  In this paper, we propose an algebraic approach to upgrade a projective
reconstruction to a Euclidean one, and aim at computing the rectifying
homography from a minimal number of 9 segments of known length. Constraints are
derived from these segments which yield a set of polynomial equations that we
solve by means of Gr\"obner bases. We explain how a solver for such a system of
equations can be constructed from simplified template data. Moreover, we
present experiments that demonstrate that the given problem can be solved in
this way.
