2.2 Algorithm of boundary cluster

Transcription

1 An Ipleenaon of he Deecng Mehod of Conou- Based Opcal Flow Feld of Defoable Bod and Is Applcaon n Ulasound B-Scan Iages fo he Hea Chan g Ln an d Yonghu a Ln Dep. Of Rado Engneeng FuZhou, Unes, Fuan 35 P. R. Of Chna Absac: -- Ths pape pesens a ehod fo deecng conou-based opcal flow feld of he hea n ulasound B-Scan ages, whch s Machng Algoh of Bounda Cluse Cenes. The hea beng a defoable bod, hs pape, as a esul, s a eseach on he opcal flow feld o defoable f bod, whch s of coon concen n he eseach of opcal flow feld. Ths beng ou fs eseach, we nend o splf ou age,.e. we do no aep o eseach on all pels of he hea age, bu ahe ou focus sudes on soe bounda cluse cenes ha can epesen he oonal condon of he hea. Fs, we oban he bounda cluse cenes of ee fae. Second, we ach he cenes of he wo neghbong faes accodng o he achng accs of coon oon and oban he wachng dffeence of ee cluse cene S ( =,, whch s, hen, dded b he neal e of neghbong faes (,.e. S / =V(=,.In hs wa we oban he opcal flow feld. The aboe accs ae he bases of he achng opeaon. If he accs ae coec, hee wll be a oe accuae wa o deec he opcal flow feld of defoable a bod. The pape also shows soe esaed esuls of B-Scan conou-based opcal flow feld b applng he ehod of achng algoh of bounda cluse cenes. Ke Wads : Copue Vson ;Opcal Flow; Iages o Defoable f Bo CSCC99 Poceedngs, Pages: Inoducon The ao clncal applcaon of ulasound B- Scan n showng he ages of he hea s sac ages of ee fae wh e led dnac Dopple nfoaon.[] To gan oe dnac poan nfoaon decl fo sequence ages, we choose he opcal flow feld as he sang pon of ou eseach wok. Unl now, he eseach on opcal flow feld s bascall esced o he aea of gd bod. The wo faous eseaches of opcal flow equaon[] E V+E =, b Hon -Schunk and new opcal flow equaon[3] E V + E V+E = b Schunk ae no ecepons. We wll fnd ha he esuls ae based on gd bodes f we eseach he fuhe. The sud of eacng oon nfoaon fo sequence ages o f defoable bodes s a focus of dscusson n he aea of copue son oall, he nfoaon of oon s obaned fo deecng he wachng dffeence of ee Pel. [4][5] If ee Pel becoes he obec of ou sud, he aoun of calculaon noled wll be eendous. Fuheoe, The oelang (dsappeang and speadng (appeang of he pels of a defoable bod hae o be aken no accoun. Thus, he algohs ae no easl asnged. Accodngl, we hae chosen he ehod of achng algoh of bounda cluse cenes and we focus ou pape on he elucdaon of hs ehod whch ncludes he followng aspec: Oeall sucue of sofwae and hadwae Algoh of bounda cluse cenes Machng accs coon oon ec. We hae used he ehod o deec he opcal flow feld of soe sequence ages of ulasound B- Scan ages. These esuls coespond o he clncal analss. Ths fuhe poes ha he ehod s applcable n cean aeas.. Mehods. Oeall Sucue of he Sse Accodng o he aboe analss, he pupose of desgnng he sse s o eac opcal flow feld fo sequence ages. The sse us nclude he followng basc sucue of sofwae and hadwae: Saplng un of sequence ages The saplng of sequence ages s dgalzed and each age s eozed n an ndependen fle. Eacng conou of hea age Ths ncludes bounda enchanceen, bounda deecon n bna ages and educon.

