Lie group method for data set registration problem with anisotropic scale deformation

By analyzing the data set registration problem with anisotropic scale deformation, we introduced the constraints to the model. Combining with the procedure of traditional iterative closest point (ICP) method, the registration problem was described as a constrained optimization problem. Using parameterized method by Lie group and quadric approximation to the objective function, the registration problem was translated into a series of quadratic programming problems. Then, a novel scale-registration algorithm was proposed. The numerical simulations showed that such method not only was rapid and accurate as the traditional ICP method, but also could deal with the registration problem with large scale deformation. By introducing the constraints to the scale parameters, the algorithm was more robust. A way for choosing the initial transformations was proposed to assume the global registration.