Detection and discrimination of relative spatial phase by V1 neurons

Neural adaptation to the eye's optics through phase compensation

How does the brain achieve a seemingly veridical and 'in-focus' perception of the world, knowing how severely corrupted visual information is by the eye's optics? Optical blur degrades retinal image quality by reducing the contrast and disrupting the phase of transmitted signals. Neural adaptation can attenuate the impact of blur on image contrast, yet vision rather relies on perceptually-relevant information contained within the phase structure of natural images. Here we show that neural adaptation can compensate for the impact of optical aberrations on phase congruency. We used adaptive optics to fully control optical factors and test the impact of specific optical aberrations on the perceived phase of compound gratings. We assessed blur-induced changes in perceived phase over three distinct exposure spans. Under brief blur exposure, perceived phase shifts matched optical theory predictions. During short-term (~1h) exposure, we found a reduction in blur-induced phase shifts over time, followed by after-effects in the opposite direction-a hallmark of adaptation. Finally, patients with chronic exposure to poor optical quality showed altered phase perception when tested under fully-corrected optical quality, suggesting long-term neural compensatory adjustments to phase spectra. These findings reveal that neural adaptation to optical aberrations compensates for alterations in phase congruency, helping restore perceptual quality over time.

Processing of visual statistics of naturalistic videos in macaque visual areas V1 and V4

Natural scenes are characterized by diverse image statistics, including various parameters of the luminance histogram, outputs of Gabor-like filters, and pairwise correlations between the filter outputs of different positions, orientations, and scales (Portilla–Simoncelli statistics). Some of these statistics capture the response properties of visual neurons. However, it remains unclear to what extent such statistics can explain neural responses to natural scenes and how neurons that are tuned to these statistics are distributed across the cortex. Using two-photon calcium imaging and an encoding-model approach, we addressed these issues in macaque visual areas V1 and V4. For each imaged neuron, we constructed an encoding model to mimic its responses to naturalistic videos. By extracting Portilla–Simoncelli statistics through outputs of both filters and filter correlations, and by computing an optimally weighted sum of these outputs, the model successfully reproduced responses in a subpopulation of neurons. We evaluated the selectivities of these neurons by quantifying the contributions of each statistic to visual responses. Neurons whose responses were mainly determined by Gabor-like filter outputs (low-level statistics) were abundant at most imaging sites in V1. In V4, the relative contribution of higher order statistics, such as cross-scale correlation, was increased. Preferred image statistics varied markedly across V4 sites, and the response similarity of two neurons at individual imaging sites gradually declined with increasing cortical distance. The results indicate that natural scene analysis progresses from V1 to V4, and neurons sharing preferred image statistics are locally clustered in V4.

Multi-Frequency Image Completion via a Biologically-Inspired Sub-Riemannian Model with Frequency and Phase

We present a novel cortically-inspired image completion algorithm. It uses five-dimensional sub-Riemannian cortical geometry, modeling the orientation, spatial frequency and phase-selective behavior of the cells in the visual cortex. The algorithm extracts the orientation, frequency and phase information existing in a given two-dimensional corrupted input image via a Gabor transform and represents those values in terms of cortical cell output responses in the model geometry. Then, it performs completion via a diffusion concentrated in a neighborhood along the neural connections within the model geometry. The diffusion models the activity propagation integrating orientation, frequency and phase features along the neural connections. Finally, the algorithm transforms the diffused and completed output responses back to the two-dimensional image plane.

A sub-Riemannian model of the visual cortex with frequency and phase

In this paper, we present a novel model of the primary visual cortex (V1) based on orientation, frequency, and phase selective behavior of V1 simple cells. We start from the first-level mechanisms of visual perception, receptive profiles. The model interprets V1 as a fiber bundle over the two-dimensional retinal plane by introducing orientation, frequency, and phase as intrinsic variables. Each receptive profile on the fiber is mathematically interpreted as rotated, frequency modulated, and phase shifted Gabor function. We start from the Gabor function and show that it induces in a natural way the model geometry and the associated horizontal connectivity modeling of the neural connectivity patterns in V1. We provide an image enhancement algorithm employing the model framework. The algorithm is capable of exploiting not only orientation but also frequency and phase information existing intrinsically in a two-dimensional input image. We provide the experimental results corresponding to the enhancement algorithm.

