Reconstruction of quadratic curves in 3-D from two or more perspective views

The issues involved in the reconstruction of a quadratic curve in 3-D space from arbitrary perspective projections are described in this paper. Correspondence between the projections of the curve on the image planes is assumed to be established. Equations for reconstruction of the 3-D curve, which give the parameters of the 3-D quadratic curve are determined. Uniqueness of the solution in the process of reconstruction is addressed and solved using additional constraints. As practical examples, reconstruction of circles, parabolas and pair of straight lines in 3-D space are demonstrated.