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3D spherical harmonic invariant features for sensitive and robust quantitative shape and function analysis.. Uthama, Ashish 2007

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oMimagi cogys sueiei w aes wca sseamai ieiowgO sucaa is e s oaiousi omagc soeimagi ( e maieam M ciquee as sucoamicaMo gsoo3images oe ai is cis e s o(geomeics ocoicaa suoicaaisucsee amus oecsOe oewcis cue o oe mosacseaMimagi moesaims  ii gio oe aiioeioi scic aco sucas moosuasksSuckwe oyiases ouuei oaioao s ugis eacke ogss ouge seases a uowe a isow emaaiac  sease  emoyi ous coma mecsms [11 Mnd ObjtO oe maicees iMimage asisicuy oimagiis ee meay com sus om a suecoa ci gueesA eseaooe oee eacsuecia commosce iscay qui o sucasisCuee moswiseaaacuseioimagi is  say a e images osuecai  acommoma oaase ai oeasy  use sowa o (ee Soo[13]s  eouge e iiscmi use osucaaacwiouegee  e  oe ueyi assumio ioe Sescomis ois aac egigeice ses; e macoe is e  oaoogicaai [7-1e co ia  ese aoaacse semomey meo(Mwas iay cciisuscei  misgisao[11]a is was coowi ee omoses [1 15]ese mio ieiee iesiaeameo  a e  cy ie suecsce wiouici eo e e aoocesssea  aesime measus ooeesucas eage oaco meae ewiiscic giooies(Is o eiasis [1 17]W ese meo  e aaage oi sime  comey cay  ioo a saioaooacowiie IsMo ce ses osea a seaaccc a scmi o seosaacoes [1 19]we ese aacs ckea  mea  accou e sucao ie I maskse ima aim ois esis was  a a seaac seiscmi oes oacoiscic gio oies ssucieuecao ioe cc e sucaowe a secaocs sea eseao I masksisiieis a sigca coo I s asis aa sie ieeccomso oe s acss suec wioua emuagisaoWe eeeeoua eseao o ioe oaiaiaa a eseaooe acasasiooacowiiIso ce e eecosucao oe I s oeseaswe a iicom suce ococique aiaseoumeos sei2 pl  Mn n In(MMagc soe imagi was ogiy e as caMagc soe(seoe ueyi ysicaemeuseiimage cau ageo e co oe cogy es oe cao (caics a s a sie o ao cay a si ceis sus ia magcmome []e eecois magc mome s oe mooa uo ia cusimyi ae emes wou  e magcoiesAemoics wi scacaeeacoeou eswi  oua masoois eec we e ci oceaiisosoemes ke oge uaiicsus ssessi a s eage ogecoe ie ma is kw  au %  mass []3is makes iaiae ma usi eeamagc es  image emaA cus wi a magc momewaceia magc e ose wi   agie a ooosi  e e co Age a es is caee w ey s a age ie oosi cois 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= M o 1e ^ (1e iemagc momeao ee ae magc momeacays au e asIaywe eeaey is ae mosics5 iaseAeis eeasoue is mo iiaics i  e seoeisuouisIaio i ck  equiium sie coomagsme oao gi  go ouoaseUsuayMoom asee me co ioeiis ooase is e Iaye maisc e is assume  u ugue sue ise we ia e e is ecy mogeusis sus ies oe oec e ey ees (1 a e e oequeies (1 e su is ae ome    is iacce iee ic iecoa e iomogei sui ia seomee   e  me co cas  measuusi acome esequeesSie e magc momes a  aue ase mag omomes ca esmausi ck ucoi aceicse cie iucecue iis coiis eoee ce e ous omes oaiaieaimage oe sue i se e sc e is augmeewi aioes caee ge es a ge e Gis aeae co is ces e eie a coesi ces eoequey (1a e   asw a e wi ey equa