Optimization of Visual Computations

The process of co-evolution pushes biological systems towards optimization. If one species improves by genetic mutation or sexual recombination, a competitor species must also improve or be eliminated. A corollary is that portions of the brain should also improve towards optimization if pushed by natural selection. The retina is a particularly interesting part of the brain where to understand this putative optimization. The tasks of the retina are relatively clear (it processes visual information) and its mechanisms are better understood that in many other parts of the brain. In addition, retinal limitations such as having limited output capacity (the optic nerve) are apparent. Recently, we began testing the hypothesis that the retina is optimally designed to contribute to extraction of particular kinds of information, dropping others. An important alternate hypothesis is that the retina transmits to the rest of the brain as much information as possible regardless of the type of information.

We tested this optimization-of-particular-tasks hypothesis in the outer retina. There, the horizontal cells’ lateral-inhibition extent displays a bell-shape behavior as function of background luminance. Theories based on the spatial redundancy in natural images and the advantage of removing this redundancy from the visual code predict a fall as luminance increases. In turn, the hypothesis that the lateral-inhibition adaptation in the early retina is part of a system to extract several image attributes predicts a bell-shape behavior. Therefore, the retina appears to be optimal for specialized, non-generic computations.

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Results of the Optimization-of-particular-tasks Hypothesis (Parametric on m, a Parameter that Describes a Property of Natural Images).
They were averaged over eighty-nine natural images, with the error bars being standard errors. For these images, the behavior of the lateral-inhibition extent as a function of intensity is similar to that observed physiologically. (This is specially true for large m, which capture the majority of natural images.)


We also tested the optimization-of-particular-tasks hypothesis in the inner retina. For this, we chose to model the time course of adaptation to contrast in ganglion cells and could account for surprising features of this time course. For example, ganglion cells show a fast-then-slow adaptation when contrasts in a image increase. In contrast, ganglion cells show an intermediate-speed adaptation when contrasts fall.

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Our Model Accounts for Complex Features of the Time Course of Contrast Adaptation.
When contrasts increase (t = 20 s; Panel A), the gain of ganglion cells to contrast stimuli fall. However, when contrasts fall (t = 60 s; Panel A), this gain rises. When the time axis is expanded (Panel B), the gain fall shows a fast phase (t ? 1 s) followed by a slow phase (t ? 15 s). Expanding the axis for the gain rise (Panel C), reveals an adaptation with a single intermediate time constant (t ? 3 s).

These results led us to develop a general optimization Bayesian framework for sensory adaptation. Adaptation allows biological sensory systems to adjust to variations in the environment and thus to deal better with them. The underlying principle of our adaptation framework is the setting of internal parameters of the system such that it can perform certain pre-specified tasks 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 the limitations of the mechanisms processing this information. Because these processes are probabilistic, we formulate the minimization with a Bayesian approach. We also speculate that such Bayesian framework may be applicable to two other forms of adaptation. The first is the adaptation that takes place during development when an animal is exposed to the environment. The second is the natural-selection adaptation that takes place over eons and which guides the evolution of sensory receptive fields. In this latter case, the errors driving adaptation would be errors of behavior, such as misjudging the speed of a prey. We are currently investigating various aspects of the new framework of adaptation, including models of development and evolution, and tasks such as the measurements of orientation and direction of motion.