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

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

Jun 22, 2023 242 likes •774 views

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

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CSCI 621: Digital Geometry Processing

Hao Li

http://cs621.hao-li.com

1

Spring 2018

13.2 Dynamic Geometry Processing II

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Registration without Correspondences

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  • Prof. Niloy J. Mitra

UCL

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Scan Registration

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Scan Registration

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Solve&for&inter,frame&mo/on:&

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Scan Registration

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Solve&for&inter,frame&mo/on:&

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The Setup

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Given:'' 'A'set'of'frames'{P0,'P1,'...'Pn}' Goal:'' 'Recover'rigid'mo<on'{α1,'α2,'...'αn}'between'' 'adjacent'frames'' ''

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The Setup

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  • Smoothly)varying)object)mo4on)
  • Unknown)correspondence)between)scans)
  • Fast)acquisi4on)!))

mo4on)happens)between)frames)

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Contributions

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  • 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
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Time Ordered Scans

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tj# tj+1# tj+2#

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Space-Time Surface

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Space-Time Surface

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!

j

t Δ

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Space-Time Surface

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!

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Space-Time Velocity Vectors

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Tangen&al(point(movement(!(velocity(vectors(orthogonal(to(surface(normals(

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Space-Time Velocity Vectors

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Tangen&al(point(movement(!(velocity(vectors(orthogonal(to(surface(normals(

) ( ). (

~ ~

=

j i j i

p n p v

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Final Steps

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(rigid)'velocity'vectors'!

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Final Steps

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(rigid)'velocity'vectors'!

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Registration Algorithm

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  • 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*(cj,cj).*
  • 4. Convert*velocity*vectors*to*rota+on*matrix*+*

transla+on*vector*using*Plücker*coordinates*and* quarternions.*

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Normal Estimation: PCA Based

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Plane&fi(ng&using&PCA&using&chosen&neighborhood&points.&

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Normal Estimation: Iterative Refinement

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Update'neighborhood'with'current'velocity'es6mate.'

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Normal Estimation: Effect of Noise

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Stable,(but(more(expensive.(

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Normal Estimation: Local Triangulation

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Perform'local'surface'triangula1on'(tetrahedraliza1on).'

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Normal Estimation

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Stable,(but(more(expensive.(

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Comparison with ICP

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ICP$point*plane$ Dynamic$registra5on$

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Rigid/Deformable: Coati Sequence (2.2K frames)

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Rigid: Bee Sequence (2,2K frames)

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Handling Large Number of Frames

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Rigid/Deformable: Teapot Sequence (2.2K frames)

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Deformable Bodies

  • Cluster)points,)and)solve)smaller)systems.)
  • Propagate)solu7ons)with)regulariza7on.)
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Deformable: Hand (100 frames)

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Deformable: Hand (100 frames)

scan%#1%!%scan%#50%% scan%#1%!%scan%#100%%

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Conclusion

  • Simple(algorithm(using(kinema3c(proper3es(of(

space63me(surface.(

  • Easy(modifica3on(for(deformable(bodies.(
  • Suitable(for(use(with(fast(scanners.(
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SLIDE 32

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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
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Animation Reconstruction “Urshapes”!

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  • Prof. Michael Wand

Utrecht University

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Correspondences

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Problem

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Variational Problem

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Scan Sequence

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Hierarchical Merging

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Hierarchical Merging

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Initial Urshape

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Initial Urshape

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Alignment

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Alignment

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Hierarchical Alignment

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Hierarchical Alignment

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Global Optimization

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Global Optimization

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Additional Term

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Results

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Results

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Extension: Animation Cartography

[Tevs et al. 2012]

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http://cs621.hao-li.com

Thanks!

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