Journal of Beijing University of Aeronautics and A stronautics. R eg istra tio n m e tho d ba sed o n IC P a lgo rithm fo r 3D surg ica l naviga tio n

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1 Journal of Bejng Unversty of Aeronautcs and A stronautcs Ap rl 2009 Vol. 35 o14 ICP (, ) (, ) : CT, ( ICP, Iteratve Closest Pont).. CT ; ; ( PCA, Prncpal Component Analyss) ;, k2d tree.,. 1mm. : ; ; ; ; : TP : A : (2009) R eg stra to n m e tho d ba sed o n IC P a lgo rthm fo r 3D surg ca l navga to n W ang Junchen W ang Tanm ao Xu Yuan ( School ofmechancal Engneerng and Automaton, Bejng Unversty of Aeronautcs and A stronautcs, Bejng , Chna) Fang L m ng ( The 2nd Hosptal of Bejng General Forces of A rmed Polce, Bejng , Chna) Ab s tra c t: Regstraton between medcal m ages and physcal space s an mportant p rocedure n 3D surg2 cal navgaton system s. A regstraton method based on ICP ( teratve closest pont) algorthm was p resented. Two pont sets, one of whch s acqured from physcal space by the op tcal localzer and the other s from a 3D model reconstructed by the marchng cube method, were used to calculate the transformaton matrx between p reoperatve CT m age space and ntraoperatve fducal m arker space. The regstraton p rocedure was dvded nto the follow ng two phases. PCA ( p rncpal component analyss) was used to calculate the egenvectors of the two pont sets respectvely to acheve ntal regstraton. ICP method was used to make the ntal transfor2 maton m atrx to converge nto the best soluton, n whch the k2d tree structure was used to accelerate the p ro2 cedure. A sp ne model experment was carred out and a vrtual 3D measurement envronment was set up to e2 valuate the accuracy of the regstraton m ethod. Error analyss was conducted by addng Gaussan nose to the pont sets. The result show s that under ths condton the fnal average regstraton accuracy s less than 1mm. Ke y wo rd s: mage regstraton; ICP ( teratve closest pont) ; surgcal navgaton; 3D reconstructon; contour extracton : : ( ) ; ( 2006BA I03A16) ; (D ) ; (BUAA ) : ( ),,,, wangjunchen@gmal. com.

2 4 : ICP, [ 1-2 ].,,. X,MR I, CT, PET., CT ( )MR I,,.,.,,., [ 3 ],,,. : ; ; 2..,,.,,,. ( ICP, Iteratve Closest Pont),. 1 : S V (, ), S V, T, S V p s p v : p s = T ( p v ). : 1) S V, F s F v, p s p vj F s F v. 2) : f = m n D ( p s, T ( p vj ) ) (1) j D. 3) T. 3.,., CT/MR I (marker ), S V, T V S, ,,. 2 ICP ICP 1992, Besl Mckay, [ 4 ]. P Q, ( 3 ), p q (3 1 ), 3 3 R s, R s: m n p k - (R q k + s) 2 2 (2) k =1, ( SVD, Sngular Value Decomposton) R s. : 1) P Q p 0 = 1 p q 0 = 1 q 2) P Q PQ = 1 ( q - q 0 ) ( p - p 0 ) T = 1 q p T - q 0 p T 0 3) PQ 4 4 ( PQ ) = tr( PQ ) PQ T + T PQ - tr ( PQ ) I 3, tr( PQ ) PQ ; I ; 435 = ( a 23, a 31, a 12 ) T a j = ( PQ - T PQ ) j 4) ( PQ ). q = (w, x, y, z), :

