Robust algebraic invariant methods with applications in geometry and imaging
Eamon B. Barrett, Paul M. Payton, Gregory O. Gheen · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1995
We introduce non-standard methods of deriving algebraic invariants and demonstrated two types of applications of these invariants. In model transfer a collection of conjugate points are determined on a set of reference images, and `transferred' to the matching conjugate points on a new view of the 3D object, without prior computation of camera geometry or scene reconstruction. In object reconstruction, general 3D object points are represented as functions of non-coplanar fiducial points and corresponding conjugate points across multiple images. In this application the object points are `reconstructed' once quantitative values are specified for the fiducial points. The methods we introduce for deriving these invariant algorithms are extensible from the linear fractional central projection camera model to weak perspective and certain non-central projection camera models. Stability to adverse geometries and measurement error can be enhanced by using redundant fiducial points and images to determine the transfer and reconstruction functions. Extensibility and stability are indications of the robustness of these methods.