@Article{ warland_decoding_1997, title = {Decoding Visual Information From a Population of Retinal Ganglion Cells}, volume = {78}, url = {http://jn.physiology.org/cgi/content/abstract/78/5/2336}, number = {5}, journal = {J Neurophysiol}, author = {David K. Warland and Pamela Reinagel and Markus Meister}, month = nov, year = {1997}, pages = {2336--2350} } @Article{ olshausen_close_2005, title = {How close are we to understanding v1?}, volume = {17}, url = {http://dx.doi.org/10.1162/0899766054026639}, doi = {10.1162/0899766054026639}, abstract = {A wide variety of papers have reviewed what is known about the function of primary visual cortex. In this review, rather than stating what is known, we attempt to estimate how much is still unknown about V1 function. In particular, we identify five problems with the current view of V1 that stem largely from experimental and theoretical biases, in addition to the contributions of nonlinearities in the cortex that are not well understood. Our purpose is to open the door to new theories, a number of which we describe, along with some proposals for testing them.}, number = {8}, journal = {Neural Comput}, author = {Bruno A Olshausen and David J Field}, month = aug, year = {2005}, keywords = {Animals; Bias {(Epidemiology);} Humans; {Models,Neurological;} Neurons; Nonlinear Dynamics; Visual Cortex; Visual Pathways}, pages = {1665―1699} } @Article{ huys_fast_2007, title = {Fast Population Coding}, volume = {19}, url = {http://neco.mitpress.org/cgi/content/abstract/19/2/404}, abstract = {Uncertainty coming from the noise in its neurons and the ill-posed nature of many tasks plagues neural computations. Maybe surprisingly, many studies show that the brain manipulates these forms of uncertainty in a probabilistically consistent and normative manner, and there is now a rich theoretical literature on the capabilities of populations of neurons to implement computations in the face of uncertainty. However, one major facet of uncertainty has received comparatively little attention: time. In a dynamic, rapidly changing world, data are only temporarily relevant. Here, we analyze the computational consequences of encoding stimulus trajectories in populations of neurons. For the most obvious, simple, instantaneous encoder, the correlations induced by natural, smooth stimuli engender a decoder that requires access to information that is nonlocal both in time and across neurons. This formally amounts to a ruinous representation. We show that there is an alternative encoder that is computationally and representationally powerful in which each spike contributes independent information; it is independently decodable, in other words. We suggest this as an appropriate foundation for understanding time-varying population codes. Furthermore, we show how adaptation to temporal stimulus statistics emerges directly from the demands of simple decoding. }, number = {2}, journal = {Neural Comp.}, author = {Quentin J. M. Huys and Richard S. Zemel and Rama Natarajan and Peter Dayan}, month = feb, year = {2007}, pages = {404--441} } @Article{ douglas_neuronal_2004, title = {Neuronal circuits of the neocortex.}, volume = {27}, url = {http://dx.doi.org/10.1146/annurev.neuro.27.070203.144152}, doi = {10.1146/annurev.neuro.27.070203.144152}, abstract = {We explore the extent to which neocortical circuits generalize, i.e., to what extent can neocortical neurons and the circuits they form be considered as canonical? We find that, as has long been suspected by cortical neuroanatomists, the same basic laminar and tangential organization of the excitatory neurons of the neocortex is evident wherever it has been sought. Similarly, the inhibitory neurons show characteristic morphology and patterns of connections throughout the neocortex. We offer a simple model of cortical processing that is consistent with the major features of cortical circuits: The superficial layer neurons within local patches of cortex, and within areas, cooperate to explore all possible interpretations of different cortical input and cooperatively select an interpretation consistent with their various cortical and subcortical inputs.}, journal = {Annu Rev Neurosci}, author = {Rodney J Douglas and Kevan A C Martin}, year = {2004}, keywords = {Animals; Cell Size; Humans; {Models,Neurological;} Neocortex; Nerve Net; Neural Inhibition; Neural Pathways; Neurons; Synaptic Transmission}, pages = {419―451} } @Article{ rapela_estimating_2006, title = {Estimating nonlinear receptive fields from natural images.}, volume = {6}, url = {http://dx.doi.org/10.1167/6.4.11}, doi = {10.1167/6.4.11}, abstract = {The response of visual cells is a nonlinear function of their stimuli. In addition, an increasing amount of evidence shows that visual cells are optimized to process natural images. Hence, finding good nonlinear models to characterize visual cells using natural stimuli is important. The Volterra model is an appealing nonlinear model for visual cells. However, their large number of parameters and the limited size of physiological recordings have hindered its application. Recently, a substantiated hypothesis stating that the responses of each visual cell could depend on an especially low-dimensional subspace of the image space has been proposed. We use this low-dimensional subspace in the Volterra relevant-space technique to allow the estimation of high-order Volterra models. Most laboratories characterize the response of visual cells as a nonlinear function on the low-dimensional subspace. They estimate this nonlinear function using histograms and by fitting parametric functions to them. Here, we compare the Volterra model with these histogram-based techniques. We use simulated data from cortical simple cells as well as simulated and physiological data from cortical complex cells. Volterra models yield equal or superior predictive power in all conditions studied. Several methods have been proposed to estimate the low-dimensional subspace. In this article, we test projection pursuit regression {(PPR),} a nonlinear regression algorithm. We compare {PPR} with two popular models used in vision: spike-triggered average {(STA)} and spike-triggered covariance {(STC).} We observe that {PPR} has advantages over these alternative algorithms. Hence, we conclude that {PPR} is a viable algorithm to recover the relevant subspace from natural images and that the Volterra model, estimated through the Volterra relevant-space technique, is a compelling alternative to histogram-based techniques.}, number = {4}, journal = {J Vis}, author = {Joaquín Rapela and Jerry M Mendel and Norberto M Grzywacz}, year = {2006}, keywords = {Algorithms; Animals; Cats; Computer Simulation; {Models,Neurological;} Neurons; Nonlinear Dynamics; Photic Stimulation; Visual Cortex}, pages = {441―474} } @Article{ adelson_spatiotemporal_1985, title = {Spatiotemporal energy models for the perception of motion}, volume = {2}, url = {http://oe.osa.org/ViewMedia.cfm?id=1945&seq=0}, journal = {Optical Society of America, Journal, A: Optics and Image Science}, author = {E. H Adelson and J. R Bergen}, year = {1985}, pages = {284―299} } @Article{ hubel_receptive_1968, title = {Receptive fields and functional architecture of monkey striate cortex.