DEGRADATION MODEL OF BREAST IMAGING BY DISPERSED RADIATION

THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Sis A, OF THE ROMANIAN ACADEMY Volum 1, Numb 4/011, pp. 347 35 DEGRADATION MODEL OF BREAST IMAGING BY DISPERSED RADIATION Migul BUSTAMANTE 1, Gastón LEFRANC 1 Univsidad Adolfo Ibañz, Facultad d Ingniía, Chil E-mail: migul.bustamant@uai.cl Pontificia Univsidad Católica d Valpaaíso, Escula d Ingniía Eléctica, Chil E-mail: gaston.lfanc@gmail.com This pap psnts a modl of intaction of adiation on bast, basd on Bosso s filt. This modl is usd to impov mammogaphic imags fo aly canc diagnosis, to b mo accuat and to dtct clust of micocalcifications. Th modl is basd on dgadation of bast imag poducd by dispsd adiation using th Bosso`s filt, dvlopd ali. Ky wods: Mammogam, Micocalcification, Comput Vision, Canc analysis. 1. INTRODUCTION On of th public halth poblms associatd with fmals, is bast canc. This disas is a majo caus of dath in womn btwn 15 and 54. Bast canc is th most common canc among womn woldwid, accounting fo 16% of all fmal cancs. It is stimatd that this disas killd mo than 500,000 womn last ya, although this canc is considd a disas of th dvlopd wold, th majoity (69%) of daths occu in dvloping countis [1]. In Chil, bast canc ankd thid in fmal canc, ising fom 11.7 in 100,000 to 13.3 in 100,000 in tn yas []. A timly clinical diagnosis and appopiat tatmnt could pvnt and duc this high motality. Th most widly usd mthod of diagnosis is mammogaphy, which implis a bast adiogaphy und contolld conditions. Condition fo a bast mammogaphy is th tansvsal plan to X-ay bams so that thy fall on th film paalll to th bast. Th adiogaphy is xamind by th spcialist who sks clusts of micocalcifications. Psnc of calcium clusts in bast is an impotant sign of th possibl fomation of canc. Micocalcifications hav a siz clos to th limit of solution of th systm, so it is impotant to impov imag quality. Th diagnosis intptation is complicatd du to ffcts of dgadation and limits of solution. Sval authos hav poposd diffnt appoachs to this poblm: On of thm is a mthod fo automatic dtction of micocalcifications in digitizd imags. Th mthod compas th txtu of mammogaphic imags to achiv btt contast of micocalcifications. This is don by lowing th lvl of gay of a matix which should b adjustd accoding to th associatd histogam. This pocdu povids a good sult, but it ducs lvls of gay (fom 56 to 64), which mans that in ou opinion, th imag loss pat of th infomation, but gains in computational tim. Ths authos claim that sults in a classification at of 95.6%, achiv a duction in computational complxity. [3] A goup of woks psnt a suvy, a viw of imag pocssing algoithms to dtct aly canc, and an algoithm basd on bilatal asymmty. Th algoithm quis a compaison of both basts to dtct th diffncs in psnt aas, which implis an additional dos of adiation. Th bst sult obtaind is 89.% with 4.9 fals positivs. This mthodology quis a pop alignmnt of th bast in a mio to b compad, which tchnically intoducs a complxity in th compaison algoithm [4 6]. A mthod fo automatic dtction of bast canc though th nhancmnt of mdical imags is basd on th concpt of factals applid to an imag with an aa of autosimila poptis. Thy hav idntifid aas of possibl canc, as wll as micocalcifications. Thy point out that it is ncssay to impov th systm to bcom an automatic pocss. This mthod was tstd, quiing futh wok and sults [7].

