Development of spatiotemporal receptive fields of simple cells: II. Simulation and analysis

In part I of this article a correlation based model for the developmental process of spatiotemporal receptive fields has been introduced. In this model the development is described as an activity-dependent competition between four types of input from the lateral geniculate nucleus onto a cortical cell, viz. non-lagged ON and OFF and lagged ON and OFF inputs. In the present paper simulation results and a first analysis are presented for this model. We study the developmental process both before and after eye-opening and compare the results with experimental data from reverse correlation measurements. The outcome of the developmental process is determined mainly by the spatial and the temporal correlations between the different inputs. In particular, if the mean correlation between non-lagged and lagged inputs is weak, receptive fields with a widely varying degree of direction selectivity emerge. However, spatiotemporal receptive fields may show rotation of their preferred orientation as a function of response delay. Even if the mean correlation between two types of temporal input is not weak, direction-selective receptive fields may emerge because of an intracortical interaction between different cortical maps. In an environment of moving lines or gratings, direction-selective receptive fields develop only if the distribution of the directions of motion presented during development shows some anisotropy. In this case, a continuous map of preferred direction is also shown to develop. Received: 18 June 1997 / Accepted: 16 September 1997     

Emergence of spatiotemporal receptive fields and its application to motion detection

A model of motion sensitivity as observed in some cells of area V1 of the visual cortex is proposed. Motion sensitivity is achieved by a combination of different spatiotemporal receptive fields, in particular, spatial and temporal differentiators. The receptive fields emerge if a Hebbian learning rule is applied to the network. Similar to a Linsker model the network has a spatially convergent, linear feedforward structure. Additionally, however, delays omnipresent in the brain are incorporated in the model. The emerging spatiotemporal receptive fields are derived explicitly by extending the approach of MacKay and Miller. The response characteristic of the network is calculated in frequency space and shows that the network can be considered as a spacetime filter for motion in one direction. The emergence of different types of receptive field requires certain structural constraints regarding the spatial and temporal arborisation. These requirements can be derived from the theoretical analysis and might be compared with neuroanatomical data. In this way an explicit link between structure and function of the network is established.     

Rabbit visual cortical neurons with simple and complex receptive fields

Receptive fields of neurons of the rabbit visual cortex selective for stimulus orientation were investigated. These receptive fields were less well differentiated than those of the analogous neurons of the cat visual cortex (large in size and circular in shape). Two mechanisms of selectivity for stimulus orientation were observed: inhibition between on and off zones of the receptive field (sample type) and oriented lateral inhibition within the same zone of the receptive field (complex type). Lateral inhibition within the same zone of the receptive field also took place in unselective neurons; "complex" selective neurons differed from them in the orientation of this inhibition. A combination of both mechanisms was possible in the receptive field of the same neuron. It is suggested that both simple and complex receptive fields are derivatives of unselective receptive fields and that "complex" neurons are not the basis for a higher level of analysis of visual information than in "simple" neurons.A. N. Severtsov Institute of Evolutionary Morphology and Ecology of Animals, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 10, No. 1, pp. 13–21, January–February, 1978.     

The receptive fields of Daphnia ommatidia.

1. The focal length and positions of the principal planes of an isolated Daphnia lens were determined, and the refractive index of the rhabdom was measured. 2. The lens can form an image, but this always lies well behind the rhabdom. This was confirmed by direct observation of images inside a clear-eye mutant Daphnia eye. 3. The rhabdom was shown to be unlikely to function as a waveguide, and a ray optics model is proposed to enable the prediction of ommatidial receptive fields from the lens data. 4. The predicted receptive fields have wide plateaus and steep sides, and there are virtually no totally blind gaps between neighbouring ommatidia.     

Two-dimensional substructure of MT receptive fields.

Neurons at progressively higher levels of the visual system have progressively larger, more complicated receptive fields, presumably constructed from simpler antecedent receptive fields. To study this hierarchical organization, we used sparse white noise to map receptive-field substructure (second order Wiener-like kernels) in an extrastriate motion processing area (MT) of alert monkeys. The maps revealed a clear substructure, on a spatial scale comparable to the receptive fields of the V1 inputs. There were both facilitatory and suppressive interactions that differed in spatial organization and time course. Directional interactions were remarkably precise over a very small spatial range, and reversed when successive stimuli reversed contrast--a neural correlate of "reverse phi" motion perception. The maps of some cells had an unexpected, curved shape, which challenges existing models for direction selectivity.     

