A Hierarchical Method for Aligning Warped Meshes - PowerPoint PPT Presentation

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A Hierarchical Method for Aligning Warped Meshes

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Title: A Hierarchical Method for Aligning Warped Meshes


1
A Hierarchical Method for Aligning Warped Meshes
  • Leslie Ikemoto1,
  • Natasha Gelfand2,
  • Marc Levoy2

1UC Berkeley, formerly Stanford 2Stanford
University
2
Scan Alignment Pipeline
3
Alignment Methods
  • Pairwise alignment
  • Iterated Closest Point (ICP)
  • Variant from Chen-Medioni 91

Global relaxation Global registration
1) Compute R, t minimizing distances from pi to
tangent plane at qi
2) Apply transform and repeat
Rigid scans
4
The Digital Michelangelo Statue Scanner
  • Large
  • High resolution (0.25 mm)
  • Reconfigurable
  • Deployed in the field

5
Registration Errors
  • ICP

Global Registration
Correct calibration
4 mm misalignment
Correct calibration 0.13 mm avg. err.
Incorrect calibration 1.81 mm avg. err.
Incorrect calibration
6
Model Generated
Spacing of range samples 0.5 mm
7
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

8
Compensating Warp
  • Smooth warp

Approximate with a piecewise rigid model of
overlapping sub-meshes
Create pieces hierarchically
13 original scans
84 sub-meshes
R, T
R1..8, T1..8
9
Proposed Pipeline
Find most misaligned pair of scans
Loop until error below threshold
Initial guess
Dice into pieces
Global registration
Pairwise alignment
Pairwise alignment
Global registration
Scan merging
10
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

11
Determining Placement of Cutting Planes
Overlap size affects hinge stiffness
  • Even aspect ratio dice along longest dimension
    of oriented bounding-box
  • Overlap determined empirically (30 of oriented
    bounding box)

12
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 translation
1 rotation
13
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
14
Running Times
  • Forma Urbis fragment, approximately 85 cm x 120
    cm
  • Hardware Intel P4, 2.80 GHz

Meshes Polygons (million) Pair Matching Global Reg. Points Selected Dicing
4 meshes 31 309 002 1200
37 scanner sweeps 31 1033 002 25,800 215
75 sub-meshes 35.8 3400 004 26,200 230
117 sub-meshes 40.2 2100 005 63,510 330
160 sub-meshes 46.1 2000 006 123,110 300
197 sub-meshes 52.2 1700 013 204,268
15
Model Generated
Original
After warping
Average error 0.8 mm
Average error 1.15 mm
16
More Results
Avg. err. 0.4 mm
Avg. err. 0.8 mm
Double lines
Original
After warping
Blurry lines
17
Conclusions
  • Alignment method for smoothly warped meshes
  • Introduce minimal compensating warp
  • Does not require a specific characterization of
    scanner warp
  • Relatively simple to implement

18
Limitations
  • Will not converge if
  • scans very noisy
  • scans do not have many features
  • warp is not smooth

19
Future Work
  • Fit smooth spline
  • yields non-rigid warp
  • retrospective scanner
  • calibration
  • One-to-many stability
  • analysis
  • Improve measurement
  • strategy

20
Acknowledgements
  • Our sponsors
  • National Science Foundation Research Grant
    IIS-0113427
  • Stanford University Presidents Fund
  • Also thanks to
  • Digital Michelangelo team
  • Forma Urbis team
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