Affine registration using graph representations of images

We consider the problem of estimating the geometric deformation of an object, with respect to some reference observation on it. Existing solutions, set in the standard coordinate system imposed by the measurement system, lead to high-dimensional, non-convex optimization problems. We present a weighted graph representation of images, and propose a global method that employs a set of non-linear functionals graph based to replace this originally high dimensional problem by an equivalent problem that is linear in the unknown transformation parameters. The method yields a very large number of independent linear constraints that enables explicit parametric estimation. Analysis and numerical examples that demonstrate the robustness of the method to noise are presented. The proposed solution is unique and exact and is applicable to any affine transformation regardless of its magnitude.