Super 4PCS Fast Global Pointcloud Registration via Smart...
Transcript of Super 4PCS Fast Global Pointcloud Registration via Smart...
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Fast Global Pointcloud Registration
via Smart Indexing
Nicolas Mellado1, Dror Aiger2, Niloy J. Mitra1
1 University College London 2 Google Inc.
Super 4PCS
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Problem Statement
• Estimate rigid transformation tr
• Large search space (6DoF)
P + tr(Q)
+ =
P Q
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Problem Statement
• Estimate rigid transformation tr
• Local registration: from an input pose
• ICP [BM92], [CM92], [RL01], [MGPG04]
• Sparse ICP [BTP13]
• Kinect Fusion [IKH*11]
P + tr(Q)
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Problem Statement
• Estimate rigid transformation tr
• Local registration: from an input pose
• ICP [BM92], [CM92], [RL01], [MGPG04]
• Sparse ICP [BTP13]
• Kinect Fusion [IKH*11]
• Global registration: arbitrary input pose
• RANSAC [FB81], [IR96], [CH99]
• and variants [GMGP05], [PB09], [PB11], [ART10], [RABT13]
• 4 Point Congruent Set [AMCO08]
3 pairs of corresponding points are sufficient to
define a rigid transformation
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• Estimate rigid transformation tr
• Local registration: from an input pose
• ICP [BM92], [CM92], [RL01], [MGPG04]
• Sparse ICP [BTP13]
• Kinect Fusion [IKH*11]
• Global registration: arbitrary input pose
• RANSAC [FB81], [IR96], [CH99]
• and variants [GMGP05], [PB09], [PB11], [ART10], [RABT13]
• 4 Point Congruent Set [AMCO08]
Problem Statement
RANSAC: O(n3)
4 Point Congruent Set (4PCS) : O(n2)
Difficult cases
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Problem Statement
• Estimate rigid transformation tr
• Local registration: from an input pose
• ICP [BM92], [CM92], [RL01], [MGPG04]
• Sparse ICP [BTP13]
• Kinect Fusion [IKH*11]
• Global registration: arbitrary input pose
• RANSAC [FB81], [IR96], [CH99]
• and variants [GMGP05], [PB09], [PB11], [ART10], [RABT13]
• 4 Point Congruent Set [AMCO08]
RANSAC: O(n3)
4 Point Congruent Set (4PCS) : O(n2)
Our approach (Super 4PCS): O(n)
Difficult cases
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Demo
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Overview
•4PCS
•Super4PCS
•Results
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4 Point Congruent Set
• Use planar 4-points basis in P
• Find congruent 4-points in Q
P Q
4-points Congruent Sets for Robust Surface Registration
Dror Aiger, Niloy J. Mitra, Daniel Cohen-Or
SIGGRAPH 2008
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a
b
e
r1 = || a - e || / || a - b ||
4 Point Congruent Set
• What does congruent mean ?
• Similar under a given transformation class
• Ratios r1 and r2
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a
b
c
d
d1 d2
4 Point Congruent Set
• What does congruent mean ?
• Similar under a given transformation class
• Ratios r1 and r2
• Distances d1 , d2
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4 Point Congruent Set
Rigid transformation
• What does congruent mean ?
• Similar under a given transformation class
• Ratios r1 and r2
• Distances d1 , d2
• Angle α
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4 Point Congruent Set
Select Base Extract pairs Extract
congruent superset
Verify and update
transformation
Filter congruent set
Ratios Distances
Ratios Distances
Angles
False positives (non congruents)
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4 Point Congruent Set
• Extract pairs
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4 Point Congruent Set
• Extract pairs
d1 ε ε
≈ d1
d1 ≈ d1
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4 Point Congruent Set
• Extract pairs
a
b e
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4 Point Congruent Set
• Extract pairs
d2 ε ε
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4 Point Congruent Set
• Extract pairs
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4 Point Congruent Set
• Extract pairs
• Extract congruent super-set
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4 Point Congruent Set
• Extract pairs
• Extract congruent super-set
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4 Point Congruent Set
• Extract pairs
• Extract congruent super-set
• Filter congruent set
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4 Point Congruent Set
Select Base Extract pairs Extract
congruent superset
Verify and update
transformation
Filter congruent set
Ratios Distances
Ratios Distances
Angles
O(n2) O(mlog(m)) O(k)
n points m pairs
k congruent sets
False positives (non congruents)
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Super 4PCS
Select Base Extract pairs Extract congruent set Verify and
update transformation
O(n) O(m+k)
O(n2) O(mlog(m) + k)
n points m pairs
k congruent sets
No more false positive
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Super 4PCS
Select Base Extract pairs Extract congruent set Verify and
update transformation
O(n) O(m+k)
O(n2) O(mlog(m) + k)
n points m pairs
k congruent sets
Our smart indexing techniques
produce the same congruent set as 4PCS but in linear time
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Super 4PCS
Select Base Extract pairs Extract congruent set Verify and
update transformation
O(n) O(m+k)
O(n2) O(mlog(m) + k)
