Transcript A Modified ICP Algorithm for Automatic Registration of

A Modified ICP Algorithm for
Automatic Registration of Range Data
sets form Unknown Viewpoints
REFERENCES
“Efficient Variants of the ICP Algorithm”
- S. Rusinkiewicz and M. Levoy, Proc. 3DIM, 2001
“Geometrical Cloning of 3D Objects via Simultaneous
Registration of Multiple Range Image”
- P. Neugbauer, Proc. SMA 1997
“Surface Registration by Matching Oriented Points”
- A. E. Johnson and M. Herbert, Proc. 3DIM, 1997
INTRODUCTION
It is not possible to scan the complete object at once
- Geometrical and Topological limitation
ICP : Iterative Closest point algorithm [Chen 91], [Besl 92]
- Based on the geometry (sometimes color or intensity)
- Widely used for registering range data sets.
- Starts with two mesh, a good initial guess of transformation.
- Iteratively refine transformation by repeatedly generating of
corresponding points pairs.
Expansion : Iterative Corresponding Point algorithm.
SIX STAGE OF ICP
1. Selection of point
2. Matching of point
3. Weighting of pairs
4. Rejecting pairs
5. Error Metric
6. Minimizing
SIX STAGE OF ICP
1. Selection of point
- Using all points
Besl, P and Mckay, N. “ A Method for Registration of 3D Shapes,”
Trans. PRMI, Vol. 14, No.2, 1992
- Uniform sub-sampling
Truk, G. and Levoy, M. “Zippered Polygon Meshes from Range Images,”
Proc. SIGGRAPH, 1994
- Random sampling (with different sampling at each iteration.
Masuda, T., Sakaue, K., and Yokoya, N. “Registeration and Integration of
Multiple Range Images for 3D Model Construction,” Proc. CVPR, 1996
- Selection of points with high intensity gradient. [Weik 97]
Weik, S. “Registration of 3D Partial Surface Models Using Luminance and
Depth Information,” Proc. 3DIM, 1997
SIX STAGE OF ICP
2. Matching of point
- Find the closest point in the other mesh
Besl, P and Mckay, N. “ A Method for Registration of 3D Shapes,”
Trans. PRMI, Vol. 14, No.2, 1992
- Acceleration of [Besl]
Fast and Accurate Shape-Based Registration, Ph. D. Dissertation,
Carnegie Mellon Univ.
- “Normal Shooting”
Chen, Y. and Medioni, G. “Object Modeling by Registration of Multiple
Range Images,” Proc. IEEE Conf. on Robotics and Automation, 1991
- “Reverse calibration”
Neugebauer, P. “Geometrical Cloning of 3D Objects via Simultaneous
Registration of Multiple Range Images,” Proc. SMA, 1997
- Based on color [Godin 94] and angle between normal [Puilli 99]
SIX STAGE OF ICP
3. Weighting of pairs
- Constant weight.
- Assigning lower weight with greater point-to-point
distances.
Godin, G., Rioux, M., and Baribeau, R. “Three-dimensional Registration
Using Range and Intensity Information,” Proc. SPIE. Vidiometrics III, 1994
Weight = 1 – { Dist (p1, p2) / Dist max }
SIX STAGE OF ICP
4. Rejecting pairs
- Rejection of corresponding points more than a given
distance.
- Rejection of worst n% of pairs based on some metric,
usually point-to-point distance
Pulli, K. Surface Reconstruction and Display from Range and Color Data,
Ph.D. Dissertation, University of Washington, 1997.
- Rejection of pairs that are not consistent with neighboring
pairs.
Dorai, C., Hung, Y., and Cheng, J. “Optimal Registration of Object Views
Using Range Data,” Trans. PAMI, Vol.21, No.11, 1999
- Rejection of pairs containing point on boundaries
Truk, G. and Levoy, M. “Zippered Polygon Meshes from Range Images,”
Proc. SIGGRAPH, 1994
SIX STAGE OF ICP
5. Error Metric and Minimization
- Sum of squared distance between corresponding points.
- Singular Value Decomposition (SVD) [Arun 87]
- Quaternions [Horn 87]
- Orthonormal matrices [Horn 88]
- Dual-Quaternions [Weiker 91]
- Sum of squared distance of point to plane.
