1 / 34

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.

fritzi
Download Presentation

Screened Poisson Surface Reconstruction

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related