White noise analysis of temporal properties in simple receptive fields of cat cortex

We studied the linear and nonlinear temporal response properties of simple cells in cat visual cortex by presenting at single positions in the receptive field an optimally oriented bar stimulus whose luminance was modulated in a random, binary fashion. By crosscorrelating a cell's response with the input it was possible to obtain the zeroth-, first-, and second-order Wiener kernels at each RF location. Simple cells showed pronounced nonlinear temporal properties as revealed by the presence of prominent second-order kernels. A more conventional type of response histogram was also calculated by time-locking a histogram on the occurrence of the desired stimulus in the random sequence. A comparison of the time course of this time-locked response with that of the kernel prediction indicated that nonlinear temporal effects of order higher than two are unimportant. The temporal properties of simple cells were well represented by a cascade model composed of a linear filter followed by a static nonlinearity. These modelling results suggested that for simple cells, the nonlinearity occurs late and probably is a soft threshold associated with the spike generating mechanism of the cortical cell itself. This result is surprising in view of the known threshold nonlinearities in preceding lateral geniculate and retinal neurons. It suggests that geniculocortical connectivity cancels the earlier nonlinearities to create a highly linear representation inside cortical simple cells.This work comprises a portion of a PhD thesis submitted by the first author. This study was supported in part by NIH Grant EY04630 and EY06679 to R.C.E., and EY01319 (Core Grant) to the Center for Visual Science     

Learning receptive fields using predictive feedback.

Previously, it was suggested that feedback connections from higher- to lower-level areas carry predictions of lower-level neural activities, whereas feedforward connections carry the residual error between the predictions and the actual lower-level activities [Rao, R.P.N., Ballard, D.H., 1999. Nature Neuroscience 2, 79-87.]. A computational model implementing the hypothesis learned simple cell receptive fields when exposed to natural images. Here, we use predictive feedback to explain tuning properties in medial superior temporal area (MST). We implement the hypothesis using a new, biologically plausible, algorithm based on matching pursuit, which retains all the features of the previous implementation, including its ability to efficiently encode input. When presented with natural images, the model developed receptive field properties as found in primary visual cortex. In addition, when exposed to visual motion input resulting from movements through space, the model learned receptive field properties resembling those in MST. These results corroborate the idea that predictive feedback is a general principle used by the visual system to efficiently encode natural input.     

Theory of spatial position and spatial frequency relations in the receptive fields of simple cells in the visual cortex

Striate cells showing linear spatial summation obey very general mathematical inequalities relating the size of their receptive fields to the corresponding spatial frequency and orientation tuning characteristics. The experimental data show that, in the preferred direction of stimulus motion, the spatial response profiles of cells in the simple family are well described by the mathematical form of Gabor elementary signals. The product of the uncertainties in signalling spatial position (x) and spatial frequency (f) has, therefore, a theoretical minimum value of xf=1/2. We examine the implications that these conclusions have for the relationship between the spatial response profiles of simple cells and the characteristics of their spatial frequency tuning curves. Examples of the spatial frequency tuning curves and their associated spatial response profiles are discussed and illustrated. The advantages for the operation of the visual system of different relationships between the spatial response profiles and the characteristics of the spatial frequency tuning curves are examined. Two examples are discussed in detail, one system having a constant receptive field size and the other a constant bandwidth.     

Recursive features of circular receptive fields

The distribution of excitability in retinal receptive fields may be well approximated by functions with recursive features. Physiological data do not exclude an implementation of recursive structures in the visual system. It is the most remarkable advantage of a recursive visual system, that cortical receptive fields tuned to different spatial frequencies will have an identical neuronal circuitry. Structural consequences for retina, LGN and visual cortex are discussed.     

The labile brain. III. Transients and spatio-temporal receptive fields

In this paper we consider an approach to neuronal transients that is predicated on the information they contain. This perspective is provided by information theory, in particular the principle of maximum information transfer. It is illustrated here in application to visually evoked neuronal transients. The receptive fields that ensue concur with those observed in the real brain, predicting, almost exactly, functional segregation of the sort seen in the visual system. This information theoretical perspective can be reconciled with a selectionist stance by noting that a high mutual information among neuronal systems and the environment has, itself, adaptive value and will be subject to selective pressure, at any level one cares to consider.     

Chemical cross-linking of class I molecules on cells creates receptive peptide binding sites.

Class I heterodimers on the surface of cells are generally unreceptive to binding peptides in the absence of exogenous beta 2-microglobulin. Paraformaldehyde covalently cross-links beta 2-microglobulin to class I heavy chains in situ and stabilizes empty class I heterodimers. Functionally, this cross-linking creates receptive class I peptide binding sites by acting on beta 2-microglobulin-associated molecules. The presentation of preexisting peptide-class I complexes is also enhanced. These findings support a model whereby a structural alteration, the dissociation of beta 2-microglobulin, limits the existence of receptive class I molecules on normal cells and may control the half-life of active class I molecules.     