}, volume = {195}, abstract = {1. The striate cortex was studied in lightly anaesthetized macaque and spider monkeys by recording extracellularly from single units and stimulating the retinas with spots or patterns of light. Most cells can be categorized as simple, complex, or hypercomplex, with response properties very similar to those previously described in the cat. On the average, however, receptive fields are smaller, and there is a greater sensitivity to changes in stimulus orientation. A small proportion of the cells are colour coded.2. Evidence is presented for at least two independent systems of columns extending vertically from surface to white matter. Columns of the first type contain cells with common receptive-field orientations. They are similar to the orientation columns described in the cat, but are probably smaller in cross-sectional area. In the second system cells are aggregated into columns according to eye preference. The ocular dominance columns are larger than the orientation columns, and the two sets of boundaries seem to be independent.3. There is a tendency for cells to be grouped according to symmetry of responses to movement; in some regions the cells respond equally well to the two opposite directions of movement of a line, but other regions contain a mixture of cells favouring one direction and cells favouring the other.4. A horizontal organization corresponding to the cortical layering can also be discerned. The upper layers {(II} and the upper two-thirds of {III)} contain complex and hypercomplex cells, but simple cells are virtually absent. The cells are mostly binocularly driven. Simple cells are found deep in layer {III,} and in {IV} A and {IV} B. In layer {IV} B they form a large proportion of the population, whereas complex cells are rare. In layers {IV} A and {IV} B one finds units lacking orientation specificity; it is not clear whether these are cell bodies or axons of geniculate cells. In layer {IV} most cells are driven by one eye only; this layer consists of a mosaic with cells of some regions responding to one eye only, those of other regions responding to the other eye. Layers V and {VI} contain mostly complex and hypercomplex cells, binocularly driven.5. The cortex is seen as a system organized vertically and horizontally in entirely different ways. In the vertical system (in which cells lying along a vertical line in the cortex have common features) stimulus dimensions such as retinal position, line orientation, ocular dominance, and perhaps directionality of movement, are mapped in sets of superimposed but independent mosaics. The horizontal system segregates cells in layers by hierarchical orders, the lowest orders (simple cells monocularly driven) located in and near layer {IV,} the higher orders in the upper and lower layers.}, number = {1}, journal = {J Physiol}, author = {D. H. Hubel and T. N. Wiesel}, month = mar, year = {1968}, keywords = {{Animals;,Color,Evoked,Fields,Haplorhini;,Light;,Lobe;,Motion,Occipital,Perception;,Potentials;,Retina;,Vision;,Visual}} , pages = {215―243} } @Article{ baker_processing_2001, title = {Processing of second-order stimuli in the visual cortex}, volume = {134}, issn = {0079-6123}, url = {http://www.ncbi.nlm.nih.gov/pubmed/11702543}, abstract = {Naturally occurring visual stimuli are rich in examples of objects delineated from their backgrounds simply by differences in luminance, so-called first-order stimuli, as well as those defined by differences of contrast or texture, referred to as second-order stimuli. Here we provide a brief overview of visual cortical processing of second-order stimuli, as well as some comparative background on first-order processing, concentrating on single-unit neurophysiology, but also discussing relationships to human psychophysics and to neuroimaging. The selectivity of visual cortical neurons to orientation, spatial frequency, and direction of movement of first-order, luminance-defined stimuli is conventionally understood in terms of simple linear filter models, albeit with some minor nonlinearities such as thresholding and gain control. However, these kinds of models fail entirely to account for responses of neurons to second-order stimuli such as contrast envelopes, illusory contours, or texture borders. Second-order stimuli constructed from sinusoidal components have been used to analyze the neurophysiological mechanisms of such responses; these experiments demonstrate that the same neuron can exhibit three distinct kinds of tuning to spatial frequency, and also to orientation. These results can be understood in terms of a type of nonlinear 'filter--{\textgreater}rectify--{\textgreater}filter' model, which has been widely used in human psychophysics. Finally, several general issues will be discussed, including potential artifacts in experiments with second-order stimuli, and strategies for avoiding or controlling for them; caveats about definitions of first- vs. second-order mechanisms and stimuli; the concept of form-cue invariance; and the functional significance of second-order processing.}, journal = {Progress in Brain Research}, author = {C L Baker and I Mareschal}, year = {2001}, note = {{PMID:} 11702543}, keywords = {{Animals,Contrast} {Sensitivity,Humans,Models,} {Neurological,Photic} {Stimulation,Visual} {Cortex,Visual} Perception}, pages = {171--91} } @Article{ cadieu_model_2007, title = {A Model of V4 Shape Selectivity and Invariance}, volume = {98}, url = {http://jn.physiology.org/cgi/content/abstract/98/3/1733}, doi = {10.1152/jn.01265.2006}, abstract = {Object recognition in primates is mediated by the ventral visual pathway and is classically described as a feedforward hierarchy of increasingly sophisticated representations. Neurons in macaque monkey area V4, an intermediate stage along the ventral pathway, have been shown to exhibit selectivity to complex boundary conformation and invariance to spatial translation. How could such a representation be derived from the signals in lower visual areas such as V1? We show that a quantitative model of hierarchical processing, which is part of a larger model of object recognition in the ventral pathway, provides a plausible mechanism for the translation-invariant shape representation observed in area V4. Simulated model neurons successfully reproduce V4 selectivity and invariance through a nonlinear, translation-invariant combination of locally selective subunits, suggesting that a similar transformation may occur or culminate in area V4. Specifically, this mechanism models the selectivity of individual V4 neurons to boundary conformation stimuli, exhibits the same degree of translation invariance observed in V4, and produces observed V4 population responses to bars and {non-Cartesian} gratings. This work provides a quantitative model of the widely described shape selectivity and invariance properties of area V4 and points toward a possible canonical mechanism operating throughout the ventral pathway. }, number = {3}, journal = {J Neurophysiol}, author = {Charles Cadieu and Minjoon Kouh and Anitha Pasupathy and Charles E. Connor and Maximilian Riesenhuber and Tomaso Poggio}, month = sep, year = {2007}, pages = {1733--1750} } @Article{ simoncelli_model_1998, title = {A model of neuronal responses in visual area {MT}}, volume = {38}, issn = {0042-6989}, url = {http://www.ncbi.nlm.nih.gov/pubmed/9604103}, doi = {9604103}, abstract = {Electrophysiological studies indicate that neurons in the middle temporal {(MT)} area of the primate brain are selective for the velocity of visual stimuli. This paper describes a computational model of {MT} physiology, in which local image velocities are represented via the distribution of {MT} neuronal responses. The computation is performed in two stages, corresponding to neurons in cortical areas V1 and {MT.} Each stage computes a weighted linear sum of inputs, followed by rectification and divisive normalization. V1 receptive field weights are designed for orientation and direction selectivity. {MT} receptive field weights are designed for velocity (both speed and direction) selectivity. The paper includes computational simulations accounting for a wide range of physiological data, and describes experiments that could be used to further test and refine the model.}, number = {5}, journal = {Vision Research}, author = {E P Simoncelli and D J Heeger}, month = mar, year = {1998}, note = {{PMID:} 9604103}, keywords = {Brain {Mapping,Humans,Mathematics,Models,} {Neurological,Motion} {Perception,Time} Factors}, pages = {743--61} } @Article{ olshausen_principles_2003, title = {Principles of image representation in visual cortex}, journal = {The Visual Neurosciences}, author = {B. A. Olshausen}, year = {2003}, pages = {1603–1615} } @Article{ bialek_readingneural_1991, title = {Reading a neural code}, volume = {252}, url = {http://www.sciencemag.org/cgi/content/abstract/252/5014/1854} , doi = {10.1126/science.2063199}, abstract = {Traditional approaches to neural coding characterize the encoding of known stimuli in average neural responses. Organisms face nearly the opposite task--extracting information about an unknown time-dependent stimulus from short segments of a spike train. Here the neural code was characterized from the point of view of the organism, culminating in algorithms for real-time stimulus estimation based on a single example of the spike train. These methods were applied to an identified movement-sensitive neuron in the fly visual system. Such decoding experiments determined the effective noise level and fault tolerance of neural computation, and the structure of the decoding algorithms suggested a simple model for real-time analog signal processing with spiking neurons. }, number = {5014}, journal = {Science}, author = {W Bialek and F Rieke and {RR} de Ruyter van Steveninck and D Warland}, month = jun, year = {1991}, pages = {1854--1857} } @Article{ theunissen_estimating_2001, title = {Estimating spatio-temporal receptive fields of auditory and visual neurons from their responses to natural stimuli.