Estimation of orientation and affine transformations of a 3-dimensional object

We consider the general problem of jointly estimating the orientation and deformations of a 3-dimensional object based on a finite set of known templates, and a single observation. The observation is obtained by projecting the object onto a plane (the observation plane) whose location relative to the object is a-priori unknown. We propose a method that formulates the original problem as an equivalent problem of analyzing a set of polynomials in a low dimensional space. In this setting, the procedure for estimating the orientation may be formulated as an iterative algorithm for deriving a maximal ideal in the minimal polynomial ring containing the above mentioned polynomial set. Once the orientation of the observation plane relative to the object has been estimated, the deformation parameters are recovered by solving a system of linear equations.