e ecoequey aa gicaooe as is ae Magc mome oics a e Y a aacaowou  sec ie is eis ocess is caesce secosie oy a isce oe oeci imageseei  iso sig cke e coi  scic ( ycaowiiis sceo mo ge es a useas swigu 1ese ge es ice a coease s ie ecessioocess oesi icse equey a ase a  ecie cue sigcke e coiese sig a sai  iK-sce sie ey eceequey com oee A uesysis om is sce yies e  imageoe sce i se is ocess is eaa e me  oaia 3eseao is is o oe mossic aacs  oaiaMmemocomee sequeeske e ec-aimagi (E[] a useiaccego  17--ii9   "GYgu 1 Ge es a e a Y as7Strt n Mous como oe sequees a measusig su ia wi aay ossie Mimagi oco []Cuee moswiseaseooco aose wcimage e suc oe ai[]SucM aims  oaigsooimages oe e s oaissuesaissue is maiy cssieio Gy Mae Maiy cois ouyeu (Myeis a oc saau a oe u Gy maecoeos ekw si coewi maieigee W Mae Maiy cois omyeuKw  ioeimessage aacss e maceous sysm Ceosui(CSA caisoc uiwcoccues e sce ii aau e maai Maiy coeie aicsSucM ays a sigca  ie agsis ougicaseases keMuie Scsis []; w scic ogicacoio ke sio aeaie w mae e goiiimageaiamy ees uscieis sec s e amy oiiaaisucs sucas e amuscs e [ 3]e moscommoy useaisuc imagi ocoa e  a    weigeimages (gu 1 e 1 sws e omes some oe aissuee 1 Momes commoy occui aissuessue   ome (ms   ome (msAse ssue (  -Ceosui - 5-1W mae 7 9Gy mae 9 1e ee iomes e ssues sws uas ee iieies ie oaiMimageAs e es ie e sw 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scic gio wiieai eieseossue css oseoe co aisucSegmeaomeo ca oay cssieio maa semi-aumac a1aumac segmeaociques [3 37]Accu segmeaooscic gioie aiis  ima giooies(Iseasis aacsIe s os osuc oaigio ke e amus emeeo isegmeaoca a  sigca imcoe asis a sueque mecaieeI segmeao a aosaays  ogsooamicascake e  1ioe com wesoosca make osio acqui a gsooamica(usuay  i me  ee segmeaoogio oiesMaaSegmeaooe amusMosoe Is oaie  useiis esis we segmeeusi maaciquesCoie eeee is qui ii a a some oeIs iMimages (gu 13 Eougis is a  me coumi ocessmaasegmeao a aiee is coia go sa isegmeaoacaoA mosowa ckages es  aiuscieisaccu a gio oe aiiMimagesIs ioeie os (eiiseco1we segmeemaay usi e Ami sowackage (Meu ComSysmsSaegoUSAoe coec imagesooese Ise  a e g amus we secsucasis sie iwas swaey ueo aoy iios sease es [32 Aumac SegmeaooaicsMaasegmeaoocesses a eque mi e ai oaiees a e me ioeie ocessAumac segmeaomeo a13eewe giooiess a gS a wi accucy asess  eougy s We usee semomey (M[39] aac segme e  a g aics om e  1scas i kwmioiag coicaas oe 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simi a iaaas usi (3eace o/ a  k  [3 wi   a  q a use ieeseas we s  I  io a si w comeio  =   aasisIc=m m=1I(q  E E  (c=1q 1 mak=16 Ah ntrnM coeuae ssuisee coecooe  om Uasuisee acaooe SA cique  mecaAU eSA-semeoa oee cauo suisee eoe SA-semeoa assisie acao mecaScoece  aU a oee maasegmeao oe amiMcoece  aU a maay segmeee  om U suisee coecooU  a assisiogicaieooe susAnlntis wo was suoe a g om E/CI C(3- (M(3798 f[I] cci  Kaca Keea Go  Sa Imiamic cisiowiseaimcomi aomeaceuc ie sagaauaouogy a Eemeaugy(1-31[ eoCaeeKCawg  iy GMgeooe cemeascicucomeiios