Continuous Projection for Fast L1 Reconstruction

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 L2 Reconstruction Input (87K points)

4. Dynamic Surface Reconstruction Weighted LOP (1.4 FPS) Online L2 Reconstruction Input (87K points)

5. Dynamic Surface Reconstruction Our Technique (10.8 FPS) Online L2 Reconstruction Input (87K points)

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

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

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

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

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

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. CLOP Overview Compute Gaussian Mixture Input Solve Continuous Attraction

20. CLOP Overview Compute Gaussian Mixture Input Solve Continuous Attraction

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

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

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

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

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

26. Gaussian Mixture Computation initialize each point with Gaussian pick parentGaussians EM: fit parents based on maximum likelihood • Hierarchical Expectation Maximization:

27. Gaussian Mixture Computation initialize each point with Gaussian pick parentGaussians EM: fit parents based on maximum likelihood Iterate over levels • Hierarchical Expectation Maximization: CLOP (8 FPS)

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. CLOP Overview Compute Gaussian Mixture Input Solve Continuous Attraction

33. Continuous Attraction from Gaussians Discrete K q p1 p2 p3

34. Continuous Attraction from Gaussians Discrete K q Continuous Θ1 Θ2

35. Continuous Attraction from Gaussians

36. Continuous Attraction from Gaussians

37. Continuous Attraction from Gaussians

38. Continuous Attraction from Gaussians

39. Continuous Attraction from Gaussians

40. Continuous Attraction from Gaussians

41. Continuous Attraction from Gaussians

42. Continuous Attraction from Gaussians

43. Continuous Attraction from Gaussians

44. Results Weighted LOP Continuous LOP

45. Results Weighted LOP Continuous LOP

46. Results Weighted LOP Continuous LOP

47. Performance 7x Speedup Weighted LOP Continuous LOP Input (87K points )

48. Performance

49. Accuracy WLOP CLOP

50. Accuracy Gargoyle