Darkness filling-in: a neural model of darkness induction.

A model of darkness induction based on a neural filling-in mechanism is proposed. The model borrows principles from both Land's Retinex theory and BCS/FCS filling-in model of Grossberg and colleagues. The main novel assumption of the induction model is that darkness filling-in signals, which originate at luminance borders, are partially blocked when they try to cross other borders. The percentage of the filling-in signal that is blocked is proportional to the log luminance ratio across the border that does the blocking. The model is used to give a quantitative account of the data from a brightness matching experiment in which a decremental test disk was surrounded by two concentric rings. The luminances of the rings were independently varied to modulate the brightness of the test. Observers adjusted the luminance of a comparison disk surrounded by a single ring of higher luminance to match the test disk in brightness.

Evidence for a noise gain control mechanism in human vision.

For small, brief targets incremental threshold is known to obey the de Vries-Rose law: threshold rises in direct proportion to the square-root of background intensity. We present data demonstrating a square-root law for brightness matching as well. The square-root law for brightness is obtained over the full range of scotopic vision, and the low intensity end of photopic vision. The classic theory of de Vries and Rose explains the square-root law on the basis of increased variability of the photon count as the background increases. Our brightness matching data instead indicates that the mean signal level is reduced by a factor which is inversely proportional to the standard deviation of the photon count. This result is consistent with the idea that in the retina there exists a gain control mechanism that is sensitive to the variance in the photon input, rather than to the mean illuminance. The importance of this idea to the modelling of retinal gain controls is discussed.

A model of Weber and noise gain control in the retina of the toad Bufo marinus.

We present several variations of a model of gain control in the retina of the toad Bufo marinus, and use them to fit the threshold-vs-intensity data of an actual toad ganglion cell [Donner et al. (1990). Journal of General Physiology, 95, 733-753]. Our models are based on a proposal by Donner et al. that the gain (neural spike per photon ratio) of toad ganglion cells is set by a sequence of two retinal gain control stages. The first stage consists of a Weber gain control mechanism at the level of the red rods. The second is a more proximal "noise gain" stage, which multiplies the (incremental) input signal by a factor that is inversely proportional to the standard deviation of the random ganglion cell input and, under conditions that produce the de Vries-Rose threshold law, is also proportional to the standard deviation of the photon fluctuations within the ganglion cell receptive field. We demonstrate that noise gain control arises naturally from modeling ganglion cell spike generation with either of two common types of spike generation models: integrate-and-fire models or threshold accommodation models. We simulate the process of spike generation in both types of models and show that either model can account for the basic overall shape of the toad t.v.i. curve. However, although integrate-and-fire models appropriately generate noise gain control, they cannot quantitatively fit the threshold data with realistic retinal parameters. Integrate-and-fire models also fail to account for the observed relationship between the generator potential of the ganglion cell and its spiking probability. A threshold accommodation model with realistic retinal parameters, on the other hand, can account for both the threshold data and the generator potential-spike probability relationship. When a Weber gain stage is added to the model at the photoreceptor level, the resulting two-stage gain control model is shown to account quantitatively for the ganglion cell t.v.i. curve of Bufo marinus over the full range of background levels studied by Donner et al.

Noise adaptation in integrate-and fire neurons.

The statistical spiking response of an ensemble of identically prepared stochastic integrate-and-fire neurons to a rectangular input current plus gaussian white noise is analyzed. It is shown that, on average, integrate-and-fire neurons adapt to the root-mean-square noise level of their input. This phenomenon is referred to as noise adaptation. Noise adaptation is characterized by a decrease in the average neural firing rate and an accompanying decrease in the average value of the generator potential, both of which can be attributed to noise-induced resets of the generator potential mediated by the integrate-and-fire mechanism. A quantitative theory of noise adaptation in stochastic integrate-and-fire neurons is developed. It is shown that integrate-and-fire neurons, on average, produce transient spiking activity whenever there is an increase in the level of their input noise. This transient noise response is either reduced or eliminated over time, depending on the parameters of the model neuron. Analytical methods are used to prove that nonleaky integrate-and-fire neurons totally adapt to any constant input noise level, in the sense that their asymptotic spiking rates are independent of the magnitude of their input noise. For leaky integrate-and-fire neurons, the long-run noise adaptation is not total, but the response to noise is partially eliminated. Expressions for the probability density function of the generator potential and the first two moments of the potential distribution are derived for the particular case of a nonleaky neuron driven by gaussian white noise of mean zero and constant variance. The functional significance of noise adaptation for the performance of networks comprising integrate-and-fire neurons is discussed.

