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An extreme occurrence of the missing data
W I D E B A S E L I N E – no point in more than 2 images!
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Difficult casesCoinciding camera centers
panorama zoom
Dominant planes
no problem
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Uneven image capture
26 images325 image pairs
Some important, but very few matches
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Uneven image capture
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Our method can solve
all previous examples.
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Algorithm
Technical contributionof this paper
• matches – uncalibrated EG [Matas et al. BMVC’02]
• focal length calibration
[Stewenius et al. CVPR’05], [Nister PAMI’04] [Chum]
• EG importance
• consistent rotations linearly
• bundle adjustment with constrained rotations
• consistent translations using SOCP [Kahl ICCV’05]
• dense stereo [Kostkova & Sara BMVC’03]
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Calibrated RANSAC and planes
The six-point algorithm found only points on the wall. [Stewenius et al. CVPR’05]
Two-View Geometry Unaffected by a Dominant Plane. [Chum et al. CVPR'05]
use inliers as a pool for drawing samples in RANSAC on epipolar geometry
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Full calibration
The “five-point algorithm” on all pairs. [Nister PAMI’04]
Partial calibration – unknown focal length
The “six-point algorithm” on all pairs. [Stewenius et al. CVPR’05]
mean focal length
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Consistent rotations – previous work
[Uyttendaele et al., CG\&A '04] – dense video self-intersecting paths vanishing points
[Martinec, Pajdla CVPR'05] – gluing projective reconstructions
metric upgrade needed!
loosely coupled components – ambiguity!
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Rotation registration into a reference framerotation matrices
rotations w.r.t. a reference framerelative rotation
consistent rotations
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Consistent rotations – solution
fast: ~ 1 sec for 1000 image pairs
close to orthonormal
orthonormal
and solve
large & sparse matrix
rewrite as
eigenvalue problem global minimum
well conditioned
rotations – projection to orthonormal matrices
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Refining rotations
• in each partial reconstruction:
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Refining rotations
• in each partial reconstruction:
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Refining rotations
• in each partial reconstruction:
replace rotations by the consistent ones,
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Refining rotations
• in each partial reconstruction:
reprojection errors grow
bundle adjustment needed
change in relative rotation
replace rotations by the consistent ones,
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Refining rotations
• in each partial reconstruction:
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Refining rotations
• in each partial reconstruction:
• refine all reconstructions together,
each in independant coordinate frame,
but with corresponding rotations constrained to be same
re-estimate camera translations and points using [Kahl ICCV'05]
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consistent rotations
same rotations,translations unknown
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0.8 / 18 pxl
consistent rotations
low errors
stability
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consistent rotations
0.8 / 18 pxl
0.20 / 1.6 pxl
refine
Refining rotations
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Translations
consistent rotations
0.8 / 18 pxl
0.20 / 1.6 pxl
refine
0.24 / 1.3 pxl
consistent translations
[Kahl ICCV'05]
0.19 / 1.1 pxl
refine
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Final reconstruction
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Experiments
ICCV’05 Contest finals
mean / maximum error 3.01 / 4.87 meters
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Experiments
ICCV’05 Contest finals
St. Martin rotunda – 104 images
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support
Experiments
ICCV’05 Contest finals
Head2
St. Martin rotunda
correct surface
use triplets
importance
uneven image capture
few data
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Summary
New algorithm for 3D reconstruction:
• EG importance
• consistent rotations linearly
• bundle adjustment with constrained rotations
Acknowledgements:• Ondrej Chum … code for EG unaffected by a dominant plane• Fred Schaffalitzki … code for the six-point algorithm (publicly available)• Lourakis et al. … base code for bundle adjustment (publicly available)• Jana Kostkova … routines for dense stereo• Richard Szeliski … the ICCV'05 Contest data (publicly available)
Difficult scenarios:
• coinciding camera centers
• only two-view matches
• uneven image capture, wide base-line
recent results on 260 viewspractical algorithm