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  • Review Article
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Velocity computation in the primate visual system

Key Points

  • The ability of primates to sense the direction and speed (together, the velocity) of moving objects depends on an elaborate sequence of computations that have been investigated in psychological, biological and theoretical studies.

  • Two cortical areas are central to this process: area V1 (the primary visual cortex) and area MT (the middle temporal area). V1 neurons are thought to measure image velocity at high spatial resolution and feed the results to area MT, which then combines the inputs to compute the overall velocity of a moving pattern.

  • The integration by the MT neurons is needed to overcome the ambiguity of the local (point-wise) velocity samples taken by the V1 neurons. This ambiguity is called the aperture problem, although fundamentally the problem stems from the sampling mechanism and not from the aperture itself.

  • Several mathematical models have been proposed to explain how the visual system measures velocity at each point in the image (local-velocity sampling). These include: gradient models, which compute the spatial and temporal intensity derivatives at each point in the image; Reichardt models, which sense the delay in activation of two spatially offset sensors; and spatiotemporal energy (STE) models, which detect motion energy with linear space–time filters. These models are not entirely distinct and are in fact mathematically equivalent under certain conditions.

  • Most experimental evidence supports an STE-like mechanism. In particular, a subclass of V1 cells (simple cells) behave like linear space–time filters with characteristics that match those postulated by the STE models.

  • Other theories have addressed the manner of integration of local-velocity samples by MT neurons. One idea holds that each MT neuron sums input from V1 neurons that have filter characteristics that situate them on a common plane in frequency space. Because a moving object has all its spectral energy on a single plane in frequency space, and because the orientation of this plane corresponds to the object's velocity, this 'planar summation' by the MT neuron would have the effect of tuning it for a certain object velocity.

  • A wide range of neurophysiological evidence is consistent with the above planar summation model, but no evidence establishes it directly. Other possibilities exist: in particular, there could be nonlinear transformations early in the visual system that obviate the aperture problem by tracking unambiguous elements called features. Studies are needed to directly compare these two basic mechanisms.

  • The mechanisms of pattern-velocity computation remain incompletely understood. However, the history of interplay between theory and experiment in this area has narrowed the possibilities to a small number of formally distinct ideas.

Abstract

Computational neuroscience combines theory and experiment to shed light on the principles and mechanisms of neural computation. This approach has been highly fruitful in the ongoing effort to understand velocity computation by the primate visual system. This Review describes the success of spatiotemporal-energy models in representing local-velocity detection. It shows why local-velocity measurements tend to differ from the velocity of the object as a whole. Certain cells in the middle temporal area are thought to solve this problem by combining local-velocity estimates to compute the overall pattern velocity. The Review discusses different models for how this might occur and experiments that test these models. Although no model is yet firmly established, evidence suggests that computing pattern velocity from local-velocity estimates involves simple operations in the spatiotemporal frequency domain.

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Figure 1: The aperture problem.
Figure 2: Summary of the spatiotemporal energy (STE) model.
Figure 3: A vector average (or sum) of local velocities can grossly misrepresent speed.
Figure 4: A geometric expression of the intersection of constraints (IOC) principle.
Figure 5: The Simoncelli–Heeger (S and H) model.

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Acknowledgements

We are grateful to E. Adelson, R. Born, A. Clark, G. DeAngelis, J. A. Movshon, W. Newsome, C. Pack, N. Priebe, G. Purushothaman, P. Wallisch and H. Wilson for assistance. Supported by US National Institutes of Health grants R01-EY013138 and R01-NS40690-01A1.

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Correspondence to David C. Bradley.

Glossary

Spatiotemporal frequency

A three-dimensional frequency vector (ωxyt) that specifies spatial frequencies ωx and ωy and temporal frequency ωt. The physical counterpart is a moving sinusoidal grating.

Band-pass filters

A type of linear filter that blocks low and high frequencies while allowing a certain range of intermediate frequencies to pass through.

