Robust Global Registration Natasha Gelfand Niloy Mitra Leonidas Guibas Helmut Pottmann.
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Transcript of Robust Global Registration Natasha Gelfand Niloy Mitra Leonidas Guibas Helmut Pottmann.
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Robust Global Registration
Natasha GelfandNiloy Mitra
Leonidas GuibasHelmut Pottmann
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Registration Problem
Given:Two shapes P and Q which partially overlap.
Goal:Using only rigid transforms, register Q against P by minimizing the squared distance between them.
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Applications
• Shape analysis– similarity, symmetry detection, rigid decomposition
• Shape acquisition[Koller 05] [Pauly 05] [Anguelov 04]
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Approaches I• Iterative minimization algorithms (ICP)
• Properties– Dense correspondence sets– Converges if starting positions
are “close”
2. Align corresponding points 3. Iterate1. Build a set of corresponding points
[Besl 92, Chen 92]
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Approaches II• Voting methods
– Geometric hashing, Hough transform, alignment method
• Rigid transform can be specified with small number of points– Try all possible transform bases– Find the one that aligns the most points
• Guaranteed to find the correct transform– But can be costly
[Stockman 87, Hecker 94, Barequet 97]
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Approaches III• Use neighborhood geometric information
• Descriptors should be– Invariant under transform– Local– Cheap
• Improves correspondence search or used for feature extraction
[Mokh 01, Huber 03, Li 05]
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Registration Problem• Why it’s hard
– Unknown areas of overlap– Have to solve the correspondence problem
• Why it’s easy– Rigid transform is specified by small number of
points– Prominent features are easy to identify
We only need to align a few points correctly.
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Method Overview
1. Use descriptors to identify features– Integral volume descriptor
2. Build correspondence search space– Few correspondences for each feature
3. Efficiently explore search space– Distance error metric– Pruning algorithms
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Integral Descriptors
•
• Multiscale
• Inherent smoothing
f(x)p
Br(p)
[Manay 04]
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Integral Volume Descriptor
•
• Relation to mean curvature
0.20
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Descriptor Computation
• Approximate using a voxel grid
– Convolution of occupancy grid with ball
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Feature Identification• Pick as features points with rare descriptor
values– Rare in the data rare in the model few correspondences
• Works for any descriptor
0
10
20
30
40
50
60
70
80
90
100
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Descriptor value
# o
ccu
ren
ces
Features
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Multiscale Algorithm
• Features should be persistent over scale change
r=0.5 r=1 r=2 r=4 r=8
Y Y Y N N
N N Y Y Y
N N Y N N
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Feature Properties
• Sparse
• Robust to noise
• Non-canonical
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• Search the whole model for correspondences– Range query for descriptor values– Cluster and pick representatives
Correspondence Space
PQ
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Evaluating Correspondences
• Coordinate root mean squared distance
– Requires best aligning transform– Looks at correspondences individually
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Rigidity Constraint
• Pair-wise distances between features and correspondences should be the same
PQ
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Rigidity Constraint
• Pair-wise distances between features and correspondences should be the same
PQ
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Rigidity Constraint
• Pair-wise distances between features and correspondences should be the same
PQ
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Evaluating Correspondences
• Distance root mean squared distance
– Depends only on internal distance matrix
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Search Algorithm• Few features, each with few potential
correspondences– Minimize dRMS– Exhaustive search still too expensive
PQ
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• Branch and bound– Initial bound using greedy assignment
• Discard partial correspondences that fail thresholding test–
• Prune if partial correspondence exceeds bound– Spaced out features make incorrect correspondences fail
quickly
• Since we explore the entire search space, we are guaranteed to find optimal alignment– Up to cluster size
Search Algorithm
pi
pjqj
qi
Rc
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Search Algorithm• Branch and bound
– Initial bound using greedy assignment
• Discard partial correspondences that fail thresholding test–
• Prune if partial correspondence exceeds bound– Spaced out features make incorrect correspondences fail
quickly
• Since we explore the entire search space, we are guaranteed to find optimal alignment– Up to cluster size
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Greedy Initialization• Good initial bound is essential• Build up correspondence set hierarchically
…
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Greedy Initialization• Good initial bound is essential• Build up correspondence set hierarchically
…
…
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Greedy Initialization• Good initial bound is essential• Build up correspondence set hierarchically
…
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Partial Alignment• Allow null correspondences, while maximizing the
number of matches points
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Alignment Results
Input: 2 scans Our alignment Refined by ICP
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Alignment Results
Input: 10 scans
Our alignment Refined by ICP
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Symmetry Detection• Symmetry detection
– Match a shape to itself
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Rigid Decomposition
• Repeated application of partial matching
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Conclusions• Simple feature identification algorithm
– Used integral volume descriptor– Applicable for any low-dimensional descriptor
• Correspondence evaluation using dRMS error– Look at pairs of correspondences, instead of
individually
• Efficient branch and bound correspondence search– Finds globally best alignment
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Future Work
• Linear features
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Future Work
• Linear features
• Fast rejection tests
• More descriptors
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Acknowledgements• Daniel Russel• An Nguyen• Doo Young Kwon • Digital Michelangelo Project
• NSF CARGO-0138456, FRG-0454543, ARO DAAD 19-03-1-033, Max Plank Fellowship, Stanford Graduate Fellowship, Austrian Science Fund P16002-N05
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Questions?