基于分支限界的三维曲面全局配准方法

Globally optimal solution to 3D surface registration based on branch and bound

在三维测量中常需要将测量点云数据与已知曲面模型进行配准。采用隐式函数建立点云数据到曲面模型的距离场,进而进行非线性优化求解可以有效提升配准效率。然而由于点到曲面的近似距离及刚性变换的约束,其误差函数呈现非凸性而导致迭代极易陷入局部最优。为实现全局配准,提出了一种利用分支限界算法搜索点到曲面近似距离平方和误差函数最小化变换参数的方法。通过确定刚体变换参数空间中误差函数的上下界限加快搜索,并结合一种等效距离公式的LevenbergMarquardt算法优化的局部配准方法加速收敛并保证配准精度。三维模型的配准实验与分析验证了本文全局配准方法的有效性。

Surface registration is significant in 3D measurement which often needs to register the obtained data point set to the known surface model. Registration efficiency can be improved by nonlinear optimization of the distance error between the data and model in the form of an implicit function. However, due to the constraints of the approximate distance matrix and rigid transformation, the cost function is often non-convex and easily leads to locally optimal solutions. To achieve globally optimal registration, a method based on Branch and Bound scheme is proposed to identify for the best transformation parameters. Searching is sped up by deriving the upper and lower bounds for the registration error function. A local method using Levenberg-Marquardt algorithm to optimize the equivalent distance error function is integrated, which enhances the convergence speed and guarantees the accuracy. Experimental results and analysis on 3D models validate of the proposed global solution.