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This article presents for the first time a global method for registering 3Dcurves with 3D surfaces without requiring an initialization. The algorithmworks with 2-tuples point+vector that consist in pairs of points augmented withthe information of their tangents or normals. A closed-form solution fordetermining the alignment transformation from a pair of matching 2-tuples isproposed. In addition, the set of necessary conditions for two 2-tuples tomatch is derived. This allows fast search of correspondences that are used inan hypothesise-and-test framework for accomplishing global registration.Comparative experiments demonstrate that the proposed algorithm is the firsteffective solution for curve vs surface registration, with the method achievingaccurate alignment in situations of small overlap and large percentage ofoutliers in a fraction of a second. The proposed framework is extended to thecases of curve vs curve and surface vs surface registration, with the formerbeing particularly relevant since it is also a largely unsolved problem.

3D Registration of Curves and Surfaces using Local Differential Information