2 Algoh of bounda cluse cenes Ths s o copue bounda cluse cenes b k-eans. Machng of Bounda Cluse cenes The obaned bounda cluse cenes of neal fae ages ae ached b he achng accs of coon oon and we ge opcal flow feld of neal fae ages. The aboe conen s he desgned basc sucue of he deecng sse, as s show n Fg. Snce he saplng sse of sequence ages [6][7] and eacng conou of hea ages [8] ae known o us all, we wll no epea. Insead, we wll onl focus on he algoh of bounda cluse and he Machng of Bounda Cluse Cenes n hs pape.. Algoh of bounda cluse A feaue pon of bounda cluse s epesenae of a goup of Pels whch s closel elaed. In ohe wods, we defne a goup of Pels as a feaue pon o an abuon. Thus, a egon of an age can be epesened b a goup of feaue pons,z,z,z 3 Z, Z, whch hae a posonal abuon. These feaue pons ae called he ke eleens of eco Z,.e. Z=[Z,Z,Z 3 Z Z ] T ( Thus, obanng he feaue pons (Z of bounda cluse becoes he ao wok. Recenl, hee ae an cluse algohs aalable, fo eaple, Isodaa, K-eans, au lkelhood ao and nu dsance classfcaon ec..[9] We choose he K-eans due o he fac ha ou obec s a ong and defoable bod and he fac ha boh ong and defong hae a posonal abuon. We use K-eans o cluse bounda pels. The cluse feaue pon s also known as bounda cluse cene. The algoh flow cha of K- eans bounda cluse n a fae s shown n Fg. Fg,Algoh flow-cha of K-eans bounda bluse As shown n Fg. If he new cluse cene Z (k+ of equaon (B oelaps he peousl obaned cluse cene Z (k, he new cluse cene Z (k+ wll sasf he followng equaon: J=n [ Z ( k ] ( G ( k J s a funcon nde [6]. The equaon shows ha he quadac su of he dsance fo ee pl o he cluse cene s nu n he eseachng aea G (k. To begn wh, we us choose soe oponal cluse pons. Bu fo accuae classfcaon and quck ascon of algoh, he selecon of begnnng cluse pons us show concen fo he geoe and defoaon shape of he age and nclude such pons as angle ops, quee pons and pons a defoable posons. I us also show concen fo he een dsbuon of cluse pons so ha he pons ae he equpaon of he bounda. The begnnng oponal pons of he ne fae can use he cluse cenes whch hae been cluseed n he las fae, because he neal e of adacen faes s lle, so he change n he shape of he bounda s hadl noceable. We use he algoh flow-cha o coplee he cluseng of he lef au of he hea n ulasound B-Scan age and he ap of bounda cluse cenes s shown n Fg3.

3 Fg3, The ap of bounda cluse cenes fo he lef au of he hea.3machng accs of coon oon The achng (followng of feaue pons depends on he achng accs o esc he possble oonal couse of he feaue pons and o oban he esaon of he opcal flow (speed feld. [] The bee he achng accs he less he possble oon aea of he feaue pons, and he oe lkel he possble oon couse wll appoach he ue couse, hus, he oe accuae esaon of he opcal flow. The acc of coon oon we pu fowad s one of he achng accs. [] We base ou eseach on he achng accs of coon oon on he obseaons and analses of he shape of he hea on oon and defoaon. We fnd ha, n a cean egon of he hea age, a goup of foces F hang he sae chaacescs acs on each feaue pon, he oon of whch s as follows: F V dd (3 As he goup of foces F has one o oe chaacescs n coon, he oon has soe coon feaues. Ths s he e coon oon of ee feaue pon n a cean egon of he hea age. The coon oon escs he possble oonal couse of he feaue pons and consues he achng accs of he coon oon. If we wan o ge accuae achng accs, we us eseach he phscal analss and he aheacal descpon of he coon oon fuhe. Machng acs of ed coon oon can be used o ge opcal flow feld fo cople oon case of hea sucue. In he followng, we choose he conscng saus of he sho-as secon age of LV whch has he anslang oon, and suppose ha feaue pon of he (kh fae wll pobabl oe o feaue pon of he (k+h fae and ha s an deal saus. Thus, he decoposng ap of he ed oon can be shown as n Fg4. In Fg4, we can fnd: (4 ( c ( In equaon(4, s he facual ong eco of feaue pon o feaue pon,.e. he oal su of oon; c s he oon deced o he cene of he ccle whle s he anslaonal oon,.e. ; ( ; ( c (5 Fs, Le us dscuss he sascal analss of he wo pas of he oeall oon. In an deal oon deced o he cene of he ccle, f he oal nube of he ccle bounda cluse cenes ae suffcen, hen he followng equaons (6,(7 wll be enable. ( c c c ( c.e. ( c c ( ( (6 (7 Equaons (6(7 also show ha he sascal esul of hs pa of he oeall coon oon equals zeo. Below s an analss on he anslaonal oon of he coon oon b sascal ehod, whch s shown as follows:.e. ( ( (8 3 Fg4, The decoposng ap of ed coon oon

