Hoip10 presentación reconstrucción de superficies_upc

Motivation and SoAPropagation AlgorithmExperimental Results

Conclusion

Surface Reconstructionby

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

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

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

Conclusion

State of the Art

Results are evaluated against a reference composed of:

Ball-Pivoting Algorithm

• Very accuratereconstruction

• Sensitive to densityvariations

Poisson Reconstruction

• Watertight reconstructedsurface

• Fast reconstructions providelow level of detail

Marching Cubes + APSS

• Voxelization required

all of them implemented in the MeshLab c© software

Conclusion

State of the Art

Conclusion

State of the Art

Conclusion

State of the Art

Conclusion

Outline

4 Conclusion

Conclusion

Algorithm overview

From 3D point clouds...

...to meshed surfaces

Conclusion

Algorithm overview

Conclusion

Algorithm overview

Conclusion

Voxelization

• The target point cloud S is composed of points pi = (Pi , Ci ) withPi = (xi , yi , zi ) and Ci = (ri , gi , bi )

• Voxels υk are associated to pi as follows

0 points in voxel

υk ← ∅

1 point p = (P, C) in voxel

υk ← (P, C)

m points pj

υk ← (P, C)

Voxels υk 6= ∅ are called seed voxels, or υS

Conclusion

Voxelization

• The target point cloud S is composed of points pi = (Pi , Ci ) withPi = (xi , yi , zi ) and Ci = (ri , gi , bi )

• Voxels υk are associated to pi as follows

0 points in voxel

υk ← ∅

1 point p = (P, C) in voxel

υk ← (P, C)

m points pj

υk ← (P, C)

Voxels υk 6= ∅ are called seed voxels, or υS

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 indi�erent

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

Conclusion

Propagation Pattern

Conclusion

Propagation Pattern

Conclusion

Propagation Pattern

Conclusion

Propagation Steps

Iterative Algorithm

• Propagation starts at every seed voxel υSi

• Voxels ∈ 6DO are associated to its seedvoxels υSi , building up seed volumes Vithat grow at every iteration

• At propagation end, intersections Vi ∩ Vjde�ne pairs of neighbors pi ! pj

• Triangular faces are obtained from the listof neighbors

Conclusion

Propagation Steps

Iterative Algorithm

Conclusion

Propagation Steps

Iterative Algorithm

Conclusion

Propagation Steps

Iterative Algorithm

Conclusion

Propagation Steps

Iterative Algorithm

Conclusion

Propagation Steps

Iterative Algorithm

Conclusion

Propagation Steps

Iterative Algorithm

Conclusion

Propagation Steps

Iterative Algorithm

Conclusion

Stop Threshold

Propagation iterations should be stopped at the appropriate moment to avoidmeshing distant points

Edge Density

• The number of created edges per iteration is called edge density or De

• De presents a �rst maximumDemax at a low number ofiterations κmax, which correspondsto the meshing of the main surface

• Propagation stops at iteration k

which veri�es:(κ ≥ 2κmax)

)∧(De(κ) <

4Demax

Conclusion

Stop Threshold

Edge Density

)∧(De(κ) <

4Demax

Conclusion

Stop Threshold

Edge Density

)∧(De(κ) <

4Demax

Conclusion

Stop Threshold

Edge Density

)∧(De(κ) <

4Demax

Conclusion

Outline

4 Conclusion

Conclusion

Evaluation of results

Quantitative Evaluation

Two main characteristics are evaluated:

δH Hausdor� Distance metric between a groundtruth surface and areconstructed 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

Conclusion

Voxelization e�ect

Voxelization resolution is ReOP's critical parameter

• Low resolution: Poor visual quality

• High resolution: Higher calculation time and memory requirements

76×57×34 voxels11,145 vertices76,124 faces

17.3 s

Conclusion

Evaluation on the (δH , tO) plane

Happy Buddha dataset (543,652 points)

