Image Modeling & Segmentation

Transcription

1 Img Moling & Sgmnion Aly Frg n Am Ali Lur #7

2 MGRF- Img Anlyi Fiing MRF mol o n img rquir h h prmr o h mol im rom mpl o h img Th lirur i rih wih work h propo irn MGRF mol whih r uil or pii ym hvior. Uully, h work iniy hir mol prmr uing n opimizion hniqu. Thi hniqu ri o mximiz ihr h liklihoo or h nropy o h propo proiliy iriuion. Mximum Liklihoo Eimion (MLE) For h Gi proiliy iriuion (GPD): Th log-liklihoo union i in y Th mximum log-liklihoo imor i in y

3 MGRF- Img Anlyi Coing Mho (Bg 74): Mximiz h log-liklihoo in oing j Color o pixl long o h m oing r oniionlly inpnn L Squr Error mho (LSQR) (Drin n Ellio PAMI 87) ` ` ` ` ` l 2 ` ` ` ` ` ` ` ` l 1 ` ` ` Th rio i im y ouning h numr o lok o yp1n iviing y h numr o lok o yp 2. olving ovrrmin ym o linr quion uing h mo rqunly ourring lok yp Drin, H. n Ellio, H. (1987). ``Moling n gmnion o noiy n xur img uing Gi rnom il''. IEEE Trnion on Prn Anlyi n Mhin Inllign, 9(1):

4 Anioropi Po Mol MGRF- Img Anlyi Dirn Typ o h ponil union Anlyil Eimion (Frg l) or Po Mol Approxim h log liklihoo i oin y runing h Tylor ri xpnion

5 Rrn Mrkov-Gi Rnom Fil in Img Anlyi n Synhi: A Rviw Thnil Rpor y Am Ali Gi Rnom Fil: Tmprur n Prmr Anlyi, Thnil Rpor y Rolin W. Pir, MIT Mi L. Mrkov/Gi moling: Txur n Tmprur, Thnil Rpor y Rolin W. Pir, MIT Mi L. Rnom il mol in img nlyi Journl o Appli ii, y Du n Jin Mrkov Rnom Fil n Img, y Prik Prz CWI Qurrly (NOTE: you on n o r h whol ppr in h, pik n hoo h rl ion)

6 Pu All Toghr 6

7 Img Moling Inniy Spil Inrion Img Lling Img Shp /11/2 Ph.D. Dn 7

8 Lling Prolm In lling Prolm w hv o i P n o ll P : rprn img ur {.g. pixl, g, img gmn,.}. Fur my hv om nurl ruur pixl r rrng in 2D rry. L : rprn innii, iprii,. Lling prolm i mpping P L. W no h lling y P = 1; 2; : : : ; ng L = l 1 ; l 2 ; : : : ; l k g = 1 ; 2 ; : : : ; n g L S o ll lling Ln i no y F Simpl Exmpl: P = 1; 2; 3; 4g L = 5; ; 15g = ; 5; 5; 15g = 5; 5; 5; 15g = ; 5; ; 15g Th o ll lling F = L 4 oni o 3 4 = 81 lling 8

9 Lling prolm onp giv ommon noion or ivr viion prolm, uh : P = 1; 2; : : : ; R Cg Img Sgmnion L = ; 255g inpu oupu Img Rorion P = 1; 2; : : : ; R Cg L = (; ; ); : : : ; (255; 255; 255)g inpu oupu 9

10 Lling prolm onp giv ommon noion or ivr viion prolm, uh : Sro Mhing x (x, y) (x +, y) y L img Righ img P = 1; 2; : : : ; R Cg L = min : mx g Dipriy rng Dph/ipriy mp /11/2 Ph.D. Dn

11 Lling prolm onp giv ommon noion or ivr viion prolm, uh : Img Mhing Shkhovov, l CVPR 7 (x, y) (x +δx, y + δy) P = 1; 2; : : : ; R Cg inpu L = (±x min ; ±y min ) : (±x mx ; ±y mx )g δ δ δ δ Diplmn rng Oupu Digil Tpry (Rohr l CVPR 5) inpu P = 1; 2; : : : ; n Blok g oupu L = I S /11/2 Ph.D. Dn 11

12 Img Sgmnion I Th inpu img n h ir gmn img r ri y join Mrkov-Gi rnom il (MGRF) MGRF mol i i wihin h Byin rmwork o Mximum-A-Poriori (MAP) imion o im = rg mx P (I j)p (): 2F In h pirwi inrion mol, Gi nrgy i in in rm o liqu o iz 2. Th img i rprn y MGRF wih join iriuion: P () = Z 1 xp( X p ; qg2n V ( p ; q )) (A) Th iriuion i MRF y uming h noi h pixl i inpnn (Du n Jin 89) P (I j ) P (I j ) = Y p2p P (I p j p ) (B)

13 Img Sgmnion Mximum-A-Poriori (MAP) Eimion From (A) & (B) h MAP imor = rg mx 2F xp(x p2p log(p (I p j p )) X p ; qg2n V ( p ; q )): Equivln o minimiz h nrgy E() = X p ; qg2n V ( p ; q ) X p2p log(p (I p j p )): Fir rm xpr moohing onrin on lling. Ll vri moohly vrywhr xp h oj ounri ioninuiy. Son rm mur how muh igning ll wih h orvion I p p o pixl p igr

