Input-output transformation in the visuo-oculomotor loop: modeling the ocular following response to center-surround stimulation in a probabilistic framework

The machinery behind Ocular Following Response (OFR) is confronted to ambiguities which are efficiently resolved in the primate visual system. We study here a model of center-surround motion integration in a probabilistic framework and try to identify its different dynamical components by using contrast gain responses to the particular bipartite stimuli. Motion integration may be modeled as an ideal observer in a probabilistic framework by using bayesian modeling [11] or statistical inference which proved to be successfully applied to the ocular following response [9]. Experiments on primates’ oculo-motor recordings concentrated on bipartite stimuli optimized to study the dynamics of information integration for different levels of noise which provide evidence for an orientation selective suppressive effect of the surround on the contrast gain control of local stimuli [1]. We extend here our previous model to integrate different spatial cues: the information propagates to give a command response for ocular response that we could compare with the human behavioral response. We present results which show that the hypothesis of independence of local measures succesfully accounts for the monotonic integration of the spatial motion signal but that another mechanism should be added to account for suppressive saturation. Adding this, we observed similar dynamics for the contrast gain control mechanisms observed in the behavioral data and in neuro-physiological through in-vivo cortical recording by optical imaging (see accompanying poster number 21 by Reynaud et al. [10]). 1 An "ideal observer" model for Ocular Following Response (OFR) FIGURE 1: Architecture of the model. The model consists in the pooling of elementary infomation bits from neurons to provide a decision which reaches the oculomotor system to close the oculomotor loop by moving the eye’s position. Every neuron integrates motion information from the image on its receptive field so as to provide a probabilistic representation of the local velocity. This information is then pooled across the different neurons (and hence across space) but also integrated in time, or potentially by other modalities (proprioception). A decision is formed —usually the Maximum A Posteriori (MAP) probability or the mean of the computed global velocity probability— which is transformed accordingly by the oculomotor system to produce an eye movement. Perceiving motion is a difficult task and we use here the tools of statistical inference to model results observed in primates (humans and macaques) on the Ocular Following Response (OFR) [4, 5, 1]. This is particularly relevant in the visual system where this task relies on the integration of different information bits, such as visual local information in a receptive field, the information already detected by neurons which should be computed quickly and efficiently. As described in [9], we model the observed change in eye position as proportional to a gain defined as the ideal response knowing the given information: γ ∝ E(~v|I) = ∫ ~vP(~v|I)dP(~v|I) (1) A difficulty is is to compute P(~v|I) and a solution which seem to be implemented in the visual system consists in pooling the information from different neurons n ∈ P, where P is the total population of neurons, which have local receptive fields. It is then possible to evaluate the velocity ~v thanks to a stochastic model of the local translation in the image : I(~x, t) = I(~x − ~vdt, t − dt) + ν, where ~x is the position in the receptive field and ν is a Gaussian noise of variance σn. This noise is inversely proportional to Michelson’s Contrast (we note the full contrast image : I100 = C−1.I). Adding a Gaussian prior of variance σp,n favoring slow speed [11], it follows log P(~v|I,n) = Z − C.DI100(~v)/σ/2 − (log ‖~v‖)/σp,n/2 (2) where DI100 = C−2.DI is the contrast-normalized gradient constraint for the local image in the receptive field. In the range of experiments that we describe here, the image is locally a grating: I100 = sin(2π f (x − ~v.t)) (3) for which DI100 is easy to compute: it is well approached by a quadratic function. Every node can thus be characterized by a mean ~vn and a covariance matrix Cn such that the density P(~v|I,n) is a Gaussian: N(~vn,Cn) = 1 √ det(2πCn) .exp( 1 2 (~v − ~vn)TC−1 n (~v − ~vn) (4) In the general case, we have Cn given by ( σn 0 0 σ2 ) ( cos(θ) sin(θ) − sin(θ) cos(θ) )