Fly Photoreceptors Encode Phase Congruency

More than five decades ago it was postulated that sensory neurons detect and selectively enhance behaviourally relevant features of natural signals. Although we now know that sensory neurons are tuned to efficiently encode natural stimuli, until now it was not clear what statistical features of the stimuli they encode and how. Here we reverse-engineer the neural code of Drosophila photoreceptors and show for the first time that photoreceptors exploit nonlinear dynamics to selectively enhance and encode phase-related features of temporal stimuli, such as local phase congruency, which are invariant to changes in illumination and contrast. We demonstrate that to mitigate for the inherent sensitivity to noise of the local phase congruency measure, the nonlinear coding mechanisms of the fly photoreceptors are tuned to suppress random phase signals, which explains why photoreceptor responses to naturalistic stimuli are significantly different from their responses to white noise stimuli.

Representation of higher-order statistical structures in natural scenes via spatial phase distributions

Natural scenes contain richer perceptual information in their spatial phase structure than their amplitudes. Modeling phase structure of natural scenes may explain higher-order structure inherent to the natural scenes, which is neglected in most classical models of redundancy reduction. Only recently, a few models have represented images using a complex form of receptive fields (RFs) and analyze their complex responses in terms of amplitude and phase. However, these complex representation models often tacitly assume a uniform phase distribution without empirical support. The structure of spatial phase distributions of natural scenes in the form of relative contributions of paired responses of RFs in quadrature has not been explored statistically until now. Here, we investigate the spatial phase structure of natural scenes using complex forms of various Gabor-like RFs. To analyze distributions of the spatial phase responses, we constructed a mixture model that accounts for multi-modal circular distributions, and the EM algorithm for estimation of the model parameters. Based on the likelihood, we report presence of both uniform and structured bimodal phase distributions in natural scenes. The latter bimodal distributions were symmetric with two peaks separated by about 180°. Thus, the redundancy in the natural scenes can be further removed by using the bimodal phase distributions obtained from these RFs in the complex representation models. These results predict that both phase invariant and phase sensitive complex cells are required to represent the regularities of natural scenes in visual systems.

Spectral characteristics of phase sensitivity and discharge rate of neurons in the ascending tectofugal visual system

Drifting gratings can modulate the activity of visual neurons at the temporal frequency of the stimulus. In order to characterize the temporal frequency modulation in the cat’s ascending tectofugal visual system, we recorded the activity of single neurons in the superior colliculus, the suprageniculate nucleus, and the anterior ectosylvian cortex during visual stimulation with drifting sine-wave gratings. In response to such stimuli, neurons in each structure showed an increase in firing rate and/or oscillatory modulated firing at the temporal frequency of the stimulus (phase sensitivity). To obtain a more complete characterization of the neural responses in spatiotemporal frequency domain, we analyzed the mean firing rate and the strength of the oscillatory modulations measured by the standardized Fourier component of the response at the temporal frequency of the stimulus. We show that the spatiotemporal stimulus parameters that elicit maximal oscillations often differ from those that elicit a maximal discharge rate. Furthermore, the temporal modulation and discharge-rate spectral receptive fields often do not overlap, suggesting that the detection range for visual stimuli provided jointly by modulated and unmodulated response components is larger than the range provided by a one response component.

BOLD human responses to chromatic spatial features

Animal physiological and human psychophysical studies suggest that an early step in visual processing involves the detection and identification of features such as lines and edges, by neural mechanisms with even- and odd-symmetric receptive fields. Functional imaging studies also demonstrate mechanisms with even- and odd-receptive fields in early visual areas, in response to luminance-modulated stimuli. In this study we measured fMRI BOLD responses to 2-D stimuli composed of only even or only odd symmetric features, and to an amplitude-matched random noise control, modulated in red-green equiluminant colour contrast. All these stimuli had identical power but different phase spectra, either highly congruent (even or odd symmetry stimuli) or random (noise). At equiluminance, V1 BOLD activity showed no preference between congruent- and random-phase stimuli, as well as no preference between even and odd symmetric stimuli. Areas higher in the visual hierarchy, both along the dorsal pathway (caudal part of the intraparietal sulcus, dorsal LO and V3A) and the ventral pathway (V4), responded preferentially to odd symmetry over even symmetry stimuli, and to congruent over random phase stimuli. Interestingly, V1 showed an equal increase in BOLD activity at each alternation between stimuli of different symmetry, suggesting the existence of specialised mechanisms for the detection of edges and lines such as even- and odd-chromatic receptive fields. Overall the results indicate a high selectivity of colour-selective neurons to spatial phase along both the dorsal and the ventral pathways in humans.

