Fourier analysis techniques applied in data registration: A survey

The data registration transforms multiple datasets into the same coordinate system, and in this way overlapping components of these sets are aligned. The registration is the fundamental of many advanced tasks, such as data fusion. There are plenty of solutions to data registration, and among them the algorithms based on Fourier analysis are efficient for large offsets but intricate. The surveys about data registration seldom focus on the approaches based on Fourier analysis. In this survey, we express the profound principles of Fourier analysis behind the obscure mathematical equations in plain language, explain the reason why the Fourier analysis techniques could be used in data registration and present how it is used in existing literatures. Transforming datasets into the Fourier domain decouples the rotation from the translation. For the rotation estimation, the algorithms could be categorized into the ones based on resampling of the Cartesian Fourier spectral and the ones adopting Spherical Fourier Transform. As to the translation recovery, the Phase Only Matched Filtering (POMF) is widely used and scarcely has a rival. In the end, we discuss the challenge of the registration methods relying on Fourier analysis and point out the future direction.