1. Dynamic Geometry Registration Maks Ovsjanikov Leonidas Guibas Natasha GelfandNiloy J. Mitra Simon Flöry Helmut Pottmann Dynamic Geometry Registration

2. Scan Registration

3. Dynamic Geometry Registration Scan Registration Solve for inter-frame motion:

4. Dynamic Geometry Registration Scan Registration Solve for inter-frame motion:

5. Dynamic Geometry Registration The Setup Given: A set of frames {P 0, P 1,... P n } Goal: Recover rigid motion {  1,  2,...  n } between adjacent frames

6. Dynamic Geometry Registration The Setup Smoothly varying object motion Unknown correspondence between scans Fast acquisition ! motion happens between frames

7. Dynamic Geometry Registration Contributions Rigid registration ! kinematic property of space- time surface (locally exact) Registration ! surface normal estimation Analysis (see paper for details) Relation to ICP (Iterated Closest Point) Stability analysis Extension to deformable/articulated bodies

8. Dynamic Geometry Registration Time Ordered Scans tjtj t j+1 t j+2

9. Dynamic Geometry Registration Space-time Surface

10. Dynamic Geometry Registration Space-time Surface !

11. Dynamic Geometry Registration Space-time Surface !

12. Dynamic Geometry Registration Spacetime Velocity Vectors Tangential point movement ! velocity vectors orthogonal to surface normals

13. Dynamic Geometry Registration Spacetime Velocity Vectors Tangential point movement ! velocity vectors orthogonal to surface normals

14. Dynamic Geometry Registration Final Steps (rigid) velocity vectors !

15. Dynamic Geometry Registration Final Steps (rigid) velocity vectors !

16. Dynamic Geometry Registration Registration Algorithm 1.Compute time coordinate spacing (  ), and form space-time surface. 2.Compute space time neighborhood using ANN, and locally estimate space-time surface normals. 3.Solve linear system to estimate (c j,c j ). 4.Convert velocity vectors to rotation matrix + translation vector using Plücker coordinates and quarternions.

17. Dynamic Geometry Registration Normal Estimation: PCA Based Plane fitting using PCA using chosen neighborhood points.

18. Dynamic Geometry Registration Normal Estimation: Iterative Refinement Update neighborhood with current velocity estimate.

19. Dynamic Geometry Registration Normal Refinement: Effect of Noise Stable, but more expensive.

20. Dynamic Geometry Registration Normal Estimation: Local Triangulation Perform local surface triangulation (tetrahedralization).

21. Dynamic Geometry Registration Normal Estimation Stable, but more expensive.

22. Dynamic Geometry Registration Comparison with ICP ICP point-planeDynamic registration

23. Dynamic Geometry Registration Rigid: Bee Sequence (2,200 frames)

24. Dynamic Geometry Registration Rigid: Coati Sequence (2,200 frames)

25. Dynamic Geometry Registration Handling Large Number of Frames

26. Dynamic Geometry Registration Rigid/Deformable: Teapot Sequence (2,200 frames)

27. Dynamic Geometry Registration Deformable Bodies Cluster points, and solve smaller systems. Propagate solutions with regularization.

28. Dynamic Geometry Registration Deformable: Hand (100 frames)

29. Dynamic Geometry Registration Deformable: Hand (100 frames) scan #1 ! scan #50 scan #1 ! scan #100

30. Dynamic Geometry Registration Deformation + scanner motion: Skeleton (100 frames)

31. Dynamic Geometry Registration Deformation + scanner motion: Skeleton (100 frames) scan #1 ! scan #50 scan #1 ! scan #100

32. Dynamic Geometry Registration Deformation + scanner motion: Skeleton (100 frames) rigid components

33. Dynamic Geometry Registration Performance Table (on 2.4GHz Athlon Dual Core, 2GB RAM)

34. Dynamic Geometry Registration Conclusion Simple algorithm using kinematic properties of space-time surface. Easy modification for deformable bodies. Suitable for use with fast scanners.

35. Dynamic Geometry Registration Conclusion Simple algorithm using kinematic properties of space-time surface. Easy modification for deformable bodies. Suitable for use with fast scanners. Limitations/Future Work Need more scans, dense scans, … Sampling condition ! time and space

36. Dynamic Geometry Registration Acknowledgements Thibaut Weise Andreas Schilling Funding sources: Austrian Science Fund grants S9206-N12 and P18865-N13 Neumaier fellowship NSF ITR 0205671 NIH grant GM-072970 DARPA grant 32905 Agilent Corporation

37. Dynamic Geometry Registration thank you