Robust and efficient Fourier-Mellin transform approximations for gray-level image reconstruction and complete invariant description

This paper addresses the gray-level image representation ability of the Fou rier-Mellin transform (FMT) for pattern recognition, reconstruction, and im age database retrieval. The main practical difficulty of the FMT lies in th e accuracy and efficiency of its numerical approximation and we propose thr ee estimations of its analytical extension. A comparison of these approxima tions is performed from discrete and finite-extent sets of Fourier-Mellin h armonies by means of experiments in: (i) image reconstruction via both visu al inspection and the computation of a reconstruction error; and (ii) patte rn 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 o bjects reliably even when a large set of descriptors is used. Finally, an e xample will be given, which illustrates both theoretical and numerical resu lts in the context of content-based image retrieval. (C) 2001 Academic Pres s.