Quadric reconstruction from dual-space geometry

Abstract

We describe the recovery of a quadric surface from its image in two or more perspective views. The recovered quadric is used in 3D modeling and image registration applications. There are three novel contributions. First, it is shown that a one parameter family of quadrics is recovered from outlines in two views. The ambiguity is reduced to twofold given a point correspondence. There is no ambiguity from outlines in three or more views. Second, it is shown that degenerate quadrics reduce the ambiguity of reconstruction. Third, it is shown that surfaces can be piecewise quadric approximated from piecewise conic approximations of their outlines. All these cases are illustrated by examples with real images. Implementation details are given and the quality of the results is assessed.