4 ( ( ( ( (9 Accodng o equaons(4 (9, he sascal analss of he ed coon oon can be epessed as follows:.e. ( ( c ( c ( ( ( ( ( ( Equaon ( ells us ha he sascal esuls of he ed coon oon ae he sae as hose of he anslaonal oon. Accodngl, we can oban he sascal esuls of he anslaonal oon b eans of he oeall ed coon oon. The oon of ee feaue pon of he anslaonal oon s bascall he sae and s equal o. Thus, f we eese he anslaon of ee feaue pon ( on he (k+h fae, he ed coon oon becoes he coon oon on he (kh fae. Accodng o he aboe, afe obanng he of he ed coon oon, we can eese he anslaon of ee feaue pon on he (k+h fae back o he ccle of he (kh fae. If he achng pon of feaue pon on he (kh fae s he feaue pon n he ccle of he (kh fae, whch has been anslaed fo he feaue pon on he (k+h fae, hen he opcal flow feld wll be as follows: F ( c ( ( [( ( ] In equaon (, s he neal e beween he (kh fae and he (k+h fae. The opcal flow feld of he sho-as LV wh anslaonal oon whch we oban b usng he achng accs s shown as n Fg5. Fg5, An opcal flow feld of sho-as LV wh anslaonal oon 3, Resuls and applcaon. The aboe s a descpon and analss of ed coon oon n cobnaon wh he acual oon of he hea. We hae also descbed he aheacal and phscal analses of ed coon oon and foulaed he achng accs. Fg5 hae shown he opcal flow feld of LV of he hea. The esuls wll be helpful n eseachng how he hea s funconng. Le s ake a look a he clncal epeens of he sho-as LV seconal age. The esaed opcal flow feld of LV can fal accuael eflec he saus of LV. Fo eaple, Fg6 shows he opcal flow feld of feaue pons a each poson on he bounda of sho-as LV of a dseased peson suffeng fo fon wall ocadal nfacon. In Fg6, hee ae a ap of an opcal flow feld of a dseased peson suffeng fo ocadal nfacon and a daa able whch s a goup of daa copang he opcal flow of ee feaue pon. In he ap and he able, o. and o. ae he posons of he fon wall of LV. The oon on he as decon s nu n all he feaue pons and he hae shown obous oon obsucon. Ths esul s close o he clncal dagnoss. 4

5 4.Dscusson In hs pape we hae noduced he deecng of opcal flow feld of copue son no sequence seconal ages. In ulasound B-Scan of he hea, whch s a new feld n he eseach on defoable bod oon. We hae also found a new ehod Coon Moon Machng Algoh of Bounda Cluse wh whch we epeened on he deecon of clncal applcaon. o onl can he algoh be used n he feld of Ulasound B-Scan age of he hea, can also be appled n he ohe aeas of defoable bod ages whose bounda can be easl eaced.[] The foulaon of he achng accs s based on soe deal saus. If he acual saus deaes uch fo he deal saus, he esuls wll be less accuae. 5.Concluson The pupose of hs eseach s o oban oe laes nfoaon fo age equpen, especall he laes oon nfoaon. The eal e, hgh accuac and auhenc of new age equpen hae ade ou eseach possble. Refenence [] Chang Ln, Pncples of Medcal Eleconc Insuens and The Clncal Applcaons Publshng House of Eleconcs Indus of Chna, pp [] B.K.Hon, B.G.Schunck, Deenng Opcal Flow Afcal Inellgence, Vol.7, pp. 85 4, 98. [3] B.G.Schunch, Iage Flow Fundaenal and Fuue eseach, Poc. of CVPR 85, San Fancsco,CA. pp [4] T.S.Huang, Iage Sequence Pocessng and Dnac Scence Analss ATO ASI Sees F,Spnge-Velag 983 [5] R.Jan and H. H. agel, On he Analss of Accuulae Dffeence Pcue fo Iage Sequences of Real Wold Scence IEEE Tans., PAM (, pp. 6 4,979 [6] Chang Ln, A Deecng Mehod Conou- Based Opcal Flow Feld of Hea n Ulasound B- Scan Iages Aca Eleconca Snca, Vol. 4, pp [7] Chang Ln, The Deelopen of a Deecng Sse of Conou-Based Opcal Flow Feld fo Defoable Bod age Jounal of Eleconc Measueen and Insuen, Vol., pp [8] Vka Chalana, Dad T. Lnke, Dad R. Hano and Yongn K, A Mulple Ace Conou Model fo Cadac Bounda Deecon on Echocadogaphc Sequences IEEE Tans. On edcal Iagng, Vol. 5, pp [9] R. M. Endlch, D. E. Wolf, D. J. Hall and A. E. Ban, Use of a Paen Recognon Technque fo Deenng Cloud Moons fo Sequences of Saelle Phoogaphs Jounal of Appled Meeoolog, Vol., pp [] D. H. Ballad, C. M. Bown, Copue Vson Pence Hall ew Jes, pp [] Chang Ln and Tan Gulan, A Inesgaon on he Machng Taccs of Coon Moon n Deecng Flow b Cluseed Algoh Aca Eleconca Snca, Vol. 5 pp [] Robe L. Lbbe, Sgnal and Iage Pocessng Soucebook ITP. Pp , 99 5 Fg6, Opcal flow feld of dseased peson of ocadal nfacon