}, volume = {12}, doi = {{10.1088/0954-898X/12/3/304}}, abstract = {We present a generalized reverse correlation technique that can be used to estimate the spatio-temporal receptive fields {(STRFs)} of sensory neurons from their responses to arbitrary stimuli such as auditory vocalizations or natural visual scenes. The general solution for {STRF} estimation requires normalization of the stimulus-response cross-correlation by the stimulus autocorrelation matrix. When the second-order stimulus statistics are stationary, normalization involves only the diagonal elements of the Fourier-transformed auto-correlation matrix (the power spectrum). In the non-stationary case normalization requires the entire auto-correlation matrix. We present modelling studies that demonstrate the feasibility and accuracy of this method as well as neurophysiological data comparing {STRFs} estimated using natural versus synthetic stimulus ensembles. For both auditory and visual neurons, {STRFs} obtained with these different stimuli are similar, but exhibit systematic differences that may be functionally significant. This method should be useful for determining what aspects of natural signals are represented by sensory neurons and may reveal novel response properties of these neurons.}, number = {3}, journal = {Network}, author = {F. E. Theunissen and S. V. David and N. C. Singh and A. Hsu and W. E. Vinje and J. L. Gallant}, month = aug, year = {2001}, keywords = {Acoustic Stimulation; Algorithms; Animals; Auditory Cortex; Auditory Perception; {Models,Afferent;} Photic Stimulation; Primates; Prosencephalon; Songbirds; Space Perception; Visual Cortex; Visual Perception; {Vocalization,Animal,Neurological;} Neurons}, pages = {289―316} } @Article{ yen_heterogeneity_2007, title = {Heterogeneity in the responses of adjacent neurons to natural stimuli in cat striate cortex.}, volume = {97}, url = {http://dx.doi.org/10.1152/jn.00747.2006}, doi = {10.1152/jn.00747.2006}, abstract = {When presented with simple stimuli like bars and gratings, adjacent neurons in striate cortex exhibit shared selectivity for multiple stimulus dimensions, such as orientation, direction, and spatial frequency. This has led to the idea that local averaging of neuronal responses provides a more reliable representation of stimulus properties. However, when stimulated with complex, time-varying natural scenes (i.e., movies), striate neurons exhibit highly sparse responses. This raises the question of how much response heterogeneity the local population exhibits when stimulated with movies, and how it varies with separation distance between cells. We investigated this question by simultaneously recording the responses of groups of neurons in cat striate cortex to the repeated presentation of movies using silicon probes in a multi-tetrode configuration. We found, first, that the responses of striate neurons to movies are brief (tens of milliseconds), decorrelated, and exhibit high population sparseness. Second, we found that adjacent neurons differed significantly in their peak firing rates even when they responded to the same frames of a movie. Third, pairs of adjacent neurons recorded on the same tetrodes exhibited as much heterogeneity in their responses as pairs recorded by different tetrodes. These findings demonstrate that complex natural scenes evoke highly heterogeneous responses within local populations, suggesting that response redundancy in a cortical column is substantially lower than previously thought.}, number = {2}, journal = {J Neurophysiol}, author = {{Shih-Cheng} Yen and Jonathan Baker and Charles M Gray}, month = feb, year = {2007}, keywords = {Algorithms; Anesthesia; Animals; Attention; Cats; Data {Interpretation,Monocular;} Visual {Cortex,Statistical;} Electroencephalography; Electrophysiology; Female; Fourier Analysis; Male; Neurons; Photic Stimulation; Reproducibility of Results; Vision}, pages = {1326―1341} } @Article{ felsen_cortical_2005, title = {Cortical sensitivity to visual features in natural scenes.}, volume = {3}, url = {http://dx.doi.org/10.1371/journal.pbio.0030342}, doi = {10.1371/journal.pbio.0030342}, abstract = {A central hypothesis concerning sensory processing is that the neuronal circuits are specifically adapted to represent natural stimuli efficiently. Here we show a novel effect in cortical coding of natural images. Using spike-triggered average or spike-triggered covariance analyses, we first identified the visual features selectively represented by each cortical neuron from its responses to natural images. We then measured the neuronal sensitivity to these features when they were present in either natural images or random stimuli. We found that in the responses of complex cells, but not of simple cells, the sensitivity was markedly higher for natural images than for random stimuli. Such elevated sensitivity leads to increased detectability of the visual features and thus an improved cortical representation of natural scenes. Interestingly, this effect is due not to the spatial power spectra of natural images, but to their phase regularities. These results point to a distinct visual-coding strategy that is mediated by contextual modulation of cortical responses tuned to the spatial-phase structure of natural scenes.}, number = {10}, journal = {{PLoS} Biol}, author = {Gidon Felsen and Jon Touryan and Feng Han and Yang Dan}, month = oct, year = {2005}, keywords = {Animals; Cats; Male; {Models,Psychological;} Neurons; Photic Stimulation; Visual Cortex; Visual Perception}, pages = {e342} } @Article{ sekuler_visual_2001, title = {Visual neuroscience: Resonating to natural images}, volume = {11}, issn = {0960-9822}, url = {http://www.ncbi.nlm.nih.gov/pubmed/11566115}, abstract = {Visual neurons may be optimized to produce sparse, distributed responses to natural scenes. This proposal, along with recent results from monkey {fMRI} and electrophysiology, may force us to re-interpret many neuroimaging results.}, number = {18}, journal = {Current Biology: {CB}}, author = {A B Sekuler and P J Bennett}, month = sep, year = {2001}, note = {{PMID:} 11566115}, keywords = {{Animals,Haplorhini,Humans,Magnetic} Resonance {Imaging,Neurons,} {Afferent,Vision,} {Ocular,Visual} {Cortex,Visual} Perception}, pages = {R733--6} } @Article{ vinje_sparse_2000, title = {Sparse Coding and Decorrelation in Primary Visual Cortex During Natural Vision}, volume = {287}, url = {http://www.sciencemag.org/cgi/content/abstract/287/5456/1273} , doi = {10.1126/science.287.5456.1273}, number = {5456}, journal = {Science}, author = {William E Vinje and Jack L Gallant}, year = {2000}, pages = {1273--1276} } @Article{ lesica_encoding_2004, title = {Encoding of natural scene movies by tonic and burst spikes in the lateral geniculate nucleus.}, volume = {24}, url = {http://dx.doi.org/10.1523/JNEUROSCI.3059-04.2004}, doi = {{10.1523/JNEUROSCI.3059-04.2004}}, abstract = {The role of the lateral geniculate nucleus {(LGN)} of the thalamus in visual encoding remains an open question. Here, we characterize the function of tonic and burst spikes in cat {LGN} X-cells in signaling features of natural stimuli. A significant increase in bursting was observed during natural stimulation (relative to white noise stimulation) and was linked to the strong correlation structure of the natural scene movies. Burst responses were triggered by specific stimulus events consisting of a prolonged inhibitory stimulus, followed by an excitatory stimulus, such as the movement of an object into the receptive field. {LGN} responses to natural scene movies were predicted using an integrate-and-fire {(IF)} framework and compared with experimentally observed responses. The standard {IF} model successfully predicted {LGN} responses to natural scene movies during tonic firing, indicating a linear relationship between stimulus and response. However, the {IF} model typically underpredicted the {LGN} response during periods of bursting, indicating a nonlinear amplification of the stimulus in the actual response. The addition of a burst mechanism to the {IF} model was necessary to accurately predict the entire {LGN} response. These results suggest that {LGN} bursts are an important part of the neural code, providing a nonlinear amplification of stimulus features that are typical of the natural environment.