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Continuous Projection for Fast L1 Reconstruction

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.

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Continuous Projection for Fast L1 Reconstruction

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  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

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