3 R ( q) = s = p 0 - R ( q) q 0 R s 4 4 T. P Q., ICP.. 1),,,. P Q, ( PCA, Prncpal Component Analyss) P Q 3,, 4, T 0. 2) k, P Q P Q, ( = ). k: = 0, Q 0 =Q, T 0 = T 0, Q 0 q 0, = 1, 2,, Q, k2d tree [ 5 ] P q 0 : D 0 ( ) = p j s. t. m n 1 j P q 0 Q k + 1 r 0 = 1 Q r k +1 = 1 Q Q q 0 w 2 + x 2 - y 2 - z 2 z ( xy - w z) 2 ( xz + w y) 2 ( xy + w z) w 2 - x 2 + y 2 - z 2 2 ( yz - w x) 2 ( xz - w y) 2 ( yz + w x) w 2 - x 2 - y 2 + z 2 - D 0 ( ) = T k Q k D k + 1 ( ) = P j s. t. m n q k +1 1 j P Q q k +1 - p j - p j - D k +1 ( ) r k r k k, T k T k - 1 T 0.. Q k + 1 D k + 1 SVD T, T k + 1 = T, k: = k + 1, (3) CT D ICOM (D gtal Imagng and Communcatons n Medcne),.. marchng cube [ 6 ],, CT. vtk (V sualzaton Toolkt),.,, P D I Po2 lars Spectra, mm ( (RMS, RootMean Square) ). marker, marker. marker. ( ),, Q..,,.,, Q P , 2, 2 P Q. 2.,, 2 a P b Q 1

4 4 : ICP 437. marker ,,.,., CT, , 1mm, x y mm. 300 CT ( 3a), 3b 3 P (7 358 ), Polars Q (1 208 ),. 4,,, 5a.,,,,,, 5b. 8 ; 13. a b 5 a b 3,.., CT,,, 4., (CT ). vtk CT. Polars, 4. 2, mm, mm x y z L mm. 13,

5 a b mm, mm. 7, 1mm. 5 8 ICP. 1mm.,.,. ( References) 7,, Q = 0, = / 3, 8. T, T + T, p q, : e = p - ( T + T) q = T q (4), ( 4) e RMS : V RM S ( e) = 1 T q 2 (5) (5),. marker,., 200mm 200 mm 200 mm, , : V RM S ( e) = 0. 56mm Polars 2. [ 1 ] olte L P, Beutler T. Basc p rncp les of CAOS [ J ]. Injury, 2004, 35 ( S1) : 6-16 [ 2 ],,. MR2 CAS [ J ]., 2008, 27 (1) : W ang Tanm ao, L u W enyong, Hu Le. Progresses of medcal robotcs and computer asssted surgery (MRCAS) [ J ]. Chnese Journal of B omedcal Engneerng, 2008, 27 ( 1 ) : ( n Chnese) [ 3 ] Lavall e S. Regstraton for computer2ntegrated surgery: meth2 odology, state of art[ C ] / /Taylor R H, Lavall e S, Burdea G C, et al. Computer2Integrated Surgery: Technology and Clncal Applcatons. Cambrdge, MA: M IT Press, 1996: [ 4 ] Besl P J, Mckay D. A method for regstraton of 32d shapes [ J ]. IEEE Transactons on Pattern Analyss and Machne Intel2 lgence, 1992, 14 (2) : [ 5 ] Bentley J L. Multdmensonal bnary search trees used for asso2 catve searchng[ J ]. Communcatons of the ACM, 1975, 18 (9) : [ 6 ] Hoppe H, DeRose T, Duchamp T, et al. Surface reconstructon from unorganzed ponts[ J ]. Computer Graphcs 1992, 26 (2) : [ 7 ] Herrng J L, Dawant B M, Maurer C R, et al. Surface2based regstraton of CT mages to physcal space for mage2guded sur2 gery of the spne: a senstvty study[ J ]. Medcal Imagng, 1998, 17 (5) : IEEE Transactons on [ 8 ] W est J B, Maurer C R. Desgnng op tcally tracked nstruments for mage2guded surgery[ J ]. agng, 2004, 23 (5) : IEEE Transactons onmedcal Im2 ( : )