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

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.

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