IMAGE ALIGNMENT BY INTEGRATED ROTATIONAL AND TRANSLATIONAL TRANSFORMATION MATRIX

This paper presents an algorithm to align 2D images with similar densi tometric patterns in the spatial domain. It performs automatic identif ication of control points through local maxima in normalized image cro ss correlations computed through projections of an image function on 2 D orthonormal bases over a predefined circular domain. The image is su bsequently subjected to translational and rotational corrections throu gh an integrated transformation matrix obtained by the least-squares m inimization technique. The algorithm restricts the corrections require d for alignment to rotation and translation only, and care is taken to see that the image does not go through scaling (isotropic or anisotro pic) or non-linear distortions. The least-squares method results in im plicit equations in three variables, theta, h, v, representing rotatio n, 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 expl icit equations that are easy to solve. The mathematical validity of th is approximation is proved and the results obtained show that the algo rithm performs well with similar biological (histological, autoradiogr aphic, and tomographic) images. The algorithm is iterative, and its co mputer implementation is discussed.