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1 Cellular ad Molecular Biology TM 52, N 6, ISSN X DOI /T Cell. Mol. Biol. TM STATISTICAL APPROACH TO BOAR SEMEN EVALUATION USING INTRACELLULAR INTENSITY DISTRIBUTION OF HEAD IMAGES L. SÁNCHEZ 1, N. PETKOV 2, E. ALEGRE 1 1 Departmet of Electrical ad Electroics Egieerig, Uiversity of Leó, Campus de Vegazaa, Leó, Spai Fax: ; lidia@uileo.es 2 Istitute of Mathematics ad Computig Sciece, Uiversity of Groige, P.O. Box 800, 9700 AV Groige, The Netherlads Abstract We propose a method for the classificatio of boar sperm heads based o their itracellular itesity distributios observed i microscopic images. The image pre-processig comprises segmetatio of cell heads ad ormalizatio for brightess, cotrast ad size. Next, we defie a model distributio of head itracellular itesity of a alive cell usig a set of head images assumed to be alive by veteriary experts. We ow cosider two other sets of cell head images, oe formed by heads assumed to be alive by experts ad aother formed by cells which preset some abormalities i their cytoplasm desities ad are cosidered as dead by the experts. We defie a measure of deviatio from the model itesity distributio ad for each head image of the two test sets we compute the deviatio from the model. While the distributios of deviatio values for alive ad dead cells overlap, it is possible to choose a optimal value of a decisio criterio for sigle cell classificatio i such a way that the error made i the estimatio of the fractio of alive cells i a sample is miimal. I the rage [0.7,1.0] of iterestig values of the fractio of alive cells, the stadard deviatio of the fractio estimatio error for samples of 100 head images is smaller tha Thus, i 95% of the cases the value of the fractio of alive cells i a sample estimated by a veteriary expert will be withi 8% of the estimatio made accordig to the proposed method. This result satisfies the requiremets of veteriary practice. Key words : image aalysis, classificatio, sperm heads, boar seme, itracellular itesity distributio, cocetratio of alive cells. INTRODUCTION Boar artificial isemiatio presets advatages over the atural oe ad it is widely used i curret practice. To avoid ifertility problems ad to idetify boars with high reproductive features, sperm quality aalysis is used. Visual assessmets of seme by veteriary experts or CASA (Computer Aided Sperm Aalysis) systems are the classical ways to determie the potetial fertility of boars. There are four factors to cosider i the evaluatio of boar sperm quality: cocetratio, motility, morphology ad acrosome itegrity of spermatozoa (13). I this work, we itroduce a method for the automatic evaluatio of acrosome itegrity usig digital image aalysis. Due to the complexity of sperm quality estimatio, computerized techiques are essetial tools. The majority of these computer methods have bee developed to aalyse huma seme morphology ad have afterwards bee adapted for other species. The developmet of ew methodologies is a ogoig research activity (4,5). These researches have eriched the available kowledge o sperm cells (15) ad furthermore, digital image aalysis had allowed to classify subpopulatios (9) or to describe shape abormalities (5). Most of these approaches use CASA systems (10,14) or propose ew descriptio ad classificatio methods (1,3,6,7). The majority of them focus o spermatozoa morphology such as abormalities relatig to shape ad size of 38 sperm heads ad it is very difficult to fid works about vitality or acrosome itegrity. I veteriary practice, stais are used to determie if a sperm cell is alive or dead. A hypothesis of practical iterest is that there is a relatio betwee particular patters of itracellular desity distributio observed i microscopic images, sperm vitality ad seme fertility. Basig o their experieces, veteriary experts assume that there is a certai correlatio betwee the itracellular desity distributio ad the alive/dead status of a cell. This hypothesis has bee studied with methods of digital image processig ad machie learig. (2,11,12). These studies aimed at idetifyig a patter that is characteristic of alive cells ad localizig regios that are diagostic for the alive/dead status of a cell. I the curret work we preset ew results that build o this hypothesis. The mai motivatio behid this ad previous studies i the same directio is to explore the potetial of digital image processig ad machie learig for sperm fertility estimatio. Beside the fudametal biological isights ito the correlatio betwee itracellular desity distributio ad alive/dead status of a cell that such studies ca provide, they ca also be of importace for veteriary practice, havig a potetial to substitute expesive staiig techiques. The latter techiques have