}, number = {47}, journal = {J Neurosci}, author = {Nicholas A Lesica and Garrett B Stanley}, month = nov, year = {2004}, keywords = {Action Potentials; Animals; Cats; Geniculate Bodies; {Models,Neurological;} Motion Pictures; Neurons; Photic Stimulation; Visual Perception}, pages = {10731―10740} } @Article{ hegde_comparative_2007, title = {A Comparative Study of Shape Representation in Macaque Visual Areas V2 and V4}, volume = {17}, url = {http://cercor.oxfordjournals.org/cgi/content/abstract/17/5/1100} , doi = {10.1093/cercor/bhl020}, abstract = {We compared aspects of shape representation in extrastriate visual areas V2 and V4, which are both implicated in shape processing and belong to different hierarchical levels. We recorded responses of cells in awake, fixating monkeys to matched sets of contour and grating stimuli of low or intermediate complexity. These included simple stimuli (bars and sinusoids) and more complex stimuli (angles, intersections, arcs, and {non-Cartesian} gratings), all scaled to receptive field size. The responses of cells within each area were substantially modulated by each shape characteristic tested, with substantial overlap between areas by many response measures. Our analyses revealed many clear and reliable differences between areas in terms of the effectiveness of, and response modulation by, various shape characteristics. Grating stimuli were on average more effective than contour stimuli in V2 and V4, but the difference was more pronounced in V4. As a population, V4 showed greater response modulation by some shape characteristics (including simple shape characteristics) and V2 showed greater response modulation by many others (including complex shape characteristics). Recordings from area V1 demonstrated complex shape selectivity in some cells and relatively modest population differences in comparison with V2. Altogether, the representation of 2-dimensional shape characteristics revealed by this analysis varies substantially among the 3 areas. But surprisingly, the differences revealed by our analyses, individually or collectively, do not parallel the stepwise organization of the anatomical hierarchy. Commonalities of visual shape representation across hierarchical levels may reflect the replication of neural circuits used in generating complex shape representations at multiple spatial scales. }, number = {5}, journal = {Cereb. Cortex}, author = {Jay Hegde and David C. Van Essen}, month = may, year = {2007}, pages = {1100--1116} } @Article{ touryan_isolation_2002, title = {Isolation of relevant visual features from random stimuli for cortical complex cells.}, volume = {22}, url = {http://www.jneurosci.org/cgi/reprint/22/24/10811}, abstract = {A crucial step in understanding the function of a neural circuit in visual processing is to know what stimulus features are represented in the spiking activity of the neurons. For neurons with complex, nonlinear response properties, characterization of feature representation requires measurement of their responses to a large ensemble of visual stimuli and an analysis technique that allows identification of relevant features in the stimuli. In the present study, we recorded the responses of complex cells in the primary visual cortex of the cat to spatiotemporal random-bar stimuli and applied spike-triggered correlation analysis of the stimulus ensemble. For each complex cell, we were able to isolate a small number of relevant features from a large number of null features in the random-bar stimuli. Using these features as visual stimuli, we found that each relevant feature excited the neuron effectively in isolation and contributed to the response additively when combined with other features. In contrast, the null features evoked little or no response in isolation and divisively suppressed the responses to relevant features. Thus, for each cortical complex cell, visual inputs can be decomposed into two distinct types of features (relevant and null), and additive and divisive interactions between these features may constitute the basic operations in visual cortical processing.}, number = {24}, journal = {J Neurosci}, author = {Jon Touryan and Brian Lau and Yang Dan}, month = dec, year = {2002}, keywords = {Animals; Cats; Evoked {Potentials,Neurological;} Neurons; Photic Stimulation; Principal Component Analysis; Visual Cortex; Visual Fields; Visual Pathways; Visual {Perception,Visual;} Models}, pages = {10811―10818} } @Article{ zhou_coding_2000, title = {Coding of border ownership in monkey visual cortex.}, volume = {20}, abstract = {Areas V1 and V2 of the visual cortex have traditionally been conceived as stages of local feature representations. We investigated whether neural responses carry information about how local features belong to objects. Single-cell activity was recorded in areas V1, V2, and V4 of awake behaving monkeys. Displays were used in which the same local feature (contrast edge or line) could be presented as part of different figures. For example, the same light-dark edge could be the left side of a dark square or the right side of a light square. Each display was also presented with reversed contrast. We found significant modulation of responses as a function of the side of the figure in {\textgreater}50\% of neurons of V2 and V4 and in 18\% of neurons of the top layers of V1. Thus, besides the local contrast border information, neurons were found to encode the side to which the border belongs ("border ownership coding"). A majority of these neurons coded border ownership and the local polarity of luminance-chromaticity contrast. The others were insensitive to contrast polarity. Another 20\% of the neurons of V2 and V4, and 48\% of top layer V1, coded local contrast polarity, but not border ownership. The border ownership-related response differences emerged soon ({\textless}25 msec) after the response onset. In V2 and V4, the differences were found to be nearly independent of figure size up to the limit set by the size of our display (21 degrees ). Displays that differed only far outside the conventional receptive field could produce markedly different responses. When tested with more complex displays in which figure-ground cues were varied, some neurons produced invariant border ownership signals, others failed to signal border ownership for some of the displays, but neurons that reversed signals were rare. The influence of visual stimulation far from the receptive field center indicates mechanisms of global context integration. The short latencies and incomplete cue invariance suggest that the border-ownership effect is generated within the visual cortex rather than projected down from higher levels.}, number = {17}, journal = {J Neurosci}, author = {H. Zhou and H. S. Friedman and R. von der Heydt}, month = sep, year = {2000}, keywords = {Animals; Color Perception; Contrast Sensitivity; Decision Making; {Fixation,Ocular;} Macaca mulatta; Neurons; Pattern {Recognition,Visual;} Vision Disparity; Visual Cortex}, pages = {6594―6611} } @Article{ heeger_normalization_1992, title = {Normalization of cell responses in cat striate cortex.}, volume = {9}, abstract = {Simple cells in the striate cortex have been depicted as half-wave-rectified linear operators. Complex cells have been depicted as energy mechanisms, constructed from the squared sum of the outputs of quadrature pairs of linear operators. However, the linear/energy model falls short of a complete explanation of striate cell responses. In this paper, a modified version of the linear/energy model is presented in which striate cells mutually inhibit one another, effectively normalizing their responses with respect to stimulus contrast. This paper reviews experimental measurements of striate cell responses, and shows that the new model explains a significantly larger body of physiological data.}, number = {2}, journal = {Vis Neurosci}, author = {D. J. Heeger}, month = aug, year = {1992}, keywords = {{Adaptation,Biological;} Visual Cortex; Visual {Pathways,Ocular;} Animals; Cats; Contrast Sensitivity; Mathematics; Models}, pages = {181―197} } @Article{ jones_two-dimensional_1987, title = {The two-dimensional spatial structure of simple receptive fields in cat striate cortex.}, volume = {58}, url = {http://jn.physiology.org/cgi/reprint/58/6/1187}, abstract = {1. A reverse correlation (6, 8, 25, 35) method is developed that allows quantitative determination of visual receptive-field structure in two spatial dimensions. This method is applied to simple cells in the cat striate cortex. 