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1967,1970’s

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1981,1984

Shape Representation

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Computer VisionComputer Graphics

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Medical Imaging

1991,1992deformable

superquadrics

DynamicsLagrangian

Physics

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1995,1996

elasticallydeformable

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1987,1988

variational models1983,1986

Heart Modeling

1994

with parameter functionsdeformable models

1989

(Terzopoulos)

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h7:

make model () % assemble meshes

compute net applied force and torque ()compute translation and rotation ()

while (!done)

clear forces ()compute forces from datapoints ()

compute model () % compute node position

compute deformation ()

compute model ()

display model ()

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C ¨

c

parametervalue

time 1 (ED)

time 2

time 3

time 5 (ES)

time 4

apex baseu

u

Sf85,2 i~" 62:,2K,1:M&?9?>"K'&?,M&?;H:1:,L8,M&?K$'C

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5879 - *@$ 5 /

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4 .+-S 8 .+-S .+-S 7 .+-S 35.+-S J

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K'&?,M&?;H:1:,MCG 6@ N yU#&?'3E 6@ N UM ,2CKg(A.S,2; 2$C^§8,&?K$'C: !#@:&?95'&?6`>G.H2$@C$'&?K'd&Y'3H;HDH?>v1$Fb?ck365,8EMC#C.4C^2?A

S,L['&?;HK6A g*0.9C25'36.D8%1$d8,M&YK$'C#?> N Un&?'3E N yUJNPSf80C: ¨ NP& *yU1UM ?!#s:&?_'1A5'362$'&?d1$%;%&Y8625'36%Y>JD02,&=X2$+,M&3DI&)AL3D],1NG Z&)A8=2$EHl@&?'3 IDl&)[CU365,8sC.C2?ATICZ&?KK,2)[6];+&?2A. © :0+ © $% W$6AL1$n8D,M&?K$E?> =#C$?!§Cf56>G,2;D02,&&)A8@2$TA8d&)[6BC"Y>'2$Lb?cs ?1$n8D,M&?K$E?> = nC^$j!aCyAC2CT01,M&q2?!w&Y,M3Cy2$#*'&C#?>y2$b?c;%& D]8q2$L*'&C^#A0 <;H,2#AÀ`]K^B:&jA a#$6ICZ,2C^56A]LC5KKg,2MCT1A`]6I:&)AvC15'36.d\''3D80Cw!L$:,2;H,2HC2,1C2CaIC@[:,223/&?@2$+&?K'[365,8=2$%b?c ;HV "&?'3t&)AICr2$:,2EICE&?=',2&C^3CW;EÀB&Y,P.r?>z2$Eb?c *'&CEC$'&?K'E2+&?_AÀ`K'C v365,8_C.C2YA] Wtd;<&C5,2>|,2D; 2$d8D,M&?K$C$?!Lr]XSf8' ¨ NP)UM g2$'&?@1$H2M&jAn3DBC^K6AB&D:;H:0H&)A8r2$CJ?l&j[0IC: "!L$6I1$,2,2C^K''3Cq201,M& &)A8X2$ J?l&)[6BC LICr&?KK,2)[0;%&Y2A. i?< = a!L$:,2 2$rA]:8D2$ ?>E2$b?cBC&?KK,2)[0;%&Y2A. C $ =z#$:,1>|,1 '2$dD02,& &jA]D8H2$ JYl&)[0IC 0?!L_&DC#A8?25'3D'&)A01,M& IC9&?KK,2)[6];+&?2A. ©?¨ >G,%1$6BCrb?cELS,2; 1$ 8D,M&?K$ Sf8' ¨ N3gUM L!#t:&?5'&?6`>G._2$E!#IC8_;<=?>n1$ bYc 365,8tC.C2?AE29&?KK,2)[0;%&Y2A.¥i<%36:8,1:C:H#$8,M&?K$HC$?!§C"2$'&Yv2$:,1#ICz&@C;%&jAAx&Y;H56v?>y!#IC8@H&?,Â].HC.C2YA]#!#2$<8,M&365'&)A6',2&CC2?!w&Y,M3C@:'36lC.C2YA]XSf'&)AÀ. T>|,1; 2$+A8&)[6ICH36>|D,2;%&?/K'&?,M&Y;H:2:,MC<N,H&)[6ICEXvC:K'&?,M&?;H:1:,MCUFC^$j!JtSf80C ¨ N:l>U V!#9*'C:,2(D%2$'&Ys1$:,2_&?,2+6A.¥CPA8$6%36>G,2;%&Y'C&?'3 ;H0CHY>s2$=36>|,1;%&? &?KKg&?,MC<2?!w&Y,M3CqMC9&?Kg[ &?'3 *'&C a:&?K25,8 & *':'3D8

