Modeling the self-organization of color selectivity in the visual cortex

How does the visual cortex represent and process color? Experimental evidence from macaque monkey suggests that cells selective for color are organized into small, spatially separated blobs in V1, and stripes in V2. This organization is strikingly different from that of orientation and ocular dominance maps, which consist of large, spatially contiguous patterns. In this dissertation, a self-organizing model of the early visual cortex is constructed using natural color image input. The modeled V1 develops realistic color-selective receptive fields, ocular dominance stripes, orientation maps, and color-selective regions, while the modeled V2 also creates realistic colorselective and orientation-selective neurons. V1 color-selective regions are generally located in the center of ocular dominance stripes as they are in biological maps; the model predicts that color-selective regions become more widespread in both cortical regions when the amount of color in the training images is increased. The model also predicts that in V1 there are three types of color-selective regions (red-selective, greenselective, and blue-selective), and that a unique cortical activation pattern exists for each of the HSV colors. In both V1 and V2, when regions of different color-selectivity are located nearby, bands of color form with gradually changing color preferences. The model also develops lateral connections between cells that are selective for similar orientations, matching previous experimental results, and predicts that cells selective for color primarily connect to other cells with similar chromatic preferences. Thus the model replicates the known data on the organization of color preferences in V1 and V2, provides a detailed explanation for how this structure develops and functions, and leads to concrete predictions to test in future experiments.Computer Science

Coordinated optimization of visual cortical maps (II) Numerical studies

It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we defined a class of analytically tractable coordinated optimization models and solved representative examples in which a spatially complex organization of the orientation preference map is induced by inter-map interactions. We found that attractor solutions near symmetry breaking threshold predict a highly ordered map layout and require a substantial OD bias for OP pinwheel stabilization. Here we examine in numerical simulations whether such models exhibit biologically more realistic spatially irregular solutions at a finite distance from threshold and when transients towards attractor states are considered. We also examine whether model behavior qualitatively changes when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. Our numerical results support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the spatially irregular architecture of the visual cortex. We discuss several alternative scenarios and additional factors that may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1102.335

Coverage, Continuity and Visual Cortical Architecture

The primary visual cortex of many mammals contains a continuous representation of visual space, with a roughly repetitive aperiodic map of orientation preferences superimposed. It was recently found that orientation preference maps (OPMs) obey statistical laws which are apparently invariant among species widely separated in eutherian evolution. Here, we examine whether one of the most prominent models for the optimization of cortical maps, the elastic net (EN) model, can reproduce this common design. The EN model generates representations which optimally trade of stimulus space coverage and map continuity. While this model has been used in numerous studies, no analytical results about the precise layout of the predicted OPMs have been obtained so far. We present a mathematical approach to analytically calculate the cortical representations predicted by the EN model for the joint mapping of stimulus position and orientation. We find that in all previously studied regimes, predicted OPM layouts are perfectly periodic. An unbiased search through the EN parameter space identifies a novel regime of aperiodic OPMs with pinwheel densities lower than found in experiments. In an extreme limit, aperiodic OPMs quantitatively resembling experimental observations emerge. Stabilization of these layouts results from strong nonlocal interactions rather than from a coverage-continuity-compromise. Our results demonstrate that optimization models for stimulus representations dominated by nonlocal suppressive interactions are in principle capable of correctly predicting the common OPM design. They question that visual cortical feature representations can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure

Coordinated optimization of visual cortical maps : 2. Numerical studies

In the juvenile brain, the synaptic architecture of the visual cortex remains in a state of flux for months after the natural onset of vision and the initial emergence of feature selectivity in visual cortical neurons. It is an attractive hypothesis that visual cortical architecture is shaped during this extended period of juvenile plasticity by the coordinated optimization of multiple visual cortical maps such as orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we introduced a class of analytically tractable coordinated optimization models and solved representative examples, in which a spatially complex organization of the OP map is induced by interactions between the maps. We found that these solutions near symmetry breaking threshold predict a highly ordered map layout. Here we examine the time course of the convergence towards attractor states and optima of these models. In particular, we determine the timescales on which map optimization takes place and how these timescales can be compared to those of visual cortical development and plasticity. We also assess whether our models exhibit biologically more realistic, spatially irregular solutions at a finite distance from threshold, when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. We show that, although maps typically undergo substantial rearrangement, no other solutions than pinwheel crystals and stripes dominate in the emerging layouts. Pinwheel crystallization takes place on a rather short timescale and can also occur for detuned wavelengths of different maps. Our numerical results thus support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the architecture of the visual cortex. We discuss several alternative scenarios that may improve the agreement between model solutions and biological observations