2. It is demonstrated that the reverse correlation method yields results with several desirable properties, including convergence and reproducibility independent of modest changes in stimulus parameters. 3. In contrast to results obtained with moving stimuli, we find that the bright and dark excitatory subregions in simple receptive fields do not overlap to any great extent. This difference in results may be attributed to confounding the independent variables space and time when using moving stimuli. 4. All simple receptive fields have subregions that vary smoothly in all directions in space. There are no sharp transitions either between excitatory subregions or between subregions and the area surrounding the receptive field. 5. Simple receptive fields vary both in the number of subregions observed, in the elongation of each subregion, and in the overall elongation of the field. In contrast with results obtained using moving stimuli, we find that subregions within a given receptive field need not be the same length. 6. The hypothesis that simple receptive fields can be modeled as either even symmetric or odd symmetric about a central axis is evaluated. This hypothesis is found to be false in general. Most simple receptive fields are neither even symmetric nor odd symmetric. 7. The hypothesis that simple receptive fields can be modeled as the product of a width response profile and an orthogonal length response profile {(Cartesian} separability) is evaluated. This hypothesis is found to be true for only approximately 50\% of the cells in our sample.}, number = {6}, journal = {J Neurophysiol}, author = {J. P. Jones and L. A. Palmer}, month = dec, year = {1987}, keywords = {Animals; Cats; Darkness; Evoked {Potentials,Neurological;} Photic Stimulation; Visual Cortex; Visual Fields; Visual {Perception,Visual;} Models}, pages = {1187―1211} } @Article{ kohn_stimulus_2005, title = {Stimulus dependence of neuronal correlation in primary visual cortex of the macaque.}, volume = {25}, url = {http://dx.doi.org/10.1523/JNEUROSCI.5106-04.2005}, doi = {{10.1523/JNEUROSCI.5106-04.2005}}, abstract = {Nearby cortical neurons often have correlated trial-to-trial response variability, and a significant fraction of their spikes occur synchronously. These two forms of correlation are both believed to arise from common synaptic input, but the origin of this input is unclear. We investigated the source of correlated responsivity by recording from pairs of single neurons in primary visual cortex of anesthetized macaque monkeys and comparing correlated variability and synchrony for spontaneous activity and activity evoked by stimuli of different orientations and contrasts. These two stimulus manipulations would be expected to have different effects on the cortical pool providing input to the recorded pair: changing stimulus orientation should recruit different populations of cells, whereas changing stimulus contrast affects primarily the relative strength of sensory drive and ongoing cortical activity. Consistent with this predicted difference, we found that correlation was affected by these stimulus manipulations in different ways. Synchrony was significantly stronger for orientations that drove both neurons well than for those that did not, but correlation on longer time scales was orientation independent. Reducing stimulus contrast resulted in a decrease in the temporal precision of synchronous firing and an enhancement of correlated response variability on longer time scales. Our results thus suggest that correlated responsivity arises from mechanisms operating at two distinct timescales: one that is orientation tuned and that determines the strength of temporally precise synchrony, and a second that is contrast sensitive, of low temporal frequency, and present in ongoing cortical activity.}, number = {14}, journal = {J Neurosci}, author = {Adam Kohn and Matthew A Smith}, month = apr, year = {2005}, keywords = {Action Potentials; Animals; Contrast Sensitivity; Macaca fascicularis; {Models,Neurological;} Neurons; Orientation; Photic Stimulation; Reaction Time; Statistics; Time Factors; Visual Cortex; Visual Perception}, pages = {3661―3673} } @Article{ albright_contextual_2002, title = {Contextual influences on visual processing.}, volume = {25}, url = {http://dx.doi.org/10.1146/annurev.neuro.25.112701.142900}, doi = {10.1146/annurev.neuro.25.112701.142900}, abstract = {The visual image formed on the retina represents an amalgam of visual scene properties, including the reflectances of surfaces, their relative positions, and the type of illumination. The challenge facing the visual system is to extract the "meaning" of the image by decomposing it into its environmental causes. For each local region of the image, that extraction of meaning is only possible if information from other regions is taken into account. Of particular importance is a set of image cues revealing surface occlusion and/or lighting conditions. These information-rich cues direct the perceptual interpretation of other more ambiguous image regions. This context-dependent transformation from image to perception has profound-but frequently under-appreciated-implications for neurophysiological studies of visual processing: To demonstrate that neuronal responses are correlated with perception of visual scene properties, rather than visual image features, neuronal sensitivity must be assessed in varied contexts that differentially influence perceptual interpretation. We review a number of recent studies that have used this context-based approach to explore the neuronal bases of visual scene perception.}, journal = {Annu Rev Neurosci}, author = {Thomas D Albright and Gene R Stoner}, year = {2002}, keywords = {Animals; Color Perception; Contrast Sensitivity; Cues; Humans; Motion Perception; Pattern {Recognition,Visual;} Retina; Visual Cortex; Visual Fields; Visual Pathways}, pages = {339―379} } @Article{ stanley_reconstruction_1999, title = {Reconstruction of Natural Scenes from Ensemble Responses in the Lateral Geniculate Nucleus}, volume = {19}, url = {http://www.jneurosci.org/cgi/content/abstract/19/18/8036}, abstract = {A major challenge in studying sensory processing is to understand the meaning of the neural messages encoded in the spiking activity of neurons. From the recorded responses in a sensory circuit, what information can we extract about the outside world? Here we used a linear decoding technique to reconstruct spatiotemporal visual inputs from ensemble responses in the lateral geniculate nucleus {(LGN)} of the cat. From the activity of 177 cells, we have reconstructed natural scenes with recognizable moving objects. The quality of reconstruction depends on the number of cells. For each point in space, the quality of reconstruction begins to saturate at six to eight pairs of on and off cells, approaching the estimated coverage factor in the {LGN} of the cat. Thus, complex visual inputs can be reconstructed with a simple decoding algorithm, and these analyses provide a basis for understanding ensemble coding in the early visual pathway. }, number = {18}, journal = {J. Neurosci.}, author = {Garrett B. Stanley and Fei F. Li and Yang Dan}, month = sep, year = {1999}, pages = {8036--8042} } @Article{ simoncelli_shiftable_1992, title = {Shiftable multiscale transforms}, volume = {38}, url = {http://www.cns.nyu.edu/ftp/eero/simoncelli91-reprint.pdf}, number = {2 Part 2}, journal = {Information Theory, {IEEE} Transactions on}, author = {E. P. Simoncelli and W. T. Freeman and E. H. Adelson and D. J. Heeger}, year = {1992}, pages = {587―607} } @Article{ franz_unifying_2006, title = {A Unifying View of Wiener and Volterra Theory and Polynomial Kernel Regression}, volume = {18}, url = {http://www.kyb.mpg.de/publications/attachments/nc05_%5B0%5D.pdf} , number = {12}, journal = {Neural Computation}, author = {M. O Franz and B. Scholkopf}, year = {2006}, pages = {3097} } @Article{ victor_responses_2006, title = {Responses of V1 Neurons to {Two-Dimensional} Hermite Functions}, volume = {95}, url = {http://jn.physiology.org/cgi/content/abstract/95/1/379}, doi = {10.1152/jn.00498.2005}, abstract = {Neurons in primary visual cortex are widely considered to be oriented filters or energy detectors that perform one-dimensional feature analysis. The main deviations from this picture are generally thought to include gain controls and modulatory influences. Here we investigate receptive field {(RF)} properties of single neurons with localized two-dimensional stimuli, the two-dimensional Hermite functions {(TDHs).