Matching wire frame objects from their two dimensional perspective projections

A wire frame object consists of a set of three dimensional arcs, each arc being a sequence of conics and line segments lying in the same plane, with different arcs being allowed to lie on different planes. Given a picture taken by a camera focusing on one wire frame object, we show how to determine what the object is and where it is situated relative to the camera when the camera viewing parameters are unknown.

To accomplish the object identification, we begin with a segmented picture. Then we construct a ray from the lens to each point on the boundary of every region. For each region, the collection of its associated rays is a cone. We show that by constructing cones, the two-dimensional to three-dimensional matching problem is transformed into an equivalent three-dimensional to three-dimensional matching problem.

This matching problem is expressed as a nonlinear optimization search procedure on the 6 camera viewing parameters: the 3 translation parameters and the 3 rotation parameters. A solution is found when a viewing position and optical axis is determined which is consistent with the world knowledge we have of possible curves and the observed image data.