Responses Of Complex Cells Research Articles

Spatial Organization of Receptive Fields of V1 Neurons of Alert Monkeys: Comparison With Responses to Gratings

We studied the spatial organization of receptive fields and the responses to gratings of neurons in parafoveal V1 of alert monkeys. Activating regions (ARs) of 228 cells were mapped with increment and decrement bars while compensating for fixational eye movements. For cells with two or more ARs, the overlap between ARs responsive to increments (INC) and ARs responsive to decrements (DEC) was characterized by a quantitative overlap index (OI). The distribution of overlap indices was bimodal. The larger group (78% of cells) was composed of complex cells with strongly overlapping ARs (OI >/= 0.5). The smaller group (14%) was composed of simple cells with minimal spatial overlap of ARs (OI </= 0.3). Simple cells were preferentially located in layers dominated by the magnocellular pathway. A third group of neurons, the monocontrast cells (8%), responded only to one sign of contrast and had more sustained responses to flashed stimuli than other cells. One hundred fourteen neurons were also studied with drifting sinusoidal gratings of various spatial frequencies and window widths. For complex cells, the relative modulation (RM, the ratio of the 1st harmonic to the mean firing rate), ranged from 0.6 +/- 0.4 to 1.1 +/- 0.5 (mean +/- SD), depending on the stimulus conditions and the mode of correction for eye movements. RM was not correlated with the degree of overlap of ARs, indicating that the spatial organization of receptive fields cannot reliably be predicted from RM values. In fact, a subset of complex cells had RM > 1, the traditional criterion for identifying simple cells. However, unlike simple cells, even those complex cells with high RM could exhibit diverse nonlinear responses when the spatial frequency or window size was changed. Furthermore, the responses of complex cells to counterphase gratings were predominantly nonlinear even harmonics. These results show that RM is not a robust test of linearity. Our results indicate that complex cells are the most frequently encountered neurons in primate V1, and their behavior needs to receive more emphasis in models of visual function.

The role of complex cells in object recognition

Primate’s primary visual cortex (V1) is dominated by complex cells. This choice of nature seems puzzling, as complex cells are insensitive to spatial phase––information which is generally believed to be essential for perceptual characterization and recognition of images. Modeling complex cells as Gabor wavelet magnitudes, we have mathematically and empirically examined the information content of their responses. Our results show that in spite of phase insensitivity of individual complex cell responses, population responses contain sufficient information to capture the perceptual essence of images. A complex cell type representation seems to be not only sufficiently discriminating for object identification, but also––due to its inherent ambiguities––robust to changes in background, lighting, and small deformations.

On the velocity tuning of area 18 complex cell responses to moving textures.

Unlike simple cells, complex cells of area 18 give a directionally selective response to motion of random textures, indicating that they may play a special role in motion detection. We therefore investigated how texture motion, and especially its velocity, is represented by area 18 complex cells. Do these cells have separable spatial and temporal tunings or are these nonseparable? To answer this question, we measured responses to moving random pixel arrays as a function of both pixel size and velocity, for a set of 63 directionally selective complex cells. Complex cells generally responded to a fairly wide range of pixel sizes and velocities. Variations in pixel size of the random pixel array only caused minor changes in the cells' preferred velocity. For nearly all cells the data much better fitted a model in which pixel size and velocity act separately, than a model in which pixel size and velocity interact so as to keep temporal-frequency sensitivity constant. Our conclusion is that the studied population of special complex cells in area 18 are true motion detectors, rather than temporal-frequency tuned neurons.

Sparse coding of natural contours

An important approach in visual neuroscience considers how the function of the early visual system relates to the statistics of its natural input. Previous work has shown how the classical receptive fields and the organization (topography) of the primary visual cortex can be viewed as efficient coding of natural images. Here, we extend the framework by considering how the responses of complex cells could be efficiently coded by a higher-order neural layer. This leads to the sparse coding of contours in natural images, and can explain certain extra-classical properties of receptive fields.

Learning the invariance properties of complex cells from their responses to natural stimuli.