} {TDHs} can be grouped into distinct complete orthonormal bases that are matched in contrast energy, spatial extent, and spatial frequency content but differ in two-dimensional form, and thus can be used to probe spatially specific nonlinearities. Here we use two such bases: Cartesian {TDHs,} which resemble vignetted gratings and checkerboards, and polar {TDHs,} which resemble vignetted annuli and dartboards. Of 63 isolated units, 51 responded to {TDH} stimuli. In 37/51 units, we found significant differences in overall response size (21/51) or apparent {RF} shape (28/51) that depended on which basis set was used. Because of the properties of the {TDH} stimuli, these findings are inconsistent with simple feedforward nonlinearities and with many variants of energy models. Rather, they imply the presence of nonlinearities that are not local in either space or spatial frequency. Units showing these differences were present to a similar degree in cat and monkey, in simple and complex cells, and in supragranular, infragranular, and granular layers. We thus find a widely distributed neurophysiological substrate for two-dimensional spatial analysis at the earliest stages of cortical processing. Moreover, the population pattern of tuning to {TDH} functions suggests that V1 neurons sample not only orientations, but a larger space of two-dimensional form, in an even-handed manner. }, number = {1}, journal = {J Neurophysiol}, author = {Jonathan D. Victor and Ferenc Mechler and Michael A. Repucci and Keith P. Purpura and Tatyana Sharpee}, year = {2006}, pages = {379--400} } @Article{ lee_role_1998, title = {The role of the primary visual cortex in higher level vision}, volume = {38}, url = {http://www.math.utah.edu/ bresslof/neuropapers/paper4.pdf}, number = {15/16}, journal = {Vision Research}, author = {T. S Lee and D. Mumford and R. Romero and V. {A.F} Lamme}, year = {1998}, pages = {2429―2454} } @Article{ felleman_distributed_1991, title = {Distributed hierarchical processing in the primate cerebral cortex.}, volume = {1}, abstract = {In recent years, many new cortical areas have been identified in the macaque monkey. The number of identified connections between areas has increased even more dramatically. We report here on (1) a summary of the layout of cortical areas associated with vision and with other modalities, (2) a computerized database for storing and representing large amounts of information on connectivity patterns, and (3) the application of these data to the analysis of hierarchical organization of the cerebral cortex. Our analysis concentrates on the visual system, which includes 25 neocortical areas that are predominantly or exclusively visual in function, plus an additional 7 areas that we regard as visual-association areas on the basis of their extensive visual inputs. A total of 305 connections among these 32 visual and visual-association areas have been reported. This represents 31\% of the possible number of pathways if each area were connected with all others. The actual degree of connectivity is likely to be closer to 40\%. The great majority of pathways involve reciprocal connections between areas. There are also extensive connections with cortical areas outside the visual system proper, including the somatosensory cortex, as well as neocortical, transitional, and archicortical regions in the temporal and frontal lobes. In the somatosensory/motor system, there are 62 identified pathways linking 13 cortical areas, suggesting an overall connectivity of about 40\%. Based on the laminar patterns of connections between areas, we propose a hierarchy of visual areas and of somatosensory/motor areas that is more comprehensive than those suggested in other recent studies. The current version of the visual hierarchy includes 10 levels of cortical processing. Altogether, it contains 14 levels if one includes the retina and lateral geniculate nucleus at the bottom as well as the entorhinal cortex and hippocampus at the top. Within this hierarchy, there are multiple, intertwined processing streams, which, at a low level, are related to the compartmental organization of areas V1 and V2 and, at a high level, are related to the distinction between processing centers in the temporal and parietal lobes. However, there are some pathways and relationships (about 10\% of the total) whose descriptions do not fit cleanly into this hierarchical scheme for one reason or another. In most instances, though, it is unclear whether these represent genuine exceptions to a strict hierarchy rather than inaccuracies or uncertainities in the reported assignment.}, number = {1}, journal = {Cereb Cortex}, author = {D. J. Felleman and D. C. Van Essen}, year = {1991}, keywords = {{Animals;,Brain,Cerebral,Cortex;,Macaca;,Mapping;,Mental,Processes}} , pages = {1―47} } @Article{ david_predicting_2005, title = {Predicting neuronal responses during natural vision.}, volume = {16}, url = {http://taylorandfrancis.metapress.com/content/g3076151261528n0/fulltext.pdf} , abstract = {A model that fully describes the response properties of visual neurons must be able to predict their activity during natural vision. While many models have been proposed for the visual system, few have ever been tested against this criterion. To address this issue, we have developed a general framework for fitting and validating nonlinear models of visual neurons using natural visual stimuli. Our approach derives from linear spatiotemporal receptive field {(STRF)} analysis, which has frequently been used to study the visual system. However, prior to the linear filtering stage typical of {STRFs,} a linearizing transformation is applied to the stimulus to account for nonlinear response properties. We used this approach to compare two models for neurons in primary visual cortex: a nonlinear Fourier power model, which accounts for spatial phase invariant tuning, and a traditional linear model. We characterized prediction accuracy in terms of the total explainable variance, given intrinsic experimental noise. On average, Fourier power {STRFs} predicted 40\% of explainable variance while linear {STRFs} were able to predict only 21\% of explainable variance. The performance of the Fourier power model provides a benchmark for evaluating more sophisticated models in the future.}, number = {2-3}, journal = {Network}, author = {Stephen V David and Jack L Gallant}, year = {2005}, keywords = {Animals; Computer Simulation; Discrimination Learning; Evoked {Potentials,Neurological;} Nerve Net; Neurons; Pattern {Recognition,Visual;} Humans; Information Storage and Retrieval; {Models,Visual;} Photic Stimulation; Visual Cortex; Visual Fields; Visual Pathways}, pages = {239―260} } @Article{ rust_spatiotemporal_2005, title = {Spatiotemporal elements of macaque v1 receptive fields.}, volume = {46}, url = {http://dx.doi.org/10.1016/j.neuron.2005.05.021}, doi = {10.1016/j.neuron.2005.05.021}, abstract = {Neurons in primary visual cortex {(V1)} are commonly classified as simple or complex based upon their sensitivity to the sign of stimulus contrast. The responses of both cell types can be described by a general model in which the outputs of a set of linear filters are nonlinearly combined. We estimated the model for a population of V1 neurons by analyzing the mean and covariance of the spatiotemporal distribution of random bar stimuli that were associated with spikes. This analysis reveals an unsuspected richness of neuronal computation within V1. Specifically, simple and complex cell responses are best described using more linear filters than the one or two found in standard models. Many filters revealed by the model contribute suppressive signals that appear to have a predominantly divisive influence on neuronal firing. Suppressive signals are especially potent in direction-selective cells, where they reduce responses to stimuli moving in the nonpreferred direction.}, number = {6}, journal = {Neuron}, author = {Nicole C Rust and Odelia Schwartz and J. Anthony Movshon and Eero P Simoncelli}, month = jun, year = {2005}, keywords = {Action Potentials; Animals; Macaca; Male; {Models,Neurological;} Motion Perception; Neural Inhibition; Neurons; Nonlinear Dynamics; Photic Stimulation; Space Perception; Visual Cortex; Visual Fields; Visual Pathways}, pages = {945―956} } @Article{ pillow_prediction_2005, title = {Prediction and decoding of retinal ganglion cell responses with a probabilistic spiking model.