A survey of visual preprocessing and shape representation techniques

Many recent theories and methods proposed for visual preprocessing and shape representation are summarized. The survey brings together research from the fields of biology, psychology, computer science, electrical engineering, and most recently, neural networks. It was motivated by the need to preprocess images for a sparse distributed memory (SDM), but the techniques presented may also prove useful for applying other associative memories to visual pattern recognition. The material of this survey is divided into three sections: an overview of biological visual processing; methods of preprocessing (extracting parts of shape, texture, motion, and depth); and shape representation and recognition (form invariance, primitives and structural descriptions, and theories of attention)

A Neural Model of How Horizontal and Interlaminar Connections of Visual Cortex Develop into Adult Circuits that Carry Out Perceptual Grouping and Learning

A neural model suggests how horizontal and interlaminar connections in visual cortical areas Vl and V2 develop within a laminar cortical architecture and give rise to adult visual percepts. The model suggests how mechanisms that control cortical development in the infant lead to properties of adult cortical anatomy, neurophysiology, and visual perception. The model clarifies how excitatory and inhibitory connections can develop stably by maintaining a balance between excitation and inhibition. The growth of long-range excitatory horizontal connections between layer 2/3 pyramidal cells is balanced against that of short-range disynaptic interneuronal connections. The growth of excitatory on-center connections from layer 6-to-4 is balanced against that of inhibitory interneuronal off-surround connections. These balanced connections interact via intracortical and intercortical feedback to realize properties of perceptual grouping, attention, and perceptual learning in the adult, and help to explain the observed variability in the number and temporal distribution of spikes emitted by cortical neurons. The model replicates cortical point spread functions and psychophysical data on the strength of real and illusory contours. The on-center off-surround layer 6-to-4 circuit enables top-clown attentional signals from area V2 to modulate, or attentionally prime, layer 4 cells in area Vl without fully activating them. This modulatory circuit also enables adult perceptual learning within cortical area Vl and V2 to proceed in a stable way.Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-95-1-0409); National Science Foundation (IRI-97-20333); Office of Naval Research (N00014-95-1-0657

Natural scene statistics and the structure of orientation maps in the visual cortex

Visual activity after eye-opening influences feature map structure in primary visual cortex (V1). For instance, rearing cats in an environment of stripes of one orientation yields an over-representation of that orientation in V1. However, whether such changes also affect the higher-order statistics of orientation maps is unknown. A statistical bias of orientation maps in normally raised animals is that the probability of the angular difference in orientation preference between each pair of points in the cortex depends on the angle of the line joining those points relative to a fixed but arbitrary set of axes. Natural images show an analogous statistical bias; however, whether this drives the development of comparable structure in V1 is unknown. We examined these statistics for normal, stripe-reared and dark-reared cats, and found that the biases present were not consistently related to those present in the input, or to genetic relationships. We compared these results with two computational models of orientation map development, an analytical model and a Hebbian model. The analytical model failed to reproduce the experimentally observed statistics. In the Hebbian model, while orientation difference statistics could be strongly driven by the input, statistics similar to those seen in experimental maps arose only when symmetry breaking was allowed to occur spontaneously. These results suggest that these statistical biases of orientation maps arise primarily spontaneously, rather than being governed by either input statistics or genetic mechanisms

Coordinated optimization of visual cortical maps : 1. Symmetry-based analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of orientation columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about a hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference. From basic symmetry assumptions we obtain a comprehensive phenomenological classification of possible inter-map coupling energies and examine representative examples. We show that each individual coupling energy leads to a different class of OP solutions with different correlations among the maps such that inferences about the optimization principle from map layout appear viable. We systematically assess whether quantitative laws resembling experimental observations can result from the coordinated optimization of orientation columns with other feature maps