Linear Estimation of Sequences of Multi-Dimensional Affine Transformations

We consider the general framework of planar object registration and tracking. Given a sequence of observations on an object, subject to an unknown sequence of affine transformations of it, our goal is to estimate the deformation that transforms some pre-chosen representation of this object (template) into the current sequence of observations. We propose a method that employs a set of non-linear operators to replace the original high dimensional and non-linear problem by an equivalent linear problem, expressed in terms of the unknown affine transformation parameters. We investigate two modelling and estimation solutions: the first, estimates the affine transformation relating any two consecutive observations, followed by a least squares fit of a global model to the estimated sequence of instantaneous deformations. The second, is a global solution that fits a time-dependent affine model to the entire set of observed data