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Presents a new method to match a 2D image to a translated, rotated and scaled reference image. The approach consists of two steps: the calculation of a Fourier-Mellin invariant (FMI) descriptor for each image to be matched, and the matching of the FMI descriptors. The FMI descriptor is translation invariant, and represents rotation and scaling as translations in parameter space. The matching of the FMI descriptors is achieved using symmetric phase-only matched filtering (SPOMF). The performance of the FMI-SPOMF algorithm is the same or similar to that of phase-only matched filtering when dealing with image translations. The significant advantage of the new technique is its capability to match rotated and scaled images accurately and efficiently. The innovation is the application of SPOMF to the FMI descriptors, which guarantees high discriminating power and excellent robustness in the presence of noise. This paper describes the principle of the new method and its discrete implementation for either image detection problems or image registration problems. Practical results are presented for various applications in medical imaging, remote sensing, fingerprint recognition and multiobject identification.