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A Hierarchical Method for Aligning Warped Meshes

A Hierarchical Method for Aligning Warped Meshes. Leslie Ikemoto 1 , Natasha Gelfand 2 , Marc Levoy 2. 1 UC Berkeley, formerly Stanford 2 Stanford University. Pairwise alignment. Global relaxation. Scan merging. Scan Alignment Pipeline. n i. q i. p i. Point constraints from ICP.

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A Hierarchical Method for Aligning Warped Meshes

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  1. A Hierarchical Method for Aligning Warped Meshes Leslie Ikemoto1, Natasha Gelfand2, Marc Levoy2 1UC Berkeley, formerly Stanford 2Stanford University

  2. Pairwise alignment Global relaxation Scan merging Scan Alignment Pipeline A Hierarchical Method for Aligning Warped Meshes

  3. ni qi pi Point constraints from ICP Alignment Methods Global relaxation: Global registration Pairwise alignment: Iterated Closest Point (ICP) [Variant from Chen-Medioni ‘91] 1) Compute R, t minimizing distances from pi to tangent plane at qi 2) Apply transform and repeat Rigid scans A Hierarchical Method for Aligning Warped Meshes

  4. 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 The Digital Michelangelo Statue Scanner • Large • High resolution (0.25 mm) • Reconfigurable • Deployed in the field A Hierarchical Method for Aligning Warped Meshes

  5. Registration Errors Global Registration ICP Correct calibration 4 mm misalignment Correct calibration 0.13 mm avg. err. Incorrect calibration 1.81 mm avg. err. Incorrect calibration A Hierarchical Method for Aligning Warped Meshes

  6. Model Generated Spacing of range samples = 0.5 mm A Hierarchical Method for Aligning Warped Meshes

  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 A Hierarchical Method for Aligning Warped Meshes

  8. Compensating Warp Approximate with a piecewise rigid model of overlapping sub-meshes Smooth warp Create pieces hierarchically 13 original scans 84 sub-meshes R, T R1..8, T1..8 A Hierarchical Method for Aligning Warped Meshes

  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 A Hierarchical Method for Aligning Warped Meshes

  10. Arbitrary cutting planes No features 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 A Hierarchical Method for Aligning Warped Meshes

  11. Smaller overlap Lower squared error Larger overlap Higher squared error Mesh dicing scheme Determining Placement of Cutting Planes • Even aspect ratio: dice along longest dimension of oriented bounding-box • Overlap: determined empirically (30% of oriented bounding box) Overlap size affects “hinge stiffness” A Hierarchical Method for Aligning Warped Meshes

  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 A Hierarchical Method for Aligning Warped Meshes

  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 A Hierarchical Method for Aligning Warped Meshes

  14. Running Times • Forma Urbis fragment, approximately 85 cm x 120 cm • Hardware: Intel P4, 2.80 GHz A Hierarchical Method for Aligning Warped Meshes

  15. Model Generated Original After warping Average error = 0.8 mm Average error = 1.15 mm A Hierarchical Method for Aligning Warped Meshes

  16. More Results Avg. err. = 0.8 mm Avg. err. = 0.4 mm Double lines After warping Original Blurry lines A Hierarchical Method for Aligning Warped Meshes

  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 A Hierarchical Method for Aligning Warped Meshes

  18. Limitations Will not converge if: • scans very noisy • scans do not have many features • warp is not smooth A Hierarchical Method for Aligning Warped Meshes

  19. Future Work • Fit smooth spline • yields non-rigid warp • retrospective scanner calibration • One-to-many stability analysis • Improve measurement strategy A Hierarchical Method for Aligning Warped Meshes

  20. Acknowledgements Our sponsors… • National Science Foundation Research Grant IIS-0113427 • Stanford University President’s Fund Also thanks to… • Digital Michelangelo team • Forma Urbis team A Hierarchical Method for Aligning Warped Meshes

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