Robust and Efficient Fourier–Mellin Transform Approximations for Gray-Level Image Reconstruction and Complete Invariant Description

Abstract

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. A comparison of these approximations is performed from discrete and finite-extent sets of Fourier–Mellin harmonics by means of experiments in: (i) image reconstruction via both visual inspection and the computation of a reconstruction error; and (ii) pattern recognition and discrimination by using a complete and convergent set of features invariant under planar similarities.Experimental results on real gray-level images show that it is possible to recover an image to within a specified degree of accuracy and to classify objects reliably even when a large set of descriptors is used. Finally, an example will be given, which illustrates both theoretical and numerical results in the context of content-based image retrieval.