L ine s Surfa c e s 3D o b je c ts Po ints P. J. Be sl a nd N. - PowerPoint PPT Presentation

L ine s Surfa c e s 3D o b je c ts Po ints

 P. J. Be sl a nd N. D. Mc K a y. A me tho d fo r re g istra tio n o f 3-D sha pe s. I E E E T rans. o n Patte rn Analysis and Mac hine I nte llig e nc e , 14(2):239–256, 1992.

 Rig id o b je c ts T ra nsla tio n Ro ta tio n Sc a ling

 Pro b le m fo rmula tio n: p i po ints o n the mo de l. › q i c o rre spo nding po ints o f p i o n the o b je c t. › F ind the line a r tra nsfo rma tio n T tha t minimize s the e rro r E : › Numb e r o f po ints in M E uc lide a n Dista nc e

 Assume s a nd R a re fixe d the n, the o ptima l t tha t minimize s:  sho uld b e :

 Re pla c e the t in the e rro r func tio n using the pre vio us re sult we g e t:  Whe re :

 E xpa nding the e rro r func tio n Re writte n a s: 

 Minimize d whe n:



 T he n we ne e d to ma ximize :  T hus the o ptima l ro ta tio n q is the e ig e n ve c to r c o rre spo nding to the la rg e st e ig e n va lue o f

 Ma ke e duc ate d gue ss . Whe n two o b je c ts a re re g iste re d.  po ints a re c lose to so me po ints o n the o the r o b je c t. › Give n a po int p i in M, the c lo se st po int q i in O sa tisfie s:  E uc lide a n dista nc e

 Re pe a t until c o nve rg e nc e : › F ind q i o f p i . › Co mpute T tha t minimize s: › Apply the T to a ll the p i .

sma lle r E  Re pe a t until c o nve rg e nc e : › F ind q i o f p i . › Co mpute T tha t minimize s: sma lle r E › Apply the T to a ll the p i .

 Va rio us da ta re pre se nta tio n Outlie r se nsitive  I nitia liza tio n se nsitive 

 Phillips J. M., L iu R., a nd T o ma si C. Outlie r ro b ust I CP fo r minimizing fra c tio na l RMSD. I n Pro c . o f I nt. Co nf. o n 3D Dig ital I mag ing and Mo de ling (2007), pp. 427–434.

 c o mple te a nd a b no rma l F ra c ture I nc o mple te sc a nning

 Mo de ls to b e re g iste re d: va ry g re a tly in size , sha pe de ta ils a nd c o mple te ne ss. 20

 I de ntify the o utlie rs Re je c t wro ng pa irs b y dista nc e b e twe e n tha t pa ire d po ints. ›



 Re pe a t until c o nve rg e nc e : › Co mpute µ: D -> M tha t minimize s RMSD Cho o se a po int se t › Co mpute f a nd D f tha t minimize s with le ss RMSD  fra c tio na l ro o t me a n sq ua re d dista nc e › Co mpute tra nsfo rma tio n T tha t minimize s RMSD o n D f Cho o se a po int se t with mo re po ints



sma lle r F RMSD  Re pe a t until c o nve rg e nc e : › Co mpute µ: D -> M tha t minimize s RMSD › Co mpute f a nd D f tha t minimize s  fra c tio na l ro o t me a n sq ua re d dista nc e sma lle r F RMSD › Co mpute T tha t minimize s RMSD o n D f sma lle r F RMSD

F I CP I CP

I CP F I CP

Co mple te Pa tie nt So urc e T a rg e t I CP re sult F I CP re sult 29

Che ng Yua n, L e o w We e K he ng , L im T ia m Chye : Auto ma tic Id e ntific a tio n o f F ra nkfurt Pla ne a nd Mid - Sa g itta l Pla ne o f Skull. In WACV 2012, pp. 233-238. F I CP I nitia liza tio n F P (a ) O rb ita le (c ) Po rio n MSP (a ) Rid g e (b ) Pe a k (c ) FMC I te ra tive re fine me nt

P. J. Be sl a nd N. D. Mc K a y. A me tho d fo r re g istra tio n o f 3-D  sha pe s. I E E E T ra ns. o n Pa tte rn Ana lysis a nd Ma c hine I nte llig e nc e , 14(2):239–256, 1992. J.M.Phillips, R. L iu, C. T o ma si. Outlie r Ro b ust I CP fo r Minimizing  F rac tio nal RMSD. I nte rna tio na l Co nfe re nc e o n 3-D Dig ita l I ma g ing a nd Mo de ling , 2007. Ho rn, B.K .P. Clo se d-fo rm so lutio n o f a b so lute o rie nta tio n using  unit q ua te rnio ns. T he Jo urna l o f the Optic a l So c ie ty o f Ame ric a A, 4(4):239–256, 1987. Ho rn, B.K .P. Clo se d-fo rm so lutio n o f a b so lute o rie nta tio n using  o rtho no rma l ma tric e s. T he Jo urna l o f the Optic a l So c ie ty o f Ame ric a A, 5(7):1127--1135, 1988.