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Statistics, Computation, and Coding in the Retina  

Gregory Schwartz

One of the most common ways to approach descriptions of the function of brains is with the language of computation. Neuroscientists often speak about what the brain computes and how it performs the computation using biological hardware. Theories of neural computation in most parts of the central nervous system of vertebrates are difficult to test in satisfying ways because often only partial information is available. Computations can be distributed over millions of neurons and vast regions of the brain, and the definitions of the computations themselves are often either abstract or lack a compelling, quantitative, causal link to a specific behavior. Although the vertebrate retina is a highly complex part of the central nervous system comprising approximately 150 different cell types, studying computation in the retina has certain advantages that have enabled the field to lead the way in some disciplines of computational neuroscience. These advantages include advanced knowledge of cell types, the repeating “mosaic” structure of retinal circuits, the ability to control precisely the full input (spatiotemporal patterns of light) while recording the full output (retinal ganglion cell spikes), and quantitative links to certain innate visual behaviors. Through the lens of statistics, many retinal computations can be framed as measurements of properties of probability distributions. The ways evolution has found to make these measurements with biological components are both elegant in their simplicity and powerful in their flexibility, in many cases far exceeding the sophistication of modern human-made digital imaging technology. Fast adaptation to both the mean and the variance of time-varying light distributions allows the retina to encode the enormous dynamic range of natural images within the limited dynamic range of neurons. Signal and noise distributions are estimated and combined in ways approaching theoretical limits. Objects are localized with precision far exceeding individual receptive fields by using a form of triangulation. Predictive information about motion statistics is represented in the population code. These examples and others enable analysis of retinal computation with tools from computer science, engineering, statistics, and information theory, serving as a model for computational neuroscience.


Evolution, Homology, Cell Classification, and Parallel Processing for Vision  

W. Martin Usrey and S. Murray Sherman

A first step in analyzing complex systems is a classification of component elements. This applies to retinal organization as well as to other circuit components in the visual system. There is great variety in the types of retinal ganglion cells and the targets of their axonal projections. Thus, a prerequisite to any deep understanding of the early visual system is developing a proper classification of its elements. How many distinct classes of retinal ganglion cells are there? Can the main classes be broken down into subclasses? What sort of functional correlates can be established for each class? Can homologous relationships between apparently similar classes between species be established? Can a common nomenclature based on homologous cell and circuit classes be developed?


The Functional Organization of Vertebrate Retinal Circuits for Vision  

Tom Baden, Timm Schubert, Philipp Berens, and Thomas Euler

Visual processing begins in the retina—a thin, multilayered neuronal tissue lining the back of the vertebrate eye. The retina does not merely read out the constant stream of photons impinging on its dense array of photoreceptor cells. Instead it performs a first, extensive analysis of the visual scene, while constantly adapting its sensitivity range to the input statistics, such as the brightness or contrast distribution. The functional organization of the retina abides to several key organizational principles. These include overlapping and repeating instances of both divergence and convergence, constant and dynamic range-adjustments, and (perhaps most importantly) decomposition of image information into parallel channels. This is often referred to as “parallel processing.” To support this, the retina features a large diversity of neurons organized in functionally overlapping microcircuits that typically uniformly sample the retinal surface in a regular mosaic. Ultimately, each circuit drives spike trains in the retina’s output neurons, the retinal ganglion cells. Their axons form the optic nerve to convey multiple, distinctive, and often already heavily processed views of the world to higher visual centers in the brain. From an experimental point of view, the retina is a neuroscientist’s dream. While part of the central nervous system, the retina is largely self-contained, and depending on the species, it receives little feedback from downstream stages. This means that the tissue can be disconnected from the rest of the brain and studied in a dish for many hours without losing its functional integrity, all while retaining excellent experimental control over the exclusive natural network input: the visual stimulus. Once removed from the eyecup, the retina can be flattened, thus its neurons are easily accessed optically or using visually guided electrodes. Retinal tiling means that function studied at any one place can usually be considered representative for the entire tissue. At the same time, species-dependent specializations offer the opportunity to study circuits adapted to different visual tasks: for example, in case of our fovea, high-acuity vision. Taken together, today the retina is amongst the best understood complex neuronal tissues of the vertebrate brain.


Physiology of Color Vision in Primates  

Robert Shapley

Color perception in macaque monkeys and humans depends on the visually evoked activity in three cone photoreceptors and on neuronal post-processing of cone signals. Neuronal post-processing of cone signals occurs in two stages in the pathway from retina to the primary visual cortex. The first stage, in in P (midget) ganglion cells in the retina, is a single-opponent subtractive comparison of the cone signals. The single-opponent computation is then sent to neurons in the Parvocellular layers of the Lateral Geniculate Nucleus (LGN), the main visual nucleus of the thalamus. The second stage of processing of color-related signals is in the primary visual cortex, V1, where multiple comparisons of the single-opponent signals are made. The diversity of neuronal interactions in V1cortex causes the cortical color cells to be subdivided into classes of single-opponent cells and double-opponent cells. Double-opponent cells have visual properties that can be used to explain most of the phenomenology of color perception of surface colors; they respond best to color edges and spatial patterns of color. Single opponent cells, in retina, LGN, and V1, respond to color modulation over their receptive fields and respond best to color modulation over a large area in the visual field.