CC

a1_normal

1.00

time1time2time3time4time5

a1(t)/a1(ED)

u

0.60

0.80

1.20

apex base

a2_normal

1.00


a2(t)/a2(ED)

u

0.60

0.80

1.20

apex base

a3_normal

0.00


mm

u-30.00

-20.00

-10.00

10.00

apex base 4 8

twist_normal

0.00


degree

u-20.00

-10.00

10.00

apex base

offx_normal

0.00


mm

u-20.00

-10.00

10.00

20.00

apex base

offy_normal

0.00


mm

u-20.00

-10.00

10.00

20.00

apex base 7 3

Sf85,1 ¨ ~"[2,M&D23+;H36AvK'&?,M&?;<:2:,MC#&CT>G5''CJ?> >|D,L2$@,2;+&)AV$&?,2

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4 .+-S 8 .+-S .+-S 7 .+-S 35.+-S J

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Wtt&?KK6A`]3 5,%12$6ID5 1¥&?D2$:,%D,2;%&)AFbYc 2(D:,`>|.X2$=,2C^56A]9&?'3 !#9>G5'32$'&?L2$q[41,M&23+K'&?,&?;H:2:,#>G5''CJ!#:,2d(:,1.CW;EÀI&?,@2<2$0CEC$?!L+oSf8' ¨ ##$j(D:,M&)AÀ D02,&=!L&C@&?KK,2)[6];+&?2A. © $ %sbx DHt2$E1$:,@,2;%&)AnbYcs y2$:,1H!L&C#AC2C01,M&XN36\'3/*0.M= U&jA]D8 1$CIl&j[0ICE2?!L&?,M3Ca1$%*'&C^H?>§2$9b?c D;HK'&?,23 !#2$2$%62,M&^]Dt2?!L&?,M3Ca2$%&YK'[Vw$CD'3t,1;%&)Az$&?,2q!L&C#0?!L 2_$'&)(H8D,2&?2:,P!wBC^8;HD 365,8 C.C2?Ak5,2K,ICW8?A. a!#9>G5'3X1$'&?%1$ b?c 5'36:,2!#:6%8D,2&?2:,8?A*'&)A0,2DM&?'&)A;HDa6]^B&jAA. *g>|D,2Z!#IC8'ZSf8' NP&6U'C$?!§Cy2$Z!#IC^]8aK'&?,M&Y;H:2:,MC&?L2$q:'36lC.4C^2?Aq>|,J*'2$=,1;%&)Aeb?c@C:L#$q!#IC8&Y8?A 365,^]8_C^.4C1?Ad!L&CLD5'&?6`\'32E*'s&YKK,2)[0;%&?1A]. © :s36:8D,2:C:' ( 5879 - *@$ 5 /

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C

a1_abnormal

1.00


a1(t)/a1(ED)

u

0.60

0.80

1.20

apex base

a2_abnormal

1.00


a2(t)/a2(ED)

u

0.60

0.80

1.20

apex base

a3_abnormal

0.00


mm

u-30.00

-20.00

-10.00

10.00

apex base 4 8

twist_abnormal

0.00


degree

u-20.00

-10.00

10.00

apex base

offx_abnormal

0.00


mm

u-20.00

-10.00

10.00

20.00

apex base

offy_abnormal

0.00


mm

u-20.00

-10.00

10.00

20.00

apex base 7 3

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a1_normal

1.00

V1V2

a1(ES)/a1(ED)

u0.60

0.70

0.80

0.90

1.10

1.20

apex base

a1_abnormal

1.00

P1P2

a1(ES)/a1(ED)

u0.60

0.70

0.80

0.90

1.10

1.20

apex baseNP&4U KJ,2;+&)AV$&?,2MC N*yU L *D,2;%&)Av$&Y,2MCSf]8D5,2 %<~e[42,&23+b?c K'&?,M&?;<:2:,A N Un&?#:'36lC.C2?A<N;EI36lG!L&)A`A|U

twist_normal

0.00

V1V2

degree

u-20.00

-10.00

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i

acquire MRI-SPAMM images

convert 2D data in image spaceinto 3D data in Cartesian space

input 3D coordinates of4 corners for image planes

N=total number of time phase

input boundary data at t=0

input SPAMM data at t=0

register SPAMM data

recover initial shape

save model parameters at t=T

extract SPAMM and boundary data from images

start

T=1

T=T+1

end

T< N

b31

no

yes

visualize and analyze motion

input boundary data at t=T

input SPAMM data at t=T

estimate rigid motion

estimate non-rigid motion

B1

B2

B3

B4

B5

b42

b41

b32

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apex base

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percentage

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percentage

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percentage

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percentage

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percentage

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percentage

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percentage

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percentage

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10.00

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percentage

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Logitudinal Contraction (average over along the long-axis)

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0

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IN MID OUT

across wall (w)

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INMIDOUT

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along long-axis (u)

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Twist (average over along the long-axis)

-4

-3

-2

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0

1

2

3

v1 v2 v3 v4 v5 v6 v7 v8 v9 v10

v11

v12

circumferential locations (v)

degr

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INMIDOUT

Twist (average over across the wall)

-3

-2

-1

0

1

2

3

v1 v2 v3 v4 v5 v6 v7 v8 v9 v10

v11

v12

circumferential location (v)

degr

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sherknie/articles/leftventricleofa... · 2001-05-18 · jnm xp_7 i_cd 5] =:] d o / h > * mtexmtd...

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