1. Wavelets for Surface Reconstruction
Josiah Manson
Guergana Petrova
Scott Schaefer

2. Convert Points to an Indicator Function

3. Data Acquisition

4. Properties of Wavelets
Fourier Series
Wavelets
Represents
all functions
Locality
Depends
on wavelet
Smoothness

5. Wavelet Bases
Haar D4

6. Example of Function using Wavelets

7. Example of Function using Wavelets

8. Example of Function using Wavelets

9. Example of Function using Wavelets

10. Example of Function using Wavelets

11. Strategy Estimate wavelet coefficients of indicator function
Use only local combination of samples to find coefficients

12. Computing the Indicator Function
[Kazhdan 2005]

13. Computing the Indicator Function
[Kazhdan 2005]

14. Computing the Indicator Function
[Kazhdan 2005]

15. Computing the Indicator Function
[Kazhdan 2005]
Divergence Theorem

16. Computing the Indicator Function
[Kazhdan 2005]
Divergence Theorem

17. Computing the Indicator Function
[Kazhdan 2005]

18. Computing the Indicator Function
[Kazhdan 2005]

19. Finding

20. Finding

21. Finding

22. Extracting the surface
Coefficients
Indicator function
Dual marching cubes
Surface

23. Smoothing the Indicator Function
Haar unsmoothed

24. Smoothing the Indicator Function
Haar unsmoothed
Haar smoothed

25. Comparison of Wavelet Bases
Haar D4

26. Advantages of Wavelets
Coefficients calculated only near surface
Fast, Low memory
Trade quality for speed
Multi-resolution representation
Out of core calculation is possible

27. Streaming Pipeline
Output
Input

28. Results Michelangelo’s Barbuto
329 million points (7.4 GB of data), 329MB memory, 112 minutes

29. Results Michelangelo’s Awakening
381 million points (8.5 GB), 573MB memory, 81 minutes
Produced 590 million polygons

30. Results Michelangelo’s Atlas
410 million points (9.15 GB), 1188MB memory, 98 minutes
Produced 642 million polygons

31. Results Michelangelo’s Atlas
410 million points (9.15 GB), 1188MB memory, 98 minutes
Produced 642 million polygons

32. Robustness to Noise in Normals
0° ° ° °

33. Comparison of Methods MPU 551 sec 750 MB Poisson 289 sec 57 MB Haar

34. Relative Hausdorff Errors

35. Conclusions Works with all orthogonal wavelets
Wavelets provide trade-off
between speed/quality
Guarantees closed, manifold
surface
Out of core

36. Future Work Better estimates of dσ Compress surfaces
Wedgelets and higher order versions thereof

38. Overview

39. Getting locality
Always in memory
Streamed tree

40. Smooth, but large error A B

41. Jagged, but low error A B

42. Hausdorf error on points – pointless