Optical coherence tomography (OCT) has recently become one of the primary methods for noninvasive probing of the human retina. The pseudoimage formed by OCT (the so-called B-scan) varies probabilistically across pixels due to complexities in the measurement technique. Hence, sensitive automatic procedures of diagnosis using OCT may exploit statistical analysis of the spatial distribution of reflectance. In this paper, we perform a statistical study of retinal OCT data. We find that the stretched exponential probability density function can model well the distribution of intensities in OCT pseudoimages. Moreover, we show a small, but significant correlation between neighbor pixels when measuring OCT intensities with pixels of about 5 microm. We then develop a simple joint probability model for the OCT data consistent with known retinal features. This model fits well the stretched exponential distribution of intensities and their spatial correlation. In normal retinas, fit parameters of this model are relatively constant along retinal layers, but varies across layers. However, in retinas with diabetic retinopathy, large spikes of parameter modulation interrupt the constancy within layers, exactly where pathologies are visible. We argue that these results give hope for improvement in statistical pathology-detection methods even when the disease is in its early stages.

Adaptation allows biological sensory systems to adjust to variations in the environment and thus to deal better with them. In this article, we propose a general framework of sensory adaptation. The underlying principle of this framework is the setting of internal parameters of the system such that certain prespecified tasks can be performed optimally. Because sensorial inputs vary probabilistically with time and biological mechanisms have noise, the tasks could be performed incorrectly. We postulate that the goal of adaptation is to minimize the number of task errors. This minimization requires prior knowledge of the environment and of the limitations of the mechanisms processing the information. Because these processes are probabilistic, we formulate the minimization with a Bayesian approach. Application of this Bayesian framework to the retina is successful in accounting for a host of experimental findings.

Recently we found that the theories related to information theory existent in the literature cannot explain the behavior of the extent of the lateral inhibition mediated by retinal horizontal cells as a function of background light intensity. These theories can explain the fall of the extent from intermediate to high intensities, but not its rise from dim to intermediate intensities. We propose an alternate hypothesis that accounts for the extent's bell-shape behavior. This hypothesis proposes that the lateral-inhibition adaptation in the early retina is part of a system to extract several image attributes, such as occlusion borders and contrast. To do so, this system would use prior probabilistic knowledge about the biological processing and relevant statistics in natural images. A key novel statistic used here is the probability of the presence of an occlusion border as a function of local contrast. Using this probabilistic knowledge, the retina would optimize the spatial profile of lateral inhibition to minimize attribute-extraction error. The two significant errors that this minimization process must reduce are due to the quantal noise in photoreceptors and the straddling of occlusion borders by lateral inhibition.

We develop a theory for the temporal integration of visual motion motivated by psychophysical experiments. The theory proposes that input data are temporally grouped and used to predict and estimate the motion flows in the image sequence. This temporal grouping can be considered a generalization of the data association techniques that engineers use to study motion sequences. Our temporal grouping theory is expressed in terms of the Bayesian generalization of standard Kalman filtering. To implement the theory, we derive a parallel network that shares some properties of cortical networks. Computer simulations of this network demonstrate that our theory qualitatively accounts for psychophysical experiments on motion occlusion and motion outliers. In deriving our theory, we assumed spatial factorizability of the probability distributions and made the approximation of updating the marginal distributions of velocity at each point. This allowed us to perform local computations and simplified our implementation. We argue that these approximations are suitable for the stimuli we are considering (for which spatial coherence effects are negligible).

We develop a theory for the temporal integration of visual motion motivated by psychophysical experiments. The theory proposes that input data are temporally grouped and used to predict and estimate motion flows in the image sequences. Our theory is expressed in terms of the Bayesian generalization of standard Kalman filtering which allows us to solve temporal grouping in conjunction with prediction and estimation. As demonstrated for tracking isolated contours the Bayesian formulation is superior to approaches which use data association as a first stage followed by conventional Kalman filtering. Our computer simulations demonstrate that our theory qualitatively accounts for several psychophysical experiments on motion occlusion and motion outliers.

Although the commonly used quadratic Hebbian-anti-Hebbian rules lead to successful models of plasticity and learning, they are inconsistent with neurophysiology. Other rules, more physiologically plausible, fail to specify the biological mechanism of bidirectionality and the biological mechanism that prevents synapses from changing from excitatory to inhibitory, and vice versa. We developed a synaptic bidirectional Hebbian rule that does not suffer from these problems. This rule was compared with physiological homosynaptic conditions in the hippocampus, with the results indicating the consistency of this rule with long-term potentiation (LTP) and long-term depression (LTD) phenomenologies. The phenomenologies considered included the reversible dynamics of LTP and LTD and the effects of N-methyl-D-aspartate blockers and phosphatase inhibitors.

