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Screened Poisson Surface Reconstruction

Screened Poisson Surface Reconstruction. Misha Kazhdan Johns Hopkins University. Hugues Hoppe Microsoft Research. Motivation. 3D scanners are everywhere: Time of flight Structured light Stereo images Shape from shading Etc. http://graphics.stanford.edu/projects/mich/. Motivation.

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Screened Poisson Surface Reconstruction

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  1. Screened PoissonSurface Reconstruction Misha Kazhdan Johns Hopkins University Hugues Hoppe Microsoft Research

  2. Motivation 3D scanners are everywhere: • Time of flight • Structured light • Stereo images • Shape from shading • Etc. http://graphics.stanford.edu/projects/mich/

  3. Motivation Surfacereconstruction Geometryprocessing Parameterization Decimation Filtering etc.

  4. Implicit Function Fitting Given point samples: • Define a function with value zero at the points. • Extract the zero isosurface. >0 F(q) =0 F(q)<0 0 F(q)>0 <0 Sample points F(q)

  5. Related work [Hoppe et al. 1992] [Curless and Levoy 1996] [Carr et al. 2001] [Kazhdan et al. 2006] [Alliez et al. 2007] [Calakli and Taubin 2011] … and many more …

  6. Poisson Surface Reconstruction [2006] • Oriented points  samples of indicator gradient. • Fit a scalar field to the gradients. (q)=0.5 (q)=-0.5

  7. Poisson Surface Reconstruction [2006] • Compute the divergence • Solve the Poisson equation

  8. Poisson Surface Reconstruction [2006] • Compute the divergence • Solve the Poisson equation • Discretize over an octree • Update coarse  fine fine + + + + coarse Solution Correction

  9. Poisson Surface Reconstruction [2006] Properties: • Supports noisy, non-uniform data • Over-smoothes • Solver time is super-linear

  10. Screened Poisson Reconstruction • Higher fidelity – at same triangle count • Faster – solver time is linear Poisson Screened Poisson

  11. Outline • Introduction • Better / faster reconstruction • Evaluation • Conclusion

  12. Better Reconstruction Add discrete interpolation to the energy: •  encouraged to be zero at samples • Adds a bilinear SPD term to the energy • Introduces inhomogeneity into the system Sample interpolation[Carr et al.,…,Calakli and Taubin] Gradient fitting

  13. Better Reconstruction Discretization: Choose basis to represent :

  14. Better Reconstruction Discretization: For an octree, use B-splines: • centered on each node • scaled to the node size

  15. Better Reconstruction Poisson reconstruction: To compute , solve: with coefficients given by: Screened ^ Bj Bi

  16. Better Reconstruction Poisson reconstruction: • Sparsityis unchanged • Entries are data-dependent Screened ^ Bj Bi Bj Bi

  17. Faster Screened Reconstruction Bj Bj Bi Bi Observation: At coarse resolutions, no need to screen as precisely.  Use average position, weighted by point count. Bj Bi

  18. Faster Reconstruction Solver inefficiency: Before updating, subtract constraints met at all coarser levels of the octree.  complexity fine + + coarse + Correction Solution

  19. Faster Reconstruction Regular multigrid: • Function spaces nest  can upsample coarser solutions to finer levels

  20. Faster Reconstruction Adaptive multigrid: • Function spaces do not nest  coarser solutions need to be stored explicitly

  21. Faster Reconstruction Naive enrichment:  Complete octree

  22. Faster Reconstruction Observation: Only upsample the part ofthe solution visible to the finer basis.

  23. Faster Reconstruction Enrichment: Iterate fine  coarse Identify support of next-finer level Add visible functions

  24. Faster Reconstruction Original Enriched

  25. Faster Reconstruction Adaptive Poisson solver: • Update coarse  fine • Get supported solution • Adjust constraints • Solve residual + + + + + + + + + + + Correction Visible Solution Solution

  26. Outline • Introduction • Better / faster reconstruction • Evaluation • Conclusion

  27. Accuracy SSD [Calakli & Taubin] Poisson Screened Poisson z z

  28. Accuracy SSD [Calakli & Taubin] Poisson Screened Poisson

  29. Performance Input: 2x106 points

  30. Performance Input: 5x106 points

  31. Limitations • Assumes clean data Poisson Screened Poisson

  32. Summary Screened Poisson reconstruction: • Sharper reconstructions • Optimal-complexity solver

  33. Future Work • Robust handling of noise • (Non-watertight reconstruction) • Extension to full multigrid

  34. Thank You! Data: Aim@Shape, Digne et al., EPFL,Stanford Shape Repository Code: Berger et al., Calakliet al.,Manson et al. Funding: NSF Career Grant (#6801727) http://www.cs.jhu.edu/~misha/Code/PoissonRecon

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