We propose a trimmed strategy for affine registration of point sets using the Lie group parameterization. All affine transformations form an affine Lie group, thus finding an optimal transformation in registration is reduced to finding an optimal element in the affine group. Given two point sets (with outliers) and an initial element in the transformation group, we seek the optimal group element iteratively by minimizing an energy functional. This is conducted by sequentially finding the closest correspondence of two point sets, estimating the overlap rate of two sets, and finding the optimal affine transformation via the exponential map of the affine group. This method improves the trimmed iterative closest point algorithm (TrICP) in two aspects: (1) We use the Lie group parameterization to implement TrICP. (2) We also extend TrICP to the case of affine transformations. The performance of the proposed algorithm is demonstrated by using the LiDAR data acquired in the Mount St. Helens area. Both visual inspections and evaluation index (root mean trimmed squared distance) indicate that our algorithm performs consistently better than TrICP and other related algorithms, especially in the presence of outliers and missing points.
|Journal||Journal of Applied Remote Sensing|
|State||Published - 2013|
Bibliographical noteFunding Information:
This work is supported by the 973 Programme (No. 2011CB707104), the National Science Foundation of China (Nos. 61273298, 11101260, and 61005002), the First-class Discipline of Universities in Shanghai, the Discipline Project at the corresponding level of Shanghai (A.13-0101-12-005), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. The authors would like to thank libLAS for providing the LAS data (http://www.liblas.org/samples/).
- Lie group
- affine transformation
- point set
- trimmed iterative closest point.
ASJC Scopus subject areas
- Earth and Planetary Sciences (all)