Receptive Fields Of Simple Cells Research Articles

Image Reconstruction of Compressed Sensing Based on the Double Density Circular Symmetric Contourlet Transform and Bivariate Model

Compressed sensing uses the sparse prior of image representation,it can reconstruct image from samples much less than Nyquist rate.The sparse image representation and sparseness measure are two key ingredients which have important role on image reconstruction performance.To achieve the better sparse image representation,we split one octave scale of circular symmetric contourlet transform into two scales according to the characteristic of simple cell receptive field,and yield the double density circular symmetric contourlet transform(DDCSCT).The radial bandwidth ratio of the DDCSCT is 1.414.According to the characteristics of the DDCSCT joint distribution,we deduce the second order sparseness measure of image reconstruction from bivariate model.The experiment results show that proposed image reconstruction algorithm which combine DDCSCT and second order sparseness measure outperforms the classical algorithms in terms of both peak signal-to-noise ratio and visual quality.

Seeing via Miniature Eye Movements: A Dynamic Hypothesis for Vision

During natural viewing, the eyes are never still. Even during fixation, miniature movements of the eyes move the retinal image across tens of foveal photoreceptors. Most theories of vision implicitly assume that the visual system ignores these movements and somehow overcomes the resulting smearing. However, evidence has accumulated to indicate that fixational eye movements cannot be ignored by the visual system if fine spatial details are to be resolved. We argue that the only way the visual system can achieve its high resolution given its fixational movements is by seeing via these movements. Seeing via eye movements also eliminates the instability of the image, which would be induced by them otherwise. Here we present a hypothesis for vision, in which coarse details are spatially encoded in gaze-related coordinates, and fine spatial details are temporally encoded in relative retinal coordinates. The temporal encoding presented here achieves its highest resolution by encoding along the elongated axes of simple-cell receptive fields and not across these axes as suggested by spatial models of vision. According to our hypothesis, fine details of shape are encoded by inter-receptor temporal phases, texture by instantaneous intra-burst rates of individual receptors, and motion by inter-burst temporal frequencies. We further describe the ability of the visual system to readout the encoded information and recode it internally. We show how reading out of retinal signals can be facilitated by neuronal phase-locked loops (NPLLs), which lock to the retinal jitter; this locking enables recoding of motion information and temporal framing of shape and texture processing. A possible implementation of this locking-and-recoding process by specific thalamocortical loops is suggested. Overall it is suggested that high-acuity vision is based primarily on temporal mechanisms of the sort presented here and low-acuity vision is based primarily on spatial mechanisms.

Spatiotemporal receptive fields of cells in V1 are optimally shaped for stimulus velocity estimation

In recent literature, particularly interesting stimulus velocity-selective behaviors were found in the response properties of neurons belonging to the primary visual cortex (V1). In this work, 93 simple and complex cell receptive fields were obtained from the recordings of different experiments made on cats (DeAngelis, Blanche, Touryan) with reverse correlation and the spike-triggered covariance methods and then fitted with a three-dimensional Gabor model, so that cells are seen as minimizers of the Heisenberg uncertainty principle over both space and time. Analysis of the model parameters' cortical distribution suggests that V1 is spatiotemporally organized to maximize the resolution on the stimulus velocity measure.

A Sparse Coding Model with Synaptically Local Plasticity and Spiking Neurons Can Account for the Diverse Shapes of V1 Simple Cell Receptive Fields

Sparse coding algorithms trained on natural images can accurately predict the features that excite visual cortical neurons, but it is not known whether such codes can be learned using biologically realistic plasticity rules. We have developed a biophysically motivated spiking network, relying solely on synaptically local information, that can predict the full diversity of V1 simple cell receptive field shapes when trained on natural images. This represents the first demonstration that sparse coding principles, operating within the constraints imposed by cortical architecture, can successfully reproduce these receptive fields. We further prove, mathematically, that sparseness and decorrelation are the key ingredients that allow for synaptically local plasticity rules to optimize a cooperative, linear generative image model formed by the neural representation. Finally, we discuss several interesting emergent properties of our network, with the intent of bridging the gap between theoretical and experimental studies of visual cortex.

