Affine Registration For Three Dimensional Range Data Under The Framework Of Lie Group

In recent years, with the continuous development of computer vision and remote sensing technology, the registration problem of three-dimensional range data has gained more and more attentions. In this article, under the registration framework of iterative closest point (ICP) algorithm and with the expectation-maximization (EM) theory, we establish an affine registration model for three dimensional range data. What is more, we can bring out the numerical solution by Lie group parametric method. Specifically, first in order to overcome the sensitivity to noise or outliers of the traditional affine ICP method, we draw the EM theory into the iteration process. Next, we use Lie group representation of the transformation to parameterize the model. And we put the reasonable constraints to the parametric model to improve the robustness of the algorithm. Once again, by the use of a series of quadratic programming problems to approximate the original problem, we achieve the approximate solution to the original problem and propose the Lie-EM-ICP algorithm. Last, by several numerical experiments, we prove our proposed algorithm is more robust to the registration problem in the presence of noise or outliers compared the traditional affine registration algorithm.