Nonlinear 2D shape registration via thin-plate spline and Lie group representation

Thin-plate spline for robust point matching (TPS-RPM) algorithm is a famous and widely used approach in nonlinear shape registration. In this paper, we improve this approach by adopting an alternatively iterative strategy of globally affine and locally nonlinear registration. Concretely, in the affine registration step, we apply the Lie group parameterization method to globally align two shapes to assume the global similarity. In which, some suitable constraints are introduced to improve the robustness of algorithm. Then, in the locally nonlinear deformation step, we apply the thin-plate spline approach. By alternatively iterating these two steps, the proposed method not only preserves the advantages of spline methods, but also overcomes an overmatching phenomenon in shape registration. Finally, we test the proposed method on several conventional data sets with comparison of TPS-RPM. The experimental results validate that our method is really effective for nonlinear shape registration as well as more robust.