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

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.