......4.... 4.... 4.....4.....6..3...6.3... 7.3....7.3....8.3.3...8... 3.... 3..... 3..... 3..3... 3..4...3 3..5...5 3....7...9...7 8 9
[8]. X [9] Hohe VoxelMa CTMRI
VoxelMa Voxel Ma VoxelMa [7] Maya Clc 7 CT MRI 3D. MRI 3D CT
3
.... m {(, )} =, φ = spa ϕ, ϕ,..., ϕ } x y * * P ( x) = a ϕ ( x) ( < m) = { m * [ P ( x ) f ( x )] = m w( x )[ P( x ) f ( x ] m = w( x ) ) = = δ () f f : R R ) y = f x m ( 4
w(x) [a,b] ( x y ) w x ), ( P * ( x) m I( a,... a ) = w( x )[ a jϕ j ( x ) f ( x )] = j= * * ( a,..., a ) I a m m = w( x )[ a ϕ ( x ) f ( x )] ϕ ( x ) = =,,..., 3 = j= j j m ( ϕ, ϕ ) = w( x ) ϕ ( x ) ϕ ( x ) j = m ( f, ϕ ) = w( x ) f ( x ) ϕ ( x ) = j j= ( ϕ, ϕ ) a = ( f, ϕ ) j j =,,... 4 G = ( ϕ, ϕ ) ( ϕ, ϕ )... ( ϕ, ϕ ) ( ϕ, ϕ ) ( ϕ, ϕ )... ( ϕ, ϕ )............ ( ϕ, ϕ ) ( ϕ, ϕ )... ( ϕ, ϕ ) } = { ϕ G 4 a = j =,,... * j a j * * P ( x) = a ϕ ( x) = 5
.. l m m {(( xj ) =, y j )} j= { w } = l φ = spa ϕ, ϕ,... ϕ } ( < m +) { l * * P ( x, x,... x ) = a ϕ ( x, x I( a =,..., x ) m *, a,..., a ) = w [ P ( x, x,... xl ) y ] = = m w [ a ϕ ( x = = *, x l,..., x l ) y ] { 4 a} = m ( ϕ, ϕ j ) = wϕ ( x, x,..., xl ) ϕ j ( x, x,..., xl ), = m ( f, ϕ j ) = w yϕ j ( x, x,..., xl ), =, j =,,..., j =,,..., 4 { l a} = * * P ( x, x,..., x ) = a ϕ ( x, x,..., xl ) =..3 6
{( y, z )} x, = φ = spa{, x, y, x, y } ( > 3) z = f + ( x, y) = a + ax + a y + a3x a4 y 4 { a } =.3.3. r. {, P,... P } P. P m P P P... P ds( Pj P ) ds( Pj P )... ds( Pj ) j j j m P m P 7
P m P P....3..3.3 t, P N 8
P L { } = L P } = P L 3 { 4 e >t e > L N, L = L 3 a P L { P } = L { P } = e false true t false L > N true L = L b. 9
3. 3.. 3 { O; xyz} E x = x( u, v) y = y( u, v) z = z( u, v) u, v ( u, v) R D 3 D E ( u, v) ( x( u, v), y( u, v), z( u, v)) 3 D E S 3. 3. ( u,v) S S r = r( u, v) = ( x( u, v), y( u, v), z( u, v)) P S, ) v = v ( u v u S P
r = r( u, v ) P u u u = u P v v r = r( u, v) S u v S P r u u= u v= v r v u= u v= v r u = u u v= v r v u= u v= v r u= u r u= u P S u v= v v v= v S P( u, v) r u r v 3. S C u = u( t) v = v( t) a t b t = u = u t ), v = v( ) t P u, ) t ( t C C P r = r( u( t), v( t)) ( v
dr dt r du r dv r du r dv = 3 ( + ) t= t = ( ) ( ) t= t + t= t u u u u t t u dt v dt u = dt v = = dt v= v v= v P r r P ω = αr u βr α, β u= u + v= v v u= u v= v P ω S P u = u v = v S + α( t t ) + β ( t t ) r = r( u + α ( t t ), v + β ( t t )) P dr dt r r = α + β = ω u u= u v u= u t= t v= v v= v P S P T T S u v P P P r u= u u v= v r T v u= u v= v P 3 P S E a, b a b a,b a,b a, b=a b T a b P T P 3..3 3 E P T P
