Robust Algorithm for Euclidean Upgrading from a Minimal Number of Segments

In this paper, a robust algebraic approach for Euclidean upgrading from a minimal number of segments is proposed, which requires just 9 segments of known length. Euclidean Upgrading based on segments have been widely used because of the advantage that self-occlusion is not easy to occur in calibration. Since the projective reconstruction can be easily obtained according to corresponding relation of multiple camera system, the key of upgrading projective reconstruction to Euclidean reconstruction is to extract infinite plane and the image of the absolute conic. The existing method is to constitute a homogeneous polynomial equation of degree 4 in 9 variables based on the segments of known length. However, the existing solver for the polynomial equations of degree 4 in 9 variables is sensitive to noise and not robust. The algorithm proposed in this paper constrains different parameters, uses elimination method to reduce the number of unknowns, and finally construct a general solving template to solve the polynomial equations with the Gröbner base method. In general, this algorithm has the advantages of robustness against noise and easy to calculate compared with the existing method. Moreover, we present experiments to demonstrate the feasibility and precision of this algorithm.