Duality between foveatization and multiscale local spectrum estimation

Rafael Fonolla Navarro; Javier Portilla; Antonio Tabernero

doi:10.1117/12.320121

17 July 1998 Duality between foveatization and multiscale local spectrum estimation

Rafael Fonolla Navarro, Javier Portilla, Antonio Tabernero

Proceedings Volume 3299, Human Vision and Electronic Imaging III; (1998) https://doi.org/10.1117/12.320121
Event: Photonics West '98 Electronic Imaging, 1998, San Jose, CA, United States

Abstract

In this work we demonstrate the relationship existing between two important issues in vision: multi-scale local spectrum analysis, and log-polar foveatization. We show that, when applying a continuous set of self-similar (rotated and scaled) band-pass filters to estimate the local spectrum at a given point of attention of the image, the inverse Fourier transform of this local spectrum is a log- polar foveated version of the original image at that position. Both the local spectrum and its associated foveated image can be obtained through log-polar warping of the spectral/spatial domain followed by a conventional invariant low-pass filtering and the corresponding inverse warping. Furthermore, the low-pass filters in the warped space and frequency domains are mirror versions of each other. Thus, filters with mirror symmetry under the log- polar warping are self-dual, and make the foveatization process commute with the Fourier transform. Nevertheless, in order to implement a fovea that can be easily moved across the image, it is preferable to use a fixed bank of steerable filters, instead of applying log-polar warpings with different centers. Using low-pass scalable filters we have implemented a real-time moving fovea. We believe that a dual finite spatial/spectral local representation of images could be a very powerful tool for many visual tasks, which could benefit from a dual explicit representation in space and spatial frequency, as well as from the rotation and scale invariance naturally achieved in both domains.

Citation Download Citation

Rafael Fonolla Navarro, Javier Portilla, and Antonio Tabernero "Duality between foveatization and multiscale local spectrum estimation", Proc. SPIE 3299, Human Vision and Electronic Imaging III, (17 July 1998); https://doi.org/10.1117/12.320121

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