Relative motion and pose from arbitrary plane curves

We show how to recover the position and orientation of a pair of known coplanar conics from a single perspective image. We describe and compare a number of methods for determining this relationship. One uses a simple four point back projection model, and the other utilizing transformation invariants. These results can be extended in a number of ways. Firstly, they can be applied to arbitrary plane curves using an invariant tting technique. Secondly, the recovery methods are applicable to higher order algebraic curves. We show examples of pose determination for both synthetic data and real images of conic and non-conic objects. For example we recognise and determine pose for a gasket containing non-conic curves. We assess the methods for stability and for accuracy against an accepted standard-Tsai's calibration method 16]. We conclude that using such methods enables accurate pose determination for arbitrary plane curves .