Analysis of medical images in frequency and space-frequency domains ; Medicininių vaizdų analizė ir tyrimas spektriniais metodais
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Analysis of medical images in frequency and space-frequency domains ; Medicininių vaizdų analizė ir tyrimas spektriniais metodais

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VI LNIUS G EDIMI NAS TECHNI CAL UNIVERSITY of Do gine) gical Scien Summar ssertation g an y2007ctoral Di Technolo ces, Vilnius Electrical En erin d Electronics (01T DOMAINS IN FREQUENCY AND SPACE-FREQUENCY ANALYSIS OF MEDICAL IMAGES Ev ara s ŽITKEVIČI US Doctoral dissertation w as pre pared at Vilniu s Gedi m ina s Technical Un ivers it y in 07. –20 2003Scienti fic superv isor Prof Dr H abil Ro manas MARTAVIČIU S ( l , Tec S , Ell Eg and E s The d issertation is being defended at the Cou ncil of Scientific Field of Electrical E ngineering an d Electronic s at Viln ius Gedi m inas Tec hnical University: Chair m a n Prof Dr Habil Stani slovas ŠT ARAS (Vil niu s Ged i mi nas Technica l Uni versit y , Technologica l Sci ences, Electrical E n gi neerin g and Electronics – T). 01Me mbers: Prof Dr Habil Gintautas D Z EMYDA (Ins tit ute of Mathe m atic s an d Infor m a tics, Technological Sc iences, In for m at ics En gi neeri n T), g – 07Dr Habil Virginija GAI GA LAI TĖ (Vil ni us U ni ve rsit y, Bio m edical Science s, Medicine – 07B), Assoc Prof Dr Šarūnas PA ULI K A S (Vil ni us Ge di mina s Technica l Uni versit y , Technologica l Sci ences, Electrical E n gi neerin g and Electronics – T) 01Prof Dr Habil Juliu s SKUD UTI S (Vil ni us Gedi m i nas Te chnica l U ni versit y , Technological Scie nces, Elect rical Engi neeri ng a nd Electronics – 01T).

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Publié le 01 janvier 2007
Nombre de lectures 48
Poids de l'ouvrage 1 Mo

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VI LNIUS G EDIMI NAS TECHNI CAL UNIVERSITY
of Do gine) gical Scien Summar ssertation g an y2007ctoral Di Technolo ces, Vilnius Electrical En erin d Electronics (01T
DOMAINS
IN FREQUENCY AND SPACE-FREQUENCY
ANALYSIS OF MEDICAL IMAGES
Ev ara s ŽITKEVIČI US Doctoral dissertation w as pre pared at Vilniu s Gedi m ina s Technical Un ivers it y in
07. –20 2003
Scienti fic superv isor
Prof Dr H abil Ro manas MARTAVIČIU S ( l
, Tec S , Ell Eg and E s
The d issertation is being defended at the Cou ncil of Scientific Field of
Electrical E ngineering an d Electronic s at Viln ius Gedi m inas Tec hnical
University:
Chair m a n
Prof Dr Habil Stani slovas ŠT ARAS (Vil niu s Ged i mi nas Technica l
Uni versit y , Technologica l Sci ences, Electrical E n gi neerin g and Electronics –
T). 01
Me mbers:
Prof Dr Habil Gintautas D Z EMYDA (Ins tit ute of Mathe m atic s an d
Infor m a tics, Technological Sc iences, In for m at ics En gi neeri n T), g – 07
Dr Habil Virginija GAI GA LAI TĖ (Vil ni us U ni ve rsit y, Bio m edical
Science s, Medicine – 07B),
Assoc Prof Dr Šarūnas PA ULI K A S (Vil ni us Ge di mina s Technica l
Uni versit y , Technologica l Sci ences, Electrical E n gi neerin g and Electronics –
T) 01
Prof Dr Habil Juliu s SKUD UTI S (Vil ni us Gedi m i nas Te chnica l U ni versit y ,
Technological Scie nces, Elect rical Engi neeri ng a nd Electronics – 01T).
