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A Generalized Point-to-Point Approach for Orthogonal Transformations

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Abstract

The known Iterative Closest Point (ICP) algorithm utilizes point-to-point or point-to-plane approaches. The point-to-plane ICP algorithm uses points coordinates and normal vectors for aligning of 3D point clouds, whereas point-to-point approach uses point coordinates only. This paper proposes a new algorithm for orthogonal registration of point clouds based on a generalized point-to-point ICP algorithm for orthogonal transformations. The algorithm uses the known Horn’s algorithm and combines point coordinates and normal vectors.

The work was supported by the Ministry of Education and Science of Russian Federation (grant N 2.1743.2017) and by the RFBR (grant N 18-07-00963).

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References

  1. Besl, P., McKay, N.: A method for registration of 3-D shapes. IEEE Trans. Pattern Anal. Mach. Intell. 14(2), 239–256 (1992)

    Article  Google Scholar 

  2. Chen, Y., Medioni, G.: Object modeling by registration of multiple range images. Image Vis. Comput. 2(10), 145–155 (1992)

    Article  Google Scholar 

  3. Turk, G., Levoy, M.: Zippered polygon meshes from range images. In: Computer Graphics Proceedings. Annual Conference Series, ACM SIGGRAPH, pp. 311–318 (1994)

    Google Scholar 

  4. Horn, B.: Closed-form solution of absolute orientation using unit quaternions. J. Opt. Soc. Am. Ser. A 4(4), 629–642 (1987)

    Article  Google Scholar 

  5. Horn, B., Hilden, H., Negahdaripour, S.: Closed-form solution of absolute orientation using orthonormal matrices. J. Opt. Soc. Am. Ser. A 5(7), 1127–1135 (1988)

    Article  MathSciNet  Google Scholar 

  6. Du, S., Zheng, N., Ying, S., You, Q., Wu, Y.: An extension of the ICP algorithm considering scale factor. In: Proceedings of the 14th IEEE International Conference on Image Processing, pp. 193–196 (2007)

    Google Scholar 

  7. Du, S., Zheng, N., Meng, G., Yuan, Z.: Affine registration of point sets using ICP and ICA. IEEE Signal Process. Lett. 15, 689–692 (2008)

    Article  Google Scholar 

  8. Du, S., Zheng, N., Ying, S., Liu, J.: Affine iterative closest point algorithm for point set registration. Pattern Recogn. Lett. 31, 791–799 (2010)

    Article  Google Scholar 

  9. Makovetskii, A., Voronin, S., Kober, V., Tihonkih, D.: An efficient point-to-plane registration algorithm for affine transformations. In: Proceedings SPIE, Applications of Digital Image Processing XL, vol. 10396, p. 103962J (2017)

    Google Scholar 

  10. Makovetskii, A., Voronin, S., Kober, V., Tihonkih, D.: Affine registration of point clouds based on point-to-plane approach. Procedia Eng. 201, 322–330 (2017)

    Article  Google Scholar 

  11. Makovetskii, A., Voronin, S., Kober, V., Voronin, A.: A non-iterative method for approximation of the exact solution to the point-to-plane variational problem for orthogonal transformations. Math. Methods Appl. Sci. 41, 9218–9230 (2018)

    Article  MathSciNet  Google Scholar 

  12. Makovetskii, A., Voronin, S., Kober, V., Voronin, A., Tihonkih, D.: Point clouds registration based on the point-to-plane approach for orthogonal transformations. In: CEUR Workshop Proceedings, vol. 2210, pp. 236–242 (2018)

    Google Scholar 

  13. Makovetskii, A., Voronin, S., Kober, V., Voronin, A.: A point-to-plane registration algorithm for orthogonal transformations. In: Proceedings of the SPIE, Applications of Digital Image Processing XLI, vol. 10752, p. 107522R (2018)

    Google Scholar 

  14. Voronin, S., Makovetskii, A., Voronin, A., Diaz-Escobar, J.: A regularization algorithm for registration of deformable surfaces. In: Proceedings of the SPIE, Applications of Digital Image Processing XLI, vol. 10752, p. 107522S (2018)

    Google Scholar 

  15. Ruchay, A., Dorofeev, K., Kober, A.: Accurate reconstruction of the 3D indoor environment map with a RGB-D camera based on multiple ICP. In: CEUR Workshop Proceedings, vol. 2210, pp. 300–308 (2018)

    Google Scholar 

  16. Ruchay, A., Dorofeev, K., Kober, A., Kolpakov, V., Kalschikov, V.: Accuracy analysis of 3D object shape recovery using depth filtering algorithms. In: Proceedings of SPIE - The International Society for Optical Engineering, vol. 10752, p. 1075221 (2018)

    Google Scholar 

  17. Ruchay, A., Dorofeev, K., Kober, A.: Accuracy analysis of 3D object reconstruction using RGB-D sensor. In: CEUR Workshop Proceedings, vol. 2210, pp. 82–88 (2018)

    Google Scholar 

  18. Rusinkiewicz, S., Levoy, M.: Efficient variants of the ICP algorithm. In: Proceedings of the International Conference on 3-D Digital Imaging and Modeling, pp. 145–152 (2001)

    Google Scholar 

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Correspondence to Artyom Makovetskii .

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Makovetskii, A., Voronin, S., Kober, V., Voronin, A. (2019). A Generalized Point-to-Point Approach for Orthogonal Transformations. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_17

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  • DOI: https://doi.org/10.1007/978-3-030-33394-2_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33393-5

  • Online ISBN: 978-3-030-33394-2

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