13.2 Dynamic Geometry Processing II Hao Li http://cs621.hao-li.com - PowerPoint PPT Presentation

Spring 2018 CSCI 621: Digital Geometry Processing 13.2 Dynamic Geometry Processing II Hao Li http://cs621.hao-li.com 1

Prof. Niloy J. Mitra UCL Registration without Correspondences 2

Scan Registration 3

Scan Registration Solve&for&inter,frame&mo/on:& 4

Scan Registration Solve&for&inter,frame&mo/on:& 5

The Setup Given:'' 'A'set'of'frames'{P 0 ,'P 1 ,'...'P n }' Goal:'' 'Recover'rigid'mo<on'{ α 1 ,' α 2 ,'...' α n }'between'' 'adjacent'frames'' '' 6

The Setup • Smoothly)varying)object)mo4on) • Unknown)correspondence)between)scans) • Fast)acquisi4on) ! )) mo4on)happens)between)frames) 7

Contributions • Rigid&registra,on& ! &kinema,c&property&of&space5,me& surface&(locally&exact)& • Registra,on& ! surface&normal&es,ma,on& & & • Analysis&(see&paper&for&details)& • Rela,on&to&ICP&(Iterated&Closest&Point)& • Stability&analysis& • Extension&to&deformable/ar,culated&bodies 8

Time Ordered Scans t j# t j+1# t j+2# 9

Space-Time Surface 10

Space-Time Surface j t Δ ! 11

Space-Time Surface ! 12

Space-Time Velocity Vectors Tangen&al(point(movement( ! (velocity(vectors(orthogonal(to(surface(normals( 13

Space-Time Velocity Vectors Tangen&al(point(movement( ! (velocity(vectors(orthogonal(to(surface(normals( j j ~ ~ v ( p ). n ( p ) 0 = i i 14

Final Steps (rigid)'velocity'vectors' ! 15

Final Steps (rigid)'velocity'vectors' ! 16

Registration Algorithm 1. Compute*+me*coordinate*spacing*( σ ),*and*form* space8+me*surface.* 2. Compute*space*+me*neighborhood*using*ANN,*and* locally*es+mate*space8+me*surface*normals.* 3. Solve*linear*system*to*es+mate*(c j ,c j ).* 4. Convert*velocity*vectors*to*rota+on*matrix*+* transla+on*vector*using*Plücker*coordinates*and* quarternions.* 17

Normal Estimation: PCA Based Plane&fi(ng&using&PCA&using&chosen&neighborhood&points.& 18

Normal Estimation: Iterative Refinement Update'neighborhood'with'current'velocity'es6mate.' 19

Normal Estimation: Effect of Noise Stable,(but(more(expensive.( 20

Normal Estimation: Local Triangulation Perform'local'surface'triangula1on'(tetrahedraliza1on).' 21

Normal Estimation Stable,(but(more(expensive.( 22

Comparison with ICP ICP$point*plane$ Dynamic$registra5on$ 23

Rigid/Deformable: Coati Sequence (2.2K frames) 24

Rigid: Bee Sequence (2,2K frames) 25

Handling Large Number of Frames 26

Rigid/Deformable: Teapot Sequence (2.2K frames) 27

Deformable Bodies • Cluster)points,)and)solve)smaller)systems.) • Propagate)solu7ons)with)regulariza7on.) 28

Deformable: Hand (100 frames) 29

Deformable: Hand (100 frames) scan%#1% ! %scan%#50%% scan%#1% ! %scan%#100%% 30

Conclusion • Simple(algorithm(using(kinema3c(proper3es(of( space63me(surface.( • Easy(modifica3on(for(deformable(bodies.( • Suitable(for(use(with(fast(scanners.( 31

Conclusion • Simple(algorithm(using(kinema3c(proper3es(of( space63me(surface.( • Easy(modifica3on(for(deformable(bodies.( • Suitable(for(use(with(fast(scanners.( Limita3ons/Future(Work( • Need(more(scans,(dense(scans,(…( • Sampling(condi3on( ! 3me(and(space 32

Prof. Michael Wand Utrecht University Animation Reconstruction “Urshapes”! 33

Correspondences 34

Problem 35

Variational Problem 36

Scan Sequence 37

Hierarchical Merging 38

Hierarchical Merging 39

Initial Urshape 40

Initial Urshape 41

Alignment 42

Alignment 43

Hierarchical Alignment 44

Hierarchical Alignment 45

Global Optimization 46

Global Optimization 47

Additional Term 48

Results 49

Results 50

Extension: Animation Cartography [Tevs et al. 2012] 51

http://cs621.hao-li.com Thanks! 52