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Modeling spatial integration in the ocular following response using a probabilistic framework

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All material (c) L. Perrinet. Please check the copyright notice.

grating_contrast grating_size full_field_barberpole

Figure Stimuli used for testing OFR. (Left) Grating in a disk aperture with varying contrast and (Middle) with varying diameters. (Right) Barberpole.

summary

Figure 1 Basic properties of human OFR. Several properties of motion integration for driving ocular following as summarized from our previous work. (a) A leftward drifting grating elicits a brief acceleration of the eye in the leftward direction. Mean eye velocity profiles illustrate that both response amplitude and latency are affected by the contrast of the sine-wave grating, given by numbers at the right-end of the curves. Quantitative estimates of the sensori-motor transformation are given by measuring the response amplitude (i.e. change in eye position) over a fixed time window, at response onset. Relationships between (b) response latency or (c) initial amplitude and contrast are illustrated for the same grating motion condition. These curves define the contrast response function (CRF) of the sensori-motor transformation and are best fitted by a Naka–Rushton function (reprinted from (Barthélemy et al., 2007)). (d) At fixed contrast, the size of the circular aperture can be varied to probe the spatial summation of OFR. Clearly, response amplitude first linearly grows up with stimulus size before reaching an optimal size, the integration zone. For larger stimulus sizes, response amplitudes are lowered (reprinted from (Barthélemy et al., 2006)). (e) OFR are recorded for center-alone and center–surround stimuli. The contrast of the center stimulus is varied to measure the contrast response function and compute the contrast gain of the sensori-motor transformation at both an early and a late phase during response onset. Open symbols are data obtained for a center-alone stimulus, similar to those illustrated in (c). When adding a flickering surround, ones can see that late (but not early) contrast gain is lowered, as illustrated by a rightward shift of the contrast response function (Barthélemy et al., 2006).

model_rog.png

Figure 2 To model spatial integration in the OFR in primates (humans and macaques), we use the tools of statistical inference with the hypothesis that information is represented in a probabilistic fashion. The architecture of the OFR system consists in this model of a stage extracting from the raw image the possible local translation velocities (V1) to represent the local probabilities of translational velocity (MT). These local bits of information are then pooled (MST) to give a single probabilistic representation of possible translational velocities to the oculomotor system, which then controls the eyes' motion as quickly and efficiently as possible to stabilize the image on the retina. The local probabilities may be often described as gaussian probabilities, and the gain response as a function to the signal to noise ratio is then given by a Naka-Rushton curve (Barthélemy et al., 2007).


This work was supported by European integrated project FP6-015879, "FACETS".


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