2 L.SANCHEZ et al. certai disadvatages, such as sesitivity to temperature variatios ad maual maipulatio of the samples, errors i ph adjustmet, ad relatively log stai preparatio time. Some simple stai techiques used to idetify alive ad dead cell like eosi-igrosi are time cosumig sice the icubatio period is at least 5 miutes, the stai has to dry ad further time is eeded for evaluatio. I cotrast, digital image processig techiques allow to aalyse 1000 or eve more sperm cells i less tha a miute. Aother disadvatage of traditioal stai procedures is their toxic effects o sperm cells that icreases the umber of dead spermatozoa. I this work we adopt the followig approach. First, veteriary experts, who assume that a certai itracellular desity distributio is characteristic of alive cells, visually ispect microscopic boar sperm images ad mark cells as alive or dead. Usig a subset of images of cell heads that were marked as alive by veteriary experts we derive a itracellular desity distributio model for alive cells ad we defie a measure of deviatio of a give itracellular distributio from this model. Usig this measure we assig a deviatio value to each image of a cell head that has bee marked as alive or dead by a expert ad we use the obtaied values to make a statistical iferece about the error made i evaluatig the fractio of alive cells accordig to this method. I Methods, we preset the derivatio of a itracellular desity distributio model, the defiitio of a measure of deviatio from this model ad the assigmet of a deviatio value to each cell head image from a large experimetal data set. The use of the set of obtaied values for evaluatio of the fractio of alive cells i a sample is explaied i the sectio Results. Fially, we summarize the results ad draw coclusios. METHODS Seme samples collected from boars are cetrifuged at 800 xg for 10 miutes. Next, the superatat is removed ad the obtaied sperm pellet is diluted with MRA util a fial sperm cocetratio of 200 millios sperm cells per ml is achieved. Fially, the sperm cells are fixed i glutaraldehide 2%. The seme sample images were acquired by meas of a digital camera Niko Coolpix 5000 coected to a phase-cotrast microscope. The magificatio used was 40x ad the resolutio of the sample images was 1600 x 1200 pixels, Fig. 1. To develop the proposed method we used Matlab ad its Image Processig Toolbox. Fig 1. Example of a boar seme sample image acquired usig a phase-cotrast microscope. The umber of spermatozoa i a image as well as their orietatio ad tilt vary. A sample image ca also preset agglutiatios of heads ad debris because of the maipulatio process. To isolate the sperm heads i a image, we first apply morphological closig which results i smooth head cotours. The we apply thresholdig deployig Otsu s method to isolate the image regios that potetially cotai heads (8). Fially, we remove those regios that are occluded by the boudaries of the image. We also do ot cosider isolated regios that are smaller tha 45% of the average head area. This value was determied experimetally. For each sample image, the above preprocessig ad segmetatio steps produce a image with the isolated heads as grey level distributios o a black backgroud, Fig. 2. Fig 2. Image obtaied from the image show i Fig.1 by pre-processig ad segmetatio. Sperm heads appear as grey level distributios o a black backgroud. I the images obtaied i this way, sperm heads appear as oval shapes with differet orietatios. Boar sperm heads, ulike other species, have a characteristic early elliptical shape. We cosider the 39

3 Statistical approach to boar seme evaluatio usig itracellular itesity distributio of head images pixels o the boudary of a head ad, usig pricipal compoet aalysis, we compute the mai axes of the ellipse that fits ito the head. We use the obtaied pricipal compoets of a head to rotate it ad alig the major ad mior axes of the fittig ellipse with the x ad y axes, respectively, Fig. 3. Fig 3. (left) Example of a head as it appears i the image preseted i Fig.2 with the pricipal compoet axes of the best fittig ellipse ad (right) a rotated head image. The experimetal measuremets of sperm heads show that a ormal head is from 4 to 5 µm wide ad from 7 to 10 µm log. Thus the aspect ratio or the ellipse eccetricity varies from 0.4 to 0.7. As a ext step we re-scale all head images to the same aspect ratio ad size of 19 