Surface Registration Gianpaolo Palma The problem 3D scanning - - PowerPoint PPT Presentation
Surface Registration Gianpaolo Palma The problem 3D scanning generates multiple range images Each contain 3D points for different parts of the model in the local coordinates of the scanner Find a rigid transformation (rotation +
multiple range images
for different parts of the model in the local coordinates of the scanner
(rotation + translation) for each scan to align them in the same reference system
Point)
corresponding points among the range scans
(MeshLab)
during the acquisition using markers
acquisition
between the correspondence point
matrix and the translation vector that minimize the point-to-point error function E
1.
Compute centroid
2.
Compute bary-centered point set
3.
Compute covariance matrix
4.
Compute Singular Value Decomposition of covariance matrix
5.
Compute Rotation
6.
Compute Translation
Q in arbitrary initial poses, with unknown percentage of
clouds can present significant amount of noise and outliers
aligning P to Q with a probabilistic approach
automatic
uniquely define a rigid transformation
the problem simpler
ratios of distances
Slides by [Aiger et al., SIGGRAPH 08]
Slides by [Aiger et al., SIGGRAPH 08]
point to ensure coplanarity
to limit the maximum distance among the points
Slides by [Aiger et al., SIGGRAPH 08]
Slides by [Aiger et al., SIGGRAPH 08]
Slides by [Aiger et al., SIGGRAPH 08]
Slides by [Aiger et al., SIGGRAPH 08]
Slides by [Aiger et al., SIGGRAPH 08]
Slides by [Aiger et al., SIGGRAPH 08]
Slides by [Aiger et al., SIGGRAPH 08]
Slides by [Aiger et al., SIGGRAPH 08]
correct relative rotation/translation
detection?
Points (ICP)
[Bels et al., PAMI92]
metric
metric
constrain all degrees of freedom of the rigid-body transformation
[Gelfand et al., 3DIM03]
UNIFORM SAMPLING STABLE SAMPLING
where
change in error when surfaces are moved from
with small eigenvalues correspond to sliding transformations
[Gelfand et al., 3DIM03]
points with uniform distribution of normals
metric
ICP algorithm
Project the point onto the destination mesh from the point of view of the destination camera
metric
point to point distance higher than a given threshold.
based on some metric.
mesh border.
consistent with their neighboring pairs
DISTANCE BORDER INCOSISTENT PAIRS
error metric
(minimization with a direct method)
regions can slide along each
metric because rotation is not a linear function
rotation
rotation
among all scans
scan that covers most surface
scan
’96]
While not converged: For each scan For each point For every other scan Find closest point
where n is number of scans
While not converged: For each scan: For each point: For every other scan Find closest point
each pair of scans with enough overlapping) Scan1 Scan4 Scan3 Scan5 Scan2 Scan6
Add most connect view in the queue While (queue is not empty) Align the current view with the neighbor in the graph If (change in error > threshold) Add neighbors to the queue
corresponding points.
[Pulli et al., 3DIM99]
Scan1 Scan4 Scan3 Scan5 Scan2 Scan6 Scan1 Queue
transformation Scan1 Scan4 Scan3 Scan5 Scan2 Scan6 Queue
in the queue and iterate Scan1 Scan4 Scan3 Scan5 Scan2 Scan6 Queue Scan5 Scan4 Scan3 Scan2
local refinement
Images by [Li et al., SGP08]
Relax regularization Correspondences Weighting Deformation
are based on the course of
ICCV Course 2005
http://www.cis.upenn.edu/~bjbrown/iccv05_course/
for robust pairwise surface registration." ACM Transactions on Graphics (TOG) 27.3 (2008): 85.
shapes." IEEE Transactions on Pattern Analysis and Machine Intelligence, 1992.
algorithm." 3-D Digital Imaging and Modeling, 2003. 3DIM 2003.
and Modeling, 1999. Proceedings. Second International Conference on. IEEE, 1999.
Optimization for Non‐Rigid Registration of Depth Scans." Computer graphics forum. Vol. 27. No. 5. Blackwell Publishing Ltd, 2008.