Image alignment by integrated rotational and translational transformation matrix

Abstract

Presents an algorithm to align 2D images with similar densitometric patterns in the spatial domain. It performs automatic identification of control points through local maxima in normalized image cross correlations computed through projections of an image function on 2D orthonormal bases over a predefined circular domain. The image is subsequently subjected to translational and rotational corrections through an integrated transformation matrix obtained by the least-squares minimization technique. The algorithm restricts the corrections required for alignment to rotation and translation only, and care is taken to see that the image does not go through scaling (isotropic or anisotropic) or nonlinear distortions. The least-squares method results in implicit equations in three variables, theta , h, upsilon , representing rotation, and translations along x and y axes. The present algorithm, on the other hand, is based on an approximation that results in a set of explicit equations that are easy to solve. The mathematical validity of this approximation is proved and the results obtained show that the algorithm performs well with similar biological (histological, autoradiographic, and tomographic) images. The algorithm is iterative, and its computer implementation is discussed.