seaseAa ougy (33-35 [3] eoCaeeKCawg  iy GMss oamicimici iogssi suacay a ios seaseccaaeuc imicaoai1( 7111[ iy GMMac  eoA comsoogeoimoamus a coeeeogssi suacay a ios seaseai1( 1[5] AymecMSoso-Ca  Mao MMu AMMo-IgoaMGoaae iego Coequees ougsiaaooe amosiaway iEuauaousciee(9-[ Keea Go  cci  Sa AymecMSoso-Ca  Oso iego Imiamic ci a Maigu osaGaassie ioeme ie oysiogy oios seaseIe saGaa IIE m Im CAMagi SieUS;331-339[7] kamu YOke Kku  e scicucus ys siu e siamaecomicsco s ie  usciee sea5173-79[ cey C m Magi a sooiies oimiamic u a eisiaocouaousciee(137[9] Kimu MMimimo  Maumo   YMo a swi ocoico-sagaa oo  e amo-siasysmuscieesea(55-3[1 Ogawa  Yos YOku  guc KKa  Uemu KSecoaamic geoaeceaiaoie mi ceaae sioeaowi Mimagiogy 199715- 1997[11] mu A Ygasma  Ki  Go  SSa Kamicaoy owi ceaiaoie i oe mi ceaaeSoke1991(55- 1991[1  i 1ieWMScack ekeCAmos e Ka oa mage a amic me cesu 11(1339-31[13] Kassuk  e wig  See cki C amic gy maeces iuioas emo a semomeic asiso3-meiomagc soe imagiusciee e 3(1-3[1 Summeie Cue Csa ESaa-  GomeAo Mai Ms mii Mea Sucaices iiosease wimeiaa semomey sAs ougy (-5[15] Kaasi Magui emeee K Coicosiacoaees o[1] o- a [1] oogcose iiosseaseuaougy 3(33-3[1 oksi"semomey" su  usewi imecygisimagesuimage 11 [17] Asue isK W semomey su  use[comme]uimage 113 [1 MieMIg M Ceg CS CIasi e weoomaoe meam  usi e aoeomoc meic maiocees oe oAcamy oSciees oe USs oAmeca 1(95-9 [19] S CE Oka YMaki memoes wiouyimeamac associawi iiamemo ao cogo uaousciee (17-53[] Yusece Mecc-mio aeSea MA Ka AKokowski Ma  Gee ocams-scic  guacoasis usi e coious meaeseao uimage 35(51153 [] McKeowM  a  Wa caascmi Asis(Iee OMuisuec IIEEE AcouscsSecaSigocessi; waii;  3[] Maiu csy Ee  Caca ACoi E ACgis  aimomey usi 3mome iaasMecaImage Asis 31-19 []   A-Gie a  McKeowM Cc  Acowiigio oIes(IsUsi 3Mome IaasIocees oCoee oComsioa e cogo ; w Yo;3[] Uama AAgie auee AMcKeowM Iaa SAS sco ComeGeomey iMgiooIesAsisIAuaIeaoCoee IEEE EM; o ae; [] Maws MAa oe ceu aecomicscoc s oamic og geoowi coicaaao uaoucygy197335- 1973[] cemi CoiemaA  osiaaeoocoeico om oeoasio ie  ysiogy o19(5797- 19[] ss Eeamic og geoowi coicaiuaeic ocess? usciee 199 35(35-55 199[] Soeau Imme e Micgaaco  oggeooaceiieamic u aeoaseomocoesio ia Eemeaaisea199 11- 199[] KumoYSakaki SWa  ka KOa SMau SYosmu Sakaka MCia uoic caeas sacogoimiecoicaiaoa amic geoisaous ei  wi caceaiscmiausciee e 199 31-1199[3 Yama KKis AKou ESakaguc  guc  Kaoka Kyakawa  sic oasgw ces amic geoaecoicaiao uaoCeaooow a Mesm 199111(3 1991[31] cksoG 3aaa oi w ocoiaa amicmogicaces aea ooacoicaaaocoswi e eecoa simisioicaaisea1995eaaisea91-7[3 aaa ess i  e is ss amic geoiosioaia-sioca aeceamisecmyaisea193(11-519[33] Ami  Soaa cas CGi MAumac segmeaooamusom aiM ieg y cs a mic coouIEEE aaco oomecaEie 51(51[3 wis MSg CSmi Auo Yi  McKeowMMaia eAa  sk scic iees oios sease oe sia-amo-coicaa ceo-amo-coicamociuiiesusciee e 1(15[35] e MMYa M iosmoe ogssioa moaugy1917(57- 19[3 masio  maaiAmy iComImages; [37] ok  Aaages ouo(omio s iccaaeemeaaacogy a ysiogyCcaa Eemeaaacogya