Point Set Processing and Surface Reconstruction (cgal)

1. Point Set Processing and Surface Reconstruction(www.cgal.org) Nader Salman, INRIA In collaboration with Pierre Alliez, INRIA Laurent Saboret, INRIA Gaël Guennebaud, INRIA Bordeaux 9th ACCV Xi’an China, Sep 25-27 2009

2. Outline • Common pipeline • Structure • Documentation • Demo • Roadmap

3. Common Pipeline Physical • Acquisition • Registration • Pre-processing • Reconstruction Digital Geometry

4. Example Pipeline (1)laser range data Acquisition Registration Pre-processing (simplification, denoising, smoothing, …) Reconstruction

5. Example Pipeline (2)multi-view passive stereo Acquisition & calibration Point cloud generation Pre-processing (simplification, denoising, smoothing, …) Reconstruction

6. Structure (pipeline-oriented) Point set Analysis Processing Normals Reconstruction Contouring • Bounding box • Bounding sphere • Centroid • Average spacing • Poisson • Algebraic point set surfaces • Surface mesh generator • Simplification • Outlier removal • Smoothing • Estimation • Orientation (grayed out = in other CGAL packages)

7. Entering the Pipeline… Clean points with oriented normals Clean point set Point set Analysis Processing Normals Reconstruction Contouring • Bounding box • Bounding sphere • Centroid • Average spacing • Poisson • Algebraic point set surfaces • Surface mesh generator • Simplification • Outlier removal • Smoothing • Estimation • Orientation Points with unoriented normals (grayed out = in other CGAL packages)

8. Output… Point set Analysis Processing Normals Reconstruction Contouring • Bounding box • Bounding sphere • Centroid • Average spacing • Poisson • Algebraic point set surfaces • Surface mesh generator • Simplification • Outlier removal • Smoothing • Estimation • Orientation Implicitfunction Surfacetriangle mesh Clean points withoriented normals (grayed out = in other CGAL packages)

9. Point_set_processing_3 Introduction Left: 275k points sampled on an elephant (Minolta laser scanner) Right: point set cleaned and simplified to 17K points

10. Analysis • Bounding box • Bounding sphere • Centroid • Average spacing • reuse orthogonal search for K nearest neighbors • used by reconstruction / contouring algorithms • takes an iterator range of 3D points and parameter K

11. Processing • Simplification • by random selection • by clustering (regular grid) • Outlier removal • sort w.r.t. sum of squared distances to KNN and cut at specified percentile. • Smoothing • jet fitting + projection

12. Example Simplification from 100K to 50k points by random simplification

13. Example Simplification from 100K to 50k points by clustering

14. Example Outlier Removal (a lion and a bunch of outliers)

15. Example Smoothing • For each point • find KNN • fit jet (smooth parametric surface) • project onto jet (noisy point set) (smoothed point set)

16. Normals • Estimation (no orientation) • KNN + PCA (fit a plane) • KNN+jet fitting (better for noisy data) • Orientation • KNN + BGL MST (Minimum Spanning Tree)[Hoppe 92]

17. Example Normal Estimation Normals estimation through PCA (7 KNN) Orientation through MST (7 KNN)

18. Example Normal Orientation Normal Orientation through MST

19. Surface_reconstruction_points_3Introduction reconstructed surface using Poisson 17K points sampled on an elephant (Minolta laser scanner) reconstructed surface using APSS (in progress)

20. Reconstruction (1) • Poissonsurface reconstruction [Kazhdan-Bolitho-Hoppe, SGP 2006] • Solves for an implicit function (~indicator function) • Isosurface extracted by CGAL surface mesh generator

21. Indicator function M Poisson Surface Reconstruction • Reconstruct the surface of the model by solving for the indicator function of the shape. 0 0 1 1 0 0 1 0

22. 0 0 0 0 0 0 Indicator gradient M Poisson Surface Reconstruction • There is a relationship between the normal field and gradient of indicator function points + oriented normals

23. Poisson Surface Reconstruction • Represent the points by a vector field • Find the function whose gradient best approximates : • Applying the divergence operator, we can transform this into a Poisson problem: 

24. Poisson Surface Reconstruction • We solve for the Poisson equation onto the vertices of a (refined) 3D Delaunay triangulation [TAUCS linear solver]

25. Example Poisson

26. Example Poisson Left: 120K points sampled on child statue (Minolta laser scanner) Right: reconstructed surface

27. Example Poisson Left: 120K points sampled on a statue (Minolta laser scanner) Right: reconstructed surface

28. Example Poisson

29. Example Poisson Left: 70K points with (emphasized) outliers Right: reconstructed surface

30. Example Poisson Left: Bimba 120K reconstructed with distance = 0.25*average spacing Right: Bimba 120K reconstructed with distance = 0.15*average spacing

31. Example Poisson Left: 65K points sampled on a hand with no data at the wrist base (Kreon laser scanner) Right: reconstructed surface

32. Example Poisson

33. Example Poisson Left: 50K points sampled on Neptune trident Right: point set simplified to 1K then reconstructed

34. Example Poisson Left: points sampled on a sphere with flipped normals Right: reconstructed surface

35. Example Poisson Left: 4K points sampled on a mechanical piece with sharp edges Right: reconstructed surface

36. Poisson duration wrt #input points

37. Surface meshing duration and error wrt approximation distance

38. Memory wrt #input points

39. Reconstruction error wrt #input points

40. Reconstruction (2) • Algebraic point set surfaces (APSS) [Guennebaud, SIGGRAPH 2007] • Evaluates an implicit function on the fly (~signed distance function) • Isosurface extracted by CGAL surface mesh generator

41. Based on Moving Least Squares fitting on algebraic spheres APSS

42. Point projection APSS

43. APSS

44. can evaluate an implicit function at any point APSS

45. APSS

46. Poisson vs APSS? INPUT = 275K points sampled on an elephant (minolta laser scanner)

47. Poisson APSS Approximation error in surface mesh generator: 0.004

48. Poisson APSS Approximation error in surface mesh generator: 0.002

49. Poisson APSS Approximation error in surface mesh generator: 0.001 always a bit smoother one extra component

50. Documentation • Current: 98 pages • Reference manual available online • User manual available online Demo • Current: 3D point set demo (QT4 + QGLViewer)