x 35 pixels; this re-scalig is doe usig earest-eighbor iterpolatio. We cosider a two dimesioal fuctio f( which is defied by the grey levels of those pixels that belog to the metioed ellipse with mior ad major axes of 19 ad 35, respectively, Fig. 4. Fig 4. The rotated image is re-scaled to 19x35 pixels (left). We apply a elliptic mask of 19x35 pixels (ceter) i order to defie the 2D grey level fuctio f( (right). Spermatozoa preset differet itracellular desity distributios. Veteriary experts mark sperm heads as alive or dead based o their experiece. Although there are cosiderable variatios i the itracellular distributios of cells marked as alive, it is possible to distiguish three head areas accordig to their itesity. There are a darker area, called the post ucleus cap where the mid-piece ad the tail develop from, a itermediate light area ad, fially, aother dark area correspodig to the acrosome which covers the aterior portio of the ucleus regio. The acrosomal status gives iformatio about the sperm fertility sice those heads that have lost their acrosomes before approachig the oocyte are uable to fertilize. To be able to fertilize, spermatozoa have to go through a capacitatio process which ivolves several chages i the orgaizatio of the plasma membrae ad the cell iterior. The acrosome reactio results i a loss of the cotets of the acrosome. Hece, the capacitatio destabilizes the membrae to be ready for the acrosome reactio, which allows the ezymes go out of the head. The acrosome reactio etails that the plasma membrae ad the acrosomal cotets are lost. For this reaso, the itracellular itesity distributios are ot the same across differet head images. Furthermore, the head images preset diverse cotrasts of the three metioed regios ad differet head brightess averages. To deal with these latter variatios, we carry out a liear trasform o the grey level fuctio f( of the itracellular itesity distributio i order to keep the same mea ad stadard deviatio across all sperm head images. Cosiderig the 2D grey level fuctio f( defied o a regio S eclosed by the above metioed ellipse with mai axes 19 ad 35 pixels, we defie a liear trasform of f( ito a fuctio g( defied o S by: g ( = a f ( + b The coefficiets a ad b are defied as follows: std( g) a =, std( f ) b = g a f I the above formula, the values f ad std(f) of the mea ad the stadard deviatio of f( are computed directly from the fuctio f. The values of the mea g ad the stadard deviatio std(g) of g( are fixed to 100 ad 8 respectively. These target values were experimetally determied sice the sperm head images assumed as potetially alive by veteriary experts take aroud those values for their meas ad stadard deviatios. We ow cosider a set of sperm heads that have bee hypothesized as potetially alive by experts based o their itracellular itesity distributios. This set cotais = 34 head images ad it is amed the model traiig set M. For each of these images we obtai a itesity distributio fuctio g i (, i = 1, as described above. Next, we defie a model grey level itesity distributio fuctio m( as a pixel-wise average of these fuctios, Fig m( = gi( i= 1 Fig 5. Model of the itracellular itesity distributio assumed as characteristic of alive sperm cells. It is computed as the average of a set of head images of sperm cells classified by experts as alive. 40

4 L.SANCHEZ et al. For each pixel which lies withi the metioed ellipse, we assess the variability of the grey levels across the model traiig set by computig the stadard deviatio s( for that pixel: 2 ( g = i ( m( ) s( i= 1 RESULTS Fig. 8 shows the distributios of the frequecies of occurrece of the values of the deviatios obtaied for the sets A ad D. The we defie ad compute a deviatio value d of the 2D grey level itesity distributio fuctio g( of a give head image from the model distributio fuctio m( usig the ifiity orm: g( m( d = max s( Next we use two sets of sperm head images that have bee obtaied from boar seme images by applyig the previously metioed pre-processig ad ormalizatio steps. Oe of these sets, that we call the alive cell set (A), cosists of 718 heads that preset itracellular itesity distributios assumed by experts as characteristic of alive sperm cells, Fig. 6. The other set, that we call the dead cell set (D), comprises 650 head images with itracellular itesity distributios that are assumed by experts to be characteristic of dead sperm cells, Fig. 7. For each head image from these sets we compute a fuctio g( ad the deviatio d of this fuctio from the model fuctio m(. Fig 8. Frequecies of occurrece (probability