Opponents:
Prof Dr Habil Arūnas LUKOŠEV IČ IUS (Kaunas University o f
Technolog y, Technological Sc iences, Electrical En gineeri n g and Electronics –
T), 01
Assoc Prof Dr Daliu s N A VAKAUSKAS (Viln iu s Ge di mina s Techn ical
Uni versit y , Technological Sc i ences, In for m atic s En gi neerin T). g – 07
The dissertation w ill be defe n ded at the public meeti n g of t he Cou ncil o f Scie nti fic
Field of Electrical E n gineeri ng and Electronics i n t he S enate Ha ll o f Vi lni u s
Gedi mi nas Technical U ni versi t y at 1 p. m. on 14 Septe m ber 2007.
Address: Sa ulėte -10223 Vilnius, kio al. 11, LT Lit h uania.
12; 01 6; fax +370 5 270 495 274 0 5 +37 952, 4 4 5 27 70 Tel.: +3
e- m ail: doktor@ad m .v gt u.lt
The su m m ar y o f the doctoral dissertation w a s distributed on 13 Au gu st 2007.
A cop y of the doctoral dissertation is available for revie w a t the Librar y of Vil ni us
Gedi mi nas Technical U ni versi t y (Sau lėtek 3 Vilniu io al. 14, LT-1022 s, Lith ua nia).
© Evaras Žit kevič iu s
,
01T).
– lectronic ngineeriectrn icaiencehsnoloUnigvicaerslity
T e c hni caGe d iminas V iln iusVI LNIAUS GE DIMINO TECHNIKOS U NIVERS
elektros ir elektronikos iTechnoloVilnius acijos santr ITETAS 2007 nžinerija (01T) gijos mokslai, auka Daktaro disert
SPEKTRINIAIS METODAIS
YRIMAS IR TMEDICININIŲ VAIALIZĖ ZDŲ AN
Ev ara s ŽITKEVIČI US Disertacija rengta 2003–20m 07 etai s Vil niau s Gedi m ino tec hni kos un ivers itete.
Moksli nis vadovas
prof. habil. dr. Ro m anas M artavičius ( s
Disertacija gina ma Vilniau s Gedi m ino techn i kos uni versiteto Ele ktros i r
elektroni ko s inži nerijos m o k slo kryptie s taryboje:
Pirmininkas
prof. habil. dr. Stanislovas ŠTAR AS (Vil nia us Ge di mino tec h niko s
uni versi tetas, tec) hnolo T gijos 1 m okslai, ele0 ktros ir elektroni kos– inžinerija .
Nariai:
prof. habil. dr. Gi ntautas D Z EMYDA (Mate m ati kos ir i nfor m a tiko s
inst itu tas, tech nologijos mo ksl ai, infor m ati kos inž), 7T inerija – 0
habil. dr. Virginija GAI G ALAI T Ė (Vilnia us uni versit etas, biomedici nos
mo k slai, medici na – 07B),
doc. dr. Šarūnas PAUL IK AS (Vil nia us Gedi m i no tec h niko s uni ver sitetas,
technolo gijos moks lai, elektro s ir elektroni kos i nžinerija – 01T),
prof. habil. dr. Julius SKUDUT IS (Vil niau s Ge di mino tech ni kos
uni versi tetas, tec hnolo gijos m okslai, ele ktros ir elektroni kos inžinerija – 01T).
Oponentai:
prof. habil. dr. Arū nas LUKOŠE VIČ IUS (Ka u no tech nologijos
uni versi tetas, tec hnolo gijos m okslai, ele ktros ir elektroni kos inžinerija – 01T),
doc. dr. Dalius NAVA KAUSKAS (Vil niau s Ge di mino tec hn ikos
uni versi tetas, tec hnolo gijos m okslai, i nfor m ati kos inži . T) nerija – 07
Disertacija bus gi na m a vie ša m e Ele ktros ir elektron ik os inži nerijos mo ksl o
kr ypties tar ybos posėd yje 2 007 m. rugsėjo 14 d. 13 v al. Vilnia us Gedi m in o
techn ikos u niver siteto se nato posėdžių salėje.
Adresas : Sau lėtek -10223 Vilnius, io al. 11, LT Liet u va.
112; 4956; faksas (8 5) 270 0 74 ) 2 (8 5 52, 4 49 27 8 5) Tel.: (
el. paštas doktor@ad m . vgt u.lt
Disertacijos santra uka i šsi u nti nėta 2007 m. ru gpjūčio 13 d.
Disertaciją gali m a peržiūrėti Vilnia us Gedi mi no tec hni kos uni versi teto bibliotekoje
(Saulėte Vilni kio al. 14, LT-10223 us, Liet u va).