348 Migul Bustamant, Gastón Lfanc A mthod of micocalcifications dtction in mammogams basd on wavlts and adaptiv thsholds has bn poposd. Bast aas a sgmntd and dividd into ovlappd squas, thn th wavlt tansfom is applid on ach squa imag and thshold of ach mammogam a calculatd to idntify th gion of intst. Thn, ths gions a analyzd to duc fals positivs. This mthod povids naly 89.39% coct classification [8]. Anoth appoach poposs automatic dtction of clusts of micocalcifications in mammogams using multiclassifis, to obtain th suspicious clusts, laving to th xpt th diagnosis sponsibility. Th systm is abl to dtct 90% of th clusts of micocalcifications, but it nds to classify as positiv o ngativ th whol mammogaphy [9]. A mthod fo bast tumo dtction in mammogams basd on Jacobi Momnts is poposd. It is capabl of dtcting suspicious aas in mammogams indpndnt of thi siz, ointation and position. Th mthod is succssful in dtcting th micocalcification in th mammogam. It has to b tstd on much lag sts of data. Futhmo, a clinically usful systm fo bast canc dtction must b abl to dtct th bast cancs, not just micocalcifications. This wok has to xtnd th Jacobi Momnts fatus fo oth typs of mammogam [10]. Anoth wok dvlops a spatial point pocss modling appoach fo dtction of clustd micocalcifications in mammogam imags. In this appoach a makd point pocss is mployd to chaactiz th spatial distibution of clusts in a mammogam imag, whin pio distibutions a dfind to dscib both th amplitud of th micocalcifications signals and thi spatial intactiv pattns. Th micocalcifications a thn simultanously dtctd though maximum a postioi stimation of th modl paamts associatd with th makd point pocss. Th paamts associatd with th pio distibutions a dtmind fom a st of taining mammogam imags. Th appoach is valuatd with 141 mammogams imags. Th mthod has computational complxity and it nds to b ducd [11]. A mthod to classify mammogams imags in fiv classs to hlp adiologist dtct canc-affctd basts. is poposd. This mthod has two stps, on is ppocssing wh th bounday os will b movd succssfully using nw mophological opations. Th scond is valuating th statistical paamts to classify and to find abnomality in bast imags. Th sults obtaind out of th xisting tchniqus hav bn found to hav btt pfomancs. Futh sach is ndd [14]. Som woks apply fuzzy logic to dvlop nw imag pocssing algoithms. A compaativ study of fuzzy imag nhancmnt tchniqus applid on digital mammogam imags has bn don. Compad to oth non-lina tchniqus, fuzzy filts a abl to psnt knowldg in a comphnsibl way [16]. Multimdia psnts powful tool fo dissmination of data and intptation of sach sults. On wok psnts an animation on bast canc asy to us pattns fo patint, studnts and sachs [17]. Optimizing th quality of th imags gos against th dgadation causd by th intaction of adiation, but also poducs dispsd adiation which in tun affcts th imag plat. This dispsd adiation is addd to th main bam adiation sulting in a dgadd imag of th objct contous, with lss quality. This pap psnts a modl of intaction of adiation on bast, basd on th Bosso s Filt. This modl is usd to impov mammogaphic imags, fo th diagnosis of canc to b mo accuat, showing th micocalcifications. Th ida is to qui only a singl dos of adiation. Th modl usd is basd on a dgadation modl by dispsd adiation and using th Bosso s Filt, dvlopd ali [1, 13].. BOSSO S FILTER Th Bosso s Filt is dfind by th quation (1), wh a and λ a th paamts, and A (N, λ, a) is a nomalizd constant dpnding on λ and a. N is th dimnsion of th matix in pixls. λ +a ( ) ( ). B N,λ,a = A λ,a +a (1)

3 Dgadation modl of bast imaging by disps adiation 349 Th Euclidan distanc is = (i + j ), wh i, j a th positions of th matix cll. Th f paamts a: N, λ, a. In th disct domain, th quation of th filt is givn fo: N λ ( ) i 0 0 0, i ( i 0) +a ( ) = A( N,λ,a, ) B N,a,λ, +a () wh 0 is th position of cntal pixl in th knl. Th application of th filt consids th convolution opation fo squa imags with M M dimnsions. In th analysis of Bosso s Filt bhavio th IDL softwa (NASA oiginal pogam) and th Foui Tansfom FT a usd. Th algoithm allows obsving th changs that tak plac whn vaying th th paamts of th filt on digital imags. Th softwa pmits to us th Foui Tansfom fo dtmining th Bosso s Filt fquncis spctum, and valuats th bhavio shown duing th xpimnt. Th sults a compad with classic filts. Th Bosso s Filt bhavio is don at diffnt valus of its a, λ and N paamts. It is found that th a gions wh th filt sms to act simila to classical filts, such as lowpass, bandpass and highpass. In som gions, th filt has a bad pfomanc and dos not act. This vsatility pmits to chang th pfomanc of th filt with small vaiations of on of th paamts. Th a angs of paamt valus wh th filt dos not wok. This λ ang is [ 5, 0]. Th gat vsatility of th Bosso s Filt pmits to b applid to imags in al tim, vaying th paamts automatically. Th Bosso s Filt can b usd in two-dimnsional imags, infing th ffct and possibl applications in on-lin vision applid to th industy o mdical applications. Ths applications a caid out in imags with a gat vaity of gay lvls. It is obsvd that th bods can b stood out, placing ctain valus to th paamts, so that th high fquncis a compltly notoious [15]. 3. DISPERSED RADIATION X adiation intacts with matt in th ways, accoding to th Rayligh ffct, photolctic ffct and Compton ffct. That is, it can dposit som o all of th ngy in it accoding to ths ffcts, which gnally dpnds on th photon ngy, th dnsity of th matial, as wll as th typ of atoms composing th matial [1]. It can b appoximatd by th lina attnuation cofficint of th photolctic ffct using q. (3) 5 Z µ =an, (3) E 7/ wh α is a constant, N th numb of lctons p unit volum, Z th atomic numb and E th photon ngy. Whn Z is incasd, attnuation and E (ngy) a gat and th damping facto of th photolctic ffct µ is low. Th Compton ffct pdominats fo ngis btwn 50 kv and 500 kv, dpnding linaly on th atomic numb Z of th matial. Ths two ffcts pdominat in adiogaphy imag. In th cas of mammogams, th photolctic ffct pdominats whn th photon ngy is 0 30 kv. Howv, th matial of th bast is lss dns compad with oth tissus (bon, intnal ogans) and th xist absoption ngis clos to kv. In th cas of photolctic ffct, an lcton is jctd fom th inn lays of th atom bcaus ths a alady occupid, poducing an mission of th ngy chaactistic of th atom lctonic tansition. Fig. 1 shows th incidnt X-ay bam into bast tissu and th poducd dispsd adiation, wh d is th mamma thicknss, ρ is th plan distanc fom point O to point (x, y). Th pincipal bam going though th matial, poducs missions in all dictions, that is to say, it poducs sphical point soucs in th way of th main bam.

