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This paper addresses the gray-level image representation ability of the Fourier-Mellin Transform (FMT) for pattern recognition, reconstruction and image database retrieval. The main practical difficulty of the FMT lies in the accuracy and efficiency of its numerical approximation and we propose three estimations of its analytical extension. Comparison of these approximations is performed from discrete and finite-extent sets of Fourier-Mellin harmonics by means of experiments in: (i) imagedoi:10.1006/cviu.2001.0922 fatcat:vcj2poljxjamdensm6nm2z7px4