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

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Pro b le m fo rmula tio n:

›

pi 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

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Assume s a nd R a re fixe d the n, the o ptima l t tha t minimize s:

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sho uld b e :

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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:

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Whe re :

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E xpa nding the e rro r func tio n

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Re writte n a s:

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Minimize d whe n:

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T he n we ne e d to ma ximize :

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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

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Ma ke e duc ate d gue ss.

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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 pi 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 pi. › Co mpute T

tha t minimize s:

› Apply the T

to a ll the pi .

 Re pe a t until c o nve rg e nc e :

› F ind q i o f pi. › Co mpute T

tha t minimize s:

› Apply the T

to a ll the pi .

sma lle r E sma lle r E

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Va rio us da ta re pre se nta tio n

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Outlie r se nsitive

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I nitia liza tio n se nsitive

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Phillips J. M., L iu R., a nd T

• 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

I nc o mple te sc a nning F ra c ture

 Mo de ls to b e re g iste re d:

20

va ry g re a tly in size , sha pe de ta ils a nd c o mple te ne ss.

 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.

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 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 Df tha t minimize s

 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

• n Df

Cho o se a po int se t with mo re po ints Cho o se a po int se t with le ss 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 Df tha t minimize s

 fra c tio na l ro o t me a n sq ua re d dista nc e

› Co mpute T tha t minimize s RMSD o n Df

sma lle r F RMSD sma lle r F RMSD sma lle r F RMSD

F I CP I CP

I CP F I CP

I CP re sult F I CP re sult So urc e T a rg e t

29

Co mple te Pa tie nt

I nitia liza tio n

F P MSP

(a ) O rb ita le (c ) Po rio n

(a ) Rid g e (b ) Pe a k (c ) FMC

F I CP

I te ra tive re fine me nt

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.



• 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

• 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

• 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.