ysiogy 199 (93- 199[3 Gcq  e-meioiaas a eiacao oeccogo Sigocess 1995(11-1995[39] ay  ckmo Moo S Ae se aacaoI 199 19913-13  13199[] ac Aimome ooiaa 3s scoseoo ocoec sesIIEEE IeaoCoee oImage ocessi; e; 57-7[] KaMuse siiewicSoiaa secaoceseaoo3s scoIocees oe  Eugics/ACMSIGG symsium oGeomey ocessiAac GeaEugicsAssociao 4 ttn d An  An ShCh M ( brn vtrl4.IntrtnMagc soe imagi (Mis iasi cogas a suie mo si e maaiamy  i Imomes i M scaewaa acquisiosequees a yiei ogssi gsoo3images 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"IaaSA S sco ComeGeomey iMgiooIesAsis"usee ocamme  iesga ces oeeimi cogimie (MCI[we ses usi meic measus  ecacas ces amig  iica ougicacea  ea  usemeaeseao  cc e suace oe cau a ii s ces isca [5]we is aacquis accu age oe Is acsse suec asis a e siaeo imuaage couaee aece susAea meo  ooai sci ac wcmay ece sucioaoiaIese as may iaa  oao a scaus ei easy comsoacsse suecis emis e emuaagesa me aiaioisies asi om gisaoeom  ea[ usesecaoc (SAseiaa iices  accu esma a s me oaisioci e eo e  suecsioIaeaiewowe usescaoa aoiaa as usi a SA eseaoo3Is  a s ces iaiM  [7] a moaeaaages ousi sucaaaca wi aomeic asiswe e meocique useioueous wo aow ss wi coegyIis  we ee oumeoa ose weaeSA s sco aa uque  a Iese as aoee e ccoocomess wi comegyi osewi muie si sWe  oumeoosyc  a moae eecss oe osecique eie esee oiesueca a misage eesuecGeg  ea [ oseusi a SA suace eseaos oaisucs ke e cs  eue ue auge ceseiaacwequis eciage oesucs a wi me aoa is oy sucs wi secagye SA as ose is mi secagy a ioos age a sca issues as  oi iaa ses [91  ao swe imae ocus a me iuei ugicasoeIis swe a e s ocs ioosuec wi ios sease a csigcaces c e coeiomeic meo4.2 MhIis seco we iey summa oueaiewo oSA-seIsco iMWe eocee ese e oseeaemes useee e s ocomeI gies i a aa useoaiuque as a I4.2. Invnt SA ftA 3I wi secagy ca esseas   a ooe use wi   a  as e aa amuaas sce eoe oaa gi(is equa e se  e suace i om eceiaose as [7]e SA eseaoois ois gi= o(siee ^ (1^ 0  (   is e comecouga oe  m  oesecaoc oge  1w/ es om  [11]e accucy ois eseaos oe e o ao caee wiIaae oe eseao aois oai si e ogioe3I  i cei com e SA coeiciesIoueous wo[7]we emoyeoy iaa as om is eseaousi (Sca aowas ace sca e coaii( wi i emewcgis a ugmeasu ome [7]=  Ec ^ (coegiesisuaces wi se occsioogies wi scoeccoms cao eseeas a ooo aesW(  sie esegies  aays  a si se e a  (   A i ae  e se om e ogica ice ee e o i sucsse augmeeo    is e e ki a  eoy iis ii e 3Ie SA eseaoosuca oisgir  i si(gk=     ^ 177(9(si0^ 0^ o(39k  is aieice accou ssie gecy [11]Sie ccomoo(3is gy iiciewe use aaea aac esei e as a seosecaoese o a oai ieec e 3 I wi   secass oiasi i    is ieecois simusami e 3I oa secagoco meio   aeace o [1e SA coeicies a eoaiaeace o  as^ C =   ,0 ( 19si9i (is sus ia SA eseaoeacsIaa as esess cae usi (as use Ka ea [13]we as eauo emsees is eseaois uquesie iee o oe s a a oe co ss wi su ie same a ceseaoeouge gies oe ss a ascay eoome is mio we ose ai e aa i(3acss eseas as i(5 is yies uque as eueiee o ae ss ace sca iaae acss e Iswe ose  keeemoss S