Neurons in primary visual cortex are typically classified as either simple or complex. Whereas simple cells respond strongly to grating and bar stimuli displayed at a certain phase and visual field location, complex cell responses are insensitive to small translations of the stimulus within the receptive field [Hubel & Wiesel (1962) J. Physiol. (Lond.), 160, 106-154; Kjaer et al. (1997) J. Neurophysiol., 78, 3187-3197]. This constancy in the response to variations of the stimuli is commonly called invariance. Hubel and Wiesel's classical model of the primary visual cortex proposes a connectivity scheme which successfully describes simple and complex cell response properties. However, the question as to how this connectivity arises during normal development is left open. Based on their work and inspired by recent physiological findings we suggest a network model capable of learning from natural stimuli and developing receptive field properties which match those of cortical simple and complex cells. Stimuli are drawn from videos obtained by a camera mounted to a cat's head, so they should approximate the natural input to the cat's visual system. The network uses a competitive scheme to learn simple and complex cell response properties. Employing delayed signals to learn connections between simple and complex cells enables the model to utilize temporal properties of the input. We show that the temporal structure of the input gives rise to the emergence and refinement of complex cell receptive fields, whereas removing temporal continuity prevents this processes. This model lends a physiologically based explanation of the development of complex cell invariance response properties.

A multi-layer sparse coding network learns contour coding from natural images

An important approach in visual neuroscience considers how the function of the early visual system relates to the statistics of its natural input. Previous studies have shown how many basic properties of the primary visual cortex, such as the receptive fields of simple and complex cells and the spatial organization (topography) of the cells, can be understood as efficient coding of natural images. Here we extend the framework by considering how the responses of complex cells could be sparsely represented by a higher-order neural layer. This leads to contour coding and end-stopped receptive fields. In addition, contour integration could be interpreted as top-down inference in the presented model.

Review: Molecular response of plant cells to UV-B stress.

UV-B radiation (UV-B: 280-320 nm) can cause a wide range of responses in plant cells. These responses depend on the perception of the UV-B radiation, signal transduction mechanisms, and modification of gene expression. Studies over the last ten years have revealed a complex molecular response of plant cells to UV-B radiation. A number of signal transduction pathways are established and specific changes in gene activity take place. In addition, other environmental parameters strongly influence the UV-B-induced response. Although molecular studies have advanced our knowledge, our understanding of UV-B-induced cellular changes remains limited compared with other areas of plant photobiology / molecular biology. This review will focus on UV-B-induced signal transduction, gene expression and defence mechanisms. Comparisons will be made with other light-regulated systems to provide an insight into UV-B responses. This review will also attempt to identify present limitations to our understanding of molecular responses of plant cells to UV-B radiation.

Modeling temporal response characteristics of V1 neurons with a dynamic normalization model

We present a dynamic normalization model to characterize both the transient and the steady-state components of V1 simple and complex cell responses. Primary receptive field properties are chiefly determined by the convergence of LGN afferents. These linear responses are rectified, and subjected to shunting inhibition through cortical feedback, which accounts for the non-linear characteristics of the neuronal responses. The duration of the transient response is determined by the time delay and the low-pass filtering of the cortical feedback. In addition to accounting for basic non-linear behaviors such as response saturation and cross-orientation inhibition, the model is also able to reproduce several short-term contrast and pattern-selective adaptation effects.

Joint-encoding of motion and depth by visual cortical neurons: neural basis of the Pulfrich effect.

Motion and stereoscopic depth are fundamental parameters of the structural analysis of visual scenes. Because they are defined by a difference in object position, either over time or across the eyes, a common neural machinery may be used for encoding these attributes. To examine this idea, we analyzed responses of binocular complex cells in the cat striate cortex to stimuli of various intra- and interocular spatial and temporal shifts. We found that most neurons exhibit space-time-oriented response profiles in both monocular and binocular domains. This indicates that these neurons encode motion and depth jointly, and it explains phenomena such as the Pulfrich effect. We also found that the relationship between neuronal tuning of motion and depth conforms to that predicted by the use of motion parallax as a depth cue. These results demonstrate a joint-encoding of motion and depth at an early cortical stage.

Predictions of the spontaneous symmetry-breaking theory for visual code completeness and spatial scaling in single-cell learning rules.