350 Migul Bustamant, Gastón Lfanc 4 Fig. 1 Incidnt and dispsd adiation insid th bast tissu. By th law of attnuation, th intnsity of incidnt bam is attnuatd accoding to quation 4. I=I (4) µ d. 0 Th atom missions within th matial can b thought of as point soucs, in a mdium that attnuats th adiation, poducing intnsity in th plat givn by (5) µ I=I s, (5) Wh = ρ + d and ρ= x + y a distancs and ρ, as shown in Fig. 1. Th quadatic tm du to th intnsity of a sphical wav and I dcass with th squa of th distanc. Equation (5) is th Bosso s Filt [1, 13]. Assuming ths conditions, th intnsity at point 0 can b wittn as (6). is µ µ d I=I 0 δ( ρ ) +I s. (6) Th bast tissu is not homognous, thfo lina attnuation cofficint µ dpnds on th position (x, y). As an appoximation, it can b assumd that th attnuation cofficint can b calculatd with q. (7). ( ) 1 I x,y µ ( x, y ) = ln. d I (7) 0 In this cas, th valu of d cosponds to th thicknss of th bast in tms of imag acquisition. This paamt is not fixd, but it givs a good fnc valu. To calculat th intnsity I s, it assums th following hypothsis: Th total intnsity dpositd in th plat is I 0. This implis that intgal I(x, y) on th sufac (q. 4) must b qual to I 0. In this way, an xpssion fo th calculation of I s is psntd in q. (8) with I =I s ( ) 0 z d = 1 +d z( d ) µ ρ +d, µ ρ ρdρ. (9) ρ +d 0 (8)

Eo 5 Dgadation modl of bast imaging by disps adiation 351 In a pvious wok [1], th infinit is placd by a valu of 100d, bcaus th function z(d) convgs apidly in th ang of valu µ. This nw imag is th contibution of dispsd adiation in th cntal pixl. Subtacting I s (x, y) to th imag I(x, y), an imag without th contibution of th dispsion, I = I (x, y) I s (x, y), is obtaind, wh th diffnc dpnds on th valu of d. 4. BOSSO S FILTER APPLIED TO BREAST MAMMOGRAM Th Bosso s Filt is pogammd using IDL softwa. Th IDL pogam outins dscib th quations psntd. Th intgation is achivd using Simpson Intgal. Within an intval, th valu of Ι is calculatd as a function of d paamt fo two adiogaphis obtaining th sults shown in Figs. and 3. Figu shows th unpocssd bast mammogam. Th imag is pocssd by using Bosso s Filt, psntd in B, which nhancs th gion with micocalcifications. Figu 3 shows C, unpocssd imag of a phantom (dvic usd fo calibation of imaging quipmnt that contains within it, lmnts simila to th body) with dfcts. Th imag D is pocssd by using Bosso s Filt, has phantom with mo dfcts that in th oiginal imag wh calcifications a appciatd. Fig. Bast unpocssd (A) and pocssd (B) imag. Fig. 3 Phantom (C) unpocssd and (D) pocssd imag. Sval valuations hav bn don, calculating I fo diffnt valus of d, to choos th bst d valu. Th ida is to obtain th btt solution. Eo v/s D.00E+07 0.00E+00 -.00E+07 9 14 19-4.00E+07-6.00E+07-8.00E+07-1.00E+08 D Gll Fantoma Fig. 4 Paamt d vsus o.