n points m pairs
k congruent sets
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Pair extraction
• Reporting incidences: all valid pairs generated from a sphere
d1
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Pair extraction
• Reporting incidences using sphere rasterization
• Complexity depends only on ε and d1
d1
ε
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Pair extraction
• Reporting incidences using sphere rasterization
• With an adaptative grid
Note: using a pre-computed tree is not optimal
d1
ε
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Pair extraction
• Reporting incidences using sphere rasterization
• With an adaptative grid
• Simultaneously for all points
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Pair extraction
• Reporting incidences using sphere rasterization
• With an adaptative grid
• Simultaneously for all points
• Theoretical complexity: O(n)
(see details in the paper)
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Pair extraction
• Reporting incidences using sphere rasterization
• With an adaptative grid
• Simultaneously for all points
• Theoretical complexity: O(n)
• In practice
• Runtime: linear
• Minimal memory overhead
Q
P
50
0
time (sec)
1049 1171 1542 2346 3117
4PCS
Super 4PCS
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4PCS Congruent set extraction
• Original approach
• Represent a pair by 2 invariants
m pairs k congruent sets
a
b
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4PCS Congruent set extraction
• Original approach
• Represent a pair by 2 invariants
• Use kd-tree to find closest invariants
m pairs k congruent sets
O(mlog(m) )
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4PCS Congruent set extraction
• Original approach
• Represent a pair by 2 invariants
• Use kd-tree to find closest invariants
• Filter non congruent quadriplets
m pairs k congruent sets
O(mlog(m) + k)
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Congruent set extraction
• Efficient indexing
• Represent pairs as invariant + direction
a
b
a
b
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Congruent set extraction
• Efficient indexing
• Represent pairs as invariant + direction
• Hash pairs by position and direction
a
b
a
b
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Congruent set extraction
• Efficient indexing
• Represent pairs as invariant + direction
• Hash pairs by position and direction
• Query
• Hash positions (closest invariants)
a
b
a
b
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Congruent set extraction
• Efficient indexing
• Represent pairs as invariant + direction
• Hash pairs by position and direction
• Query
• Hash positions (closest invariants)
a
b
a
b
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Congruent set extraction
• Efficient indexing
• Represent pairs as invariant + direction
• Hash pairs by position and direction
• Query
• Hash positions (closest invariants)
• Theoretical complexity: O(n)
(see details in the paper)
a
b
a
b
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Congruent set extraction
• Efficient indexing
• Represent pairs as invariant + direction
• Hash pairs by position and direction
• Query
• Hash positions (closest invariants)
• Theoretical complexity: O(n)
• In practice
• Runtime: linear
• Memory overhead: similar to kd-tree
Q
P
4PCS
Super 4PCS
time (sec)
1049 1171 1542 0
2346 3117
200
400
600
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Results
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Outliers
Before ICP
After ICP
Input 1.4 sec 15 sec 30 sec
35k points
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Low overlap
(no ICP)
32k points
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Low overlap
• Other examples
Model Points (x1000)
Overlap (%)
4PCS (in sec)
Super 4PCS
(in sec)
Bubba 10 5 5 2.5
Buddha 37 20 63 37
Hippo 32 25 11 0.5
10k points 37k points 32k points
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Low overlap + featureless
2 500 points
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Multi-modal models
• P: 2.5M points, multiview stereo
• Q: 2.5M points, LIDAR
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Range Images alignment
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Kinect scans
• Chaining pairwise registration (5/6 frames)
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Limitations
• Sampling sensitivity
• Region Of Interest (ROI)
• Cannot match between the points
• Metric
Select Base Extract pairs Extract congruent set Verify
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Conclusion
• Global matching algorithm
• Running in linear time
• Unstructured point clouds without normals
• Can be combined with local descriptors
• Future work
• Real-time using GPGPU programming
• Alternative to Kinect Fusion
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Thank you for your attention
• Super 4PCS
• Global matching running in linear time
• Acknowledgements • Feedback&discussion: Duygu Ceylan, Aron Monszpart
• SparseICP data and comparisons: Sofien Bouaziz, Andrea Tagliasacchi
• Pisa dataset: Matteo Dellepiane
• Funding • Marie Curie Career Integration Grant
• ERC Starting Grant SmartGeometry
• Adobe Research
Code and data goo.gl/uQrhJU
github.com/smartgeometry-ucl/Super4PCS
Features: • C++ • Based on Eigen • Structures implemented in arbitrary dimensions