Three-dimensional reconstruction using the perpendicularity constraint

This paper proposes a new method for calculating the Euclidean 3D structure of a scene using only two uncalibrated images and the basic Euclidean constraint resulting from the 3D perpendicularity. Instead of using the nonlinear self-calibration methods to estimate the intrinsic parameters, a linear search for the best values of these parameters is carried out. The criteria measuring the goodness of the intrinsic parameters' values is based on the Euclidean quality of the calculated 3D reconstruction using the 3D perpendicularity constraint. Experimental results on both simulated and real data have validated our method and have shown that the proposed method could be a better alternative to calibration-based reconstruction.