r u r v r r r ± u r v u v r = r( u, v) r r r 3. u r v u v 3. S = r r u u v r r v 3..4 r(u P ( u, v) P '( u + u, v + v) S r( u, v) + u,v + v) PP' = r = r( u + u, v + v) r( u, v) = r u + r v +... u u, v r dr = r du u + r dv v v 3
' P P u, v PP' E 3 ds S ds ds = dr = dr dr = ( ru du + rv dv) ( ru du + rv dv) = ru ru ( du) + ru rv dudv + rv rv ( dv ) E = r u r u F r u rv = G = r v rv E, F, G ds = Edu + Fdudv + Gdv E, F, G Ι P P' ( u + u, v + v) P T δ 3.3 P ( r 3.3 PP' = r = r( u + u, v + v) r( u, v) = r u + r v + u v uu ( u) + r uv u v + r vv ( v) ) +... u, v δ = PP ' = ( ruu ( u) + ruv u v + rvv ( v) ) +... (4) 4
L = r, M = r N = r uu uv δ = L( u) + M u v + N v +... δ > ' P u, v P T δ < ' P P vv δ C = Ldu + + L M N Mdudv Ndv 3..5 Ldu + Mdudv + Ndv = C 5 Gdv Ι = Edu + Fdudv + 4 C 5 P 5 ( E L) du + ( F M ) dudv + ( du dv = µ 6 dv ( G N) dv = 6 E L) µ + ( F M ) + ( G N) = 7 µ 5
µ 7 µ d ( E L) µ + ( F M ) + ( Eµ + Fµ + G) = 8 dµ d = 8 dµ 7 ( E L) µ + F M = 9 µ [( E L) µ + F M ] + [( F M ) + G N] = µ 9 ( F M ) µ + G N = 9 µ E L F M F M G N = () ( EG F ) ( EN FM + GL) + ( LN M ) = () Edu + Fdv Ldu + Mdv Fdu + Gdv Mdu + Ndv = ( EM FL) du w = µ r u + ηr v + ( EN GL) dudv + ( FN GM ) dv = φ = µ φ η ( LF EM ) φ + ( LG EN) φ + ( MG FN) = 6
3 K = H = ( + ), K H = = LN EG M F EN FM + GL ( EG F ) 3. z = f ( x, y) p ( x, y) = ( x, y, z) = ( x, y, f ( x, y)) f ( x, y) u = x f ( x, y) v = y p x = (,, u) p y = (,, v) p xx u u v v = (,, ) p xy = (,, ) = (,, ) p yy = (,, ) x y x y 7
= ( u, v, ) + u + v E = + u F = u v G = + v u L = x M + u + v u v = y = x, + u + v + u + v N = + v y + u v z = f = + + + + ( x, y) a ax a y a3x a4 y p ( x, y) = ( x, y, f ( x, y)) p x =,, a + a ), p y =,, a + a ) ( 3x ( 4 y p xx =,,a ), p = (,,), p yy =,,a ) ( 3 xy ( 4 = ( a + ( a + a x, a 3 + a 3 x) + a + ( a 4 y, ) + a 4 y) E, F, G, L, M, N 8
FastSca Vrual C++6. OpeGLMatlab FastSca 887 4. 4. 4.3 4.4 4. 4. 4.3 4.4 4.5 4.6 3. 5. 4.7 3.., 4.6, λ,λ g m e t r 9
4. 9 6 4 7.8 9 4. 4 4 4.3 4.4. r t e 9. 37 5. 4.87 9. 36 4..7899 3 9. 35..8386 4 9. 3. 9.75 5 9. 8 9. 7.89
