— Scan matching techniques have been widely used to compute the displacement of robots. This estimate is part of many algorithms addressing navigation and mapping. This paper addresses the scan matching problem in three dimensional workspaces. We propose an generalization of the Metric based Iterative Closest Point (MbICP) to the 3D case. The main contribution is the development of all the mathematical tools required to formulate the ICP with this new metric, including the derivation of point to plane distances based on the new metric. We also provide experimental results to evaluate the algorithms and different combinations of ICP and MbICP to illustrate the advantages of the metric based approach.