Chen, Y. and Medioni, G. “Object Modeling by Registration of Multiple
Range Images,” Proc. IEEE Conf. on Robotics and Automation, 1991
SIX STAGE OF ICP
Several ways to formulate
- Repeatedly generating a set of corresponding points
using current transformation, and finding a new
transformation that minimizes the error metric [Chen 91]
- Performing the iterative minimization using various
random-selected subsets of points, then selecting the
optimal result using a robust metric. [Masuda 96]
- Stochastic search for the best transform, using simulated
annealing. [Blais 95]
Efficient Variants of the ICP algorithm
S. Rusinkiewicz and M. Levoy, Proc. 3DIM, 2001
Goal : Comparison of convergence characteristics of several ICP
Variants.
Proposed combination of ICP :
- Registering in a few milliseconds.
- Real-time ICP is possible
- New applications in model based tracking and 3D scanning
Concept of normal-space-directed sampling
- Improve convergence.
Efficient Variants of the ICP algorithm
Baseline combination of variants
- Random sampling on both meshes.
- Matching selected point to closest sample within 45 degree
of source normal.
- Uniform weighting of point pairs
- Rejecting of pairs of edge vertices, percentage of pairs with
the largest point to point distance.
- Point-to-plane error metric
- The classic “selected-match-minimize” iteration.
Pulli, K. “Multiview Registration for Large Data sets”
Proc. 3DIM, 1999
Efficient Variants of the ICP algorithm
Test Scenes
Wave
Fractal landscape
Incised plane
Efficient Variants of the ICP algorithm
Comparisons of sampling method
Wave mesh : Sampling strategy is not
Critical.
Incised plane : Only normal –space
sampling is able to converge.
Efficient Variants of the ICP algorithm
Comparisons of matching method
Fractal mesh :
Norma shooting – Projection algorithm
- Closest point algorithm
Incised plane : Only the closest-point
algorithm converge.
Efficient Variants of the ICP algorithm
Comparisons of matching method
Conclusions :
Although the closest-point algorithm
might not have the fastest
convergence rate for “easy” scenes,
they are the most robust for “difficult”
geometry.
Fractal mesh : Convergence rate vs. time
Efficient Variants of the ICP algorithm
Comparisons of Weighting method
Wave mesh :
Geometrical Cloning of 3D Object via
Simultaneous Registration of Multiple
Range Images
Peter J. Neugebauer, Proc. SMA, 1997
Main contribution : simultaneous registration of all range images
acquired from different views
Registration process : Based on a least-squares approach.
(distance metric minimization)
After registration, a volumetric model of the object is carved out.
 Visibility criterion.
 Need not integration process.
Geometrical Cloning of 3D Object……
Problems
1. Parts of the 3D object are occluded or may lie in shadow.
2. The Object might be larger than the scanner is able to capture.
Assume : Different scanner views are unknown.
The registration is a highly nonlinear problem
- Initial estimation of the relative orientation is required.
 User input (at least 3 corresponding points)
For reconstruct of large object
- registration errors are not accumulated.
Geometrical Cloning of 3D Object……
For the generate of a model
- It is very important to handle self-occlusions and scan errors.
- Develop a visible criterion.
- The idea : A point in 3D space lying between the camera and
the surface cannot belong to the object.
- By applying this test to all voxel of a volume.
- Easy to sculpture a volumetric model of the object.
- By finding isosurfaces in the volumetric model
- Polygonal representation is generated.
Geometrical Cloning of 3D Object……
Registration : Point-based registration
Visibility Criterion :
Surface Registration by Matching Oriented Points
Andrew Edie Johnson and Martial Hebert
Appearing in the International Conference on Recent Advances in 3D Digital Imaging and Modeling, Ottawa,
Ontario, May 12-15, 1997
Fundamental contribution : called a spin-image.
The spin-image is the projection of the relative position of 3D points that lie on the
surface to a 2D space where some of the 3D metric information is preserved.
Oriented Point So;
* The vertex-based spin image  The face-based spin-image
Spin Image
Feature Matching