Several models of cortical development postulate that a Hebbian process fed by spontaneous activity amplifies orientation biases occurring randomly in early wiring, to form orientation selectivity. These models are not applicable to the development of retinal orientation selectivity, since they neglect the polarization of the retina's poorly branched early dendritic trees and the wavelike organization of the retina's early noise. There is now evidence that dendritic polarization and spontaneous waves are key in the development of retinal receptive fields. When models of cortical development are modified to take these factors into account, one obtains a model of retinal development in which early dendritic polarization is the seed of orientation selectivity, while the spatial extent of spontaneous waves controls the spatial profile of receptive fields and their tendency to be isotropic.

Waves of action-potential bursts propagate across the ganglion-cell surface of isolated developing retinas. It has been suggested that the rise of extracellular potassium concentration following a burst of action potentials in a cell may underlie these waves by depolarizing neighbor cells. This suggestion is sensible for developing tissues, since their glial system is immature. We tested whether this extracellular-potassium suggestion is feasible. For this purpose, we built a realistic biophysical model of the ganglion-cell layer of the developing retina. Simulations with this model show that increases of extracellular potassium are sufficiently high (about fourfold) to mediate the waves consistently with experimental physiological and pharmacological data. Even if another mechanism mediates the waves, these simulations indicate that extracellular potassium should significantly modulate the waves' properties.

Humans can recover the three-dimensional structure of moving objects from their changing two-dimensional retinal image, in the absence of other cues to three-dimensional structure (Wallach and O'Connell 1953; Braunstein 1976). In this paper, we describe a patient, A.F., with bilateral lesions involving the visual cortex who is severely impaired on computing local-speed and global-motion fields, but who can recover structure from motion. The data suggest that although possibly useful, global-motion fields are not necessary for deriving structure from motion. We discuss these results from the perspective of theoretical models for this computation.

A winner-take-all mechanism is a device that determines the identity and amplitude of its largest input (Feldman and Ballard 1982). Such mechanisms have been proposed for various brain functions. For example, a theory for visual velocity estimate (Grzywacz and Yuille 1989) postulates that a winner-take-all selects the strongest responding cell in the cortex's middle temporal area (MT). This theory proposes a circuitry that links the directionally selective cells in the primary visual cortex to MT cells, making them velocity selective. Generally, several velocity cells would respond, but only the winner would determine the perception. In another theory, a winner-take-all guides the spotlight of attention to the most salient image part (Koch and Ullman 1985). Also, such mechanisms improve the signal-to-noise ratios of VLSI emulations of brain functions (Lazzaro and Mead 1989). Although computer algorithms for winner-take-all mechanisms exist (Feldman and Ballard 1982; Koch and Ullman 1985), good biologically motivated models do not. A candidate for a biological mechanism is lateral (mutual) inhibition (Hartline and Ratliff 1957). In some theoretical mutual-inhibition networks, the inhibition sums linearly to the excitatory inputs and the result is passed through a threshold non linearity (Hadeler 1974). However, these networks work only if the difference between winner and losers is large (Koch and Ullman 1985). We propose an alternative network, in which the output of each element feeds back to inhibit the inputs to other elements. The action of this presynaptic inhibition is nonlinear with a possible biophysical substrate. This paper shows that the new network converges stably to a solution that both relays the winner's identity and amplitude and suppresses information on the losers with arbitrary precision. We prove these results mathematically and illustrate the effectiveness of the network and some of its variants by computer simulations.

Tliere are a number of important phenom- ena in motion perception involving colicrcnce. Examples include motion capture and motion cooperativity. We propose a theoretical model, called the motion coherence tlieory, that gives a possible explanation for these effects (Yuille and Grzywacz, 1988a,b). In this framework, the aperture problem can also be thought of as a problem of coherence and given a similar explanation. We propose the concept of a velocity field dcfined everywhere in the image, even where there is no explicit motion information available. Through a cost function, tlie model imposes smoothness on the velocity field in a more general way than previous theories. In this paper, we provide a de- tailed theoretical analysis of the motion coherence theory. We discuss its relations with previous theories and show that some of t1ic.m arc approximations to it. A sccorid pa- per (Grzywacz, Smith, and Yuillc, 1088) provides exten- sions and cletnilcd comparisons to psychophysical plienom- cna. Tlic theory applies to both short-range and long- range motion. It places them in the same computational framework aiid provides a way to define interactions be- twcr:11 the two 1)roccsses.