Simple cells

V1 neurons with essentially linear properties. They act as linear space–time filters that perform the first and most basic step of motion detection. Subsequent stages (performed by complex cells and MT cells) elaborate on the outputs of simple cells.

Rectification

A sinusoidal wave (whatever its dimensions) oscillates symmetrically about a value of zero. If we take the absolute value of the negative parts, we obtain a full-wave rectified signal. If we set the negative parts to zero, we obtain a half-wave rectified signal.

Quadrature pair

A pair of sinusoidal functions of the same dimension and frequency but with phases that differ by 90°. Notably, sine and cosine functions have a quadrature relationship to each other.

Gabor function

A sinusoidal function multiplied by a Gaussian function. The sinusoid is said to be in a Gaussian 'envelope'.

Least-squares sampling

Noisy measurements often have a basic trend, such as a mean or a linear slope. If the measurements are normally distributed, then the maximum-likelihood estimate of the underlying trend is obtained by minimizing the sum of squared differences between the samples and the estimated trend. This is least-squares sampling.

Kernel

A weighting function, characteristic of a particular filter, that is used to convolve input to the system.

Response saturation

The levelling off of a neuron's response (at some maximum value) as stimulus intensity increases.

Gain normalization

In a population of neurons that are tuned for a specific parameter and that share lateral, inhibitory connections, gain normalization removes the nonspecific effect of the overall intensity of the stimulus. This allows each neuron's firing rate to reflect the strength of the image at that neuron's preferred (tuned) value.

Recurrent inhibition

Inhibition that comes from lateral connections that the inhibited cells make with neurons in the same cortical area.

Complex cells

V1 neurons that are thought to represent a stage that lies one level above simple cells in the motion-processing stream. Complex cells probably combine input from simple cells with similar frequencies but different phase tuning. They tend to be phase-insensitive.

Spike-triggered correlation and covariance

Neurons are sometimes responsive to specific combinations of stimulus properties (for example, luminance at different locations). As a result, these combinations tend to occur just before a spike. Spike-triggered correlation and covariance measure the average pattern of correlation that occurs in the moments preceding a spike.

Vector sum

Every two-dimensional velocity has two components: the horizontal velocity, Vx, and the vertical velocity, Vy. Given a set of velocity vectors, the vector sum itself has two components: one the sum of the Vx, the other the sum of the Vy. The vector average is the vector sum divided by the number of vectors.

Surround inhibition

Modulation of a visual neuron that results from the presence of a stimulus in a defined 'surround' region outside the classical receptive field of a visual neuron; as the name implies, the effect is usually but not always inhibitory.

Static nonlinearities

Static nonlinearities occur when a (temporally) linear filtering operation is performed and then the output (the firing rate) is transformed with some nonlinear mechanism, such as rectification or saturation. Static nonlinearities tend to scale the output but do not affect the overall selectivity of the mechanism.

Maximum-likelihood estimation

A process in which the probability of each of a sample of multiple random variables (such as neural firing rates for a certain stimulus) is inspected and then an overall estimate of the probability (termed the likelihood) of this set of observations is taken. Thus, one method of stimulus discrimination is to choose the stimulus for which the likelihood estimate is greatest.

Endstopping

A process in which neurons respond well to small spots but poorly to long contours that go beyond their receptive field. Endstopped neurons were first defined by Hubel and Wiesel as hypercomplex cells. The idea is that the ends of the contour tend to stop the response.

Spectral power

Taking the Fourier transform of a function gives its amplitude and its phase as a function of its frequency. The amplitude portion is called the amplitude spectrum, and the square of this is the power spectrum. The area under the power spectrum over any specific range of frequencies is called the spectral power in that frequency band.

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Bradley, D., Goyal, M. Velocity computation in the primate visual system. Nat Rev Neurosci 9, 686–695 (2008). https://doi.org/10.1038/nrn2472

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