Design principles of columnar organization in visual cortex

Visual space is represented by cortical cells in an orderly manner. Only little variation in the cell behavior is found with changing depth below the cortical surface, that is, all cells in a column with axis perpendicular to the cortical plane have approximately the same properties (Hubel and Wiesel 1962, 1963, 1968). Therefore, the multiple features of the visual space (e.g., position in visual space, preferred orientation, and orientation tuning strength) are mapped on a two-dimensional space, the cortical plane. Such a dimension reduction leads to complex maps (Durbin and Mitchison 1990) that so far have evaded an intuitive understanding. Analyzing optical imaging data (Blasdel 1992a, b; Blasdel and Salama 1986; Grinvald et al. 1986) using a theoretical approach we will show that the most salient features of these maps can be understood from a few basic design principles: local correlation, modularity, isotropy, and homogeneity. These principles can be defined in a mathematically exact sense in the Fourier domain by a rather simple annulus-like spectral structure. Many of the models that have been developed to explain the mapping of the preferred orientations (Cooper et al. 1979; Legendy 1978; Linsker 1986a, b; Miller 1992; Nass and Cooper 1975; Obermayer et al. 1990, 1992; Soodak 1987; Swindale 1982, 1985, 1992; von der Malsburg 1973; von der Malsburg and Cowan 1982) are quite successful in generating maps that are close to experimental maps. We suggest that this success is due to these principles, which are common properties of the models and of biological maps

Rules for the Cortical Map of Ocular Dominance and Orientation Columns

Three computational rules are sufficient to generate model cortical maps that simulate the interrelated structure of cortical ocular dominance and orientation columns: a noise input, a spatial band pass filter, and competitive normalization across all feature dimensions. The data of Blasdel from optical imaging experiments reveal cortical map fractures, singularities, and linear zones that are fit by the model. In particular, singularities in orientation preference tend to occur in the centers of ocular dominance columns, and orientation contours tend to intersect ocular dominance columns at right angles. The model embodies a universal computational substrate that all models of cortical map development and adult function need to realize in some form.Air Force Office of Scientific Research (F49620-92-J- 0499, F49620-92-J-0334); Office of Naval Research (N00014-92-J-4015, N00014-91-J-4100); National Science Foundation (IRI-90-24877); British Petroleum (BP 89A-1204

Linking Visual Development and Learning to Information Processing: Preattentive and Attentive Brain Dynamics

National Science Foundation (SBE-0354378); Office of Naval Research (N00014-95-1-0657

Subset Warping: Rubber Sheeting with Cuts

Image warping, often referred to as "rubber sheeting" represents the deformation of a domain image space into a range image space. In this paper, a technique is described which extends the definition of a rubber-sheet transformation to allow a polygonal region to be warped into one or more subsets of itself, where the subsets may be multiply connected. To do this, it constructs a set of "slits" in the domain image, which correspond to discontinuities in the range image, using a technique based on generalized Voronoi diagrams. The concept of medial axis is extended to describe inner and outer medial contours of a polygon. Polygonal regions are decomposed into annular subregions, and path homotopies are introduced to describe the annular subregions. These constructions motivate the definition of a ladder, which guides the construction of grid point pairs necessary to effect the warp itself

Cortical column design: a link between the maps of preferred orientation and orientation tuning strength?