A bio-inspired, motion-based analysis of crowd behavior attributes relevance to motion transparency, velocity gradients, and motion patterns

The analysis of motion crowds is concerned with the detection of potential hazards for individuals of the crowd. Existing methods analyze the statistics of pixel motion to classify non-dangerous or dangerous behavior, to detect outlier motions, or to estimate the mean throughput of people for an image region. We suggest a biologically inspired model for the analysis of motion crowds that extracts motion features indicative for potential dangers in crowd behavior. Our model consists of stages for motion detection, integration, and pattern detection that model functions of the primate primary visual cortex area (V1), the middle temporal area (MT), and the medial superior temporal area (MST), respectively. This model allows for the processing of motion transparency, the appearance of multiple motions in the same visual region, in addition to processing opaque motion. We suggest that motion transparency helps to identify "danger zones" in motion crowds. For instance, motion transparency occurs in small exit passages during evacuation. However, motion transparency occurs also for non-dangerous crowd behavior when people move in opposite directions organized into separate lanes. Our analysis suggests: The combination of motion transparency and a slow motion speed can be used for labeling of candidate regions that contain dangerous behavior. In addition, locally detected decelerations or negative speed gradients of motions are a precursor of danger in crowd behavior as are globally detected motion patterns that show a contraction toward a single point. In sum, motion transparency, image speeds, motion patterns, and speed gradients extracted from visual motion in videos are important features to describe the behavioral state of a motion crowd.

Standardized F1: a consistent measure of strength of modulation of visual responses to sine-wave drifting gratings

The magnitude of spike-responses of neurons in the mammalian visual system to sine-wave luminance-contrast-modulated drifting gratings is modulated by the temporal frequency of the stimulation. However, there are serious problems with consistency and reliability of the traditionally used methods of assessment of strength of such modulation. Here we propose an intuitive and simple tool for assessment of the strength of modulations in the form of standardized F1 index, zF1. We define zF1 as the ratio of the difference between the F1 (component of amplitude spectrum of the spike-response at temporal frequency of stimulation) and the mean value of spectrum amplitudes to standard deviation along all frequencies in the spectrum. In order to assess the validity of this measure, we have: (1) examined behavior of zF1 using spike-responses to optimized drifting gratings of single neurons recorded from four 'visual' structures (area V1 of primary visual cortex, superior colliculus, suprageniculate nucleus and caudate nucleus) in the brain of commonly used visual mammal - domestic cat; (2) compared the behavior of zF1 with that of classical statistics commonly employed in the analysis of steady-state responses; (3) tested the zF1 index on simulated spike-trains generated with threshold-linear model. Our analyses indicate that zF1 is resistant to distortions due to the low spike count in responses and therefore can be particularly useful in the case of recordings from neurons with low firing rates and/or low net mean responses. While most V1 and a half of caudate neurons exhibit high zF1 indices, the majorities of collicular and suprageniculate neurons exhibit low zF1 indices. We conclude that despite the general shortcomings of measuring strength of modulation inherent in the linear system approach, zF1 can serve as a sensitive and easy to interpret tool for detection of modulation and assessment of its strength in responses of visual neurons.

A model of motion transparency processing with local center-surround interactions and feedback

Motion transparency occurs when multiple coherent motions are perceived in one spatial location. Imagine, for instance, looking out of the window of a bus on a bright day, where the world outside the window is passing by and movements of passengers inside the bus are reflected in the window. The overlay of both motions at the window leads to motion transparency, which is challenging to process. Noisy and ambiguous motion signals can be reduced using a competition mechanism for all encoded motions in one spatial location. Such a competition, however, leads to the suppression of multiple peak responses that encode different motions, as only the strongest response tends to survive. As a solution, we suggest a local center-surround competition for population-encoded motion directions and speeds. Similar motions are supported, and dissimilar ones are separated, by representing them as multiple activations, which occurs in the case of motion transparency. Psychophysical findings, such as motion attraction and repulsion for motion transparency displays, can be explained by this local competition. Besides this local competition mechanism, we show that feedback signals improve the processing of motion transparency. A discrimination task for transparent versus opaque motion is simulated, where motion transparency is generated by superimposing large field motion patterns of either varying size or varying coherence of motion. The model's perceptual thresholds with and without feedback are calculated. We demonstrate that initially weak peak responses can be enhanced and stabilized through modulatory feedback signals from higher stages of processing.

