Soft Shape Registration Under Lie Group Frame

Image registration is a basic topic in the field of image processing and plays an im-portant role in many applications such as the object recognition, computer vision, medical processing, motion target detection and tracking. As an important issue of feature registra-tion problems, shape registration has achieved a lot of developments recently. Firstly, we introduce some shape registration problems in this paper. Then, we establish a new model by using Lie group parameterized method and Expectation Maximization (EM) method.Specifically, we understand shape registration problem as a general point registration problem. Based on the Iterative Closest Point (ICP) model, the Expectation Maximization (EM) principle is applied to overcome the effect of noise. Then, a Riemannian structure of Lie groups is used to parameterize the proposed model, which provides a unified framework to deal with the shape registration problem. Furthermore, to improve the robustness in terms of parameters, the2D shape registration problem is translated into a constrained problem on the matrix Lie group by introducing some suitable constraints to the model. In addition, a sequence of quadratic programming is designed to approximate the solution of the mod-el. Finally, a series of comparative experiments validated that the proposed algorithm was more robust than many existing algorithms with regards to noise and parameters under the premise of maintaining the computational efficiency.