}, volume = {25}, url = {http://dx.doi.org/10.1523/JNEUROSCI.3305-05.2005}, doi = {{10.1523/JNEUROSCI.3305-05.2005}}, abstract = {Sensory encoding in spiking neurons depends on both the integration of sensory inputs and the intrinsic dynamics and variability of spike generation. We show that the stimulus selectivity, reliability, and timing precision of primate retinal ganglion cell {(RGC)} light responses can be reproduced accurately with a simple model consisting of a leaky integrate-and-fire spike generator driven by a linearly filtered stimulus, a postspike current, and a Gaussian noise current. We fit model parameters for individual {RGCs} by maximizing the likelihood of observed spike responses to a stochastic visual stimulus. Although compact, the fitted model predicts the detailed time structure of responses to novel stimuli, accurately capturing the interaction between the spiking history and sensory stimulus selectivity. The model also accounts for the variability in responses to repeated stimuli, even when fit to data from a single (nonrepeating) stimulus sequence. Finally, the model can be used to derive an explicit, maximum-likelihood decoding rule for neural spike trains, thus providing a tool for assessing the limitations that spiking variability imposes on sensory performance.}, number = {47}, journal = {J Neurosci}, author = {Jonathan W Pillow and Liam Paninski and Valerie J Uzzell and Eero P Simoncelli and E. J. Chichilnisky}, month = nov, year = {2005}, keywords = {Action Potentials; Animals; Macaca; {Models,Neurological;} {Models,Statistical;} Photic Stimulation; Retinal Ganglion Cells}, pages = {11003―11013} } @Article{ arathorn_computation_2004, title = {Computation in the higher visual cortices: map-seeking circuit theory and application to machine vision}, url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1409678} , journal = {Applied Imagery Pattern Recognition Workshop, 2004. Proceedings. 33rd}, author = {D. Arathorn}, year = {2004}, pages = {73―78} } @Book{ arathorn_map-seeking_2002, title = {{Map-Seeking} Circuits in Visual Cognition: A Computational Mechanism for Biological and Machine Vision}, publisher = {Stanford University Press}, author = {D. W Arathorn}, year = {2002} } @Article{ vinje_natural_2002, title = {Natural Stimulation of the Nonclassical Receptive Field Increases Information Transmission Efficiency in V1}, volume = {22}, url = {http://www.jneurosci.org/cgi/reprint/22/7/2904}, number = {7}, journal = {Journal of Neuroscience}, author = {W. E Vinje and J. L Gallant}, year = {2002}, pages = {2904} } @Article{ ringach_mapping_2004, title = {Mapping receptive fields in primary visual cortex}, volume = {558}, url = {http://jp.physoc.org/cgi/content/abstract/558/3/717}, doi = {10.1113/jphysiol.2004.065771}, abstract = {Nearly 40 years ago, in the pages of this journal, Hubel and Wiesel provided the first description of receptive fields in the primary visual cortex of higher mammals. They defined two classes of cortical cells, simple' and complex', based on neural responses to simple visual stimuli. The notion of a hierarchy of receptive fields, where increasingly intricate receptive fields are constructed from more elementary ones, was introduced. Since those early days we have witnessed the birth of quantitative methods to map receptive fields and mathematical descriptions of simple and complex cell function. Insights gained from these models, along with new theoretical concepts, are refining our understanding of receptive field structure and the underlying cortical circuitry. Here, I provide a brief historical account of the evolution of receptive field mapping in visual cortex along with the associated conceptual advancements, and speculate on the shape novel theories of the cortex may take as a result these measurements. }, number = {3}, journal = {J Physiol}, author = {Dario L. Ringach}, month = aug, year = {2004}, pages = {717--728} } @Article{ carandini_do_2005, title = {Do we know what the early visual system does?}, volume = {25}, issn = {1529-2401}, url = {http://www.ncbi.nlm.nih.gov/pubmed/16291931}, doi = {25/46/10577}, abstract = {We can claim that we know what the visual system does once we can predict neural responses to arbitrary stimuli, including those seen in nature. In the early visual system, models based on one or more linear receptive fields hold promise to achieve this goal as long as the models include nonlinear mechanisms that control responsiveness, based on stimulus context and history, and take into account the nonlinearity of spike generation. These linear and nonlinear mechanisms might be the only essential determinants of the response, or alternatively, there may be additional fundamental determinants yet to be identified. Research is progressing with the goals of defining a single "standard model" for each stage of the visual pathway and testing the predictive power of these models on the responses to movies of natural scenes. These predictive models represent, at a given stage of the visual pathway, a compact description of visual computation. They would be an invaluable guide for understanding the underlying biophysical and anatomical mechanisms and relating neural responses to visual perception.}, number = {46}, journal = {The Journal of Neuroscience: The Official Journal of the Society for Neuroscience}, author = {Matteo Carandini and Jonathan B Demb and Valerio Mante and David J Tolhurst and Yang Dan and Bruno A Olshausen and Jack L Gallant and Nicole C Rust}, month = nov, year = {2005}, note = {{PMID:} 16291931}, keywords = {{Animals,Humans,Photic} {Stimulation,Visual} {Cortex,Visual} {Pathways,Visual} Perception}, pages = {10577--97} } @Article{ hubel_receptive_1962, title = {Receptive fields, binocular interaction and functional architecture in the cat's visual cortex.}, volume = {160}, journal = {J Physiol}, author = {D. H. {HUBEL} and T. N. {WIESEL}}, year = {1962}, keywords = {{Cerebral,Cortex}}, pages = {106―154} } @Book{ mumford_neuronal_1994, title = {Neuronal architectures for pattern-theoretic problems}, url = {citeseer.ist.psu.edu/mumford94neuronal.html}, author = {D. Mumford}, year = {1994} } @Article{ qiu_figure_2005, title = {Figure and ground in the visual cortex: v2 combines stereoscopic cues with gestalt rules.}, volume = {47}, url = {http://dx.doi.org/10.1016/j.neuron.2005.05.028}, doi = {10.1016/j.neuron.2005.05.028}, abstract = {Figure-ground organization is a process by which the visual system identifies some image regions as foreground and others as background, inferring {3D} layout from {2D} displays. A recent study reported that edge responses of neurons in area V2 are selective for side-of-figure, suggesting that figure-ground organization is encoded in the contour signals (border ownership coding). Here, we show that area V2 combines two strategies of computation, one that exploits binocular stereoscopic information for the definition of local depth order, and another that exploits the global configuration of contours {(Gestalt} factors). These are combined in single neurons so that the "near" side of the preferred {3D} edge generally coincides with the preferred side-of-figure in {2D} displays. Thus, area V2 represents the borders of {2D} figures as edges of surfaces, as if the figures were objects in {3D} space. Even in {3D} displays, Gestalt factors influence the responses and can enhance or null the stereoscopic depth information.}, number = {1}, journal = {Neuron}, author = {Fangtu T Qiu and Rüdiger von der Heydt}, month = jul, year = {2005}, keywords = {Algorithms; Animals; Cues; Data {Interpretation,Ocular;} Macaca mulatta; Microelectrodes; Neurons; Photic Stimulation; Vision Disparity; Visual Cortex; Visual {Perception,Statistical;} Electrophysiology; Eye Movements; Fixation}, pages = {155―166} } @Article{ schwartz_spike-triggered_2006, title = {Spike-triggered neural characterization.}, volume = {6}, url = {http://dx.doi.org/10.1167/6.4.13}, doi = {10.1167/6.4.13}, abstract = {Response properties of sensory neurons are commonly described using receptive fields. This description may be formalized in a model that operates with a small set of linear filters whose outputs are nonlinearly combined to determine the instantaneous firing rate. Spike-triggered average and covariance analyses can be used to estimate the filters and nonlinear combination rule from extracellular experimental data. We describe this methodology, demonstrating it with simulated model neuron examples that emphasize practical issues that arise in experimental situations.