VGTU leidy klos „Techni ka “ 1391 mokslo literat ūros knyga.
© Evaras Žit kevič iu s, 2007

universitetas, technologijos mokslai, elektros ir elektronikos inžinerija – 01T) .
technikos Gedimino Vilniau1. Introduction
Relevancy of the work. I m a ge processi ng is quic kl y dev eloping branc h o f
digital sig nal processi n g. I m a ges a s a con ve nien t and hu m an friendl y i nfor m atio n
for m are u sed in m an y fields of li fe and science i ncludi n g medici ne. O ne o f t he
ai ms of m odern medici ne are non -i nva si ve wa y s of diag nos tics. There are nu mber
of no n- in vasi ve m et hods use d in m edical diag nostic s; a m ong t he m m et hods w it h
vis ualizat ion capabilit y are m ost releva nt. These me thods use ultraso und, X -ra y s
either Nuclear Ma gnet ic Reso nance to vi sua lize interior of hu m a n body. Met hods
w it h v is ualizatio n capabilities are most i m porta nt in t he diagnos tics of disease s of
hu m a n brain. Disease s of th e brain mos tl y deve lop as a result of contraction s
(stenosi s) and dilatatio ns (ane ur y s m s) of blood vesse ls. Wh en blood vessel s ha v e
lesion s t hen probability of brain s troke i ncreases becau s e of t hro mbosi s eit her
interna l spill o f blood. After the stro ke ha s occurred it i s esse ntial to describe
precisel y t he diag nosis. The f irst sta ge of dia gnos is i s localization w h ic h ma y be
performed b y Co mp uted To mo graph y ( CT) or Magneti c Reso nance I m a gi n g
(MRI). In t he earl y sta ges of v essels disease s t here i s releva nt Ma g netic Resona nc e
A n giograph y (MR A ) dia g nos tics w h ic h allo w s to eval uat e the le sion s of blood
ves sels. The pro blem of s trok e diagnosis e nco mpas ses vi s u al anal y sis of m ul tiple
slices perfor m ed b y trai ned radiolog y person nel. If t here are sig ns o f regio ns o f
diseases the n i t i s necessar y to eval uate i ts n u m erical c haract eristics that are critical
in select ion of proper treatme n t.
I m age s of CT and M R I are gr a yscale i m a ge s a nd u sual l y th e y are a nal yzed b y
radiologists on displa y eit her on tran sparenc y scree n. Then objects in i m a ges ar e
recognized b y their properties like a verage l u m inos it y o f the region, localizatio n,
shape, di me nsio ns, etc. The process of vis ual recog nitio n is af fected b y m an y
factors. The totalit y o f factors deter m i nes u ncertaint ies of diagnost ics. More and
more o ften t here are used so ft w are u tilitie s i n the a nal y si s of i m age s w h ich help to
lo wer t he uncertai ntie s and speed up the a nal y si s ti m e. Co mpu ter soft w are i n
compariso n w it h traditional vis ual ana l y sis has an adva ntage o f more precise
evalua tion and calc ulation of i m age c haracteristics usi n g f ull d y na m ic range a nd
resolution of i m a ges. Applicat ions of so ft w are cover auto m a tic anal y si s of i m a ges,
calculatio n of areas and vol u m es of lesio ns, deter m i nation of opti m al treat me nt,
planni n g or assisti n g in c hir urgical operation, traini ng o f radiologists.
For m ulation of the proble m . In i m a ge processi ng a nd ana l ysi s t here are used
various m at he m atical approa ches. General l y m et hods m a y be divided by th e
domai n o f processi n g i nto spatial m et hods a nd m et hods w it h coordinate
trans for ms. The mo st i m porta nt a nd act ual are spectral tra ns for m s w h ic h con vert
i m a ge (spatial) do mai n i nto fr equenc y or space- freque nc y d oma in s. These k inds o f
trans for ms gi ve a n adva ntag e in t he anal y s is a nd eval uat ion of periodicit y a nd
stationarit y of si gna ls. Applications of spectral trans for m s in the processin g of CT
and MRI i m a ges are not i nv estiga ted widel y ; t here are o pen question s on ho w
spectra ma y be adopted to enhance or seg m ent t he reg ions o f stroke diseases.
