Abstract: The aim of 2D-3D point set registration is to find the optimal transformation and correspondence between 3D source point set and 2D target projection point set. In order to obtain the closed-form solution to the registration problem and avoid the volume degradation caused by projection, a volume-preserving 2D-3D point set registration algorithm based on Lie group representation was proposed. Firstly, considering the non-commutativity of the projection matrix and the rotation matrix, the Lie group representation is introduced to formalize the registration problem into an optimization problem based on Lie group. The Lie group optimization problem is transformed into a computationally quadratic programming problem by the local linearization method. Secondly, in order to avoid volume degradation, the projection of 3D transformed point set is constrained to have the same volume as that of 2D target point set. In order to facilitate calculation, the Jensen-Bregman LogDet divergence is introduced as a volume-preserving regularization term, converting the volume difference calculation into a covariance matrix difference calculation. Subsequently, a complete and solvable iteration strategy is developed by alternately solving for the correspondence and the optimal transformation. Finally, comparative experiments and ablation experiments on two classical data sets verify the accuracy and effectiveness of the proposed approach.

Key words: 2D-3D point set registration, Lie group, volume-preserving regularization, quadratic programming