Cyclic Shift Matrix—A New Tool for the Translation Matching Problem

For numerous applications in image registration, sub-pixel translation estimation is a fundamental task, and increasing attention has been given to methods based on image phase information. However, we have found that none of these methods is universal. In other words, for any one of these methods, we can always find some image pairs which will not be well matched. In this paper, by introducing the cyclic shift matrix (CSM), we present a new model for the translation matching problem and derive a least squares solution for the model. In addition, by repeatedly applying the CSM to the matching image, an iterative CSM method is proposed to further improve the matching accuracy. Furthermore, we show that the traditional phase-based matching algorithms can only achieve an exact solution when there is a cyclic shift relationship between the images to be matched. The proposed method is evaluated using simulated and real images and demonstrates a better performance in both accuracy and robustness compared with the state-of-the-art methods.