Presentación de la Universidad Politécnica de Catalunya sobre reconstrucciónde superficies realizada durante las jornadas HOIP 2010 organizadas por la Unidad de Sistemas de Información e Interacción TECNALIA. Más información en http://www.tecnalia.com/es/ict-european-software-institute/index.htm

1. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Surface Reconstruction
by
Restricted and Oriented Propagation
Xavier Suau Josep R. Casas Javier Ruiz-Hidalgo
{xavier.suau, josep.ramon.casas, j.ruiz}@upc.edu
Universitat Politècnica de Catalunya
November 16, 2010

2. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Outline
1 Motivation and state of the art
2 Propagation Algorithm
3 Experimental Results
4 Conclusion
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 1 / 20

3. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Context
Large 3D point clouds are very common datasets, being mostly obtained from:
Laser scans Multiview datasets Virtual datasets
The objective is to have a meshed representation of these type of datasets
in this case, for visualization purposes
in a fast, up to real-time, way
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 2 / 20

4. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
State of the Art
Results are evaluated against a reference composed of:
Ball-Pivoting Algorithm Poisson Reconstruction Marching Cubes + APSS
• Very accurate • Watertight reconstructed • Watertight reconstructed
reconstruction surface surface
• Sensitive to density • Fast reconstructions provide • Voxelization required
variations low level of detail
all of them implemented in the MeshLab software c
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 3 / 20

5. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
State of the Art
Results are evaluated against a reference composed of:
Ball-Pivoting Algorithm Poisson Reconstruction Marching Cubes + APSS
• Very accurate • Watertight reconstructed • Watertight reconstructed
reconstruction surface surface
• Sensitive to density • Fast reconstructions provide • Voxelization required
variations low level of detail
all of them implemented in the MeshLab software c
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 3 / 20

6. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
State of the Art
Results are evaluated against a reference composed of:
Ball-Pivoting Algorithm Poisson Reconstruction Marching Cubes + APSS
• Very accurate • Watertight reconstructed • Watertight reconstructed
reconstruction surface surface
• Sensitive to density • Fast reconstructions provide • Voxelization required
variations low level of detail
all of them implemented in the MeshLab software c
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 3 / 20

7. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
State of the Art
Results are evaluated against a reference composed of:
Ball-Pivoting Algorithm Poisson Reconstruction Marching Cubes + APSS
• Very accurate • Watertight reconstructed • Watertight reconstructed
reconstruction surface surface
• Sensitive to density • Fast reconstructions provide • Voxelization required
variations low level of detail
all of them implemented in the MeshLab software c
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 3 / 20

8. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Outline
1 Motivation and state of the art
2 Propagation Algorithm
3 Experimental Results
4 Conclusion
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 4 / 20

9. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Algorithm overview
From 3D point clouds...
...to meshed surfaces
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 5 / 20

10. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Algorithm overview
From 3D point clouds...
...to meshed surfaces
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 5 / 20

11. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Algorithm overview
From 3D point clouds...
...to meshed surfaces
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 5 / 20

12. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Voxelization
• The target point cloud S is composed of points pi = (Pi , Ci ) with
Pi = (xi , yi , zi ) and Ci = (ri , gi , bi )
• Voxels υk are associated to pi as follows
0 points in voxel 1 point p = (P, C) in voxel m points pj
υk ← ∅ υk ← (P, C) υk ← (P, C)
Voxels υk = ∅ are called seed voxels, or υS
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 6 / 20

13. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Voxelization
• The target point cloud S is composed of points pi = (Pi , Ci ) with
Pi = (xi , yi , zi ) and Ci = (ri , gi , bi )
• Voxels υk are associated to pi as follows
0 points in voxel 1 point p = (P, C) in voxel m points pj
υk ← ∅ υk ← (P, C) υk ← (P, C)
Voxels υk = ∅ are called seed voxels, or υS
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 6 / 20

14. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Propagation Pattern
Propagation, why? To nd close neighbors in the discretized space
How? With a propagation pattern or set of positions relative to a seed voxel
Omni-26 Omni-18 Omni-6 6DO Oriented Pattern
Knowing that direction of neighbor nding is indierent
Omni patterns check both directions, redundant!
The 6DO Oriented Pattern
• Reduces the amount of redundant edges
• Is faster than Omni-18 with the same spatial coverage
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 7 / 20

15. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Propagation Pattern
Propagation, why? To nd close neighbors in the discretized space
How? With a propagation pattern or set of positions relative to a seed voxel
Omni-26 Omni-18 Omni-6 6DO Oriented Pattern
Knowing that direction of neighbor nding is indierent
Omni patterns check both directions, redundant!
The 6DO Oriented Pattern
• Reduces the amount of redundant edges
• Is faster than Omni-18 with the same spatial coverage
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 7 / 20

16. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Propagation Pattern
Propagation, why? To nd close neighbors in the discretized space
How? With a propagation pattern or set of positions relative to a seed voxel
Omni-26 Omni-18 Omni-6 6DO Oriented Pattern
Knowing that direction of neighbor nding is indierent
Omni patterns check both directions, redundant!
The 6DO Oriented Pattern
• Reduces the amount of redundant edges
• Is faster than Omni-18 with the same spatial coverage
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 7 / 20

17. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Propagation Pattern
Propagation, why? To nd close neighbors in the discretized space
How? With a propagation pattern or set of positions relative to a seed voxel
Omni-26 Omni-18 Omni-6 6DO Oriented Pattern
Knowing that direction of neighbor nding is indierent
Omni patterns check both directions, redundant!
The 6DO Oriented Pattern
• Reduces the amount of redundant edges
• Is faster than Omni-18 with the same spatial coverage
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 7 / 20

18. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Propagation Steps
Iterative Algorithm
• Propagation starts at every seed voxel υiS
• Voxels ∈ 6DO are associated to its seed
voxels υiS , building up seed volumes Vi
that grow at every iteration
• At propagation end, intersections Vi ∩ Vj
dene pairs of neighbors pi pj
• Triangular faces are obtained from the list
of neighbors
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 8 / 20

19. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Propagation Steps
Iterative Algorithm
• Propagation starts at every seed voxel υiS
• Voxels ∈ 6DO are associated to its seed
voxels υiS , building up seed volumes Vi
that grow at every iteration
• At propagation end, intersections Vi ∩ Vj
dene pairs of neighbors pi pj
• Triangular faces are obtained from the list
of neighbors
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 8 / 20

20. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Propagation Steps
Iterative Algorithm
• Propagation starts at every seed voxel υiS
• Voxels ∈ 6DO are associated to its seed
voxels υiS , building up seed volumes Vi
that grow at every iteration
• At propagation end, intersections Vi ∩ Vj
dene pairs of neighbors pi pj
• Triangular faces are obtained from the list
of neighbors
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 8 / 20

21. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Propagation Steps
Iterative Algorithm
• Propagation starts at every seed voxel υiS
• Voxels ∈ 6DO are associated to its seed
voxels υiS , building up seed volumes Vi
that grow at every iteration
• At propagation end, intersections Vi ∩ Vj
dene pairs of neighbors pi pj
• Triangular faces are obtained from the list
of neighbors
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 8 / 20

22. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Propagation Steps
Iterative Algorithm
• Propagation starts at every seed voxel υiS
• Voxels ∈ 6DO are associated to its seed
voxels υiS , building up seed volumes Vi
that grow at every iteration
• At propagation end, intersections Vi ∩ Vj
dene pairs of neighbors pi pj
• Triangular faces are obtained from the list
of neighbors
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 8 / 20

23. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Propagation Steps
Iterative Algorithm
• Propagation starts at every seed voxel υiS
• Voxels ∈ 6DO are associated to its seed
voxels υiS , building up seed volumes Vi
that grow at every iteration
• At propagation end, intersections Vi ∩ Vj
dene pairs of neighbors pi pj
• Triangular faces are obtained from the list
of neighbors
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 8 / 20

24. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Propagation Steps
Iterative Algorithm
• Propagation starts at every seed voxel υiS
• Voxels ∈ 6DO are associated to its seed
voxels υiS , building up seed volumes Vi
that grow at every iteration
• At propagation end, intersections Vi ∩ Vj
dene pairs of neighbors pi pj
• Triangular faces are obtained from the list
of neighbors
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 8 / 20

25. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Propagation Steps
Iterative Algorithm
• Propagation starts at every seed voxel υiS
• Voxels ∈ 6DO are associated to its seed
voxels υiS , building up seed volumes Vi
that grow at every iteration
• At propagation end, intersections Vi ∩ Vj
dene pairs of neighbors pi pj
• Triangular faces are obtained from the list
of neighbors
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 8 / 20

26. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Stop Threshold
Propagation iterations should be stopped at the appropriate moment to avoid
meshing distant points
Edge Density
• The number of created edges per iteration is called edge density or De
• D e presents a rst maximum
D e
max
at a low number of
iterations κmax , which corresponds
to the meshing of the main surface
• Propagation stops at iteration k
which veries:
1
κ ≥ 2κmax ) ∧ e (κ)
4 e
D D max
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 9 / 20

27. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Stop Threshold
Propagation iterations should be stopped at the appropriate moment to avoid
meshing distant points
Edge Density
• The number of created edges per iteration is called edge density or De
• D e presents a rst maximum
D e
max
at a low number of
iterations κmax , which corresponds
to the meshing of the main surface
• Propagation stops at iteration k
which veries:
1
κ ≥ 2κmax ) ∧ e (κ)
4 e
D D max
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 9 / 20

28. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Stop Threshold
Propagation iterations should be stopped at the appropriate moment to avoid
meshing distant points
Edge Density
• The number of created edges per iteration is called edge density or De
• D e presents a rst maximum
D e
max
at a low number of
iterations κmax , which corresponds
to the meshing of the main surface
• Propagation stops at iteration k
which veries:
1
κ ≥ 2κmax ) ∧ e (κ)
4 e
D D max
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 9 / 20

29. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Stop Threshold
Propagation iterations should be stopped at the appropriate moment to avoid
meshing distant points
Edge Density
• The number of created edges per iteration is called edge density or De
• D e presents a rst maximum
D e
max
at a low number of
iterations κmax , which corresponds
to the meshing of the main surface
• Propagation stops at iteration k
which veries:
1
κ ≥ 2κmax ) ∧ e (κ)
4 e
D D max
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 9 / 20

30. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Outline
1 Motivation and state of the art
2 Propagation Algorithm
3 Experimental Results
4 Conclusion
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 10 / 20

31. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Evaluation of results
Quantitative Evaluation
Two main characteristics are evaluated:
δH Hausdor Distance metric between a groundtruth surface and a
reconstructed surface
tO Overall calculation time on a 64-bit Intel Xeon CPU @ 3.00GHz processor
(includes memory allocation and mesh writing)
Results are presented on an Accuracy Vs. Speed (δH , tO ) plane
Qualitative Evaluation
Global visual inspection
Four 3D models provided by the Stanford 3D Scanning Repository are tested:
Bunny Hand Dragon Happy Buddha
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 11 / 20

32. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Evaluation of results
Quantitative Evaluation
Two main characteristics are evaluated:
δH Hausdor Distance metric between a groundtruth surface and a
reconstructed surface
tO Overall calculation time on a 64-bit Intel Xeon CPU @ 3.00GHz processor
(includes memory allocation and mesh writing)
Results are presented on an Accuracy Vs. Speed (δH , tO ) plane
Qualitative Evaluation
Global visual inspection
Four 3D models provided by the Stanford 3D Scanning Repository are tested:
Bunny Hand Dragon Happy Buddha
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 11 / 20

33. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Evaluation of results
Quantitative Evaluation
Two main characteristics are evaluated:
δH Hausdor Distance metric between a groundtruth surface and a
reconstructed surface
tO Overall calculation time on a 64-bit Intel Xeon CPU @ 3.00GHz processor
(includes memory allocation and mesh writing)
Results are presented on an Accuracy Vs. Speed (δH , tO ) plane
Qualitative Evaluation
Global visual inspection
Four 3D models provided by the Stanford 3D Scanning Repository are tested:
Bunny Hand Dragon Happy Buddha
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 11 / 20

34. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Evaluation of results
Quantitative Evaluation
Two main characteristics are evaluated:
δH Hausdor Distance metric between a groundtruth surface and a
reconstructed surface
tO Overall calculation time on a 64-bit Intel Xeon CPU @ 3.00GHz processor
(includes memory allocation and mesh writing)
Results are presented on an Accuracy Vs. Speed (δH , tO ) plane
Qualitative Evaluation
Global visual inspection
Four 3D models provided by the Stanford 3D Scanning Repository are tested:
Bunny Hand Dragon Happy Buddha
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 11 / 20

35. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Evaluation of results
Quantitative Evaluation
Two main characteristics are evaluated:
δH Hausdor Distance metric between a groundtruth surface and a
reconstructed surface
tO Overall calculation time on a 64-bit Intel Xeon CPU @ 3.00GHz processor
(includes memory allocation and mesh writing)
Results are presented on an Accuracy Vs. Speed (δH , tO ) plane
Qualitative Evaluation
Global visual inspection
Four 3D models provided by the Stanford 3D Scanning Repository are tested:
Bunny Hand Dragon Happy Buddha
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 11 / 20

36. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Voxelization eect
Voxelization resolution is ReOP's critical parameter
• Low resolution: Poor visual quality
• High resolution: Higher calculation time and memory requirements
76×57×34 voxels 226×170×101 voxels 376×283×168 voxels
11,145 vertices 85,082 vertices 181,509 vertices
76,124 faces 529,916 faces 994,578 faces
1.2 s 8.9 s 17.3 s
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 12 / 20

37. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Evaluation on the (δH , tO ) plane
Happy Buddha dataset (543,652 points)
(δH , tO ) plane Point Cloud
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 13 / 20

38. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Evaluation on the (δH , tO ) plane
Happy Buddha dataset (543,652 points)
(δH , tO ) plane Ball-Pivoting
238, 193 faces
(δH , tO ) = (0.000719, 1429 s )
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 13 / 20

39. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Evaluation on the (δH , tO ) plane
Happy Buddha dataset (543,652 points)
(δH , tO ) plane MCubes+APSS
2, 641, 481 faces
(δH , tO ) = (0.000046, 528 s )
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 13 / 20

40. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Evaluation on the (δH , tO ) plane
Happy Buddha dataset (543,652 points)
(δH , tO ) plane Poisson Reconstruction
631, 480 faces
(δH , tO ) = (0.000184, 65.1 s )
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 13 / 20

41. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Evaluation on the (δH , tO ) plane
Happy Buddha dataset (543,652 points)
(δH , tO ) plane ReOP
1, 367, 336 faces
(δH , tO ) = (0.000031, 22.2 s )
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 13 / 20

42. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Comparative (Happy Buddha - 543,652 points)
Ball-Pivoting MCubes+APSS Poisson Rec. ReOP
238, 193 faces 2, 641, 481 faces 631, 480faces 1, 367, 336 faces
tO ) =
(δH , tO ) =
(δH , tO ) =
(δH , tO ) =
(δH ,
(0.000719, 1429 s ) (0.000046, 528 s ) (0.000184, 65.1 s ) (0.000031, 22.2 s )
Results on Happy Buddha, largest dataset
• About 23x faster than MCubes+APSS for a similar good quality
• Reasonable amount of faces, about 2.5 · Npoints
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 14 / 20

43. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Comparative (Happy Buddha - 543,652 points)
Ball-Pivoting MCubes+APSS Poisson Rec. ReOP
238, 193 faces 2, 641, 481 faces 631, 480faces 1, 367, 336 faces
tO ) =
(δH , tO ) =
(δH , tO ) =
(δH , tO ) =
(δH ,
(0.000719, 1429 s ) (0.000046, 528 s ) (0.000184, 65.1 s ) (0.000031, 22.2 s )
Results on Happy Buddha, largest dataset
• About 23x faster than MCubes+APSS for a similar good quality
• Reasonable amount of faces, about 2.5 · Npoints
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 14 / 20

44. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Comparative (Happy Buddha - 543,652 points)
Ball-Pivoting MCubes+APSS Poisson Rec. ReOP
238, 193 faces 2, 641, 481 faces 631, 480faces 1, 367, 336 faces
tO ) =
(δH , tO ) =
(δH , tO ) =
(δH , tO ) =
(δH ,
(0.000719, 1429 s ) (0.000046, 528 s ) (0.000184, 65.1 s ) (0.000031, 22.2 s )
Results on Happy Buddha, largest dataset
• About 23x faster than MCubes+APSS for a similar good quality
• Reasonable amount of faces, about 2.5 · Npoints
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 14 / 20

45. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Evaluation on the (δH , tO ) plane
Stanford Bunny dataset (35,947 points)
(δH , tO ) plane Point Cloud
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 15 / 20

46. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Evaluation on the (δH , tO ) plane
Stanford Bunny dataset (35,947 points)
(δH , tO ) plane Ball-Pivoting
238, 193 faces
(δH , tO ) = (0.000113, 8.2 s )
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 15 / 20

47. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Evaluation on the (δH , tO ) plane
Stanford Bunny dataset (35,947 points)
(δH , tO ) plane MCubes+APSS
2, 641, 481 faces
(δH , tO ) = (0.000042, 23 s )
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 15 / 20

48. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Evaluation on the (δH , tO ) plane
Stanford Bunny dataset (35,947 points)
(δH , tO ) plane Poisson Reconstruction
631, 480 faces
(δH , tO ) = (0.000285, 10.3 s )
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 15 / 20

49. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Evaluation on the (δH , tO ) plane
Stanford Bunny dataset (35,947 points)
(δH , tO ) plane ReOP
1, 367, 336 faces
(δH , tO ) = (0.000044, 0.96 s )
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 15 / 20

50. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Comparative (Stanford Bunny - 35,947 points)
Ball-Pivoting MCubes+APSS Poisson Rec. ReOP
70, 832faces 769, 029faces 70, 438faces 147, 029faces
(δH ,tO ) = tO ) =
(δH , tO ) =
(δH , tO ) =
(δH ,
(0.000113, 8.2 s ) (0.000042, 23 s ) (0.000285, 10.3 s ) (0.000044, 0.96 s )
Results on Stanford Bunny, smallest dataset
• About 23x faster than MCubes+APSS for a the same quality
• Reasonable amount of faces, about 3 · Npoints
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 16 / 20

51. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Comparative (Stanford Bunny - 35,947 points)
Ball-Pivoting MCubes+APSS Poisson Rec. ReOP
70, 832faces 769, 029faces 70, 438faces 147, 029faces
(δH ,tO ) = tO ) =
(δH , tO ) =
(δH , tO ) =
(δH ,
(0.000113, 8.2 s ) (0.000042, 23 s ) (0.000285, 10.3 s ) (0.000044, 0.96 s )
Results on Stanford Bunny, smallest dataset
• About 23x faster than MCubes+APSS for a the same quality
• Reasonable amount of faces, about 3 · Npoints
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 16 / 20

52. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Comparative (Stanford Bunny - 35,947 points)
Ball-Pivoting MCubes+APSS Poisson Rec. ReOP
70, 832faces 769, 029faces 70, 438faces 147, 029faces
(δH ,tO ) = tO ) =
(δH , tO ) =
(δH , tO ) =
(δH ,
(0.000113, 8.2 s ) (0.000042, 23 s ) (0.000285, 10.3 s ) (0.000044, 0.96 s )
Results on Stanford Bunny, smallest dataset
• About 23x faster than MCubes+APSS for a the same quality
• Reasonable amount of faces, about 3 · Npoints
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 16 / 20

53. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Outline
1 Motivation and state of the art
2 Propagation Algorithm
3 Experimental Results
4 Conclusion
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 17 / 20

54. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
The presented ReOP algorithm is...
• Surface reconstruction is performed about 23x faster than the reference,
for a given quality
• ReOP quality is similar to the best reference method
• ReOP reconstructed mesh is visually clear and presents few artifacts
• The seed voxel/volume structure is suitable to be parallelized on GPU
• The output mesh has no manifold properties
ReOP is suitable for...
• Real-time applications with small datasets (50,000 points in
experiments)
• Large datasets reconstruction (millions of points), such those obtained in
multiview applications
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 18 / 20

55. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
The presented ReOP algorithm is...
• Surface reconstruction is performed about 23x faster than the reference,
for a given quality
• ReOP quality is similar to the best reference method
• ReOP reconstructed mesh is visually clear and presents few artifacts
• The seed voxel/volume structure is suitable to be parallelized on GPU
• The output mesh has no manifold properties
ReOP is suitable for...
• Real-time applications with small datasets (50,000 points in
experiments)
• Large datasets reconstruction (millions of points), such those obtained in
multiview applications
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 18 / 20

56. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
The presented ReOP algorithm is...
• Surface reconstruction is performed about 23x faster than the reference,
for a given quality
• ReOP quality is similar to the best reference method
• ReOP reconstructed mesh is visually clear and presents few artifacts
• The seed voxel/volume structure is suitable to be parallelized on GPU
• The output mesh has no manifold properties
ReOP is suitable for...
• Real-time applications with small datasets (50,000 points in
experiments)
• Large datasets reconstruction (millions of points), such those obtained in
multiview applications
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 18 / 20

57. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
The presented ReOP algorithm is...
• Surface reconstruction is performed about 23x faster than the reference,
for a given quality
• ReOP quality is similar to the best reference method
• ReOP reconstructed mesh is visually clear and presents few artifacts
• The seed voxel/volume structure is suitable to be parallelized on GPU
• The output mesh has no manifold properties
ReOP is suitable for...
• Real-time applications with small datasets (50,000 points in
experiments)
• Large datasets reconstruction (millions of points), such those obtained in
multiview applications
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 18 / 20

58. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
The presented ReOP algorithm is...
• Surface reconstruction is performed about 23x faster than the reference,
for a given quality
• ReOP quality is similar to the best reference method
• ReOP reconstructed mesh is visually clear and presents few artifacts
• The seed voxel/volume structure is suitable to be parallelized on GPU
• The output mesh has no manifold properties
ReOP is suitable for...
• Real-time applications with small datasets (50,000 points in
experiments)
• Large datasets reconstruction (millions of points), such those obtained in
multiview applications
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 18 / 20

59. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
The presented ReOP algorithm is...
• Surface reconstruction is performed about 23x faster than the reference,
for a given quality
• ReOP quality is similar to the best reference method
• ReOP reconstructed mesh is visually clear and presents few artifacts
• The seed voxel/volume structure is suitable to be parallelized on GPU
• The output mesh has no manifold properties
ReOP is suitable for...
• Real-time applications with small datasets (50,000 points in
experiments)
• Large datasets reconstruction (millions of points), such those obtained in
multiview applications
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 18 / 20

60. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
The presented ReOP algorithm is...
• Surface reconstruction is performed about 23x faster than the reference,
for a given quality
• ReOP quality is similar to the best reference method
• ReOP reconstructed mesh is visually clear and presents few artifacts
• The seed voxel/volume structure is suitable to be parallelized on GPU
• The output mesh has no manifold properties
ReOP is suitable for...
• Real-time applications with small datasets (50,000 points in
experiments)
• Large datasets reconstruction (millions of points), such those obtained in
multiview applications
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 18 / 20

61. Motivation and SoA
Propagation Algorithm
Experimental Results
Conclusion
Future work
• Adapt propagation pattern to topology and sampling density of surfaces
• Find faster structures for close neighbor queries (eg. kdtree)
• Obtain manifold meshes while preserving execution speed
• GPU implementation
Xavier Suau, Josep R. Casas, Javier Ruiz-Hidalgo Surface Reconstruction by ReOP 19 / 20

62. Thank You
Questions