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Fourier-based and Poisson surface reconstruction

Fourier-based and Poisson surface reconstruction. Reporter: Lincong Fang 24th Dec, 2008. Implicit surfaces. F ( x , y ) =0. F ( x , y )>0. F ( x , y )<0. Papers. Michael Kazhdan. Reconstruction of solid models from oriented point set. SGP2005.

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Fourier-based and Poisson surface reconstruction

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  1. Fourier-based and Poisson surface reconstruction Reporter: Lincong Fang 24th Dec, 2008

  2. Implicit surfaces F (x,y) =0 F (x,y)>0 F (x,y)<0

  3. Papers • Michael Kazhdan. Reconstruction of solid models from oriented point set. SGP2005. • Oliver Schall, Alexander Belyaev, Hans-Peter Seidel. Error-guided adaptive Fourier-based surface reconstruction. CAD 2007. • Michael Kazhdan, Matthew Bolitho, Hugues Hoppe. Poisson surface reconstruction. SGP 2006. • Kun Zhou, Minmin Gong, Xin Huang, Baining Guo. Highly parallel surface reconstruction. Technique report 2008.

  4. Papers • Michael Kazhdan. Reconstruction of solid models from oriented point set. SGP2005. • Oliver Schall, Alexander Belyaev, Hans-Peter Seidel. Error-guided adaptive Fourier-based surface reconstruction. CAD 2007. • Michael Kazhdan, Matthew Bolitho, Hugues Hoppe. Poisson surface reconstruction. SGP 2006. • Kun Zhou, Minmin Gong, Xin Huang, Baining Guo. Highly parallel surface reconstruction. Technique report 2008.

  5. Characteristic Function M

  6. M Reconstruction 0 0 1 1 0 0 1 0

  7. Fourier Coefficients • The Fourier coefficients of the characteristic function give an expression of Mas a sum of complex exponentials:

  8. Divergence Theorem =

  9. Monte-Carlo integration

  10. Fourier Coefficients

  11. Anisotropic

  12. Iso-surface

  13. Non-Uniform Samples

  14. Non-Uniform Samples i=1/2

  15. Non-Uniform Samples i=1/1

  16. Non-Uniform Samples i=1/3

  17. Non-Uniform Samples i=1/4

  18. Results (Resolution) 100,000 Points 100,000 Points 100,000 Points res=643 tris=11,672 time<0:01 res=1283 tris=49,008 time=0:01 res=2563 tris=199,796 time=0:07

  19. Results (Sample Count) 10,000 Points 100,000 Points 1000 Points res=2563 tris=200,704 time=0:07 res=2563 tris=199,796 time=0:07 res=2563 tris=206,216 time=0:07

  20. Results (Non-Uniform Sampling) 100,000 Points 100,000 Points 100,000 Points res=2563 tris=199,712 time=0:09 res=2563 tris=111,680 time=0:09 res=2563 tris=220,324 time=0:09

  21. Results (Positional Noise) disp=0 res=2563 tris=141,808 time=0:07 points=100,000 disp=radius/64 res=2563 tris=134,848 time=0:07 points=100,000 disp=radius/128 res=2563 tris=139,468 time=0:07 points=100,000 disp=radius/32 res=2563 tris=124,300 time=0:07 points=100,000

  22. Results (Normal Noise) angle=0o res=2563 tris=141,808 time=0:07 points=100,000 angle=30o res=2563 tris=141,876 time=0:07 points=100,000

  23. Results (Normal Noise) angle=15o res=2563 tris=141,776 time=0:07 points=100,000 angle=45o res=2563 tris=142,048 time=0:07 points=100,000

  24. Papers • Michael Kazhdan. Reconstruction of solid models from oriented point set. SGP2005. • Oliver Schall, Alexander Belyaev, Hans-Peter Seidel. Error-guided adaptive Fourier-based surface reconstruction. CAD 2007. • Michael Kazhdan, Matthew Bolitho, Hugues Hoppe. Poisson surface reconstruction. SGP 2006. • Kun Zhou, Minmin Gong, Xin Huang, Baining Guo. Highly parallel surface reconstruction. Technique report 2008.

  25. Error-guided adaptive

  26. Error-guided adaptive

  27. Error-guided adaptive

  28. Results

  29. Comparison FFT time: 1min15s, peak memory: 1.4GB AdFFT time: 21min10s, peak memory: 1.6GB

  30. Papers • Michael Kazhdan. Reconstruction of solid models from oriented point set. SGP2005. • Oliver Schall, Alexander Belyaev, Hans-Peter Seidel. Error-guided adaptive Fourier-based surface reconstruction. CAD 2007. • Michael Kazhdan, Matthew Bolitho, Hugues Hoppe. Poisson surface reconstruction. SGP 2006. • Kun Zhou, Minmin Gong, Xin Huang, Baining Guo. Highly parallel surface reconstruction. Technique report 2008.

  31. Indicator function M Indicator function Oriented points

  32. 0 0 0 0 0 0 Indicator gradient M Poisson surface reconstruction

  33. Octree

  34. Reconstruction

  35. Function Space

  36. Function Space

  37. Function Space

  38. Function Space

  39. Function Space

  40. Splat the samples

  41. Splat the samples

  42. Splat the samples

  43. Vector Field

  44. Indicator Function

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