Geometric Analysis of the Conformal Camera for Intermediate-Level Vision and Perisaccadic Perception

A binocular system developed by the author in terms of projective Fourier transform (PFT) of the conformal camera, which numerically integrates the head, eyes, and visual cortex, is used to process visual information during saccadic eye movements. Although we make three saccades per second at the eyeball's maximum speed of 700 deg/sec, our visual system accounts for these incisive eye movements to produce a stable percept of the world. This visual constancy is maintained by neuronal receptive field shifts in various retinotopically organized cortical areas prior to saccade onset, giving the brain access to visual information from the saccade's target before the eyes' arrival. It integrates visual information acquisition across saccades. Our modeling utilizes basic properties of PFT. First, PFT is computable by FFT in complex logarithmic coordinates that approximate the retinotopy. Second, a translation in retinotopic (logarithmic) coordinates, modeled by the shift property of the Fourier transform, remaps the presaccadic scene into a postsaccadic reference frame. It also accounts for the perisaccadic mislocalization observed by human subjects in laboratory experiments. Because our modeling involves cross-disciplinary areas of conformal geometry, abstract and computational harmonic analysis, computational vision, and visual neuroscience, we include the corresponding background material and elucidate how these different areas interwove in our modeling of primate perception. In particular, we present the physiological and behavioral facts underlying the neural processes related to our modeling. We also emphasize the conformal camera's geometry and discuss how it is uniquely useful in the intermediate-level vision computational aspects of natural scene understanding.