Harmonic Analysis for Cognitive Vision: Perisaccadic Perception

The data model for image representation in terms of projective Fourier transform (PFT) is well adapted to both image perspective transformations and the retinotopic mappings of the brain visual pathways. Here we model first aspects of the human visual process in which the understanding of a scene is built up in a sequence of fixations for visual information acquisition followed by fast saccadic eye movements that reposition the fovea on the next target. We make about three saccades per second with an eyeball’s maximum speed of 700 deg/sec. The visual sensitivity is markedly reduced during saccadic eye movements such that, three times per second, there are instant large changes in the retinal images without almost any information consciously carried across fixations. Inverse Projective Fourier transform is computable by FFT in coordinates given by a complex logarithm that also approximates the retinotopy. Thus, it gives the cortical image representation, and a simple translation in log coordinates brings the presaccadic scene into the postsaccadic reference frame, eliminating the need for starting processing anew three times per second at each fixation