An unsupervised, iterative $N$-dimensional point-set registration algorithm

  • P. Hosseinbor BIO-key International, Eagan, MN, USA
  • R. Zhdanov CyberOptics, Minneapolis, MN, USA
  • A. Ushveridze Algostream, Plymouth, MN, USA
Keywords: Unsupervised method, point-registration algorithm, least square optimization


UDC 517.9

An unsupervised, iterative $N$-dimensional point-set registration algorithm for unlabeled data (i.e., correspondence between points is unknown) and based on linear least squares is proposed. The algorithm considers all possible point pairings and iteratively aligns the two sets until the number of point pairs does not exceed the maximum number of allowable one-to-one pairings.



K. S. Arun, T. S. Huang, S. D. Blostein, Least-squares fitting of two 3-D point sets, IEEE Trans. Pattern Anal. Machine Intell., 9, 698 – 700 (1987),

S. Chang, F. Cheng, W. Hsu, G. Wu, Fast algorithm for point pattern matching: Invariant to translations, rotations and scale changes, Pattern Recognition, 30, 311 – 320 (1997),

S. Gold, A. Rangarajan, C. P. Lu, S. Pappu, E. Mjolsness, New algorithms for 2d and 3d point matching: pose estimation and correspondence, Pattern Recognition, 31, 1019 – 1031 (1998).

A. P. Hosseinbor, R. Zhdanov, A. Ushveridze, An unsupervised 2d point-set registration algorithm for unlabeled feature points: Application to fingerprint matching, Pattern Recognition Letters, 100, 137 – 143 (2017),

B. Jian, B. C. Vemuri, Robust point set registration using gaussian mixture models, IEEE PAMI, 33, 1633 – 1645 (2010),

W. Kabsch, A solution for the best rotation to relate two sets of vectors, Acta Cryst., 32, 922 – 923 (1976),

S. Lan, Z. Guo, J. You, A non-rigid registration method with application to distorted fingerprint matching, Pattern Recognition, 95, 48 – 57 (2019),

A. Rangarajan, H. Chui, F. L. Bookstein, The softassign procrustes matching algorithm, IPMI, 29 – 42 (1997),

A. Rangarajan, H. Chui, E. Mjolsness, S. Pappu, L. Davachi, P. S. Goldman-Rakic, J. S. Duncan, A robust point matching algorithm for autoradiograph alignment, Med. Image Anal., 1, 379 – 398 (1997),

Y. Tsin, T. Kanade, A correlation-based approach to robust point set registration, ECCV, 558 – 569 (2004),

S. Umeyama, Least-squares estimation of transformation parameters between two point sets, IEEE Trans. Pattern Anal. Machine Intell., 13, 376 – 380 (1991),

How to Cite
Hosseinbor, P., R. Zhdanov, and A. Ushveridze. “ An Unsupervised, Iterative $N$-Dimensional Point-Set Registration Algorithm”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 3, Apr. 2022, pp. 427-36, doi:10.37863/umzh.v74i3.6969.
Research articles