This article shows analytically that single-cell learning rules that give rise to oriented and localized receptive fields, when their synaptic weights are randomly and independently initialized according to a plausible assumption of zero prior information, will generate visual codes that are invariant under two-dimensional translations, rotations, and scale magnifications, provided that the statistics of their training images are sufficiently invariant under these transformations. Such codes span different image locations, orientations, and size scales with equal economy. Thus, single-cell rules could account for the spatial scaling property of the cortical simple-cell code. This prediction is tested computationally by training with natural scenes; it is demonstrated that a single-cell learning rule can give rise to simple-cell receptive fields spanning the full range of orientations, image locations, and spatial frequencies (except at the extreme high and low frequencies at which the scale invariance of the statistics of digitally sampled images must ultimately break down, because of the image boundary and the finite pixel resolution). Thus, no constraint on completeness, or any other coupling between cells, is necessary to induce the visual code to span wide ranges of locations, orientations, and size scales. This prediction is made using the theory of spontaneous symmetry breaking, which we have previously shown can also explain the data-driven self-organization of a wide variety of transformation invariances in neurons' responses, such as the translation invariance of complex cell response.

A complex cell-like receptive field obtained by information maximization.

The energy model (Pollen & Ronner, 1983; Adelson & Bergen, 1985) for a complex cell in the visual cortex is investigated theoretically. The energy model describes the output of a complex cell as the squared sum of outputs of two linear operators. An information-maximization problem to determine the two linear operators is investigated assuming the low signal-to-noise ratio limit and a localization term in the objective function. As a result, two linear operators characterized by a quadrature pair of Gabor functions are obtained as solutions. The result agrees with the energy model, which well describes the shift-invariant and orientation-selective responses of actual complex cells, and thus suggests that complex cells are optimally designed from an information-theoretic viewpoint.

Specific Roles of NMDA and AMPA Receptors in Direction-Selective and Spatial Phase-Selective Responses in Visual Cortex

Cells in the superficial layers of primary visual cortex (area 17) are distinguished by feedforward input from thalamic-recipient layers and by massive recurrent excitatory connections between neighboring cells. The connections use glutamate as transmitter, and the postsynaptic cells contain both NMDA and AMPA receptors. The possible role of these receptor types in generating emergent responses of neurons in the superficial cortical layers is unknown. Here, we show that NMDA and AMPA receptors are both involved in the generation of direction-selective responses in layer 2/3 cells of area 17 in cats. NMDA receptors contribute prominently to responses in the preferred direction, and their contribution to responses in the nonpreferred direction is reduced significantly by GABAergic inhibition. AMPA receptors decrease spatial phase-selective simple cell responses and generate phase-invariant complex cell responses.

A role for chemokine receptor transactivation in growth factor signaling.

Complex cell responses require the integration of signals delivered through different pathways. We show that insulin-like growth factor (IGF)-I induces specific transactivation of the Gi-coupled chemokine receptor CCR5, triggering its tyrosine phosphorylation and Galpha recruitment. This transactivation occurs via a mechanism involving transcriptional upregulation and secretion of RANTES, the natural CCR5 ligand. CCR5 transactivation is an essential downstream signal in IGF-I-induced cell chemotaxis, as abrogation of CCR5 function with a transdominant-negative KDELccr5A32 mutant abolishes IGF-I-induced migration. The relevance of this transactivation pathway was shown in vivo, as KDELccr5A32 overexpression prevents invasion by highly metastatic tumor cells; conversely, RANTES overexpression confers built-in invasive capacity on a non-invasive tumor cell line. Our results suggest that this extracellular growth factor-chemokine network represents a general mechanism connecting tumorigenesis and inflammation.

The simultaneous coding of orientation and contrast in the responses of V1 complex cells.

The responses of 30 V1 complex cells were recorded using a complete set of transiently presented, oriented stimuli of different contrasts. A back-propagation neural network was used to predict the multivariate visual stimuli from the neuronal responses on a trial-by-trial basis. For single neurons, the strength of the response was much better at predicting the orientation of a visual stimulus than its contrast. Using the temporal modulation of the response improved the ability to predict the contrast of a stimulus without affecting the ability to predict the orientation. Removing stimulus latency from the responses, by time-shifting the individual responses an amount equal to the average latency, significantly reduced the ability to predict stimulus contrast, demonstrating that the response latency is reliable enough, even for a single neuron and a single trial, for it to be used to help determine stimulus contrast. Pooling the responses from a group of 11 neurons demonstrated that small groups of neurons can accurately represent multivariate stimuli in a single trial.

