On the optimal parameterization of the phase correlation method for image registration

Image registration aims to align images of the same scene, useful for several applications. Phase Correlation is a technique based on (log-)polar mapping of the image magnitude spectrum coordinates that has proven to be effective for estimating translation, rotation, and scaling parameters. It is well established that the interpolations required for Cartesian-(log-)polar mapping introduce spurious correlations, which degrade the rotation estimation performance. However, no suitable solution has been proposed so far. Although investigated for several decades, Phase Correlation-based registration still lacks clear design guidelines. Moreover, seemingly reasonable design choices may lead to counterintuitive degradation. In this work, an optimal parameterization of coordinate mapping is proposed. It preserves the information contained in the Cartesian plane while minimizing factors that cause spurious correlations and unnecessary memory consumption. Beyond its application to Phase Correlation, the proposed approach has the potential to benefit any signal processing task that requires lossless discrete-discrete Cartesian-polar mapping.