Showing papers by "Shihui Ying published in 2012"

Lie-EM-ICP algorithm: a novel frame for 2D shape registration

Abstract: In this paper, a 2D shape registration algorithm for noisy data is established by combining the Iterative Closest Point (ICP) method, Expectation Maximization (EM) method, and Lie Group representation. First, the problem is formulated by a minimization problem with two sets of variables: the point-to-point correspondence, and the transformation (i.e., rotation, scaling and translation) between two data sets. The conventional way for solving this model is by iterating alternatively the following two steps: 1) having the transformation fixed, solve the correspondence, and 2) having the correspondence fixed, solve the transformation. In our approach, to enhance the robustness, the EM algorithm is introduced to find the correspondence by a probability which covers the relationship of all points, instead of one-to-one closest correspondence in ICP. Meanwhile, Lie group is used to parameterize transformation, i.e., in the iteration, the rotation, scaling and translation are all elements within respective Lie groups, and we use the element of Lie algebra to represent that of Lie group near the identity via exponential map. This forms a unified framework for registration algorithms. Then, transformation is estimated by solving a quadratic programming. The experimental result in 2D shape registration demonstrates that, compared with Lie-ICP, our algorithm is robuster and more accurate.

A novel statistical method for 3D range data registration based on Lie group framework

Abstract: Registration of 3D range data is to find the transformation that best maps one data set to the other. In this paper, Lie group parametric representation is combined with the Expectation Maximization (EM) method to provide a unified framework. First, having a transformation fixed, the EM algorithm is introduced to find the correspondence between two data sets through correspondence probability, which covers the relationship of all points, instead of using exact correspondence such as the classical Iterative Closest Point (ICP) method. With this type of ststistical correspondence, we could deal with the presence of the degradations such as outliers and incomplete point sets. Second, having the updated correspondence fixed, and introducing Lie group parametric representation, the transformation is updated by minimizing a quadratic programming. Then, an alternative iterative strategy by the above two steps is used to approximate the desired correspondence and transformation. The comparative experiment between our Lie-EM-ICP algorithm and Lie-ICP algorithm using point cloud is presented. Our algorithm is demonstrated to be accurate and robust, especially in the presence of incomplete point sets and outliers.