A reaction-diffusion model to capture disparity selectivity in primary visual cortex.

Decades of experimental studies are available on disparity selective cells in visual cortex of macaque and cat. Recently, local disparity map for iso-orientation sites for near-vertical edge preference is reported in area 18 of cat visual cortex. No experiment is yet reported on complete disparity map in V1. Disparity map for layer IV in V1 can provide insight into how disparity selective complex cell receptive field is organized from simple cell subunits. Though substantial amounts of experimental data on disparity selective cells is available, no model on receptive field development of such cells or disparity map development exists in literature. We model disparity selectivity in layer IV of cat V1 using a reaction-diffusion two-eye paradigm. In this model, the wiring between LGN and cortical layer IV is determined by resource an LGN cell has for supporting connections to cortical cells and competition for target space in layer IV. While competing for target space, the same type of LGN cells, irrespective of whether it belongs to left-eye-specific or right-eye-specific LGN layer, cooperate with each other while trying to push off the other type. Our model captures realistic 2D disparity selective simple cell receptive fields, their response properties and disparity map along with orientation and ocular dominance maps. There is lack of correlation between ocular dominance and disparity selectivity at the cell population level. At the map level, disparity selectivity topography is not random but weakly clustered for similar preferred disparities. This is similar to the experimental result reported for macaque. The details of weakly clustered disparity selectivity map in V1 indicate two types of complex cell receptive field organization.

Sparse correlation coefficient for objective image quality assessment

Image quality assessment (IQA) is of fundamental importance to numerous image processing applications. Generally, image quality metrics (IQMs) regard image quality as fidelity or similarity with a reference image in some perceptual space. Such a full-reference IQA method is a kind of comparison that involves measuring the similarity or difference between two signals in a perceptually meaningful way. Modeling of the human visual system (HVS) has been regarded as the most suitable way to achieve perceptual quality predictions. In fact, natural image statistics can be an effective approach to simulate the HVS, since statistical models of natural images reveal some important response properties of the HVS. A useful statistical model of natural images is sparse coding, which is equivalent to independent component analysis (ICA). It provides a very good description of the receptive fields of simple cells in the primary visual cortex. Therefore, such a statistical model can be used to simulate the visual processing at the level of the visual cortex when designing IQMs. In this paper, we propose a fidelity criterion for IQA that relates image quality with the correlation between a reference and a distorted image in the form of sparse code. The proposed visual signal fidelity metric, which is called sparse correlation coefficient (SCC), is motivated by the need to capture the correlation between two sets of outputs from a sparse model of simple cell receptive fields. The SCC represents the correlation between two visual signals of images in a cortical visual space. The experimental results after both polynomial and logistic regression demonstrate that SCC is superior to recent state-of-the-art IQMs both in single-distortion and cross-distortion tests.

Development of cortical orientation selectivity in the absence of visual experience with contour

Visual cortical neurons are selective for the orientation of lines, and the full development of this selectivity requires natural visual experience after eye opening. Here we examined whether this selectivity develops without seeing lines and contours. Juvenile ferrets were reared in a dark room and visually trained by being shown a movie of flickering, sparse spots. We found that despite the lack of contour visual experience, the cortical neurons of these ferrets developed strong orientation selectivity and exhibited simple-cell receptive fields. This finding suggests that overt contour visual experience is unnecessary for the maturation of orientation selectivity and is inconsistent with the computational models that crucially require the visual inputs of lines and contours for the development of orientation selectivity. We propose that a correlation-based model supplemented with a constraint on synaptic strength dynamics is able to account for our experimental result.

A Differential Model of the Complex Cell

The receptive fields of simple cells in the visual cortex can be understood as linear filters. These filters can be modeled by Gabor functions or gaussian derivatives. Gabor functions can also be combined in an energy model of the complex cell response. This letter proposes an alternative model of the complex cell, based on gaussian derivatives. It is most important to account for the insensitivity of the complex response to small shifts of the image. The new model uses a linear combination of the first few derivative filters, at a single position, to approximate the first derivative filter, at a series of adjacent positions. The maximum response, over all positions, gives a signal that is insensitive to small shifts of the image. This model, unlike previous approaches, is based on the scale space theory of visual processing. In particular, the complex cell is built from filters that respond to the 2D differential structure of the image. The computational aspects of the new model are studied in one and two dimensions, using the steerability of the gaussian derivatives. The response of the model to basic images, such as edges and gratings, is derived formally. The response to natural images is also evaluated, using statistical measures of shift insensitivity. The neural implementation and predictions of the model are discussed.