35 Migul Bustamant, Gastón Lfanc 6 5. CONCLUSIONS This pap psnts a modl of intaction of adiation on bast, basd on Bosso s filt. This modl is usd to impov mammogaphic imags fo aly canc diagnosis, to b mo accuat and to dtct clust of micocalcifications. Th modl is basd on dgadation of bast imag poducd by dispsd adiation using th Bosso s filt, dvlopd ali. Th Bosso s Filt stimats th d paamt fo impoving mammogams imags, which allow a btt diagnosis of bast canc nhancing micocalcifications. Bosso s Filt quis a paamt d to good bhavio and its calculation can tak a long tim. Th dgadation phnomna of X-ays in matt a stimatd valus of th f vaiabls of th modl and dfin an o function of th paamt d, obtaining a minimum o. Th filt is applid to a mammogaphic imag and a phantom, giving nw imags with nw dtails, such as micocalcifications. In tun, th phantom highlights th micocalcifications. Th sults a valuatd by sval mdical xptiss, saying that th pocssd imags (aft applying Bosso s Filt pocdu) hav btt contast in th mammogaphic imag, nhancing micocalcifications and pmitting btt possibilitis in th dtction of bast canc. This opinion is also valid with phantom bast imags. Futh studis a quid to chck th validity of th sults and fin th paamts of th filt. REFERENCES 1. Wold Halth Oganization (WHO), Load wold halth suvy, bast canc pvntion and contol; http://www.who.int/topics/canc/bastcanc/s/indx.html. *** Guia Clinica Canc d Mama n psonas d 15 Años y mas, Ministio D Salud MINSAL, Santiago d Chil, 010; http://www.dsalud.gov.cl/potal/ul/itm/713d5c443d104001011f011398.pdf 3. EDDAOUDI FATIMA, REGRARI FAKHITA, Micocalcifications dtction in mammogaphic imags using txtu coding, Applid Mathmatical Scincs, 5, 8, pp. 381 393, 011. 4. KUMAR B. SAMIR, Dtction of bast asimmty using anatomical fatus-a viw, Jounal of Global Rsach in Comput Scinc, 3, pp. 1 4, 010. 5. KUMAR B. SAMIR, Imag pocssing algoithms fo bilatal asymmty dtction-a suvy, Jounal of Global Rsach in Comput Scinc, 8, pp. 39 43, 010. 6. KUMAR B. SAMIR, Diagnosis of Bast Abnomalitis in Mammogaphic Imag, Intnational Jounal of Comput Scinc and Tchnology,, 1, 011. 7. CHARAN PATEL B., SINHA G.R., Ealy dtction of bat canc using slf simila factal mthod, Intnational Jounal of Comput Applications, 4, pp. 39 43, 010. 8. PING W., JUNLI L., SHANXU Z., DONMING L., GANG C., A mthod of micocalcifications dtction in mamogams using wavlts and adaptiv thsholds, Th nd Intnational Confnc on Bioinfomatics and Biomdical Engining, ICBBE 008. 9. D`ELIA C., MARROCCO C., MOLINARA M., TORTORELLA F., Dtction of clusts of micocalcifications in mammogams: a multi-classifi appoach, 1st IEEE Intnational Symposium on Comput/Basd Mdical Systms, 008. 10. LAKSHMI N. V. S., MANOHARAN C., An automatd systm fo classification of micocalcification in mammogam basd on Jacobi momnts, Intnational Jounal of Comput Thoy and Engining, 3, 3, 011. 11. JING H., YANG Y., NISHIKAWA R., Dtction of clustd micocalcifications using spatial point pocss modling, Phys.Md.Biol., 56, 1 17, 011. 1. LEFRANC G., BUSTAMANTE M., NUÑEZ A., GUARDIA M., Dtmination of th dispsd amplitud in mammogams, using th Bosso s Filt, IASTED Symposium on, Tampa, USA, Novmb 001. 13. BUSTAMANTE M., LEFRANC G., Optimización d aplicación dl filto d bosso a imágns mamogáficas, XV Congso d la Asociación chilna d Contol Automático, Santiago, Chil, 00. 14. CHERUKURI M., NAGARJU C., VHERUKURI P., A poposd mthod fo classiffication od digitizd mammogam imags fo tumo analysis psnt in th bast, Jounal-CP, Novmb 010, pp. 3 6. 15. BUSTAMANTE M., GAJARDO G., GONZÁLEZ N., LEFRANC G., Análisis dl compotaminto dl filto d Bosso al pocsaminto d imágns, XII Congso Chilno d Ingniía Eléctica, Tmuco, Chil, Vol., 1997, pp. 65 68. 16. HASSANIEN A. E., BADR A., A compaativ study on digital mamogaphy nhancmnt algoithms basd on fuzzy thoy, Studis in Infomatics and Contol. (SIC), 11,, 003. 17. CHEN YJ, RAJENDRAN S., TAGNEY M., TABIRCA S., Multimdia visualisation fo bast canc, Jounal of Computs, Communications & Contol (IJCCC), 5, 5, 010. Rcivd July 1, 011