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

Stéphane Derrode (1) , F. Ghorbel (2)

1 FRESNEL - Institut FRESNEL
2 CRISTAL - Centre de Recherche Réseau Image SysTème Architecture et MuLtimédia

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 di±culty of the FMT lies in the accuracy and e±ciency of its numerical approximation and we propose three estimations of its analytical extension. Comparison of these approximations is performed from discrete and ¯nite-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 speci¯ed 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.

Domaines: Recherche d'information [cs.IR]

Stéphane Derrode, F. Ghorbel. Robust and efficient Fourier-Mellin transform approximations for invariant grey-level image description and reconstruction. Computer Vision and Image Understanding, 2001, 83 (1), pp.57-78. ⟨hal-00325095⟩