Abstract
This article presents for the first time a global method
for registering 3D curves with 3D surfaces without requiring an initialization. The algorithm works with 2-tuples
point+vector that consist in pairs of points augmented with
the information of their tangents or normals. A closed-form
solution for determining the alignment transformation from
a pair of matching 2-tuples is proposed. In addition, the
set of necessary conditions for two 2-tuples to match is derived. This allows fast search of correspondences that are
used in an hypothesise-and-test framework for accomplishing global registration. Comparative experiments demonstrate that the proposed algorithm is the first effective solution for curve vs surface registration, with the method
achieving accurate alignment in situations of small overlap and large percentage of outliers in a fraction of a second. The proposed framework is extended to the cases of
curve vs curve and surface vs surface registration, with the
former being particularly relevant since it is also a largely
unsolved problem