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

5. 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.

6. 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.

7. Characteristic Function M

8. Reconstruction MM 0 1 0 0 0 0 1 1

9. Fourier Coefficients The Fourier coefficients of the characteristic function give an expression of  M as a sum of complex exponentials:

10. Divergence Theorem =

11. Monte-Carlo integration

12. Fourier Coefficients

13. Anisotropic

18. Iso-surface

19. Non-Uniform Samples

20.  i =1/2

21. Non-Uniform Samples  i =1/1

22. Non-Uniform Samples  i =1/3

23. Non-Uniform Samples  i =1/4

24. Results (Resolution) res=128 3 tris=49,008 time=0:01 res=256 3 tris=199,796 time=0:07 100,000 Points res=64 3 tris=11,672 time<0:01

25. Results (Sample Count) res=256 3 tris=200,704 time=0:07 res=256 3 tris=206,216 time=0:07 100,000 Points 1000 Points res=256 3 tris=199,796 time=0:07 10,000 Points

26. Results (Non-Uniform Sampling) res=256 3 tris=111,680 time=0:09 res=256 3 tris=220,324 time=0:09 100,000 Points res=256 3 tris=199,712 time=0:09

27. Results (Positional Noise) disp=radius/128 res=256 3 tris=139,468 time=0:07 points=100,000 disp=0 res=256 3 tris=141,808 time=0:07 points=100,000 disp=radius/32 res=256 3 tris=124,300 time=0:07 points=100,000 disp=radius/64 res=256 3 tris=134,848 time=0:07 points=100,000

28. Results (Normal Noise) angle=0 o res=256 3 tris=141,808 time=0:07 points=100,000 angle=30 o res=256 3 tris=141,876 time=0:07 points=100,000

29. Results (Normal Noise) angle=15 o res=256 3 tris=141,776 time=0:07 points=100,000 angle=45 o res=256 3 tris=142,048 time=0:07 points=100,000

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. Error-guided adaptive

34. Results

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

36. 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.

37. Indicator function MM Oriented points

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

39. Octree

40. Reconstruction

41. Function Space

46. Splat the samples

49. Vector Field

50. Indicator Function

51. Surface Extraction

52. Resolution

53. Results (Resolution) Octree depths 6Octree depths 8Octree depths 10

54. Comparison to FFT

55. 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.

56. 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.