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.

Laminar and orientation-dependent characteristics of spatial nonlinearities: implications for the computational architecture of visual cortex

A full understanding of the computations performed in primary visual cortex is an important yet elusive goal. Receptive field models consisting of cascades of linear filters and static nonlinearities may be adequate to account for responses to simple stimuli such as gratings and random checkerboards, but their predictions of responses to complex stimuli such as natural scenes are only approximately correct. It is unclear whether these discrepancies are limited to quantitative inaccuracies that reflect well-recognized mechanisms such as response normalization, gain controls, and cross-orientation suppression or, alternatively, imply additional qualitative features of the underlying computations. To address this question, we examined responses of V1 and V2 neurons in the monkey and area 17 neurons in the cat to two-dimensional Hermite functions (TDHs). TDHs are intermediate in complexity between traditional analytic stimuli and natural scenes and have mathematical properties that facilitate their use to test candidate models. By exploiting these properties, along with the laminar organization of V1, we identify qualitative aspects of neural computations beyond those anticipated from the above-cited model framework. Specifically, we find that V1 neurons receive signals from orientation-selective mechanisms that are highly nonlinear: they are sensitive to phase correlations, not just spatial frequency content. That is, the behavior of V1 neurons departs from that of linear-nonlinear cascades with standard modulatory mechanisms in a qualitative manner: even relatively simple stimuli evoke responses that imply complex spatial nonlinearities. The presence of these findings in the input layers suggests that these nonlinearities act in a feedback fashion.

Complex Cells Increase Their Phase Sensitivity at Low Contrasts and Following Adaptation

One of the best-known dichotomies in neuroscience is the division of neurons in the mammalian primary visual cortex into simple and complex cells. Simple cells have receptive fields with separate on and off subregions and give phase-sensitive responses to moving gratings, whereas complex cells have uniform receptive fields and are phase invariant. The phase sensitivity of a cell is calculated as the ratio of the first Fourier coefficient ( F1) to the mean time-average ( F0) of the response to moving sinusoidal gratings at 100% contrast. Cells are then classified as simple ( F1/ F0>1) or complex ( F1/ F0<1). We manipulated cell responses by changing the stimulus contrast or through adaptation. The F1/ F0ratios of cells defined as complex at 100% contrast increased at low contrasts and following adaptation. Conversely, the F1/ F0ratios remained constant for cells defined as simple at 100% contrast. The latter cell type was primarily located in thalamorecipient layers 4 and 6. Many cells initially classified as complex exhibit F1/ F0>1 at low contrasts and after adaptation (particularly in layer 4). The results are consistent with the spike-threshold hypothesis, which suggests that the division of cells into two types arises from the nonlinear interaction of spike threshold with membrane potential responses.

Speed dependence of tuning to one-dimensional features in V1

Using drifting compound grating stimuli matched in energy and frequency spectrum, we previously showed that neurons in the primary visual cortex (V1) were tuned to line-like, edge-like, and intermediate one-dimensional features. Because these compound grating stimuli were drifting, allowing for potential interaction between shape and motion, we examine here the dependence of V1 feature tuning on drift speed. We find that the feature selectivity and specificity of individual V1 neurons strongly depend on speed. A simple model explains these observations in terms of an interaction between linear filtering by the receptive field and the static nonlinearity of spike threshold, embedded in a recurrent network. Although the speed-dependent behaviors in single V1 neurons preclude their acting as extractors of one-dimensional features, the population as a whole retains a representation of a full suite of features.

Heterogeneity in the responses of adjacent neurons to natural stimuli in cat striate cortex

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.