5In the doctoral dissertation there is anal y zed the proble m o f medical i m ag e
processing in the freque nc y and joint space- freque nc y do m ai ns w i th t he ai m o f
evalua tion of capabilitie s of s pectral met hods. The solutio n of problem is based o n
developing o f tec hniq ues a nd algorith m s for detection o f regions o f disea ses or
other specific reg ions o f i m a g es.
The ai m and tas ks of the work. The ai m of the wor k is i nve sti gation o f
m edical i m age processi n g an d anal ys is usi n g freque nc y an d j oint space- freque nc y
domai ns and developin g o f algorith m s s uitable for se g m entation of regio ns o f
diseases. The follo w i ng ta sk s m u st be solved to achie ve t he purpose:
1. inve sti gate particularitie s of spectra of CT ima ge s contai nin g t he region of
ische m ic brain stroke;
2. ose techniqprop ues for seg m entation o f regio n of i sche m ic brain stroke b y
usi n g anal y si s of CT ima ges i n freque nc y a nd space- freque nc y do mai n s;
3. create corresp onding al gorith m s a nd experi me ntall y in ves t igate properties of
the tech niq ues;
4. create a tech nique and corr espondin g al gorith m for t he seg m e ntatio n of
regions o f blood vessels i n t he MR A i m age s;
5. anal yze capabilitie s of application of spectral me thods for the processin g o f
i m a ges w it h periodic regions.
Scientific novelty and practical value of the dissertation. The follo wi n g
result s w ere obtained duri ng PhD st udies w h ic h are relevant in the scie nce o f
electrical eng ineeri n g and elec tronics:
Created tech niq ues for seg m entation of brain re gion and for calc ulatio n o f
quasi s y m m e tr y a xis i n CT i m ages b y usi n g Fourier spectru m .
Created tech nique a nd correspondin g algorit h m for t he se g m entation of reg ion
of isc he m ic brai n stroke b y us ing Fourie r spectru m .
Created tech nique a nd correspondin g algorit h m for t he se g m entation of reg ion
of isc he m ic brai n stroke b y us ing Haar wa velet spectru m.
posed technique Pro for the se g m e ntat ion of reg ions o f blood vessel s in M R A
images.
Experi me ntall y te sted created algorith m s and in ves tiga ted their capabilities to
anal yze cl inica l i m a ges.
posed algorithPro m s m a y b e i m ple m e nted in to medical i m a ge processi n g
soft w are either i nto personal comp uters for the i ndivid ual i m a ge anal y si s savi n g
ti me of dia gnos tics.
ofthodologyMe research. he folloT w i ng m et hods and tec hniq ues w ere u sed
in t he wor k: Fourier a nd wa velet spectr u m a nal y si s, processi ng i n t he freque nc y
and space-freq uenc y do ma in s, eleme nt s of mat he m atical mo rpholog y and theor y of
sets, geo m etrical m ethods.
Presented for defence.
Technique for se g m e ntat ion of t he re gion o f brain i n CT i m a ges u sin g
spectru m a nal y si s.
6 • • • • • • Technique for est i m a tion of quasi s y m m etr y a xis based o n Fo urier spectr u m
anal y sis.
Techniques for seg m e ntation of the regio n of isc he m ic brain stroke i n CT
i m a ges based on Fourier and Haar wa velet spectra.
Technique for seg m e ntation o f regio ns o f blood vessel s i n MR A i m a ges based
on wa velet spectru m.
Experi me ntal res ult s of se g m e ntation o f regio ns o f brain, isc he m ic brain stro ke
and blood vessels; res ult s of e sti m ation of q uasi s y m m etr y a xis.
Approbation of the dis sertation. The results o f t he w ork w ere disc us sed i n
nine sc ienti fic con ference s i n Lit h uania a nd other co un t ries. Ni ne article s are
printed: one article is referred in ISI Master List database; t w o are referred in ISI
dings; Procee t w o article s are cited in I nspec database, thre e articles are pri nted i n
revie w ed confere nce proce eding s; one article printed in other conferenc e
proceedings.
Structure of the dissertation. The dissertation m an uscript i s co mposed of si x
chapters; fir st one is Introduction, last one – General conclusio ns. L ist s of
references a nd aut hor‘s p ublic ations are presented af ter conclusio ns.
The volu m e o f the w ork i s 110 pages wit hout a n nexe s; t h ere are 39 form ula s,
45 figure s and t w o tables u sed. The list of references co ntai n ds. s 96 recor
2. Content of the dissertation
Chapter 1. Introduction. Rel evanc y of the wor k, for m ula ti on of t he problem ,
the purpose and ta sk s of t he w ork, objects of defe nce and work approbation are
presented in t he chapter.