A recurrent network model for the phase invariance of complex cell responses

Cortical amplification is a mechanism for modifying the selectivity of neurons through recurrent interactions. Although conventionally used to enhance selectivity, cortical amplification can also broaden it, de-tuning neurons. Here we show that the spatial-phase invariance of complex cell responses in primary visual cortex can arise using recurrent amplification of feedforward input. Neurons in the model network respond like simple cells when recurrent connections are weak and complex cells when they are strong. Simple or complex cells can coexist in such a network, and they can have a range of selectivities for image characteristics such as spatial frequency.

Spatial pooling in the second-order spatial structure of cortical complex cells

We investigate what computational mechanisms give rise to the nonlinearity of complex cell responses in the primary visual cortex. Complex cells are characterized by their nonlinear spatial properties such as spatial phase invariance and nonlinear spatial additivity. We carried out network simulations to estimate the second-order Wiener-like kernels for several different models. Models with nonlinear spatial pooling of simple-cell-like linear subunits reproduce the second-order kernels in good agreement with physiologically estimated kernels, while models without the pooling mechanism fail to reproduce the kernel. The results support the cascade mechanism consisting of simple cells’ local feature extraction followed by spatial pooling.

Neural mechanisms for processing binocular information II. Complex cells.

Complex cells in the striate cortex exhibit extensive spatiotemporal nonlinearities, presumably due to a convergence of various subunits. Because these subunits essentially determine many aspects of a complex cell receptive field (RF), such as tuning for orientation, spatial frequency, and binocular disparity, examination of the RF properties of subunits is important for understanding functional roles of complex cells. Although monocular aspects of these subunits have been studied, little is known about their binocular properties. Using a sophisticated RF mapping technique that employs binary m-sequences, we have examined binocular interactions exhibited by complex cells in the cat's striate cortex and the binocular RF properties of their underlying functional subunits. We find that binocular interaction RFs of complex cells exhibit subregions that are elongated along the frontoparallel axis at different binocular disparities. Therefore responses of complex cells are largely independent of monocular stimulus position or phase as long as the binocular disparity of the stimulus is kept constant. The binocular interaction RF is well described by a sum of binocular interaction RFs of underlying functional subunits, which exhibit simple cell-like RFs and a preference for different monocular phases but the same binocular disparity. For more than half of the complex cells examined, subunits of each cell are consistent with the characteristics specified by an energy model, with respect to the number of subunits as well as relationships between the subunit properties. Subunits exhibit RF binocular disparities that are largely consistent with a phase mechanism for encoding binocular disparity. These results indicate that binocular interactions of complex cells are derived from simple cell-like subunits, which exhibit multiplicative binocular interactions. Therefore binocular interactions of complex cells are also multiplicative. This suggests that complex cells compute something analogous to an interocular cross-correlation of images for a local region of visual space. The result of this computation can be used for solving the stereo correspondence problem.

Learning invariance manifolds

A new algorithm for learning invariance manifolds is introduced that allows a neuron to learn a non-linear input–output function to extract invariant or rather slowly varying features from a vectorial input sequence. This is demonstrated by a simple model of learning complex cell responses. The algorithm is generalized to a group of neurons, referred to as a Gibson-clique, to learn slowly varying features that are uncorrelated. Since the input–output functions are non-linear, this technique can be applied iteratively. This is demonstrated by a hierarchical network of Gibson-cliques learning translation invariance.

Complex cells as cortically amplified simple cells.

The majority of synapses in primary visual cortex mediate excitation between nearby neurons, yet the role of local recurrent connections in visual processing remains unclear. We propose that these connections are responsible for the spatial-phase invariance of complex-cell responses. In a network model with selective cortical amplification, neurons exhibit simple-cell responses when recurrent connections are weak and complex-cell responses when they are strong, suggesting that simple and complex cells are the low- and high-gain limits of the same basic cortical circuit. Given the ubiquity of invariant responses in cognitive processing, the recurrent mechanism we propose for complex cells may be widely applicable.

Collinearity and Parallelism are Statistically Significant Second-Order Relations of Complex Cell Responses

By investigating the second-order statistics of Gabor wavelet responses derived from natural images, we show that collinearity and parallelism are conspicuous relations. We give a precise mathematical characterization of these Gestalt principles by the conditional probability of two responses. Essential for our investigations is a non-linear transformation, initially utilized within the object recognition system [5], which transforms continuous Gabor wavelet responses into a binary code indicating the presence or absence of local oriented line segments.