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.