14 Prolm Solvr Morn nrgy minimizion mho uh : Grph u (Zih PAMI 1) Bli Propgion (BP) (Flznzwl CVPR 4) Tr-RWigh mg ping (TRW) (Winwrigh Ino Thory 5) Exn Roo uliy (Kolmogorov CVPR 7) Clil mho uh : Ir Coniionl Mo (ICM) (Bg 74) Simul Annling (Gmn & Gmn 84)

15 ICM: (Szliki, ECCV6) F hniqu Vry niiv o h iniil lling Lol nrgy opimizion hniqu SA: (Szliki, ECCV6) Fin h glol oluion wih rin mprur hul Th hul h l o h glol r vry low in pri. BP: (Szliki, ECCV6) I giv x minimizion i h grph o h nrgy i r, I ivrg in h o grph h hv loop I giv oluion wih highr nrgy hn grph u TRW-S: (Kolmogorov CVPR 7) Similr o h BP lgorihm. Gurn h onvrgn; h lowr oun im i no o r Sm prormn o h roo uliy, u i i muh lowr. Grph Cu: (Szliki, ECCV6) Ouprorm h ohr ompiiv mho (ury n im iiny). Appli o umoulr union. Roo uliy: (Kolmogorov CVPR 7) A gnrlizion o h nr grph u lgorihm. For umoulr union, m prormn (ury n im). non-umoulr union, roo uliy prou pr o n opiml oluion. /11/2 Ph.D. Dn Prolm Solvr Conluion

16 Img Sgmnion Mximum-A-Poriori (MAP) Eimion Iriv rrh o MAP im ohi (.g., imul nnling) or rminii (.g., ir oniionl mo) Simul Annling (Gmn & Gmn 84) Simul pro in mllurgy whih rmin h low nrgy o mril y grully lowring h nrgy Fin MAP imor or ll pixl imulnouly Fin h glol oluion wih rin mprur hul Compuionlly xpniv; h hul h l o h glol r vry low in pri.

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18 Ir Coniionl Mo (ICM) (Bg 74) Pixl r pro qunilly, n or h pixl h lgorihm l h ll h mximiz P (I P j p )P ( p j ^ Np ) Fr hn imul Annling Vry niiv o h iniil lling Lol nrgy opimizion hniqu

19 Exmpl On row img Orv img Piwi Conn Prior Po mol V ( p ; q ) = ½ 5 i p 6= q ; i p = q D pnly rm P (I p j p ) / xp( ji p p j)

20 E() = Exmpl X 5 ( p 6= q ) + X δ p2p p ; qg2n j I p pj : B lling Thrhol lling E = = 48 E = = 59

21 Grph Cu Grph Cu Bi Diniion & Noion Thwigh grph G = hv; Ei V i h o vri in grph orrpon o pixl. ; g E (ink & our) r wo iinguih vri ll rminl. (p; q) u o pir o lmn rom Eg V A ph i qun o g. N-link: onn pir o nighoring vri. Co/wigh: pnly or ioninuii wn vri T-link: onn vrx wih rminl. Co/wigh : pnly or igning h orrponing ll o h vrx 21

22 Min-Cu & Mx-Flow Grph Cu A u grph C ½ E i o g uh h rminl r pr in h inu G(C) = hv; E Ci No propr u o C pr h rminl in G(C) C Co o h u, no, h um o i g wigh jcj Min-u i o in h u wih minimum o mong ll u. Min-Cu n olv y ompuing Mx-Flow wn rminl For& Fulkron 62 g h i g h i Cu g h i g h i g h i g No Cu h i 22

23 Grph Cu Min-Cu =Min Cpiy= Mx-Flow 2 5 Cu Co = Cu Co = Cu Co =3

24 Grph Cu Min-Cu & Mx-Flow Exmpl Mx low = Th Grph Nw Grph Mx low = Nw Grph Mx Flow= Nw Grph Mx Flow= Nw Grph Min Cu= - Min-Cu/Mx-Flow lgorihm o Boykov & Kolmogorov 4

25 Grph Cu Grph u minimizion hniqu E() = X p;q g2n V ( p ; q ) X p 2P log(p (I p j p )): Evry pixl rprn vrx in h grph. N-link (p; q) wigh V ( p j q ) T-link (; p); (; p) wigh log P (I p j p ) Compu - MinCu

26 Grph Cu Grph u minimizion hniqu (Exmpl) Mx-Flow =

27 Grph Cu Grph u minimizion hniqu (Exmpl) Mx-Flow =

28 Summry Inpu I CT lung li 1. Compu h mpiril niy o CT li P(I p Lung ) P(I p Bkgroun ) 2. Uing EM i N Guin o im h niy Eim h mrginl niy o h l Finl oupu Fi MGRF on h img y ling Ingr E( ) Minimiz 1. Nighorhoo ym 2. Cliqu orr 3. Ponil union 4. Compu ponil prmr rom iniil Iniil oupu

29 Thnk You 29

30 1 Mirm Exm Wny OCT 13 -WHERE..? In l -HOW LONG..? On Hour -TOPICS..? Lur#1 #7 - MATERIALS..? Clo Book, BUT wri wh you wn in ingl i h 3