A New Close-Form Solution for Initial Registration of ICP

Abstract:

The paper proposed a original matching algorithm using the feature vectors of rigid points sets matrix and a online matching intersection testing algorithm using the bounding sphere. The relationship searching between points in each set is took place by the corresponding eigenvectors that is a closed form solution relatively. The affine transformed eigenvalue and eigenvector is also used instead of the affine transformed points sets for the non-rigid matching that do not need the complicated global goal function. The characteristics matching for the initial registration can give a well initial value for the surfaces align that improve the probability of global solution for the following-up ICP

• Periodical: Advanced Materials Research (Volumes 143-144)
• Pages: 287-292
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.143-144.287
• Online since: October 2010
• Authors: Li Zhao Liu, Xiao Jing Hu, Yu Feng Chen, Tian Hua Zhang, Mao Qing Li
• Keywords: Eigenvector Rigid Matching, ICP, Intersection Test, Registration

References

[1] AMBERG B., ROMDHANI S., VETTER T.: Optimal step nonrigid icp algorithms for surface registration. In Proceedings of IEEE CVPR (June 2009).

DOI: 10.1109/cvpr.2007.383165

[2] ALLEN B., CURLESS B., POPOVI´C Z.: The space of human body shapes: reconstruction and parameterization from range scans. ACM Trans. Graph. 22, 3 (2003).

DOI: 10.1145/882262.882311

[3] PAULY M., MITRA N. J., GIESEN J., GROSS M., GUIBAS L. J.: Example-based 3d scan completion. In Symposium on Geometry Processing (2007).

[4] BROWN B., RUSINKIEWICZ S.: Non-rigid range-scan alignment using thin-plate splines. In Symp. on 3D Data Processing, Visualization, and Transmission (2006).

DOI: 10.1109/tdpvt.2004.1335392

[5] GELFAND N., IKEMOTO L., RUSINKIEWICZ S., LEVOY M.: Geometrically stable sampling for the icp algorithm. In Proc. Int. Conf. on 3D Digital Imaging and Modeling (2005).

DOI: 10.1109/im.2003.1240258

[6] MADSEN K., NIELSEN H., TINGLEFF O.: Methods for Non-Linear Least Squares Problems. Tech. rep., Technical University of Denmark, (2006).

[7] BROWN B. J., RUSINKIEWICZ S.: Global non-rigid alignment of 3-d scans. ACM Trans. Graph. 26, 3 (2009), 21.

DOI: 10.1145/1276377.1276404

[8] WAND M., JENKE P., HUANG Q., BOKELOH M., GUIBAS L., SCHILLING A.: Reconstruction of deforming geometry from time-varying point clouds. In Symposium on Geometry processing (2009), pp.49-58.

[9] HARALICK R. M., STERNBERG S. R., ZHUANG X.: Image analysis using mathematical morphology. IEEE PAMI 9, 4 (1987), 532-550.

DOI: 10.1109/tpami.1987.4767941

[10] B. K. P. Horn, B. G. Schunk. Determing optical flow [J]. Artificial Intelligence, 1987. 17: 185-203.

[11] K. S. Arun, T. S Huang, S. D. Blostein. Least-squares fitting of two 3-D point sets[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1987. 9(5): 698-700.

DOI: 10.1109/tpami.1987.4767965

[12] Paul J. Besl, Neil D. McKay. A method for registration of 3-D shapes [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1992. 14(2): 239-256.

DOI: 10.1109/34.121791

[13] Y. Chen, G. Medioni. Object Modeling by Registration of Multiple Range Images [J]. Image and Vision Computing, 1992. 10: 145-155.

DOI: 10.1016/0262-8856(92)90066-c

[14] IKEMOTO L., GELFAND N., LEVOY M.: A hierarchical method for aligning warped meshes. In Proc. of 4th Int. Conference on 3D Digital Imaging and Modeling (2005).

DOI: 10.1109/im.2003.1240279

[15] WENDLAND H.: Scattered Data Approximation. Cambridge University Press, (2007).

[16] X. Sun, D. Gong. Interactive genetic algorithms with individual's fuzzy and stochastic fitness[J]. Chinese Journal of Electronics, 2009, 18(4): 619 - 624.

[17] Forsyth D A，Mundy J L，Zisserman A et al. Invariant descriptors for 3D object recognition and pose [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence ， 1991 ， 13(10): 971~991.

DOI: 10.1109/34.99233

[18] V. Vapnik, S. E. Golowich, A. Smola. Support vector method for function approximation, regression estimation, and signal processing[C]/The 10th Annual Conference on Neural Information Processing Systems (NIPS). Cambridge: MIT Press, 1996: 281 - 287.