(δH , tO) plane Point Cloud

Conclusion

(δH , tO) plane Ball-Pivoting

238, 193 faces

(δH , tO ) = (0.000719, 1429 s)

Conclusion

(δH , tO) plane MCubes+APSS

2, 641, 481 faces

(δH , tO ) = (0.000046, 528 s)

Conclusion

(δH , tO) plane Poisson Reconstruction

631, 480 faces

(δH , tO ) = (0.000184, 65.1 s)

Conclusion

(δH , tO) plane ReOP

1, 367, 336 faces

(δH , tO ) = (0.000031, 22.2 s)

Conclusion

Comparative (Happy Buddha - 543,652 points)

Ball-Pivoting

238, 193 faces

(δH , tO ) =

(0.000719, 1429 s)

MCubes+APSS

2, 641, 481 faces

(δH , tO ) =

(0.000046, 528 s)

Poisson Rec.

631, 480 faces

(δH , tO ) =

(0.000184, 65.1 s)

1, 367, 336 faces

(δH , tO ) =

(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

Conclusion

Ball-Pivoting

238, 193 faces

(δH , tO ) =

(0.000719, 1429 s)

MCubes+APSS

2, 641, 481 faces

(δH , tO ) =

(0.000046, 528 s)

Poisson Rec.

631, 480 faces

(δH , tO ) =

(0.000184, 65.1 s)

1, 367, 336 faces

(δH , tO ) =

(0.000031, 22.2 s)

Conclusion

Ball-Pivoting

238, 193 faces

(δH , tO ) =

(0.000719, 1429 s)

MCubes+APSS

2, 641, 481 faces

(δH , tO ) =

(0.000046, 528 s)

Poisson Rec.

631, 480 faces

(δH , tO ) =

(0.000184, 65.1 s)

1, 367, 336 faces

(δH , tO ) =

(0.000031, 22.2 s)

Conclusion

Stanford Bunny dataset (35,947 points)

(δH , tO) plane Point Cloud

Conclusion

(δH , tO) plane Ball-Pivoting

238, 193 faces

(δH , tO ) = (0.000113, 8.2 s)

Conclusion

(δH , tO) plane MCubes+APSS

2, 641, 481 faces

(δH , tO ) = (0.000042, 23 s)

Conclusion

(δH , tO) plane Poisson Reconstruction

631, 480 faces

(δH , tO ) = (0.000285, 10.3 s)

Conclusion

(δH , tO) plane ReOP

1, 367, 336 faces

(δH , tO ) = (0.000044, 0.96 s)

Conclusion

Comparative (Stanford Bunny - 35,947 points)

Ball-Pivoting

70, 832 faces

(δH , tO ) =

(0.000113, 8.2 s)

MCubes+APSS

769, 029 faces

(δH , tO ) =

(0.000042, 23 s)

Poisson Rec.

70, 438 faces

(δH , tO ) =

(0.000285, 10.3 s)

147, 029 faces

(δH , tO ) =

(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

Conclusion

Ball-Pivoting

70, 832 faces

(δH , tO ) =

(0.000113, 8.2 s)

MCubes+APSS

769, 029 faces

(δH , tO ) =

(0.000042, 23 s)

Poisson Rec.

70, 438 faces

(δH , tO ) =

(0.000285, 10.3 s)

147, 029 faces

(δH , tO ) =

(0.000044, 0.96 s)

Conclusion

Ball-Pivoting

70, 832 faces

(δH , tO ) =

(0.000113, 8.2 s)

MCubes+APSS

769, 029 faces

(δH , tO ) =

(0.000042, 23 s)

Poisson Rec.

70, 438 faces

(δH , tO ) =

(0.000285, 10.3 s)

147, 029 faces

(δH , tO ) =

(0.000044, 0.96 s)

Conclusion

Outline

4 Conclusion

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 inexperiments)

• Large datasets reconstruction (millions of points), such those obtained inmultiview applications

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

Thank You

Questions

Hoip10 presentación reconstrucción de superficies_upc

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