On Calibration and Reconstruction from Planar Curves

We describe in this paper closed-form solutions to the following problems in multi-view geometry of n'th order curves: (i) recovery of the fundamental matrix from 4 or more conic matches in two views, (ii) recovery of the homography matrix from a single n'th order (n 3) matching curve and, in turn, recovery of the fundamental matrix from two matching n'th order planar curves, and (iii) 3D reconstruction of a planar algebraic curve from two views. Although some of these problems, notably (i) and (iii), were introduced in the past [15, 3], our derivations are analytic with resulting closed form solutions. We have also conducted synthetic experiments on (i) and real image experiments on (ii) and (iii) with subpixel performance levels, thus demonstrating the practical use of our results.