Pattern Analysis and Applications

, Volume 14, Issue 2, pp 127–137 | Cite as

Iwasawa decomposition: a new approach to 2D affine registration problem

  • Shihui YingEmail author
  • Yaxin Peng
  • Zhijie Wen
Theoretical Advances


In this paper, 2D affine registration problem was studied. First, combining with the procedure of traditional iterative closest point method, the registration problem was modeled as an optimization problem on Lie group \(GL(2,{\mathfrak{R}})\). To assure the registration non-degenerate, some reasonable constraints were introduced into the model by Iwasawa decomposition. Then, a series of quadratic programming were used to approximate the registration problem and a novel affine registration algorithm was proposed. At last, several illustration and comparison experiments were presented to demonstrate the performance and efficiency of the proposed algorithm. Particularly, a way of selecting a good initial registration based on ICA method to achieve the global minimum was suggested.


Affine registration ICP Iwasawa decomposition Quadratic programming Initial parameters 



The authors would like to thank the editor and the anonymous reviewers for their helpful comments and suggestions. The research is supported by NSFC (61005002), Shanghai Leading Academic Discipline Project (S30104) and the Excellent Young Teachers Program of Shanghai (B.37-0101-08-008).


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Copyright information

© Springer-Verlag London Limited 2010

Authors and Affiliations

  1. 1.Department of Mathematics, School of ScienceShanghai UniversityShanghaiChina

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