a hierarchical method for aligning warped meshes leslie ikemoto 1, natasha gelfand 2, marc levoy 2 1...
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A Hierarchical Method for Aligning Warped Meshes
Leslie Ikemoto1,Natasha Gelfand2,
Marc Levoy2
1UC Berkeley, formerly Stanford2Stanford University
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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Scan Alignment Pipeline
Globalrelaxation
Scanmerging
Pairwisealignment
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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Alignment MethodsPairwise alignment:
Iterated Closest Point (ICP)[Variant from Chen-Medioni ‘91]
pi
qi
ni
Global relaxation: Global registration
Point constraints from ICP
Rigid scans
1) Compute R, t minimizing distances from pi to tangent plane at qi
2) Apply transform and repeat
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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The Digital Michelangelo Statue Scanner
• Large • High resolution (0.25 mm)• Reconfigurable• Deployed in the field
Calibrated motions: pitch (yellow), pan (blue), horizontal translation (orange)
Uncalibrated motions: vertical translation (red), remounting the scan head, reconfiguring the scanner, moving the entire scanner
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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Registration Errors
ICP Global Registration
Correct calibration0.13 mm avg. err.
Incorrect calibration1.81 mm avg. err.
4 mm misalignment
Correct calibration
Incorrect calibration
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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Model Generated
Spacing of range samples = 0.5 mm
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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Possible Solutions
• Calibrate the scanner better• Learn warp by self-calibration• Introduce compensating warp
– fit low-order polynomial to warp– use piecewise rigid approximation to curved warp
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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Compensating WarpSmooth warp Approximate with a piecewise rigid
model of overlapping sub-meshes
Create pieces hierarchically
R, T R1..8, T1..8
13 original scans 84 sub-meshes
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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Proposed Pipeline
Pairwisealignment
Globalregistration
Find most misaligned
pair of scans
Globalregistration
Dice intopieces
Pairwise alignment
Scanmerging
Loop until error below threshold
Initial guess
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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Design Criteria for Dicing a Scan
• Isotropic warp– Keep even aspect ratio
• Overlap with neighbors– Needed for alignment– Use size to control
tendency to warp• Sufficiently
constraining features for alignment– Pre-analyze meshes for ICP
stability
No features
Arbitrary cutting planes
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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Determining Placement of Cutting Planes
• Even aspect ratio: dice along longest dimension of oriented bounding-box
• Overlap: determined empirically (30% of oriented bounding box)
Smaller overlap
Lower squared error
Larger overlap
Higher squared errorMesh dicing scheme
Overlap size affects “hinge stiffness”
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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Determining Whether to Dice Using Stability Analysis
• Sufficiently constraining features: stability analysis to determine degenerate geometries [Gelfand et al. 3DIM03]
2 translations, 1 rotation 3 rotations 1 rotation, 1 translation
1 rotation 1 translation
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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Sampling Technique
• Sample to constrain transformations during alignment [Gelfand et al. 3DIM03]
Translation in the plane
Rotation in the plane
Rotation out of the plane
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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Running Times
MeshesPolygons (million)
Pair Matching
Global Reg.# Points Selected
Dicing
4 meshes 31 3:09 0:02 1200
37 scanner sweeps
31 10:33 0:02 25,800 2:15
75 sub-meshes
35.8 34:00 0:04 26,200 2:30
117 sub-meshes
40.2 21:00 0:05 63,510 3:30
160 sub-meshes
46.1 20:00 0:06 123,110 3:00
197 sub-meshes
52.2 17:00 0:13 204,268
• Forma Urbis fragment, approximately 85 cm x 120 cm• Hardware: Intel P4, 2.80 GHz
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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Model Generated
OriginalAfter warping
Average error = 0.8 mmAverage error = 1.15 mm
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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More Results
OriginalAfter warping
Avg. err. =0.4 mm
Avg. err. =0.8 mm
Blurry lines
Double lines
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Conclusions
• Alignment method for smoothly warped meshes– Introduce minimal compensating warp– Does not require a specific characterization of
scanner warp– Relatively simple to implement
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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Limitations
Will not converge if:
• scans very noisy
• scans do not have many features
• warp is not smooth
October 9, 2003 A Hierarchical Method for Aligning Warped Meshes
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Future Work
• Fit smooth spline – yields non-rigid warp– retrospective scanner
calibration
• One-to-many stability
analysis• Improve measurement
strategy
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