desities) of alive ad dead cells as fuctios of the deviatio d. from the model distributio of a alive cell. The two distributios overlap ad this meas that error-free classificatio of sigle cells as alive or dead is ot possible for values of d that lie i the overlap regio. Fig. 9 shows the misclassificatio errors obtaied from the distributios show i Fig. 8 as fuctios of the value d c of a classificatio criterio which is used to classify cells as alive if d d c ad dead if d > d c. For small values of d c the false rejectio error e r (d c ) (of alive cells) is high because may alive cells whose d-values are larger tha d c are misclassified as dead. For large values of d c the false acceptace error e a (d c ) (of dead cells) is large because there are may dead cells whose d-values are smaller tha d c so that these cells are misclassified as alive. Fig 6. Examples of head images of sperm cells that were assumed to be alive by experts accordig to their itracellular distributios. Fig 7. Examples of head images of sperm cells that were classified as dead by veteriary experts based o their itracellular distributios. The two sets of values of the deviatio d obtaied for the two sets A ad D form the basis of the further aalysis. Fig 9. Misclassificatio errors e r (d c ) ad e a (d c ) as a fuctios of a classificatio criterio d c which is used to classify cells as alive if d d c ad dead if d > d c. The false rejectio error e r (d c ) is defied as the fractio of alive cells for which holds d > d c ad which will be misclassified as dead. The false acceptace error e a (d c ) is defied as the fractio of dead cells for which holds d d c ad which, therefore, will be misclassified as alive. 41

5 Statistical approach to boar seme evaluatio usig itracellular itesity distributio of head images I practice, oe is iterested ot i the classificatio of sigle cells but rather i a estimatio of the fractio p of alive cells i a give sample. Whe this fractio is estimated by meas of sigle cell classificatio, the fractios of misclassified alive ad dead cells i a very large sample will be p e r (d c ) ad (1-p) e a (d c ), respectively. Note that while some alive cells are misclassified as dead, some dead cells will be misclassified as alive, ad the latter umber ca partially compesate the former. The error i the estimatio of p will thus be: e(d c,p) = p e r (d c ) - (1-p) e a (d c ) ad Fig. 10 shows e(d c,p) as a fuctio of the decisio criterio d c for three differet values of p. As ca be see from this figure, for each value of p the error e(d c,p) as a fuctio of the decisio criterio d c has a miimum for a give value of that criterio ad we deote this value with d c (p). This is the value of d c for which the umber of misclassified alive cells is equal to the umber of misclassified dead cells so that the error i the fractio estimatio is zero. Fig. 11 shows d c (p). Sice the fractio p of alive cells i a give sample is ot kow i advace, the questio of how to determie the value of the decisio criterio d c that has to be applied to the head images of the cells i the sample deserves special attetio. We suggest the followig iterative procedure. I a first step the sigle cell classificatio is doe usig d c (0.5), i.e. assumig a equal umber of alive ad dead cells i the sample (p = 0.5). The result of this sigle cell classificatio delivers a first estimatio p 1 of p. Now the sigle cell classificatio is repeated with a value of the decisio criterio d c (p 1 ) ad this ew classificatio results i a ew estimatio p 2 of p. I practice, we foud that the cosecutive estimatios of p coverge to a stable value after oly a few iteratios (less tha 5). The ext iterestig questio is how large the error is whe p is estimated as proposed above. To determie this error, we take a sample of 100 head images by radomly selectig p100 head images from set A ad (1-p)100 images from set D. For such a sample we estimate the fractio of alive cells accordig to the iterative procedure give above ad we deote the resultig value by p. The fractio estimatio error p-p will be differet from sample to sample. Therefore, we quatify the fractio estimatio error for fiite samples (of 100 head images) by the stadard deviatio of p-p for 100 samples. I the rage p > 0.7 that is iterestig for veteriary practice, the stadard deviatio of p-p is smaller tha 0.04 which meas that i 95% of the cases the real value of the fractio p of alive cells i a sample will be withi 8% of the estimatio p made accordig to the method proposed above, Fig. 12. This is withi the requiremets of the veteriary practice. Fig 10. The error e(d c, p) i the estimatio of the fractio p of alive cells i a (very large) sample as a fuctio of the decisio criterio d c for three differet values of p. Fig % cofidece iterval of the fractio of alive cells p as a fuctio of the estimatio p. Fig 11. Value d c (p) of the decisio criterio for which the error i estimatig the fractio p of alive cells i a very large sample is miimal (0). DISCUSSION We propose a method to classify sperm head images by meas of the itracellular itesity distributio that they preset. We defie a model itracellular 42