'Simplification' of responses of complex cells in cat striate cortex: suppressive surrounds and 'feedback' inactivation

In mammalian striate cortex (V1), two distinct functional classes of neurones, the so-called simple and complex cells, are routinely distinguished. They can be quantitatively differentiated from each other on the basis of the ratio between the phase-variant (F1) component and the mean firing rate (F0) of spike responses to luminance-modulated sinusoidal gratings (simple, F1/F0 > 1; complex, F1/F0 < 1). We investigated how recurrent cortico-cortical connections affect the spatial phase-variance of responses of V1 cells in the cat. F1/F0 ratios of the responses to optimally oriented drifting sine-wave gratings covering the classical receptive field (CRF) of single V1 cells were compared to those of: (1) responses to gratings covering the CRFs combined with gratings of different orientations presented to the 'silent' surrounds; and (2) responses to CRF stimulation during reversible inactivation of postero-temporal visual (PTV) cortex. For complex cells, the relative strength of the silent surround suppression on CRF-driven responses was positively correlated with the extent of increases in F1/F0 ratios. Inactivation of PTV cortex increased F1/F0 ratios of CRF-driven responses of complex cells only. Overall, activation of suppressive surrounds or inactivation of PTV 'converted' substantial proportions (50 and 30%, respectively) of complex cells into simple-like cells (F1/F0 > 1). Thus, the simple-complex distinction depends, at least partly, on information coming from the silent surrounds and/or feedback from 'higher-order' cortices. These results support the idea that simple and complex cells belong to the same basic cortical circuit and the spatial phase-variance of their responses depends on the relative strength of different synaptic inputs.

Phase noise and the classification of natural images

We measured the effect of global phase manipulations on a rapid animal categorization task. The Fourier spectra of our images of natural scenes were manipulated by adding zero-mean random phase noise at all spatial frequencies. The phase noise was the independent variable, uniformly and symmetrically distributed between 0 degrees and +/-180 degrees . Subjects were remarkably resistant to phase noise. Even with +/-120 degrees phase noise subjects were still performing at 75% correct. The high resistance of the subjects' animal categorization rate to phase noise suggests that the visual system is highly robust to such random image changes. The proportion of correct answers closely followed the correlation between original and the phase noise-distorted images. Animal detection rate was higher when the same task was performed with contrast reduced versions of the same natural images, at contrasts where the contrast reduction mimicked that resulting from our phase randomization. Since the subjects' categorization rate was better in the contrast experiment, reduction of local contrast alone cannot explain the performance in the phase noise experiment. This result obtained with natural images differs from those obtained for simple sinusoidal stimuli were performance changes due to phase changes are attributed to local contrast changes only. Thus the global phase-change accompanying disruption of image structure such as edges and object boundaries at different spatial scales reduces object classification over and above the performance deficit resulting from reducing contrast. Additional color information improves the categorization performance by 2%.

A natural approach to studying vision

An ultimate goal of systems neuroscience is to understand how sensory stimuli encountered in the natural environment are processed by neural circuits. Achieving this goal requires knowledge of both the characteristics of natural stimuli and the response properties of sensory neurons under natural stimulation. Most of our current notions of sensory processing have come from experiments using simple, parametric stimulus sets. However, a growing number of researchers have begun to question whether this approach alone is sufficient for understanding the real-life sensory tasks performed by the organism. Here, focusing on the early visual pathway, we argue that the use of natural stimuli is vital for advancing our understanding of sensory processing.

Spike train metrics

Quantifying similarity and dissimilarity of spike trains is an important requisite for understanding neural codes. Spike metrics constitute a class of approaches to this problem. In contrast to most signal-processing methods, spike metrics operate on time series of all-or-none events, and are, thus, particularly appropriate for extracellularly recorded neural signals. The spike metric approach can be extended to multineuronal recordings, mitigating the 'curse of dimensionality' typically associated with analyses of multivariate data. Spike metrics have been usefully applied to the analysis of neural coding in a variety of systems, including vision, audition, olfaction, taste and electric sense.

Cortical sensitivity to visual features in natural scenes

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.

Responses of V1 neurons to two-dimensional hermite functions

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.

