(2) Hints on terminology and the literature: it is important to properly denote the new 2D spectral registration method as “Fourier-SOFT in 2D (FS2D)”. Just as rough academic timeline and background
- translation estimation in 2D with the (Fast) Fourier Transform (FT) goes back to the earliest days of Computer Vision in 1970 [1]; this is often called “Fourier registration”
- estimating 2D rotation (and scale) in addition with the Mellin transform (MT) was introduced in the 1990s [2][3]; this is the Fourier-Mellin-Transform (FMT) also know as Fourier-Mellin-Invariant (FMI)
- while feature-based methods using SIFT&co started to dominate from end of the 1990s on, there was a rise in using variants of FMT registration due to their robustness from about 2010 again; this includes also work from our group – mainly by Heiko (Bülow) using some signal processing add-ons, which was then dubbed “improved FMI” (iFMI)
- a major new contribution from our group was “Fourier Mellin SOFT (FMS)” [4], the very first, highly non-trivial extension of FMT (aka FMI) to 3D, i.e., it provides 7-dof (translation, rotation, scale in 3D)
- the new “Fourier-SOFT in 2D (FS2D)” [5] also uses SOFT, but it is fundamentally different from both FMT (aka FMI) as well as FMS; as very short description: it projects the 2D data onto a 3D sphere where the SO(3)-Fourier-Transform (SOFT) is used
- hence important: Fourier Mellin SOFT (FMS) as 3D registration method and Fourier-SOFT in 2D (FS2D) for 2D registration are two fundamentally different, new methods – and either their full names should be spelled out or the proper abbreviations used
- just as info: Tim currently also works on a quaternion formulation of FMS (which has some advantages)
[X] X. Tong, Z. Ye, Y. Xu, S. Gao, H. Xie, Q. Du, S. Liu, X. Xu, S. Liu, K. Luan, and U. Stilla, “Image Registration With Fourier-Based Image Correlation: A Comprehensive Review of Developments and Applications,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 12, pp. 4062-4081, 2019. https://doi.org/10.1109/JSTARS.2019.2937690
[1] P. E. Anuta. Spatial registration of multispectral and multitemporal digital imagery using Fast Fourier Transform techniques. IEEE Transactions on Geoscience Electronics 8(4): 353–368, 1970
[2] Q.-S. Chen, M. Defrise, and F. Deconinck. Symmetric phase-only matched filtering of Fourier-Mellin transforms for image registration and recognition. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 16 (12), pp. 1156-1168, 1994
[3] B. S. Reddy and B. N. Chatterji. An FFT-based technique for translation, rotation, and scale-invariant image registration. Image Processing, IEEE Transactions on, 5 (8), pp. 1266-1271. 1996
[4] H. Bülow and A. Birk, “Scale-Free Registrations in 3D: 7 Degrees of Freedom with Fourier-Mellin-SOFT transforms,” International Journal of Computer Vision (IJCV), vol. 126, pp. 731-750, 2018. https://doi.org/10.1007/s11263-018-1067-5. 2018 (open access)
[5] T. Hansen and A. Birk, “Using Registration with Fourier-SOFT in 2D (FS2D) for Robust Scan Matching of Sonar Range Data,” in IEEE International Conference on Robotics and Automation (ICRA), 2023. https://doi.org/10.1109/ICRA48891.2023.10160519 (see also https://www.researchgate.net/publication/372130798_Using_Registration_with_Fourier-SOFT_in_2D_FS2D_for_Robust_Scan_Matching_of_Sonar_Range_Data)