6 9. 4 7. 5.53839 7 9. 9 4. 3.8654 8 4. 7 3..456 9 4. 4..437 4...8776 4. 8..65594 4. z = a + a x + a y + a x + a 3 4 y a a a a3 a4 69.88-5.858 -.6.4944 -.969 558.5-3.59 -.7688.777.383 3 585.58-4.69 -.89.48.3744 4 58.83-3.9745 -.99974.36574 -.5848 5 6.34-5.38 -.556.494 -.79 6 635.46-6.3484 -.7537.636 -.96 7 86.658-35.733 -.94.3654 -.54396 8 77.75-9.8546 -.433869.99 -.5393 9 646.8 6.9696 -.587.6768 -.69896 876.43-78.34 -.87.86788 -.7985 73.5-7.54 -.699.73987 -.3497 4.. r t e. 4. 9.9983. 37 9. 8.89854 3. 35 8. 7.794 4. 9 7. 6.668 5. 3 6. 5.937 6. 7 5. 4.99983 7. 4. 3.8888 8. 99 3..946 9. 9..9387. 9..9387. 7..958366. 64.8.7448
3. 39..9557 4. 35..965576 4.3 z = a + a x + a y + a x + a 3 4 y a a a a3 a4 5.4 -.4467 -.89735 -.9589 -.595393 4.8846 -.453934 -.58 -.849 -.8475 3 4.47 -.46653 -.38 -.57 -.335 4 4.668 -.46686 -.4 -.389 -.3573 5 4.9 -.463539 -.9963 -.49 -.789837 6 4.5596 -.473337 -.775 -.634 -.937 7 4.665 -.47764 -.986 -.7745 -.959636 8 5. -.4644 -.9 -.374 -.77448 9 4.4 -.479599 -.8996 -.8733 -.33655 4.4 -.479599 -.8996 -.8733 -.33655 4.7 -.483539 -.9849 -.3 -.399 5.95 -.47 -.9897 -.755 -.766 3 6.79 -.438869 -.97943 -.57.53455 4 5.5874 -.569 -.44 -.3736.3499 4.4 3. r = 4. t = 3. e =.456 = 7 =.349 =.7945 g = m =.8977 4.
λ = (.4568,.99837,.36937), λ = (.54,.445,.8575) z = 77.75 9.8546x.433869y.99x.5393y + r = 4. t =. e =.437 = 4 =.85374 =.79936 g = m =.39968 4. λ = (.5888,.963658,.96), λ = (.499953,.53,.86596) z = 646.8 6.9696x.587y.6768x.69896y + r = 4. t =. e =.8776 = =.657 =.665 g = m =.835 4.3 3 3
λ = (.335478,.996,.6), λ = (.46399,.55989,.9979) z = 876.43 78.34x.87y.86788x.7985y + 4.4 4 r =. t =. e =.9557 = 39 =.3999 =.39784 g = m =.6489 λ = (.996833,.6765,.79553), λ = (.435,.9984,.4667) z = + 6.79.438869x.97943y.57x.53455y 4.5 5 r =. t =. e =.965576 = 35 =.394573 =.3988 g = m =.95544 λ = (.9966,.8575,.858), λ = (.74,.9993,.4446) z = + 5.5874.569x.44y.3736x.3499y 4
4.6 r = 3., t = 3. 5
4.7 r = 3., t =. 6
7
[] Hogb ZhaStudes O 3-D Feature Measuremet Ad Object Recogto Based O Surface Characterzato. PhD Thess,Kyushu Uversty,99 []. 979 [3]. 989 [4]. 985 [5]. 996 [6]. 989 [7] Dael Sord ad Samuel K. Moore,The Vrtual Surgeo.IEEE Spectrum, pp.6-3, [8] Steve Seger,Vsualzg Ad Segmetg Large Volumetrc Data Sets. IEEE Computer Graphcs ad Applcatos,pp.3-37,999 [9],. 999 8
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