GDC-WED: A Novel Method for Featureless Point Cloud Registration Using Geometry Distance Constraints and Weighted Enhanced Distance

In featureless point clouds, such as cylinder-ruled surfaces or shapes with lots of flattened areas, we observe that some classic iterative closest point variants, including point-to-point, point-to-plane, and symmetric metrics, are trapped in local minima. To explain the above phenomenons, we derive that the upper bounds error of landscapes (UBEL) of point-to-plane and symmetric metrics are nearly zero in the above scenes, resulting in slow convergence or local minima. To address the above challenges, we introduce a constrained registration method, which integrates geometry distance constraints (GDC) and weighted enhanced distance metric. Specifically, WED combines point-to-point and point-to-plane metrics, resulting in a steeper UBEL than point-to-plane and symmetric; GDCs constrain the transformation matrix into a feasible subset to escape local minima. Moreover, we introduce a dynamic slack of constraint algorithm to improve the stability of the linear perturbation in the constrained registration problem. Simulations and experiments are conducted on typical featureless objects, including a turbine blade, a cylinder-ruled surface, an outlet guide vane, and a rotor engine, to verify the effectiveness and efficiency of the presented registration framework.