Learning Features of Simple and Complex Cells: A Generative Approach via Multiplicative Interactions

AbstractWe develop a hierarchical generative model to learn features of simple and complex cells in the primary visual cortex via multiplicative interactions and address the problem of learning invariant visual representation from natural image sequences. Generally, the overall objective of a generative sparse coding model (Olshausen and Field, Nature, 1996) is to reconstruct the input *x* via a linear combination of feature bases *A = [A~1~,A~2~,...,A~M~]*, such that *x = As*, where s is the latent representation with a sparse constraint.In the proposed model, we added another hidden layer with complex cells to modulate the latent representation *s*, such that *s* is generated via an element-wise product of bottom-up representation *y = A^T^x* and top-down representation *z = Bc*, i.e., *s = y.*z* . Here *c* represents the top layer with complex cells, and *B* is the feature matrix connecting from the simple cell layer to the complex cell layer. Similar to the well known bilinear models (Tenenbaum and Freeman, Neural Computation, 2000) for invariant representation, the complex cell layer here represents the content variables and the simple cell layer represents the style variables. However, instead of using three-order tensor weight parameters as in the bilinear models, our model provides a factorized approach by the product of two two-order tensor weight parameters *A* and *B*, and thus makes learning simpler and more efficient. Moreover, while bilinear models dealt with two latent variables, our model contains only one latent variable *c* for invariant representation.The penalties of sparseness and slowness priors are integrated into this model as well. In addition, non-negativity constraints of the latent variable c and weight matrices *A* and *B* are enforced to fit the known neurophysiology better. We utilize the gradient descent algorithm to train our model from natural image sequences. A dictionary of Gabor-like orientation selective features is developed in the simple cell layer, where topography of receptive fields is automatically generated. In this way, similar simple cell receptive fields are pooled together to produce locally-invariant representation in complex cells.

Online competitive incremental-decremental clustering with the Winner-Kill-Loser rule

Event Abstract Back to Event Online competitive incremental-decremental clustering with the Winner-Kill-Loser rule Jasmin Leveille1*, Isao Hayashi2, Kunihiko Fukushima2 and Massimiliano Versace1 1 Boston University, Center of Excellence for Learning in Education, Science, and Technology, United States 2 Kansai University, Faculty of Informatics, Japan Incremental clustering techniques are general-purpose methods for clustering where the number of cluster nodes is determined online, and in particular increased, upon presentation of training data. Examples include the Leader algorithm (Hartigan, 1975), and adaptive resonance theory (Carpenter and Grossberg, 2003). Incremental learning rules for clustering are attractive for their simplicity and ease of application, and have generally led to good results on a number of tasks. Recently, a variant of incremental learning which considers online removal of tuned nodes was proposed to train simple cells in a hierarchical network (Fukushima, 2010). The learning rule presented therein, termed winner-kill-loser (WKL), is a kind of competitive rule in which only sufficiently active units enter the competition and where the losing units are effectively removed from the network. In this work, we extend the WKL learning rule to study the structure and formation of simple cell receptive fields. We start with an analysis of the properties of the WKL rule and demonstrate that, unlike many clustering techniques, in its simplest form the learning rule does not seek to approximate maximum-likelihood estimates of the node parameters. Instead, the WKL learning rule converges asymptotically to a uniform covering of the input space, irrespective of the data probability distribution. Even in the case of a uniform data distribution, our analysis also highlights conditions for the presence of irreducible gaps in this covering. We can compute a lower bound on the size of these gaps, and show how this bound relates to clustering performance in sample simulations. In particular, we investigate through simulation whether this lower bound can account for improvements in performance reported when using the dual-threshold rule, in which the net input activation threshold for each simple cell is lowered after learning (Fukushima, 2010). Based on these results, we propose to complement the WKL learning rule by inserting activity-dependent thresholds that govern the selectivity of learned receptive fields. We show through simulation that the structure of the newly developed receptive fields approximates the input data distribution.

