Fourier-based and Poisson surface reconstruction

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. M Reconstruction 0 0 1 1 0 0 1 0

9. Fourier Coefficients • The Fourier coefficients of the characteristic function give an expression of Mas 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. Non-Uniform Samples 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) 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

25. 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

26. 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

27. 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

28. 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

29. 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

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

32. Error-guided adaptive

33. Error-guided adaptive

34. Results

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

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 Indicator function Oriented points

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

39. Octree

40. Reconstruction

41. Function Space

42. Function Space

43. Function Space

44. Function Space

45. Function Space

46. Splat the samples

47. Splat the samples

48. Splat the samples

49. Vector Field

50. Indicator Function