}, number = {4}, journal = {J Vis}, author = {Odelia Schwartz and Jonathan W Pillow and Nicole C Rust and Eero P Simoncelli}, year = {2006}, keywords = {Action Potentials; Computer Simulation; Humans; Linear Models; {Models,Afferent;} Nonlinear Dynamics; Poisson {Distribution,Neurological;} Neurons}, pages = {484―507} } @Article{ david_natural_2004, title = {Natural stimulus statistics alter the receptive field structure of v1 neurons.}, volume = {24}, url = {http://dx.doi.org/10.1523/JNEUROSCI.1422-04.2004}, doi = {{10.1523/JNEUROSCI.1422-04.2004}}, abstract = {Studies of the primary visual cortex {(V1)} have produced models that account for neuronal responses to synthetic stimuli such as sinusoidal gratings. Little is known about how these models generalize to activity during natural vision. We recorded neural responses in area V1 of awake macaques to a stimulus with natural spatiotemporal statistics and to a dynamic grating sequence stimulus. We fit nonlinear receptive field models using each of these data sets and compared how well they predicted time-varying responses to a novel natural visual stimulus. On average, the model fit using the natural stimulus predicted natural visual responses more than twice as accurately as the model fit to the synthetic stimulus. The natural vision model produced better predictions in {\textgreater}75\% of the neurons studied. This large difference in predictive power suggests that natural spatiotemporal stimulus statistics activate nonlinear response properties in a different manner than the grating stimulus. To characterize this modulation, we compared the temporal and spatial response properties of the model fits. During natural stimulation, temporal responses often showed a stronger late inhibitory component, indicating an effect of nonlinear temporal summation during natural vision. In addition, spatial tuning underwent complex shifts, primarily in the inhibitory, rather than excitatory, elements of the response profile. These differences in late and spatially tuned inhibition accounted fully for the difference in predictive power between the two models. Both the spatial and temporal statistics of the natural stimulus contributed to the modulatory effects.}, number = {31}, journal = {J Neurosci}, author = {Stephen V David and William E Vinje and Jack L Gallant}, month = aug, year = {2004}, keywords = {Animals; Fourier Analysis; Macaca; Male; {Models,Neurological;} Photic Stimulation; Visual Cortex}, pages = {6991―7006} } @Article{ rao_dynamic_1997, title = {Dynamic Model of Visual Recognition Predicts Neural Response Properties in the Visual Cortex}, volume = {9}, url = {ftp://ftp.cs.rochester.edu/pub/u/rao/papers/dynmem.ps.Z}, number = {4}, journal = {Neural Computation}, author = {R. {P.N} Rao and D. H Ballard}, year = {1997}, pages = {721―763} } @Article{ nakayama_visual_1995, title = {Visual surface representation: A critical link between lower-level and higher-level vision}, volume = {2}, url = {http://visionlab.harvard.edu/Members/Ken/Ken%20papers%20for%20web%20page/077NKHeShimojoMIT1995b.pdf} , journal = {Visual Cognition}, author = {K. Nakayama and Z. J He and S. Shimojo}, year = {1995}, pages = {1―70} } @Article{ heeger_pyramid-based_1995, title = {Pyramid-based texture analysis/synthesis}, url = {http://www.cns.nyu.edu/ david/ftp/reprints/Heeger-siggraph95.pdf}, journal = {Proceedings of the 22nd annual conference on Computer graphics and interactive techniques}, author = {D. J Heeger and J. R Bergen}, year = {1995}, pages = {229―238} } @Article{ berkes_slow_2005, title = {Slow feature analysis yields a rich repertoire of complex cell properties}, volume = {5}, number = {6}, journal = {Journal of Vision}, author = {P. Berkes and L. Wiskott}, year = {2005}, pages = {579―602} } @Article{ christianson_consequences_2008, title = {The Consequences of Response Nonlinearities for Interpretation of Spectrotemporal Receptive Fields}, volume = {28}, url = {http://www.jneurosci.org/cgi/content/abstract/28/2/446}, doi = {{10.1523/JNEUROSCI.1775-07.2007}}, abstract = {Neurons in the central auditory system are often described by the spectrotemporal receptive field {(STRF),} conventionally defined as the best linear fit between the spectrogram of a sound and the spike rate it evokes. An {STRF} is often assumed to provide an estimate of the receptive field of a neuron, i.e., the spectral and temporal range of stimuli that affect the response. However, when the true stimulus-response function is nonlinear, the {STRF} will be stimulus dependent, and changes in the stimulus properties can alter estimates of the sign and spectrotemporal extent of receptive field components. We demonstrate analytically and in simulations that, even when uncorrelated stimuli are used, interactions between simple neuronal nonlinearities and higher-order structure in the stimulus can produce {STRFs} that show contributions from time-frequency combinations to which the neuron is actually insensitive. Only when spectrotemporally independent stimuli are used does the {STRF} reliably indicate features of the underlying receptive field, and even then it provides only a conservative estimate. One consequence of these observations, illustrated using natural stimuli, is that a stimulus-induced change in an {STRF} could arise from a consistent but nonlinear neuronal response to stimulus ensembles with differing higher-order dependencies. Thus, although the responses of higher auditory neurons may well involve adaptation to the statistics of different stimulus ensembles, stimulus dependence of {STRFs} alone, or indeed of any overly constrained stimulus-response mapping, cannot demonstrate the nature or magnitude of such effects. }, number = {2}, journal = {J. Neurosci.}, author = {G. Bjorn Christianson and Maneesh Sahani and Jennifer F. Linden}, year = {2008}, pages = {446--455} } @Article{ barlow_single_1972, title = {Single units and sensation: a neuron doctrine for perceptual psychology?}, volume = {1}, number = {4}, journal = {Perception}, author = {H. B. Barlow}, year = {1972}, keywords = {{Adaptation,Neurological;} Neural Conduction; Neural Inhibition; Neurons; Perception; Psychophysics; Sensation; Synaptic Transmission; Touch; Visual {Cortex,Physiological;} Animals; Cats; Cerebral Cortex; Color Perception; Electroencephalography; Haplorhini; Humans; Information Theory; Models}, pages = {371―394} } @Article{ wu_complete_2006, title = {Complete Functional Characterization Of Sensory Neurons By System Identification}, volume = {29}, url = {http://arjournals.annualreviews.org/doi/abs/10.1146/annurev.neuro.29.051605.113024} , doi = {10.1146/annurev.neuro.29.051605.113024}, number = {1}, journal = {Annual Review of Neuroscience}, author = {Michael C. {-K} Wu and Stephen V David and Jack L Gallant}, year = {2006}, pages = {477--505} } @Article{ lee_image_1996, title = {Image Representation Using {2D} Gabor Wavelets}, volume = {18}, url = {http://portal.acm.org/citation.cfm?id=244015}, doi = {10.1.1.52.3893}, abstract = {{Abstract¿This} paper extends to two dimensions the frame criterion developed by Daubechies for one-dimensional wavelets, and it computes the frame bounds for the particular case of {2D} Gabor wavelets. Completeness criteria for {2D} Gabor image representations are important because of their increasing role in many computer vision applications and also in modeling biological vision, since recent neurophysiological evidence from the visual cortex of mammalian brains suggests that the filter response profiles of the main class of linearly-responding cortical neurons (called simple cells) are best modeled as a family of self-similar {2D} Gabor wavelets. We therefore derive the conditions under which a set of continuous {2D} Gabor wavelets will provide a complete representation of any image, and we also find self-similar wavelet parameterizations which allow stable reconstruction by summation as though the wavelets formed an orthonormal basis. Approximating a "tight frame" generates redundancy which allows low-resolution neural responses to represent high-resolution images, as we illustrate by image reconstructions with severely quantized {2D} Gabor coefficients.}, number = {10}, journal = {{IEEE} Trans. Pattern Anal. Mach. Intell.}, author = {Tai Sing Lee}, year = {1996}, keywords = {coarse coding,gabor wavelets,image reconstruction.,image representation,visual cortex}, pages = {959--971} }