Geometric Structure Computation from Conics

This paper presents several results on images of various configurations of conics. We extract information about the plane from single and multiple views of known and unknown conics, based on planar homography and conic correspondences. We show that a single conic section cannot provide sufficient information. Metric rectification of the plane can be performed from a single view if two conics can be identified to be images of circles without knowing their centers or radii. The homography between two views of a planar scene can be computed if two arbitrary conics are identified in them without knowing anything specific about them. The scene can be reconstructed from a single view if images of a pair of circles can be identified in two planes. Our results are simpler and require less information from the images than previously known results. The results presented here involve univariate polynomial equations of degree 4 or 8 and always have solutions. Applications to metric rectification, homography calculation, 3D reconstruction, and projective OCR are presented to demonstrate the usefulness of our scheme.