1. Spectral processing of point-sampled geometry
Mark Pauly and Markus Gross
Presented by Benjamin Haas
Seminar on graphical data processing
June 13, 2001

2. Spectral processing of point-sampled geometry
Introduction
Motivation
Algorithm overview
Algorithm details
Results
Conclusion

3. Spectral processing of point-sampled geometry
Introduction
Research area
General description
Motivation
Algorithm overview
Algorithm details
Results
Conclusion

4. Point-sampled geometry
Introduction
Point-sampled geometry
Typically from laser range scanner
Model sizes ~ 106 points
No connectivity information
Contains noise
Fast rendering possible

5. Introduction
Surface patches

6. Surface (distance map) as a 2-d signal
Introduction
Surface (distance map) as a 2-d signal

7. Spectral processing of point-sampled geometry
Introduction
Motivation
Point-sampled geometry
Fourier methods for geometry
Algorithm overview
Algorithm details
Results
Conclusion

8. Why using point samples?
Motivation
Point-sampled geometry
Why using point samples?
Increasing model size
Decreasing triangle/quadrilateral size
Smaller memory requirements
Less computation time
Hardware rendering to be expected soon

9. Why using Fourier methods?
Motivation
Fourier methods for geometry
Why using Fourier methods?
Frequency for curvature / LOD
Filters expressed in frequency domain
Convolution theorem
Parseval's theorem (error estimation)
O(n2)
O(n)

10. Spectral processing of point-sampled geometry
Introduction
Motivation
Algorithm overview
The spectral processing pipeline
Algorithm details
Results
Conclusion

11. The spectral processing pipeline
Algorithm overview
The spectral processing pipeline

12. Spectral processing of point-sampled geometry
Introduction
Motivation
Algorithm overview
Patch layout creation
Scattered data approximation
(Spectral analysis)
Resampling
Patch blending
Algorithm details
Results
Conclusion

13. Two-step patch layout creation
Algorithm details
Patch layout creation
Two-step patch layout creation
Point samples
Clusters
Patches

14. Neighborhood detection using BSP tree
Algorithm details
Patch layout creation
Clustering
Neighborhood detection using BSP tree

15. Score function for optimization
Algorithm details
Patch layout creation
Patch merging
Score function for optimization

16. Algorithm details
Patch layout creation
Normal cone condition

17. Example: Patch layout for human face
Algorithm details
Patch layout creation
Example: Patch layout for human face

18. Scattered data approximation
Algorithm details
Scattered data approximation
Scattered data approximation

19. Scattered data approximation
Algorithm details
Scattered data approximation
Scattered data approximation

20. The spectral processing pipeline
Algorithm overview
The spectral processing pipeline

21. Low-pass filtered signal  Band limitation Sampling theorem (Nyquist)
Algorithm details
Resampling
Resampling
Low-pass filtered signal
 Band limitation
Sampling theorem (Nyquist)
 Optimal sampling rate
Parseval’s theorem
 Error control

22. Patch blending (reconstruction)
Algorithm details
Patch blending
Patch blending (reconstruction)
overlapping
patch boundaries
Blending of sampling rates
Blending of points
Blending of normals

23. Spectral processing of point-sampled geometry
Introduction
Motivation
Algorithm overview
Algorithm details
Noise removal
Enhancement
Restoration
Subsampling
Results
Conclusion

24. Smoothing and enhancement
Results
Smoothing and enhancement

25. Flexible spectral filtering
Results
Flexible spectral filtering

26. Noise removal Gaussian filter Wiener filter Original Results
filtered with
Gaussian filter
filtered with
Wiener filter
Original
(with noise)

27. Results
Subsampling
Original resolution
Adapted resolution

28. Spectral processing of point-sampled geometry
Introduction
Motivation
Algorithm overview
Algorithm details
Results
Pros and cons
Discussion
Conclusion

29. + Sound concept of frequency + Flexible, elegant and fast filtering
Conclusion
Pros and cons
+ Sound concept of frequency
+ Flexible, elegant and fast filtering
- Patch merging, SDA and reconstruction are costly
- Inconsistencies at patch boundaries (no mathematical foundation at present)
Well suitable for interactive surface processing