co aa Is i a   is e usmeasu i oe smaescommose eomssi eacoe I ieei sei a91   si gkcm^  ^(^ k = E ^  1k^ =^ (5Sie is aa is aeacss eace o   as swi(5 e ccm mus oe same  eacsewe use a commoe o  asswse mimum e is oai equa e suace aa oeeomssi se  e equiausami g( =   = ^ (e uquescaaoa oiaa as a as i(7ese es a esio a si w  o e a ck=mam=/A q q=  E^= 1 1 ma^(4.k =1 m=-1gu 1 sws w is meocou  use a 3Is ke e maaics9gu 1 Ieecooa  aic wi oe 1 ss use oaieSA eseao e coesi samesuaces oe o ss a aosw4.2.2 Stt An  e a c us oaia oa gmeio e oe e o cse Moo e ge oes oese as a uw We usemoy a meic uose sscaasis oese assie  assumio oe a me a quiIuosa se measu eeo gu oss (eseeeia cis sagaie se oai a ssie uo93oe c acss e o guWe use e Eucase eee ac as e se measuAoas e a  ea [5] we use a MoeCao aac oaia suicie gmouosie s agaia ssie uo is asieA   e is oaias e o oemouo wcyieea Eucase gaae ogioe oe sames a e mouo oe Ie oai e is ss aa sscasa s oe o gu a c sigca ees eeemIousis is a so iicaoaess ie o gu  a sysmac ee isuc4.2.A tn  thl vtrle segmeaooe cs was oaiusi e semomey aac[1e cs we segmeeie suecsce  wiousaao e  a g cs we segmeeoe ssueo ma(Moe ceosui is Ma wi ose wa gy maewe gis e  amicascaoeacsuec esegisaome we euse oaie cs segmeaoie suecaisceAumac 3coec meo a mogicao we euse im e sus osegmeao gu 1 sws e su ooe sucsegmeao94.td Inis secoscs e geoa acquisioo use souoseaac wci syc o as we as asucM  oes a co4.Sth Strt tGn  e oae oe oses sciociquewe seSA as osyc  wi simu ss asc iesuecaSimi [e sic s use ge ese  is aeioias i(w  (yc is e ceiwi  (a cG as me e 3me oe eioi(e aaage osucaeemeaseis ia  quai coe  s  oe oec is  us gauge eoae oSA as wi iasi ise a aKee eequaai a  a   coe us  cG ca sysmacay eca ss wi sime eese a oe SA as iscmi o gu oeioi gewi a sma ee ieisc i ca useas a measu oi sei  y ^  qq y = ^ +  + ^ a^ ^ cG( eu amossoues oao oeeia a coiiiseemeeaceioi geia 1 g was ugsome e-ocessi  ca a mo asc iegusuace seeiI masksu siom ise was ae e geeioi mask95(a (is was owe a 3Gaussiasmooi wi a 5 keewi asa aoo ye su was coeeck io a  mask usi as o5ese es we oaiuscay om e oeaooaIs oe ami iasuec simu e eec oieuecai si a sA e e i es we ueiee  uusui ia mamum cou (mece ou %isce is come  e ao oeeia (SecoI simue eec osuecsiowiie scae e ceieaceioiwasom ue u 5  aue commoogiae ce oeg(  e eioiwas eaua omcomoo  y a/o  as  aa geom a u sioeegu (aSuace e oa a amus ( a g amus (omom a  e e ugees( GuA syc sames (see gewi mese( 51(cGusyc same gewimese( 5 e asc oki ees ie syc 94.2  Strt MtAtne  useiis s coisoM sca o2cosuec a 2es. o sca we oewi a gaoo u, o  a o aeeaisaooe ug . e M we acquioa 0 s Siemescae(Sieme, Eae Geawi a cage  sa quaa acoia aaaecamagc soe ecasysm. e iciawas sioa e camea. am i was use miamoowiie coi gsoo weigeamicaimages ( S=ms, =ms, ia=2, meio 0.0.0mm, 6, 0 sceswe acqui4.4 ltd is secoeses quai sus oemoyi e oseSA sas oe syc a aM oui.4.4.ln  Sth tSyc  geas sceaiecoisoy o  se eacse o gu, A a  eacguwi ey same ss. 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