We demonstrate that the map of the preferred orientations and the corresponding map of the orientation tuning strengths as measured with optical imaging are not independent, but that band-pass filtering of the preferred orientation map at each location yields a good approximation of the orientation tuning strength. Band-pass filtering is performed by convolving the map of orientation preference with its own autocorrelation function. We suggest an interpretation of the autocorrelation function of the preferred orientations as synaptic coupling function, i.e., synaptic strength as a function of intracortical distance between cortical cells. In developmental models it has been shown previously that a “Mexican hat”-shaped synaptic coupling function (with a shape similar to that of the autocorrelation function) can produce a realistical-looking pattern of preferred orientations. Since optical imaging performs surface averaging, we discuss the possibility that the connection between the two maps is a measurement artifact of optical imaging. Whether this is the case can only be decided by combining electrode penetrations with optical imaging techniques for which we suggest experiments. We present a model for the generation of both maps from a single computational concept. The model is based on inverse Fourier transform of rather simple two-dimensional annulus-shaped spectra which will produce a column structure very similar to real data. Thus, our approach shows that the complex appearance of cortical orientation columns has a rather simple description in the Fourier domain. Our theoretical analysis explains why singularities in the cortex do not have vorticities other than ±1/2, a result which corresponds to recent experimental findings. This study combines the results from several modeling approaches with recently available optical imaging data to construct a model of both aspects (angle and strength) of the cortical orientation column system. This could alter ideas about cortical development if the link between the two maps can be established as a physiological result

A Neural Network Model for the Development of Simple and Complex Cell Receptive Fields Within Cortical Maps of Orientation and Ocular Dominance

Prenatal development of the primary visual cortex leads to simple cells with spatially distinct and oriented ON and OFF subregions. These simple cells are organized into spatial maps of orientation and ocular dominance that exhibit singularities, fractures, and linear zones. On a finer spatial scale, simple cells occur that are sensitive to similar orientations but opposite contrast polarities, and exhibit both even-symmetric and odd-symmetric receptive fields. Pooling of outputs from oppositely polarized simple cells leads to complex cells that respond to both contrast polarities. A neural network model is described which simulates how simple and complex cells self-organize starting from unsegregated and unoriented geniculocortical inputs during prenatal development. Neighboring simple cells that are sensitive to opposite contrast polarities develop from a combination of spatially short-range inhibition and high-gain recurrent habituative excitation between cells that obey membrane equations. Habituation, or depression, of synapses controls reset of cell activations both through enhanced ON responses and OFF antagonistic rebounds. Orientation and ocular dominance maps form when high-gain medium-range recurrent excitation and long-range inhibition interact with the short-range mechanisms. The resulting structure clarifies how simple and complex cells contribute to perceptual processes such as texture segregation and perceptual grouping.Air Force Office of Scientific Research (F49620-92-J-0334); British Petroleum (BP 89A-1204); National Science Foundation (IRI-90-24877); Office of Naval Research (N00014-91-J-4100); Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-95-1-0409

A Neural Model of How the Cortical Subplate Coordinates the Laminar Development of Orientation and Ocular Dominance Maps

Air Force Office of Scientific Research (F49620-98-1-0108, F49620-0 1-1-0397); Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-95-1-0409); National Science Foundation (IIS-97-20333); Office of Naval Research (N00014-01-1-0624

A Neural Model for Self Organizing Feature Detectors and Classifiers in a Network Hierarchy

Many models of early cortical processing have shown how local learning rules can produce efficient, sparse-distributed codes in which nodes have responses that are statistically independent and low probability. However, it is not known how to develop a useful hierarchical representation, containing sparse-distributed codes at each level of the hierarchy, that incorporates predictive feedback from the environment. We take a step in that direction by proposing a biologically plausible neural network model that develops receptive fields, and learns to make class predictions, with or without the help of environmental feedback. The model is a new type of predictive adaptive resonance theory network called Receptive Field ARTMAP, or RAM. RAM self organizes internal category nodes that are tuned to activity distributions in topographic input maps. Each receptive field is composed of multiple weight fields that are adapted via local, on-line learning, to form smooth receptive ftelds that reflect; the statistics of the activity distributions in the input maps. When RAM generates incorrect predictions, its vigilance is raised, amplifying subtractive inhibition and sharpening receptive fields until the error is corrected. Evaluation on several classification benchmarks shows that RAM outperforms a related (but neurally implausible) model called Gaussian ARTMAP, as well as several standard neural network and statistical classifters. A topographic version of RAM is proposed, which is capable of self organizing hierarchical representations. Topographic RAM is a model for receptive field development at any level of the cortical hierarchy, and provides explanations for a variety of perceptual learning data.Defense Advanced Research Projects Agency and Office of Naval Research (N00014-95-1-0409