Biomimetic Construction of Category Mental Imagery Based on Recognition Mechanism of Visual Cortex of Human Brain

The principle of homology-continuity in Multi-Dimensional Biomimetic Informatics Space is applied to construct the identifying mechanism of category of deep representation of mental imagery. The model of each cerebral region involved in recognizing is established respectively and a feedforward method for establishing category mental imagery is proposed. First, the model of feature acquisition is developed based on Hubel-Wiesel model, and Gaussian function is used to simulate the simple cell receptive field to satisfy the specific function of visual cortex. Second, multiple input aggregation operation is employed to simulate the feature output of complex cells to get the invariance representation in feature space. Then, imagery basis is extracted by unsupervised learning algorithm based on the primary feature and category mental imagery is obtained by building Radial Basis Function (RBF) network. Finally, the system model is tested by training set and test set composed of real images. Experimental results show that the proposed method can establish valid deep representation of these samples, based on which the biomimetic construction of category mental imagery can be achieved. This method provides a new idea for solving imagery problem and studying imagery thinking.

Structural theorems for simple cell receptive fields

Structural theorems for simple cell receptive fields

Neural computation of visual imaging based on Kronecker product in the primary visual cortex.

BackgroundWhat kind of neural computation is actually performed by the primary visual cortex and how is this represented mathematically at the system level? It is an important problem in the visual information processing, but has not been well answered. In this paper, according to our understanding of retinal organization and parallel multi-channel topographical mapping between retina and primary visual cortex V1, we divide an image into orthogonal and orderly array of image primitives (or patches), in which each patch will evoke activities of simple cells in V1. From viewpoint of information processing, this activated process, essentially, involves optimal detection and optimal matching of receptive fields of simple cells with features contained in image patches. For the reconstruction of the visual image in the visual cortex V1 based on the principle of minimum mean squares error, it is natural to use the inner product expression in neural computation, which then is transformed into matrix form.ResultsThe inner product is carried out by using Kronecker product between patches and function architecture (or functional column) in localized and oriented neural computing. Compared with Fourier Transform, the mathematical description of Kronecker product is simple and intuitive, so is the algorithm more suitable for neural computation of visual cortex V1. Results of computer simulation based on two-dimensional Gabor pyramid wavelets show that the theoretical analysis and the proposed model are reasonable.ConclusionsOur results are:1. The neural computation of the retinal image in cortex V1 can be expressed to Kronecker product operation and its matrix form, this algorithm is implemented by the inner operation between retinal image primitives and primary visual cortex's column. It has simple, efficient and robust features, which is, therefore, such a neural algorithm, which can be completed by biological vision.2. It is more suitable that the function of cortical column in cortex V1 is considered as the basic unit of visual image processing (such unit can implement basic multiplication of visual primitives, such as contour, line, and edge), rather than a set of tiled array filter. Fourier Transformation is replaced with Kronecker product, which greatly reduces the computational complexity. The neurobiological basis of this idea is that a visual image can be represented as a linear combination of orderly orthogonal primitive image containing some local feature. In the visual pathway, the image patches are topographically mapped onto cortex V1 through parallel multi-channels and then are processed independently by functional columns. Clearly, the above new perspective has some reference significance to exploring the neural mechanisms on the human visual information processing.

Synaptic and Network Mechanisms of Sparse and Reliable Visual Cortical Activity during Nonclassical Receptive Field Stimulation

During natural vision, the entire visual field is stimulated by images rich in spatiotemporal structure. Although many visual system studies restrict stimuli to the classical receptive field (CRF), it is known that costimulation of the CRF and the surrounding nonclassical receptive field (nCRF) increases neuronal response sparseness. The cellular and network mechanisms underlying increased response sparseness remain largely unexplored. Here we show that combined CRF + nCRF stimulation increases the sparseness, reliability, and precision of spiking and membrane potential responses in classical regular spiking (RS(C)) pyramidal neurons of cat primary visual cortex. Conversely, fast-spiking interneurons exhibit increased activity and decreased selectivity during CRF + nCRF stimulation. The increased sparseness and reliability of RS(C) neuron spiking is associated with increased inhibitory barrages and narrower visually evoked synaptic potentials. Our experimental observations were replicated with a simple computational model, suggesting that network interactions among neuronal subtypes ultimately sharpen recurrent excitation, producing specific and reliable visual responses.