Chapter 2. Princip les an d m ethods of m ed ical i m age ana lysis. The c hapter
is dedicated for revie w of brain diagnostic met hods, principles of vis ual
inve sti gatio n of medical i m a ges, esti m atio n of i m a ge ch aracteristics of h u m a n
brain. Atte ntio n is paid to rier Fou a nd wa velet spectra applications.
Chapter 3. Analysis of Fourier spectru m of m edical i m ages. The chapter
enco mpas ses rev ie w of Fourie r spectru m est i m a tion a nd its r elation w it h properties
of i m age. Then it i s proposed spectru m s y m m etr y es ti m ation tec hniq ue w h ic h
allo w s to calc ulate rotation an gle of qua si s y m m etr y axi s of CT i m a ge. Re su lts o f
esti m ation w ere co mpared w i th ellipse approxi matio n and falx cerebri detectio n
result s. Al so there are prop osed t w o tech nique s for seg m e n tation of brain area and
for seg m enta tion of t he region of isc he m ic brain stro ke based on the enha nce m e n t
of lo w freque nc y co mpo nent s of spectru m and application of thres hold fu nctio n.
Segmentation of brai n regio n. One of the ai m s of i m ag e prepr ocessin g i s
detection of region of a nal y sis. This is u se ful w h e n i m age m ust be anal y zed
locall y. In t he case of CT ther e are region s i n t he slice s w h i ch do not belong to t he
region o f brain, e.g. re gion s c orresponding to tis sue s o f bones, fat, s kin, e ye s, etc .
These regions ma y be eli m i nated by creati n g the m as k of brain region. The
advanta ge o f usi n g m a sk is dual: fir st, t he n u m ber o f a nal y zable points is reduced;
second, reliabilit y of f urt her a nal y si s sta ge s is h ig her. There are t w o case s of brain
••7 •• region detectio n. In t he first case ( m ost u sual) regio n o f brain is si n gle a nd
complete l y s urrounded b y re gion of bone. In t he second case t here are m u ltiple
regions of brain w h ic h are (pa rtiall y) s urrounded b y region of bone. Second case is
more co mplicated becau se it leads to the solution of t he f ollo wi ng ta sk s: 1. it is
neces sar y to detect fro m 1 to 3 regions of brain; 2. seg m e nt s m ust not overlap wit h
regions o f s kin, fat or e yes.
Detection of region o f brain ma y be performed u si ng proposed algorith m
w h ic h consi sts of t w o sta ges: approxima te seg m e ntatio n sta ge and correction stage.
A n adva ntage o f algorit h m i s its capabilit y to detect regi on of brain in t he f irst
stage i n the case of co mpletel y surrou nded sin gle region o f brain. Second stage is
required if region of brain i s fr ag me nted or has a contact w i t h other si m ilar regio ns.
A n algorit h m of t he fir st sta g e is based on the fact t hat re gion of brain i s a
compact group of gre y level pixels; t he nu m ber of groups often is one ho w e ver in
complica ted CT slices there m a y be up to three si g ni fican t groups. The region of
brain us uall y does n ’t ha ve direct connection w i th a regi on of backgrou nd and
lu m ino sit y variation s i n t hat region are lo wer in co mparis on w it h re gion of sk in .
These properties have a con n ection w it h a m plit udes of lo w freque nc y co m pone nt s
of Fourier spectr u m ; t he big g er the group of gre y pi xels, t h e hi gher are a m plit udes
of lo w frequenc y co mpone nt s . Thus lo w pass filter m a y be used to enha nce s uch
groups of pixe ls. A nother i m portant fac t is t hat a m p lit udes of spectru m
compone nt s decrease accordin g to expone nt la w w he n frequ enc y ri ses. This m ea ns
that pa ss -band o f lo w pa s filt er m ust be ver y narro w. To o btain t he m a sk of brai n
region a thre shold f u nction m ust be applied.
