基于Lie群表示的保体积2D-3D点集配准算法

Volume-preserving 2D-3D point set registration algorithm based on Lie group representation

2D-3D点集配准的目标是寻找三维原始点集与二维目标投影点集之间的对应关系和最优变换.为了给出配准问题的解析解,避免投影引起的体积退化,提出基于Lie群表示的保体积2D-3D点集配准算法.首先,考虑投影矩阵和旋转矩阵的非交换性,引入Lie群表示,将配准问题形式化为一个Lie群优化问题.利用局部线性化方法,将Lie群优化问题转化为一个可计算的二次规划问题.其次,为了避免体积退化,考虑约束变换后的三维点集的投影与二维目标点集的投影具有相同的体积.为便于计算,引入Jensen-Bregman LogDet散度作为保体积正则项,将计算点集的体积差异转化为计算协方差矩阵之间的差异.然后,通过交替求解对应关系和最优变换,形成完整且可解的迭代策略.最后,在两个经典数据集上进行对比实验和消融实验,验证了该算法的精确性和有效性.

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.