Sparseness is not actively optimized in V1

Event Abstract Back to Event Sparseness is not actively optimized in V1 Pietro Berkes1*, Benjamin L. White1 and Jozsef Fiser1 1 Brandeis University, United States Sparse coding is a powerful idea in computational neuroscience referring to the general principle that the cortex exploits the benefits of representing every stimulus by a small subset of neurons. Advantages of sparse coding include reduced dependencies, improved detection of co-activation of neurons, and an efficient encoding of visual information. Computational models based on this principle have reproduced the main characteristics of simple cell receptive fields in the primary visual cortex (V1) when applied to natural images. However, direct tests on neural data of whether sparse coding is an optimization principle actively implemented in the brain have been inconclusive so far. Although a number of electrophysiological studies have reported high levels of sparseness in V1, these measurements were made in absolute terms and thus it is an open question whether the observed high sparseness indicates optimality or simply high stimulus selectivity. Moreover, most of the recordings have been performed in anesthetized animals, but it is not clear how these results generalize to the cell responses in the awake condition. To address this issue, we have focused on relative changes in sparseness. We analyzed neural data from ferret and rat V1 to verify two basic predictions of sparse coding: 1) Over learning, neural responses should become increasingly sparse, as the visual system adapts to the statistics of the environment. 2) An optimal sparse representation requires active competition between neurons involving recurrent connections. Thus, as animals go from awake state to deep anesthesia, which is known to eliminate recurrent and top-down inputs, neural responses should become less sparse, since the neural interactions that support active sparsification of responses are disrupted. To test the first prediction empirically, we measured the sparseness of neural responses in awake ferret V1 to natural movies at various stages of development, from eye opening to adulthood. Contrary to the prediction of sparse coding, we found that the neural code does adapt to represent natural stimuli over development, but sparseness steadily decreases with age. In addition, we observed a general increase in dependencies among neural responses. We addressed the second prediction by analyzing neural responses to natural movies in rats that were either awake or under different levels of anesthesia ranging from light to very deep. Again, contrary to the prediction, sparseness of cortical cells increased with increasing levels of anesthesia. We controlled for reduced responsiveness of the direct feedforward connections under anesthesia, by using appropriate sparseness measures and by quantifying the signal-to-noise ratio across levels of anesthesia, which did not change significantly. These findings suggest that the representation in V1 is not actively optimized to maximize the sparseness of neural responses. A viable alternative is that the concept of efficient coding is implemented in the form of optimal statistical learning of parameters in an internal model of the environment. This work has been supported by the Swartz Foundation and the Swiss National Science Foundation. Conference: Computational and Systems Neuroscience 2010, Salt Lake City, UT, United States, 25 Feb - 2 Mar, 2010. Presentation Type: Poster Presentation Topic: Poster session III Citation: Berkes P, White BL and Fiser J (2010). Sparseness is not actively optimized in V1. Front. Neurosci. Conference Abstract: Computational and Systems Neuroscience 2010. doi: 10.3389/conf.fnins.2010.03.00310 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 08 Mar 2010; Published Online: 08 Mar 2010. * Correspondence: Pietro Berkes, Brandeis University, Waltham, United States, berkes@brandeis.edu Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Pietro Berkes Benjamin L White Jozsef Fiser Google Pietro Berkes Benjamin L White Jozsef Fiser Google Scholar Pietro Berkes Benjamin L White Jozsef Fiser PubMed Pietro Berkes Benjamin L White Jozsef Fiser Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Auditory Cortex: Representation through Sparsification?

The recent discovery of combination-sensitive neurons in the primary auditory cortex of awake marmosets may reconcile previous, apparently contradictory, findings that cortical neurons produce strong, sustained responses, but also represent stimuli sparsely.

Intervening inhibition underlies simple-cell receptive field structure in visual cortex

Synaptic inputs underlying spike receptive fields (RFs) are key to understanding mechanisms for neuronal processing. Here, whole-cell voltage-clamp recordings from neurons in mouse primary visual cortex revealed the spatial patterns of their excitatory and inhibitory synaptic inputs evoked by On and Off stimuli. Surprisingly, neurons with either segregated or overlapped On/Off spike subfields exhibited substantial overlaps between all the four synaptic subfields. The segregated RF structures are generated by the integration of excitation and inhibition with a stereotypic pattern: the peaks of excitatory On/Off subfields are separated and flank co-localized peaks of inhibitory On/Off subfields. The small mismatch of excitation/inhibition leads to an asymmetric inhibitory shaping of On/Off spatial tunings, resulting in a great enhancement of their distinctiveness. Thus, slightly separated On/Off excitation together with intervening inhibition can create simple-cell RF structure, and the dichotomy of RF structures may arise from a fine-tuning of the spatial arrangement of synaptic inputs.

Spatial and Temporal Features of Synaptic to Discharge Receptive Field Transformation in Cat Area 17

The aim of the present study was to characterize the spatial and temporal features of synaptic and discharge receptive fields (RFs), and to quantify their relationships, in cat area 17. For this purpose, neurons were recorded intracellularly while high-frequency flashing bars were used to generate RFs maps for synaptic and spiking responses. Comparison of the maps shows that some features of the discharge RFs depended strongly on those of the synaptic RFs, whereas others were less dependent. Spiking RF duration depended poorly and spiking RF amplitude depended moderately on those of the underlying synaptic RFs. At the other extreme, the optimal spatial frequency and phase of the discharge RFs in simple cells were almost entirely inherited from those of the synaptic RFs. Subfield width, in both simple and complex cells, was less for spiking responses compared with synaptic responses, but synaptic to discharge width ratio was relatively variable from cell to cell. When considering the whole RF of simple cells, additional variability in width ratio resulted from the presence of additional synaptic subfields that remained subthreshold. Due to these additional, subthreshold subfields, spatial frequency tuning predicted from synaptic RFs appears sharper than that predicted from spiking RFs. Excitatory subfield overlap in spiking RFs was well predicted by subfield overlap at the synaptic level. When examined in different regions of the RF, latencies appeared to be quite variable, but this variability showed negligible dependence on distance from the RF center. Nevertheless, spiking response latency faithfully reflected synaptic response latency.

Statistical models of natural images and cortical visual representation.

A fundamental question in visual neuroscience is: Why are the response properties of visual neurons as they are? A modern approach to this problem emphasizes the importance of adaptation to ecologically valid input, and it proceeds by modeling statistical regularities in ecologically valid visual input (natural images). A seminal model was linear sparse coding, which is equivalent to independent component analysis (ICA), and provided a very good description of the receptive fields of simple cells. Further models based on modeling residual dependencies of the ''independent" components have later been introduced. These models lead to emergence of further properties of visual neurons: the complex cell receptive fields, the spatial organization of the cells, and some surround suppression and Gestalt effects. So far, these models have concentrated on the response properties of neurons, but they hold great potential to model various forms of inference and learning.

Simple cell response properties imply receptive field structure: balanced Gabor and/or bandlimited field functions.

The classical receptive fields of simple cells in mammalian primary visual cortex demonstrate three cardinal response properties: (1) they do not respond to stimuli that are spatially homogeneous; (2) they respond best to stimuli in a preferred orientation (direction); and (3) they do not respond to stimuli in other, nonpreferred orientations (directions). We refer to these as the balanced field property, the maximum response direction property, and the zero response direction property, respectively. These empirically determined response properties are used to derive a complete characterization of elementary receptive field functions defined as products of a circularly symmetric weight function and a simple periodic carrier. Two disjoint classes of elementary receptive field functions result: the balanced Gabor class, a generalization of the traditional Gabor filter, and a bandlimited class whose Fourier transforms have compact support (i.e., are zero valued outside of a bounded range). The detailed specification of these two classes of receptive field functions from empirically based postulates may prove useful to neurophysiologists seeking to test alternative theories of simple cell receptive field structure and to computational neuroscientists seeking basis functions with which to model human vision.