersbecause itwasshownthat thesefiltershaveaverygoodperformance,beingf10betterthanf18(Solorza&Álvarez-Borrego,2010).

Each filter f10 and f18 of each species was correlated withthe 360 images rotated of each species, deg. In otherwords, we worked with 7560 images (21 times 360) in each cor-relation. Considering this number of images, the computer timeused in the first method (Fig. 23) with the nonlinear filter with-out high frequencies enhanced was so short. Moreover theconfidence level for this case was 100%. The second best timewas for the average filter f18 where the difference is less thanoneminute.

One of the advantages of these kinds of methodologies isthat an entire process can be repeated in the same way withoutmistakes and the diatoms images are kept save in a hard disk ofthecomputer,soeverybodycanseeagainthediatominformationofsomespeciallocalizationoftheocean.

Takingaccountalltheworksinthepastabouttoidentifyau-tomaticallyzooplankton,themethodologypresentedintheFig.23isfasterandhasthebestlevelofconfidence.

Thesecondmethodologywithallitsvariants(Fig.26)didnothave a good performance when the diatoms images were ana-lyzed; however it had a very good performance when copepodswere studied (Álvarez-Borrego & Castro-Longoria, 2003) using a

Figure28.Methodologyofthefigure26appliedtospeciesMshowingthedifferentsvariantsintheprocess.


Hidrobiológica

linear filter with the high frequencies enhanced of the variancespectrum.

With those results we see that each particular problem hasitsownparticularsolution,howevertheideaistrytofindamorewideapplicationtoeachparticularalgorithm.

Thenovelofthealgorithmpresentedinthispaperistheintro-ductionofthenonlinearfilterassociatedwiththebinaryringmaskandtheuseofaverageone-dimensionalsignature.Thisalgorithmpermits100%ofconfidenceintherecognitionofthediatomsandarecordtimeconsuminginalltheprocedure.

ACKNOWLEDGEMENT

This document is based on work partially supported by CONACyTwithgrantNo.102007.

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Recibido:4dediciembrede2009.

Aceptado:22dejuliode2010.

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Comparative analysis of several digital methods to ...scielo.unam.mx/pdf//hbio/v20n2/v20n2a7.pdf · Comparative analysis of several digital methods to recognize diatoms Análisis