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Space and time in visual context

An Erratum to this article was published on 01 November 2007

Key Points

  • Visual processing of a feature or object is powerfully affected by its context, that is, its spatial and temporal neighbourhood. It is important to achieve a comprehensive understanding of how and why this is the case, from neural, perceptual and functional perspectives. We focus on tilt as a paradigmatic example, given the large body of historical and recent literature. We also emphasize similarities with other visual attributes and sensory domains.

  • Spatial and temporal context have often been treated separately in the literature. Nevertheless, despite quite different demands on their neural substrate (for example, memory for temporal context, but horizontal intraareal interactions for spatial context), they are closely tied, both functionally and in terms of their impact on vision.

  • Spatial and temporal context exhibit strikingly similar effects in many experimental circumstances. Psychophysical effects include perceptual biases, which are apparent in illusions and after-effects; physiological effects include suppression of the mean firing rate and changes in tuning curves.

  • Mechanistic population models of orientation tuning suggest a link between changes at the neural population level and perceptual changes. In these models, perceptual biases arise due to the 'coding catastrophe' (or decoding ambiguity): downstream mechanisms are unaware of the changes in tuning caused by contextual stimuli, and therefore err when such changes take place.

  • From a functional viewpoint, two main questions exist. First, why are these biases so similar for spatial and temporal contexts; and second, why do contextual stimuli induce perceptual biases at all? In answer to the first question, the obvious source of similarities is the shared statistical regularity in natural visual scenes, with a small patch of image in a scene being typically similar (in properties such as orientation) to patches observed simultaneously in nearby spatial regions and to patches that were recently observed.

  • The reason behind the functional benefit of contextual biases is more contentious: we discuss exciting directions in recent literature, focusing on computational frameworks of efficient coding and Bayesian inference. Natural scene statistics over space and time can inform both of the above frameworks.

  • These directions have the potential to unify our understanding of spatial and temporal contextual processing. Such unified approaches also highlight the many gaps in our current understanding and suggest future perspectives for physiological, psychophysical and computational investigations.


No sensory stimulus is an island unto itself; rather, it can only properly be interpreted in light of the stimuli that surround it in space and time. This can result in entertaining illusions and puzzling results in psychological and neurophysiological experiments. We concentrate on perhaps the best studied test case, namely orientation or tilt, which gives rise to the notorious tilt illusion and the adaptation tilt after-effect. We review the empirical literature and discuss the computational and statistical ideas that are battling to explain these conundrums, and thereby gain favour as more general accounts of cortical processing.

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Figure 1: Examples of contextual tilt.
Figure 2: Example experimental data for spatial and temporal context effects.
Figure 3: Mechanistic population model for spatial and temporal context.
Figure 4: Statistics of natural movies for time and space.
Figure 5: Correlation within a tuning curve population model.


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This work was funded by the Howard Hughes Medical Institute (O.S.), the Gatsby Charitable Foundation (A.H., P.D.), the Biotechnology and Biological Sciences Research Council, the Engineering and Physical Sciences Research Council and the Wellcome Trust (P.D). We are very grateful to C. Clifford, A. Kohn, A. Stocker and J. Solomon for comments on the manuscript and discussion, and to T. Sejnowski and E. Simoncelli for discussion.

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A rapid eye movement (with speeds of up to 800° per second) that brings the point of maximal visual acuity — the fovea — to the image of interest.

Orientation tuning

The property of visual neurons to only respond to stimuli (images) with a certain orientation or tilt (for example, vertically orientated bars).

Tuning curve

A tuning curve to a feature (such as orientation) is the curve describing the average response of a neuron as a function of the feature values.

Rotation invariance

When each input angle is treated in the same way; that is, when the input rotates, the output rotates.

Discrimination threshold

The smallest difference between two visual stimuli (for example, vertical versus tilted bars) that can reliably (that is, with a given probability of error) be reported by an observer.

Population code

Sensory events that are encoded by neuronal populations rather than by individual neurons.

Poisson spiking neuron

A simple model neuron for which the number of spikes emitted in a given time is Poisson distributed about a mean firing rate. Spikes are assumed to be independent both in time and across neurons.

Fisher information

Measures how quickly the likelihood of the population responses changes with stimulus parameters, and thereby provides a decoder-independent quantification of the potential accuracy of decoding (the Cramér-Rao lower bound).

Mean square estimation error

Estimation error can be quantified by the squared difference between the (population-based) estimate and its true value. The mean of this over trials is one measure of the accuracy of an estimate.

Efficient coding

When information is coded in an efficient and non-redundant manner, for instance, when the outputs of neurons in the population are statistically independent.

Bayes (Bayesian approach)

A statistical method that allows the use of prior information to evaluate the posterior probabilities of different hypotheses.

Kalman filter

A recursive formulation that estimates the present outcome dynamically in time, based on prior information and noisy measurements.

Markov random field

An undirected graphical model that represents statistical dependencies between a set of variables. The Markov property is that a variable associated with one location in the image is only directly influenced by variables associated with neighbouring locations.

Linear (or second order) de-correlation

Random variables are de-correlated if the off-diagonal elements of their covariance matrix (representing the second order statistics) are equal to zero. De-correlation is in general a weaker requirement than independence, because higher order statistics may still exhibit dependencies.

Divisive normalization

Strictly speaking, when (for example) sum output across a population is kept constant by dividing each response by a (trial-dependent) quantity. Looser versions model gain control mechanisms in V1 and elsewhere.

Gain control

When the (for example) sum output across a population is used to adjust the gain to an appropriate level for a range of input signal levels, with higher signal levels resulting in higher gain and reduced response. Stricter versions are denoted divisive normalization.

anti-Hebbian learning

A learning rule whereby whenever two units or neurons are active simultaneously, the effective connection between them becomes less excitatory or more inhibitory.

Bayesian inference

Inference according to the standard laws of probability, notably including Bayes theorem. Conclusions are based on posterior distributions arising from combining observations (as probabilistic likelihoods) with prior information.


A probability distribution that captures the belief or expectation about a variable, in the absence of observations or evidence. Here, priors are specified through personal or evolutionary experience of environmental statistics.

Decision-theoretic loss function

The loss (or cost) associated with a particular decision about a quantity as a function of its true values. Bayesian decision theory suggests that choices should be made by minimizing expected losses under posterior distributions.

Gibson's normalization

The hypothesis that replusive biases arise in the orientation domain due to a long-run prior favouring absolute cardinal axes.

Power law synapses

A synaptic adaptation that is (time) scale invariant; for example, having the same response shape at multiple timescales. This is in contrast to an exponential adaptation process with a single time constant.

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Schwartz, O., Hsu, A. & Dayan, P. Space and time in visual context. Nat Rev Neurosci 8, 522–535 (2007).

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