Image Registration using the Rigid Group

Image registration is the process of approximate matching of the source image to the target so that they resemble each other. In this study, two-dimensional image registration is presented using the rigid group. This group is a finite dimensional group (four-dimensional in this case) under composition. The dimensions of the rigid group are scaling, rotation, and translations along the axes. In this paper, an algorithm for the construction of rigid transformation is presented using the discretized objective function. This objective function is based on SSD (sum of the squares of the distances between the pixels intensities) and calculates the discrepancy between the images. The coarse search and the gradient descent approaches have been used for the optimization. The proposed algorithm is implemented on variety of images. The numerical examples illustrate the ability of the proposed algorithm.