6 L.SANCHEZ et al. itesity distributio that is derived from the images of heads assumed to be alive by veteriary experts. We also defie a measure of deviatio from this model. Usig the model ad the deviatio measure we study the distributios of deviatio values obtaied for two test sets A ad D of head images that are hypothesized as alive ad dead by experts, respectively. Based o these distributios we make a estimatio of the fractio of alive cells i a give sample ad the error of this estimatio. I 95% of the cases the real value of the fractio p of alive cells i a sample will be withi 8% of the estimatio p made accordig to the proposed method. This result satisfies the requiremets of veteriary practice. I future works will compare the results obtaied with the proposed method with the results of stais. Ackowledgemets We would like to thak Dr. Jua Carlos Domíguez ad Ferado Tejeria, both members of the Departmet of Aimal Pathology at the Uiversity of Leó, for the useful discussios about boar seme aalysis. We also thak Cetrotec S.A. for providig the images used i this study. REFERENCES 1. Beletti, M., Costa, L. ad Viaa, M., A compariso of morphometric characteristics of sperm from fertile bos taurus ad bos idicus bulls i Brazil. Aimal Reproductio Sciece. 2005, 85: Biehl, M., Pasma, P., Pijl, M., Sáchez, L., ad Petkov, N., Classificatio of boar sperm head images usig Learig Vector Quatizatio. Proc. Europea Symposium o Artificial Neural Networks (ESANN) (D-side, Evere, Belgium), Garrett, C. ad Baker, H., A ew fully automated system for the morphometric aalysis of huma sperm heads. Fertil. Steril. 1995, 63: Gravace, C., Garer, D., Pitt, C., Vishwaath, R., Sax- Gravace, S. ad Casey, P., Replicate ad techicia variatio associated with computer aided bull sperm head morphometry aalysis (ASMA). Iteratioal Joural of Adrology. 1999, 22: Hirai, M., Boersma, A., Hoeflich, A., Wolf, E., Foll, J., Aumuller, T. ad Brau, J., Objectively measured sperm motility ad sperm head morphometry i boars (Sus scrofa): relatio to fertility ad semial plasma growth factors. J. Adrol. 2001, 22: Lieberg, C., Salamo, P., Svarer, C. ad Hase, L., Towards seme quality assessmet usig eural etworks. I: Proc. IEEE Neural Networks for Sigal Processig IV. 1994, Ostermeier, G., Sargeat, G., Yadell, T. ad Parrish, J., Measuremet of bovie sperm uclear shape usig Fourier harmoic amplitudes. J. Adrol. 2001, 22: Otsu, N., A threshold selectio method from gray-level histograms, IEEE Trasactios o Systems, Ma ad Cyberetics, 1979, 9: Quitero-Moreo, A., Rigaub, T. ad Rodríguez-Gil, J.E., Regressio aalyses ad motile sperm subpopulatio structure study as improvig tools i boar seme quality aalysis. Theriogeology. 2004, 61: Rijsselaere, T., Soom, A.V., Hoflack, G., Maes, D. ad de Kruif, A., Automated sperm morphometry ad morphology aalysis of caie seme by the Hamilto-Thore aalyser. Theriogeology. 2004, 62: Sáchez, L., Petkov, N., ad Alegre, E., Statistical approach to boar seme head classificatio based o itracellular itesity distributio, i A. Gagalowicz ad W. Philips (Eds.), Proc. It. Cof. o Computer Aalysis of Images ad Patters, CAIP 2005, Lecture Notes i Computer Sciece. 2005, 3691: Sáchez, L., Petkov, N., ad Alegre, E., Classificatio of boar spermatozoid head images usig a model itracellular desity distributio, i M. Lazo ad A. Safeliu (Eds.), Progress i Patter Recogitio, Image Aalysis ad Applicatios: Proc. 10th. Iberoamerica Cogress o Patter Recogitio, CIARP 2005, Lecture Notes i Computer Sciece. 2005, 3773: Thursto, L., Holt, W. ad Watso, P., Post-thaw fuctioal status of boar spermatozoa cryopreserved usig three cotrolled rate freezers: a compariso. Theriogeology. 2003, 60: Verstege, J., Iguer-Ouada, M. ad Ocli, K., Computer assisted seme aalyzers i adrology research ad veteriary practice. Theriogeology. 2002, 57: Wijchma, J., Wolf, B.D., Graafe, R. ad Arts, E., Variatio i seme parameters derived from computer-aided seme aalysis, withi doors ad betwee doors. J. Adrol. 2001, 22: