An invariant, closed-form solution for matching sets of 3D lines'

Existing algorithms for finding the best match between two sets of 3D lines are not completely satisfactory in the sense that they either yield approximate solutions, or are iterative which means they may not converge to the globally optimal solution. An even more serious shortcoming of the existing algorithms is that they are all non-invariant with respect to the translation of the coordinate system. Thus, any best match found becomes rather meaningless. In this paper, we discuss the source of this non-invariance and present a new algorithm that is invariant to coordinate transforms. Moreover, the algorithm is closed-form which implies that it always yields the best global match.