At t he seco nd sta ge i m a ge i s divided into equaled size squar es; the n ce nters o f
squares are calculated; in t he next step there are used onl y t hose cen ters w hose
squares overlap w it h m as k from t he first stage. Fro m e ver y selected point t here are
dra w n radii w it h a gi ve n ste p of angle; o nl y t hose sq uares w hic h radii cross th e
region o f bone are selected. Then it m u st be tested ho w m an y radii crossed t he
region of bone; if the nu m ber of radii is greater than thres h old pa rameter t hen t he
region of square i s tran s ferred into in itial m as k. A fter all obtained initia l ma s k i s
dilated by iterati ve reg ion grow i n g a nd eval uati n g ratio bet w ee n m as k peri m eter i n
the re gion o f bone and total peri meter of se g m en t of ma s k. The ma xi m u m o f thi s
onds to stop condition of iteratiratio corresp ve regio n gro w i ng.
It wa s e xperi me ntall y eval ua ted an i nte gral u ncertaint y o f re gion gro w i n g
w h ic h w as calc ulated b y adding over - gro w n and u nder- grow n areas and dividi n g
result b y t he area o f re gion o f brain. In t he ca se o f co mpli cated CT i m a ges (tota l
of 124) the integral uncertai nt y w as lo w er tha n 20 % in 75 % of processed i m a ges.
The algorith m s w ere i m ple m ented usi n g fa st calcu lation m et hods and total
ti me of processi n g w as i n the r ange o f one second on t he mo dern PC.
Calculation of quasi-symmetry axis . In t he a nal y si s of CT im age s so meti m e s
it is required to appl y co mpa rison tec hniq ues w h ic h are u sef ul w h e n object has
so me s y m m etr y properties. The region o f brain a lso ha s particular s y m m etr y
because he m isphere s are si m i lar b y s ize a nd s hape. This m a y be used to co mpare
8 the regio ns of he m isp heres a nd detect irregular or su scep tible regions. For this
purpose it is needed to estim ate s y m m etr y a xi s. Ho we v er the regions of he m i -
spheres are not ideall y s y m m etrical by its nature and axi s (as a straight li ne) ma y
be evaluated onl y approxi ma tel y. There are pro posed three techn iques o f quas i
s y m m etr y a xis calcu lation b ased on ellipse fitti ng, detec tion of region of falx
cerebri and anal y s is of Fourie r spectru m in polar coordinate s ys te m .
Special objects of hu m a n brain to mo graph y i m age s are hea d bones w hic h ar e
easil y detectable i n ever y sl ice as bright ri n g- shaped areas. It is able to approxima te
the bone re gion b y us in g el lipse f itti ng al gorith m s base d on opti m izat ion a nd
clusteri n g (votin g) met hods. In the res ult geo m etrical fea tur es of head bone as wel l
as of brain area ma y be eval ua ted, for insta nce, s y m m etr y ax is, center, eccentric it y .
Ellipse fitt in g is also use fu l in identifica tion of brain regio n because ellipse conto ur
can separate brain fro m other tiss ue s. Both opti m ization an d clusteri n g al gorith m s
are suitable for a nal y si s of c omp uted to mo graph y i m a ges if u sed toget her w it h
special preprocessing. It w as applied optimizat ion m e thod of least squares
criterion. Appropriate results w ere obtained w h e n i m a ges w ere preprocessed b y
applyi n g thres hold f unct ion a nd morphological f ilter of the biggest particle. Fro m
the clas s of cl us terin g al gorith m s i t w as selected and i m p le m en ted algorit h m w hic h
use s 1D array -accu m u lator. It was noticed that clu steri ng al gorith m s are not
sen siti ve to extraneou s points ho we ver processin g speed is appr opriate w hen t he
nu m ber of point s does not e xceed couple of hu ndreds. T he speed require me n t
li mit s application of selected votin g al gorit h m because regi on of bone cons ist s o f
m an y tho usa nds o f poi nts. Co nseque ntl y it is needed to appl y hi gh ratio deci m ation
techn iques w h ich ha ve direct connec tion w it h t he res ult s of fitti n g. Opti m izatio n
m et hod of ellipse fi tti ng w it h morphological fi lter w as app lied to CT slices o f 18
patients (total 341 i m a ges). In ever y slice it w a s m an uall y dr a w n re ference a xi s a nd
its para meter s w ere co mpare d wi th auto m aticall y fit ted (m ajor) axis of ellipse .
Co mparison res ult s sho w t hat angle bet w ee n real and model ed sy m m etr y a xes does
not exceed 10 degrees in more than 60% of processed ima ges and brain area wa s
detected wit hout deviat ions i n more tha n 40% of anal y ze d slices. Uncertai nt y i s
related to eccentricit y of e ll ipse: i f > 0,6 the n a ng le de viation drops u nder the
li mit o f fi ve degrees.