Spatial structure of complex cell receptive fields measured with natural images

Neuronal receptive fields (RFs) play crucial roles in visual processing. While the linear RFs of early neurons have been well studied, RFs of cortical complex cells are nonlinear and therefore difficult to characterize, especially in the context of natural stimuli. In this study, we used a nonlinear technique to compute the RFs of complex cells from their responses to natural images. We found that each RF is well described by a small number of subunits, which are oriented, localized, and bandpass. These subunits contribute to neuronal responses in a contrast-dependent, polarity-invariant manner, and they can largely predict the orientation and spatial frequency tuning of the cell. Although the RF structures measured with natural images were similar to those measured with random stimuli, natural images were more effective for driving complex cells, thus facilitating rapid identification of the subunits. The subunit RF model provides a useful basis for understanding cortical processing of natural stimuli.

Principal and independent components of macaque vocalizations: constructing stimuli to probe high-level sensory processing

Neurons in high-level sensory cortical areas respond to complex features in sensory stimuli. Feature elimination is a useful technique for studying these responses. In this approach, a complex stimulus, which evokes a neuronal response, is simplified, and if the cell responds to the reduced stimulus, it is considered selective for the remaining features. We have developed a feature-elimination technique that uses either the principal or the independent components of a stimulus to define a subset of features, to which a neuron might be sensitive. The original stimulus can be filtered using these components, resulting in a stimulus that retains only a fraction of the features present in the original. We demonstrate the use of this technique on macaque vocalizations, an important class of stimuli being used to study auditory function in awake, behaving primate experiments. We show that principal-component analysis extracts features that are closely related to the dominant Fourier components of the stimuli, often called formants in the study of speech perception. Conversely, independent-component analysis extracts features that preserve the relative phase across a set of harmonically related frequencies. We have used several statistical techniques to explore the original and filtered stimuli, as well as the components extracted by each technique. This novel approach provides a powerful method for determining the essential features within complex stimuli that activate higher-order sensory neurons.

Non-Euclidean properties of spike train metric spaces

Quantifying the dissimilarity (or distance) between two sequences is essential to the study of action potential (spike) trains in neuroscience and genetic sequences in molecular biology. In neuroscience, traditional methods for sequence comparisons rely on techniques appropriate for multivariate data, which typically assume that the space of sequences is intrinsically Euclidean. More recently, metrics that do not make this assumption have been introduced for comparison of neural activity patterns. These metrics have a formal resemblance to those used in the comparison of genetic sequences. Yet the relationship between such metrics and the traditional Euclidean distances has remained unclear. We show, both analytically and computationally, that the geometries associated with metric spaces of event sequences are intrinsically non-Euclidean. Our results demonstrate that metric spaces enrich the study of neural activity patterns, since accounting for perceptual spaces requires a non-Euclidean geometry.

Neural coding of spatial phase in V1 of the macaque monkey

We examine the responses of single neurons and pairs of neurons, simultaneously recorded with a single tetrode in the primary visual cortex of the anesthetized macaque monkey, to transient presentations of stationary gratings of varying spatial phase. Such simultaneously recorded neurons tended to have similar tuning to the phase of the grating. To determine the response features that reliably discriminate these stimuli, we use the metric-space approach extended to pairs of neurons. We find that paying attention to the times of individual spikes, at a resolution of approximately 30 ms, and keeping track of which neuron fires which spike rather than just the summed local activity contribute substantially to phase coding. The contribution is both quantitative (increasing the fidelity of phase coding) and qualitative (enabling a 2-dimensional "response space" that corresponds to the spatial phase cycle). We use a novel approach, the extraction of "temporal profiles" from the metric space analysis, to interpret and compare temporal coding across neurons. Temporal profiles were remarkably consistent across a large subset of neurons. This consistency indicates that simple mechanisms (e.g., comparing the size of the transient and sustained components of the response) allow the temporal contribution to phase coding to be decoded.

Fast algorithm for the metric-space analysis of simultaneous responses of multiple single neurons

Spike train metrics quantify the notion of dissimilarity, or distance, between spike trains and between multineuronal responses (J. Neurophysiol. 76 (1996) 1310, Network 8 (1997) 127). We present a new algorithm for the implementation of a metric based on the timing of individual spikes and on their neurons of origin. This algorithm surpasses the earlier approach in speed by a factor that grows exponentially with the number of neurons, substantially extending the applicability of metric space methods to the study of coding in larger neuronal populations.