Parametric estimation of two-dimensional affine transformations

We consider the general problem of object recognition based on a set of known templates. While the set of templates is known, the tremendous set of possible transformations and deformations between the template and the observed signature, makes any detection and recognition problem ill-defined unless this variability is taken into account. We propose a method that reduces the high dimensional problem of evaluating the orbit created by applying the set of all possible transformations in the group to a template, into a problem of analyzing a function in a low dimensional Euclidian space. In this setting, the problem of estimating the parametric model of the affine deformation is expressed using a set on non-linear operators, by a set of linear equations. This system of linear equations is then solved for the transformation parameters.