A nother tec hn ique of qua si s y m m etr y a xis es ti m ation i s based on detection of
region of falx cerebri w hic h s eparates left and righ t he m isp heres. This approach is
more precise i n co mpari son w it h geo m etrical me thods since it trie s to fi nd
ph ys iological feat ure o f t he br ain. Fro m t he ot her side the region of fal x cerebri i s
detectable only i n slice s of head vertex. Temporal CT slices require other axis
evalua tion tech nique s ei ther i nfor m ation obtained b y processi ng verte x slice s m a y
be extended to other slices b y approxima tion of pla ne.
Technique of detection of fa lx cerebri w as i m ple m e nted by calc ulatio n of
center of m a ss, reduc tion o f anal y sis regio n, detection o f potential se g m en ts a nd
noise fi lterin g based on Hough principle. There were eva luated u ncertaint ies of
e9 e a c b
symmerty
axis detection. For this purpos e there were take n total of 61 i m age of 9 patients a nd
compared res ult s of a uto matic and e xpert give n s y m m etr y a xis. Stati stical anal y s i s
of resu lts s ho w tha t m axi m u m dista nce bet w ee n a xes in th e region o f brain do not
exceed 9 pixels for more tha n hal f of processed slices, and 5 pixels for one t hird of
processed slices. The speed of algorit h m depends on t he siz e of i m a ge a nd i s i n th e
range of couple seconds per sl ice usi n g P4/2,4 GHz/256 MB machi ne.
Quasi s y m m etr y a xis m a y a l so be evaluated b y Fourier s pectru m ana l y sis.
The main idea is t hat spectru m of s y m m etrica l object has s y m m etr y w i th re spect to
line crossi ng zero freque nc y c ompo nent a nd its direction corresponds to the angle
of rotation of an object. The mo st appropriate wa y of f indi ng spectru m s y m m etr y
line i s based on con version o f Fourier spectr u m into polar coordinate s yste m . I n
polar coor dinate s y ste m it i s neces sar y to find a n gle w h i ch e ns ures di vis ion o f
spectru m i nto t w o “ the mo st si m ilar” parts. Least sq uares criterion wa s u sed as a
si m ilarit y factor. Quali tati ve anal y sis o f resu lts s ho w ed that an gle of rotatio n
correlates w ith geo m etrical properties of brig ht objects of i m age. (Fi g 1). If regio n
of brain do mi nates o ver ot her region s a nd has s y m m etr y fe atures (bone regio n i s
eli m i nated) the n s y m m etr y e st i m atio n f u nction ) has clear mi ni m u m at the a n gle
of rotain. When angle is known the image may be back rotaed ensuring vertical
position of qua si s y m m etr y a xis. I f region o f bone ex ist s in t he CT i m a ge the n
angle of rotation corresponds t o the bone regio n si nce it s l u m i nosit y is m u c h h ig her
in co mpari son to re gion of brain. If object in i m a ge i s not s y m m etrical t he n
spectru m s y m m etr y e sti m atio n f u nction has m an y m i ni m a w it h s i m ilar val ues.
Segmentation of region of ischemic brain stroke in CT images . It wa s created
techn ique for se g m enta tion o f isc he m ic brain stroke i n CT i m a ges us in g m a ski n g
of us ual dark regio ns of brai n and appl y in g lo w pa ss filteri ng. Experi m enta l te sts
w it h standard size spectra correspondin g to 512 × m T i age512 C s s ho w ed that dat a
related wit h isc he m ic brain st roke is concen trated in narrow lo w frequenc y ban d
li mited to 20 × 20 size. H o we ver this band incl udes data about other com m on brain
jects. The infob lue nce of the m to detection of ische m ic strok e ma y be decreased by
usi n g additional processin g w h ic h is related w it h t he f ollo wi ng a ss u mpt ions :
1. ische m ic brain stroke i s co nti nuo us, local spot, occup y in g 5–40 % of brain area;
2. brain contai ns so me co m m on objects that are co nsiderabl y darker t ha n i sche m i c
10
mation infwith region of b (c) olar cofunctionof spectrum m of CT imagmu mini p estiing toone removed (a), function ee corresponde e rotated by degr tem (b) and imag nate sysordi(ρ
Fig 1.

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