一种基于BFGS修正的正态分布变换点云配准方法

点云配准是点云数据处理中的关键问题，针对原始正态分布变换算法求解Hessian矩阵时间复杂度高的问题，本文提出一种基于BFGS算法修正的正态分布变换点云的配准方法。通过利用目标函数的梯度值及增量参数更新正定矩阵，以正定矩阵近似代替Hessian矩阵的逆矩阵，确保算法每次迭代方向均为函数值下降方向，降低了算法的时间复杂度；通过模拟数据试验及实测数据试验，验证了本文算法的可行性，其在保持原始正态分布变换算法精度的前提下，提高了算法的配准效率。

A normal distribution transform point cloud registration method based on BFGS correction

Point cloud registration is a key problem in point cloud data processing. For the problem of solving the Hessian matrix with high time complexity for the original normal distribution transformation algorithm, a modified normal distribution transform point cloud registration method based on the BFGS algorithm is proposed. The positive definite matrix is updated with the gradient value and incremental parameters of the objective function. The inverse matrix of the Hessian matrix is almost replaced by a positive definite matrix, which reduces the time complexity of the algorithm, ensures that the direction of each iteration of the algorithm is the direction where the function value drops in. The feasibility of this algorithm is verified by simulated data and measured data experiments. This algorithm improves the registration efficiency of the algorithm while maintaining the accuracy of the original normal distribution transformation algorithm.