December 2008
Volume 8, Issue 17
OSA Fall Vision Meeting Abstract  |   December 2008
Projective fourier analysis and erisaccadic perception
Author Affiliations
  • Jacek Turski
    Computer and Mathematical Sciences, University of Houston-Downtown
Journal of Vision December 2008, Vol.8, 87. doi:
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      Jacek Turski; Projective fourier analysis and erisaccadic perception. Journal of Vision 2008;8(17):87.

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      © ARVO (1962-2015); The Authors (2016-present)

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Recently we have developed projective Fourier analysis for computational vision [1,2,3]. An important result emerging from this work is the fact that the conformal camera, which models eye's imaging functions, comes with its own harmonic analysis-projective Fourier analysis. It provides image representation that is well adapted to both the perspective transformations and the retinotopic mapping of the brain's oculomotor and visual pathways. Here, using projective Fourier transform, we model first aspects of the human visual process in which the understanding of a scene is built up in a sequence of attentional visual information acquisition fallowed by a fast saccadic eye movement that repositions the fovea on the next target. This sequence, called the scanpath, is the most basic feature of the foveate vision. We make three saccades per second with the maximum eyeball's speed of 700 deg/sec. The visual sensitivity is reduced during saccadic movements as we do not see moving images on the retinas. Therefore, three times per second, there are instant large changes in the retinal images without any information consciously carried between images. Inverse projective Fourier transform is computable by FFT in complex logarithmic coordinates that also approximates the retinotopy. Thus the output from it resembles the cortical image and a simple translation in logarithmic coordinates brings the presaccadic scene into the postsaccadic reference frame [4]. It eliminates the need for starting processing anew three times per second at each fixation, but it introduces perisaccadic mislocalization [5]. It may also build up perceptual continuity across fixations in the scanpath.

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TurskiJ. (2005). Geometric Fourier Analysis for Computational Vision, Journal of Fourier Analysis and Applications, 11, 1–23.

TurskiJ. (2006). Computational Harmonic Analysis for Human and Robotic Vision Systems, Neurocomputing, 69, 1277–1280.

VanRullenR. (2004). A simple translation in cortical log-coordinates may account for the pattern of saccadic localization errors. Biological Cybernetics, 91, 131–137.

LappeM.AwaterH.KrekelbergB. (2000). Postsaccadic visual references generate presaccadic compression of space. Nature, 403, 892–895.

Turski, J. (2008). Projective fourier analysis and erisaccadic perception [Abstract]. Journal of Vision, 8(17):87, 87a,, doi:10.1167/8.17.87. [CrossRef]

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