Geodesic
Closed form solution of ICP error minimization problem for affine transformations
Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 3, pp. 282-294.

Voir la notice de l'article provenant de la source Math-Net.Ru

The iterative closest point (ICP) algorithm is one of the most popular approaches to shape registration. The aim of the algorithm is to calculate the optimal geometric transformation relative to the given metric, combining the two given clouds. An important step in the ICP algorithm is the solution of the problem of minimizing the functional corresponding to a given metric for a given class of geometric transformations. In this paper, a method is presented for solving the variational problem of the ICP algorithm for the point-to-point metric in the class of affine transformations. With the help of computer simulation, the correctness of the proposed method is demonstrated.
Keywords: 3D reconstruction, registration of point clouds, localization, affine transformation. 
@article{CHFMJ_2017_2_3_a2,
     author = {A. Yu. Makovetskii and S. M. Voronin and D. V. Tihonkih and M. N. Alekseev},
     title = {Closed form solution of {ICP} error minimization problem for affine transformations},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {282--294},
     publisher = {mathdoc},
     volume = {2},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a2/}
}
TY  - JOUR
AU  - A. Yu. Makovetskii
AU  - S. M. Voronin
AU  - D. V. Tihonkih
AU  - M. N. Alekseev
TI  - Closed form solution of ICP error minimization problem for affine transformations
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2017
SP  - 282
EP  - 294
VL  - 2
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a2/
LA  - ru
ID  - CHFMJ_2017_2_3_a2
ER  - 
%0 Journal Article
%A A. Yu. Makovetskii
%A S. M. Voronin
%A D. V. Tihonkih
%A M. N. Alekseev
%T Closed form solution of ICP error minimization problem for affine transformations
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2017
%P 282-294
%V 2
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a2/
%G ru
%F CHFMJ_2017_2_3_a2
A. Yu. Makovetskii; S. M. Voronin; D. V. Tihonkih; M. N. Alekseev. Closed form solution of ICP error minimization problem for affine transformations. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 3, pp. 282-294. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a2/

[1] Y. Chen, G. Medioni, “Object modeling by registration of multiple range images”, Image and Vision Computing, 10:3 (1992), 145–155 | DOI

[2] P. Besl, N. McKay, “A method for registration of 3-D shapes”, IEEE Transactions of Pattern Analysis and Machine Intelligence, 14:2 (1992), 239–256 | DOI

[3] G. Turk, M. Levoy, “Zippered polygon meshes from range images”, Computer Graphics Proceedings, ACM SIGGRAPH (1994), Annual Conference Series, 311–318

[4] B. Horn, “Closed-form solution of absolute orientation using unit quaternions”, Journal of the Optical Society of America. Series A, 4:4 (1987), 629–642 | DOI

[5] B. Horn, H. Hilden, S. Negahdaripour, “Closed-form solution of absolute orientation using orthonormal matrices”, Journal of the Optical Society of America. Series A, 5:7 (1988), 1127–1135 | DOI | MR

[6] S. Du, N. Zheng, S. Ying, Q. You, Y. Wu, “An extension of the ICP algorithm considering scale factor”, Proceedings of the 14th IEEE International Conference on Image Processing, 2007, 193–196

[7] S. Du, N. Zheng, G. Meng, Z. Yuan, “Affine registration of point sets using ICP and ICA”, IEEE Signal Processing Letters, 15 (2008), 689–692 | DOI

[8] S. Du, N. Zheng, S. Ying, J. Liu, “Affine iterative closest point algorithm for point set registration”, Pattern Recognition Letters, 31 (2010), 791–799 | DOI

[9] S. Rusinkiewicz, M. Levoy, “Efficient variants of the ICP algorithm”, Proceedings of the International Conference on 3-D Digital Imaging and Modeling, 2001, 145–152 | DOI

[10] D. Tihonkih, A. Makovetskii, V. Kuznetsov, “A modified iterative closest point algorithm for shape registration”, Applications of Digital Image Processing XXXIX, Proceedings SPIE, 9971, 2016, 99712D | DOI