A computational theory of visual receptive fields

A receptive field constitutes a region in the visual field where a visual cell or a visual operator responds to visual stimuli. This paper presents a theory for what types of receptive field profiles can be regarded as natural for an idealized vision system, given a set of structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world. These symmetry properties include (i) covariance properties under scale changes, affine image deformations, and Galilean transformations of space–time as occur for real-world image data as well as specific requirements of (ii) temporal causality implying that the future cannot be accessed and (iii) a time-recursive updating mechanism of a limited temporal buffer of the past as is necessary for a genuine real-time system. Fundamental structural requirements are also imposed to ensure (iv) mutual consistency and a proper handling of internal representations at different spatial and temporal scales. It is shown how a set of families of idealized receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic, and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives, or closely related operators. Such image filters have been successfully used as a basis for expressing a large number of visual operations in computer vision, regarding feature detection, feature classification, motion estimation, object recognition, spatio-temporal recognition, and shape estimation. Hence, the associated so-called scale-space theory constitutes a both theoretically well-founded and general framework for expressing visual operations. There are very close similarities between receptive field profiles predicted from this scale-space theory and receptive field profiles found by cell recordings in biological vision. Among the family of receptive field profiles derived by necessity from the assumptions, idealized models with very good qualitative agreement are obtained for (i) spatial on-center/off-surround and off-center/on-surround receptive fields in the fovea and the LGN, (ii) simple cells with spatial directional preference in V1, (iii) spatio-chromatic double-opponent neurons in V1, (iv) space–time separable spatio-temporal receptive fields in the LGN and V1, and (v) non-separable space–time tilted receptive fields in V1, all within the same unified theory. In addition, the paper presents a more general framework for relating and interpreting these receptive fields conceptually and possibly predicting new receptive field profiles as well as for pre-wiring covariance under scaling, affine, and Galilean transformations into the representations of visual stimuli. This paper describes the basic structure of the necessity results concerning receptive field profiles regarding the mathematical foundation of the theory and outlines how the proposed theory could be used in further studies and modelling of biological vision. It is also shown how receptive field responses can be interpreted physically, as the superposition of relative variations of surface structure and illumination variations, given a logarithmic brightness scale, and how receptive field measurements will be invariant under multiplicative illumination variations and exposure control mechanisms.     

Construction of complex receptive fields in cat primary visual cortex.

In primary visual cortex, neurons are classified into simple cells and complex cells based on their response properties. Although the role of these two cell types in vision is still unknown, an attractive hypothesis is that simple cells are necessary to construct complex receptive fields. This hierarchical model puts forward two main predictions. First, simple cells should connect monosynaptically to complex cells. Second, complex cells should become silent when simple cells are inactivated. We have recently provided evidence for the first prediction, and here we do the same for the second. In summary, our results suggest that the receptive fields of most layer 2+3 complex cells are generated by a mechanism that requires simple cell inputs.     

Experience-dependent asymmetric shape of hippocampal receptive fields

We propose a novel parameter, namely, the skewness, or asymmetry, of the shape of a receptive field to characterize two properties of hippocampal place fields. First, a majority of hippocampal receptive fields on linear tracks are negatively skewed, such that during a single pass the firing rate is low as the rat enters the field but high as it exits. Second, while the place fields are symmetric at the beginning of a session, they become highly asymmetric with experience. Further experiments suggest that these results are likely to arise due to synaptic plasticity during behavior. Using a purely feed forward neural network model, we show that following repeated directional activation, NMDA-dependent long-term potentiation/long-term depotentiation (LTP/LTD) could result in an experience-dependent asymmetrization of receptive fields.     

A simulation model of AIDS in San Francisco: I. Model formulation and parameter estimation.

A model is formulated for the spread of the human immunodeficiency virus (HIV) and the subsequent development of acquired immunodeficiency syndrome (AIDS) in the population of homosexual men in San Francisco. The dynamic simulation model includes sexually very active and active subpopulations, migration, and a staged progression of HIV-infected persons to AIDS and death. Numerous data sources are used to estimate parameter values in the model. In a companion paper, simulations using the model and parameter estimates are found that are consistent with HIV and AIDS incidence data.     

The Alopex process: Visual receptive fields by response feedback

The determination of trigger features of single neurons in afferent pathways has been one of the central problems in sensory physiology. A novel method, called Alopex, has been developed, in which response feedback is used to construct visual patterns that optimize the responses. Data are presented which show the emergence of trigger features of cells monitored in frog visual tectum. The method is checked against results obtained by scanning the visual field with a small spot. Correlations between Alopex patterns and scan patterns are generally between 0.3 and 0.5 but may be as high as 0.9 when smoothing and/or averaging procedures are applied to the Alopex patterns. The dynamics of the Alopex process are discussed and details of the algorithms are presented. The series of experiments presented here has established the validity of the method and suggests that this approach should find wide application in receptive field studies. For that purpose data on the instrumentation and software are also presented.This research has been supported by the National Institutes of Health, under grant EY 01215