Stochastic retinal mechanisms of light adaptation and gain control.

Under appropriate experimental conditions, the threshold intensity of a visual stimulus varies as the square-root of the background illuminance. This square-root law has been observed in both psychophysical threshold experiments and in measurements of the thresholds of individual ganglion cells. A signal detection theory developed in the 1940s by H. L. de Vries and A. Rose, and since elaborated by H. B. Barlow and others, explains the square-root law on the basis of 'noise' due to fluctuations in the number of photon absorptions per unit area and unit time at the cornea. An alternative account of the square-root law--and also other threshold-vs-intensity slopes--is founded on the assumption of physiological gain control (W. A. H. Rushton, Proc, Roy. Soc. (London) B 162, 20-46, 1965; W. S. Geisler, J. Physiol. (London) 312, 165-179, 1979). In this paper, a neural model of light adaptation and gain control is described that shows how these two accounts of the square-root law can be reconciled by a stochastic gain control mechanism whose gain depends on the photon fluctuation level. The process by which spikes are generated in a ganglion cell is modeled in terms of a stochastic integrate-and-fire mechanism; this model is used to quantitatively fit toad retinal ganglion cell threshold data. A psychophysical model is then outlined showing how a statistical observer could analyze the ganglion cell spike trains generated by 'signal' and 'noise' trials in order to statistically discriminate the two conditions. The model is also shown to account for some dynamic aspects of ganglion cell responses, including ON- and OFF-responses. The neural light adaptation model predicts that--under the proper conditions--brightness matching judgments will also be subject to a square-root law. Experimental tests of the model under superthreshold conditions are proposed.

Cortical dynamics of visual motion perception: short-range and long-range apparent motion.

This article describes further evidence for a new neural network theory of biological motion perception. The theory clarifies why parallel streams V1----V2, V1----MT, and V1----V2----MT exist for static form and motion form processing among the areas V1, V2, and MT of visual cortex. The theory suggests that the static form system (Static BCS) generates emergent boundary segmentations whose outputs are insensitive to direction-of-contrast and to direction-of-motion, whereas the motion form system (Motion BCS) generates emergent boundary segmentations whose outputs are insensitive to direction-of-contrast but sensitive to direction-of-motion. The theory is used to explain classical and recent data about short-range and long-range apparent motion percepts that have not yet been explained by alternative models. These data include beta motion, split motion, gamma motion and reverse-contrast gamma motion, delta motion, and visual inertia. Also included are the transition from group motion to element motion in response to a Ternus display as the interstimulus interval (ISI) decreases; group motion in response to a reverse-contrast Ternus display even at short ISIs; speed-up of motion velocity as interflash distance increases or flash duration decreases; dependence of the transition from element motion to group motion on stimulus duration and size, various classical dependencies between flash duration, spatial separation, ISI, and motion threshold known as Korte's laws; dependence of motion strength on stimulus orientation and spatial frequency; short-range and long-range form-color interactions; and binocular interactions of flashes to different eyes.

Quantal fluctuation limitations on reaction time to sinusoidal gratings.

A model of sinusoidal grating detection based on the output of many parallel-processing spatial frequency-bandpass receptive fields is developed. The receptive fields are assumed to be of similar shape but to differ in scale and retinal location. Because the retinal image is inherently noisy due to photon noise a signal detection analysis is carried out. For a stimulus grating having a particular spatial frequency there is a most sensitive mechanism: one with a receptive field of ideal size and retinal location with respect to the stimulus. We hypothesize that subjects make reliable judgements concerning the physical presence of a grating based on the time-integrated output of the most sensitive mechanism. This leads to the prediction that reaction time to grating onset will be linearly related to the square of the grating frequency. This prediction is confirmed by data from Breitmeyer [1975, Experiment 1 (Vision Res. 15, 1411-1412)].