A Modified ICP Algorithm for Automatic Registration of Range Data sets form Unknown Viewpoints

1. A Modified ICP Algorithm for Automatic Registration of Range Data sets form Unknown Viewpoints

2. 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

3. 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.

4. SIX STAGE OF ICP 1. Selection of point 2. Matching of point 3. Weighting of pairs 4. Rejecting pairs 5. Error Metric 6. Minimizing

5. SIX STAGE OF ICP • 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

6. 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]

7. 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 }

8. 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

9. 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

10. 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]

11. Efficient Variants of the ICP algorithmS. 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.

12. 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

13. Efficient Variants of the ICP algorithm Test Scenes Wave Fractal landscape Incised plane

14. 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.

15. 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.

16. 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

17. Efficient Variants of the ICP algorithm Comparisons of Weighting method Wave mesh :

18. Geometrical Cloning of 3D Object via Simultaneous Registration of Multiple Range ImagesPeter 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.

19. 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.

20. 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.

21. Geometrical Cloning of 3D Object…… Registration : Point-based registration Visibility Criterion :

22. 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

23. Spin Image

24. Feature Matching