Review and improvement of the linear transformation of images

A common problem in the field of image processing is recovering a geometrical distortion such as scaling, rotation, translation, shearing, and others. These types of distortions can be described by a general affine transform. In this work, the problem of recovering a transformation applied on a reference image f is considered. A review on the most known methods for recovering a general linear transformation, or a distortion from an inspected image g and a reference image f, is conducted. A new efficient estimation method without using a prior knowledge or assumptions is proposed. The proposed algorithms use the moments of the Radon projections of f and g. In some cases, our proposed algorithm needs only two orthogonal projections such as the view angles 0, and π/2. Mathematical formulations are given for recovering the transformation of shifting, scaling, rotation, and general reflection.