Rigid Registration of Point Clouds Based on Indirect Lie Group Approach - Almeida, Liliane; Giraldi, Gilson; Vieira, Marcelo (Anais do Simpósio de Realidade Virtual e Aumentada (SVR); 2019: Anais do XXI Simpósio de Realidade Virtual e Aumentada, 2019)
In this paper we focus on application of Lie groups and Lie algebras to find the rigid transformation that best register two surfaces represented by point clouds. The so called pairwise rigid registration can be formulated by comparing intrinsic second-order orientation tensors that encode local geometry. In this work we interpret the obtained tensor field as a multivariate normal model. So, we apply the fact that the space of Gaussians can be equipped with a Lie group structure that can be embedded into the linear space defined by the Lie algebra of the symmetric matrices. This process enables us to handle Gaussians using the associated Lie algebra structure and, consequently, to compare orientation tensors with Euclidean operations. We apply this methodology to variants of the Iterative Closest Point (ICP), and compare the obtained results with the original implementations that use the comparative tensor shape factor (CTSF), as well as with two other methods. The experimental results show that ICP-LIE outperforms ICP-CTSF in situations without missing data or with missing data but smaller rotation. On the other hand, SWC-LIE achieves outstanding results if compared with SWC-ICP in more challenging setups: with moderate missing data and larger rotation, or, higher level of missing data.