Closed-form solutions for rigid transformations between heterogeneous groups of noisy geometric primitives

Computing the transformation between noisy collections of geometric primitives is a classic problem in three-dimensional computer vision and geometric computing. In this paper, we consider minimum sets of noisy objects and provide closed-form formulae to compute the Euclidean transformation that best transforms from one of these sets to another set. We enumerate these for all primitive object groups that appear in common three-dimensional computer vision problems and describe example applications. This article is part of the theme issue 'Modern applications of geometric algebra'.