1. Continuous Projection for Fast L1 Reconstruction Reinhold Preiner*Oliver Mattausch†Murat Arikan* Renato Pajarola†Michael Wimmer* * Institute of Computer Graphics and Algorithms, Vienna University of Technology † Visualization and Multimedia Lab, University of Zurich

2. Dynamic Surface Reconstruction Input (87K points)

3. Dynamic Surface Reconstruction Online L 2 ReconstructionInput (87K points)

4. Dynamic Surface Reconstruction Online L 2 ReconstructionInput (87K points) Weighted LOP (1.4 FPS)

5. Dynamic Surface Reconstruction Online L 2 ReconstructionInput (87K points) Our Technique (10.8 FPS)

6. Recap: Locally Optimal Projection LOP [Lipman et al. 2007], WLOP [Huang et al. 2009] Attraction

7. Recap: Locally Optimal Projection Attraction LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]

8. Recap: Locally Optimal Projection Attraction LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]

9. Recap: Locally Optimal Projection Attraction LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]

10. Recap: Locally Optimal Projection Repulsion LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]

11. Recap: Locally Optimal Projection LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]

12. Recap: Locally Optimal Projection LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]

13. Recap: Locally Optimal Projection LOP [Lipman et al. 2007], WLOP [Huang et al. 2009]

14. Performance Issues Attraction: performance strongly depends on the # of input points

15. Acceleration Approach Reduce number of spatial components! Naïve subsampling  information loss

16. Our Approach Model data by Gaussian mixture  fewer spatial entities

17. Our Approach Model data by Gaussian mixture  fewer spatial entities Requires continuous attraction of Gaussians ?

18. Our Approach Model data by Gaussian mixture  fewer spatial entities Requires continuous attraction of Gaussians  Continuous LOP (CLOP)

19. Solve Continuous Attraction CLOP Overview

20. Solve Continuous Attraction CLOP Overview

21. Gaussian Mixture Computation Hierarchical Expectation Maximization: 1.initialize each point with Gaussian

22. Gaussian Mixture Computation Hierarchical Expectation Maximization: 1.initialize each point with Gaussian

23. Gaussian Mixture Computation Hierarchical Expectation Maximization: 1.initialize each point with Gaussian

24. Gaussian Mixture Computation Hierarchical Expectation Maximization: 1.initialize each point with Gaussian

25. Gaussian Mixture Computation Hierarchical Expectation Maximization: 1.initialize each point with Gaussian 2.pick parent Gaussians

26. Gaussian Mixture Computation Hierarchical Expectation Maximization: 1.initialize each point with Gaussian 2.pick parent Gaussians 3.EM: fit parents based on maximum likelihood

27. Gaussian Mixture Computation Hierarchical Expectation Maximization: CLOP (8 FPS) 1.initialize each point with Gaussian 2.pick parent Gaussians 3.EM: fit parents based on maximum likelihood 4.Iterate over levels

28. Gaussian Mixture Computation Conventional HEM: blurring CLOP (8 FPS)

29. Gaussian Mixture Computation Conventional HEM: blurring

30. Gaussian Mixture Computation Conventional HEM: blurring Introduce regularization

31. Gaussian Mixture Computation Conventional HEM: blurring Introduce regularization

32. Solve Continuous Attraction CLOP Overview

33. Solve Continuous Attraction CLOP Overview

34. K Continuous Attraction from Gaussians q p1p1 p3p3 p2p2 Discrete

35. K q Continuous Attraction from Gaussians Discrete Continuous Θ1Θ1 Θ2Θ2

36. Continuous Attraction from Gaussians K q Θ1Θ1

46. Solve Continuous Attraction CLOP Overview

47. Results Weighted LOPContinuous LOP

48. Results Weighted LOPContinuous LOP

49. Results Weighted LOPContinuous LOP

50. Performance Input (87K points ) 7x Speedup Weighted LOPContinuous LOP

51. Performance

52. WLOP Accuracy CLOP

53. Accuracy Gargoyle

54. L1 Normals

56. LOP on Gaussian mixtures faster more accurate See the paper: Faster repulsion L 1 normals Conclusion Come to our Birds of a Feather! Harvest4D – Harvesting Dynamic 3D Worlds from Commodity Sensor Clouds Tuesday, 1:00 PM - 2:00 PM, East Building, Room 4 =