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1.  Initial Ocular Following in Humans Depends Critically on the Fourier Components of the Motion Stimulus 
Visual motion is sensed by low-level (energy-based) and high-level (feature-based) mechanisms. Our interest is in the motion detectors underlying the initial ocular following responses (OFR) that are elicited at ultrashort latencies by sudden motions of large images. OFR were elicited in humans by applying horizontal motion to vertical square-wave gratings lacking the fundamental. In the frequency domain, a pure square wave is composed of the odd harmonics—first, third, fifth, seventh, etc.—such that the third, fifth, seventh, etc., have amplitudes that are one-third, one-fifth, one-seventh, etc., that of the first, and the missing fundamental stimulus lacks the first harmonic. Motion consisted of successive quarter-wavelength steps, so the features and 4n+1 harmonics (where n = integer) shifted forward, whereas the 4n-1 harmonics—including the strongest Fourier component (the third harmonic)—shifted backward (spatial aliasing). Thus, the net Fourier energy and the non-Fourier features moved in opposite directions. Initial OFR, recorded with the search coil technique, had minimum latencies of 60 to 70 ms and were always in the direction of the third harmonic, for example, leftward steps resulted in right-ward OFR. Thus, the earliest OFR were strongly dependent on the motion of the major Fourier component, consistent with mediation by oriented spatiotemporal visual filters as in the well-known energy model of motion detection. Introducing interstimulus intervals of 10 to 100 ms (during which the screen was uniform gray) reversed the initial direction of tracking, consistent with extensive neurophysiological and psychophysical data suggesting that the visual input to the motion detectors has a biphasic temporal impulse response.
doi:10.1196/annals.1325.025
PMCID: PMC1383627  PMID: 15826980
visual motion; energy-based mechanisms; biphasic temporal impulse response; missing fundamental
2.  Short-Latency Disparity Vergence in Humans: Evidence for Early Spatial Filtering 
Our study was concerned with the disparity detectors underlying the initial disparity vergence responses (DVRs) that are elicited at ultrashort latencies by binocular disparities applied to large images. DVRs were elicited in humans by applying horizontal disparity to vertical square-wave gratings lacking the fundamental (termed here, the “missing fundamental”). In the frequency domain, a pure square wave is composed of odd harmonics—first, third, fifth, seventh, etc.—such that the third, fifth, seventh, etc., have amplitudes that are one-third, one-fifth, one-seventh, etc., that of the first, and the missing fundamental lacks the first harmonic. The patterns seen by the two eyes have a phase difference of one-quarter wavelength, so the disparity of the features and 4n + 1 harmonics (where n = integer) has one sign (crossed or uncrossed), whereas the 4n - 1 harmonics—including the strongest Fourier component (the third harmonic)—has the opposite sign (uncrossed or crossed): spatial aliasing. The earliest DVRs, recorded with the search-coil technique, had minimum latencies of 70 to 80 ms and were generally in the direction of the third harmonic, that is, uncrossed disparities resulted in convergent eye movements. In other experiments on the DVRs, one eye saw a missing fundamental and the other saw a pure sine wave with the contrast and wavelength of the third harmonic but differing in phase by one-quarter wavelength. This resulted in short-latency vergence in accordance with matching of the third harmonic. These data all indicate the importance of the Fourier components, consistent with early spatial filtering prior to binocular matching.
doi:10.1196/annals.1325.024
PMCID: PMC1369053  PMID: 15826979
missing fundamental; binocular disparity; vergence eye movements

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