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

Stéphane Derrode, Faouzi Ghorbel
2001 Computer Vision and Image Understanding  
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) image
more » ... truction 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, illustrating both theoretical and numerical results in the context of content-based image retrieval.
doi:10.1006/cviu.2001.0922 fatcat:vcj2poljxjamdensm6nm2z7px4