Computational Model of Neurons in Visual Area MT
Electrophysiological studies indicate that neurons in the Middle
Temporal (MT) area of the primate brain are selective for the velocity
(both direction and speed) of visual stimuli. We've developed a descriptive computational model of MT
physiology, in which local image velocities are represented via the
distribution of MT neuronal responses. The computation is performed
in two stages of identical architecture, corresponding to neurons in
cortical areas V1 and MT. Each stage computes a weighted linear sum
of inputs, followed by rectification and divisive normalization. The
output of the model corresponds to the steady-state firing rates of a
population of MT neurons, which form a distributed representation
(population encoding) of image velocity for each local spatial region
of the visual stimulus. One can think of the distributed set of responses
as representing a probability density over local image velocity.
The model accounts for a wide range of
physiological data.
Model Structure
The diagram shows the essential aspects of the model. In the first
(V1) stage, each neuron computes an inner product of the image
contrast with a space-time oriented receptive field. Our receptive
fields are directional third derivatives of a Gaussian. The use of
directional derivatives is a fundamental aspect of the model, as it
allows us to interpolate responses at arbitrary space-time
orientations from a fairly small (28) fixed population of V1 neurons.
[NOTE: The
Gaussian is chosen for simplicity: alternative choices would lead to
beneficial properties such as causality or spatio-temporal
separability, without fundamentally changing the steady-state responses].
These linear outputs are half-squared (halfwave-rectified and
squared), and then divisively normalized. The normalization factor is
a sum of a semisaturation constant (sigma) and the responses of
neurons at all space-time orientations, and within a local spatial
neighborhood.
The second (MT) stage of the model performs a summation over V1
afferents consistent with a given pattern velocity. These are
illustrated in the spatio-temporal frequency domain. This is
essentially a neural implementation of the
"intersection-of-constraints" construction (see references).
Note: this is a model of steady-state responses to
spatio-temporally homogeneous stimuli.
Software
(10/14/05)
A matlab implementation of the model is now (finally!!)
available here.
A brief description may be found in the
README file, and
updates and changes are listed in the
ChangeLog file.
An older software implementation for Macintosh OS 9 on non-fpu
68000 machines (circa 1995), is also available. A brief description
may be found in the README file.
PostScript Description & Documentation (2.2 M)
is also available.
Macintosh Executable (1.7M).
Partial List of References
This Model
- N C Rust, V Mante, E P Simoncelli and J A Movshon,
How MT cells analyze the motion of visual patterns
Nature Neuroscience, 9(11):1421-1431, Nov 2006.
Abstract
/
Reprint
- E P Simoncelli and D J Heeger,
A Model of Neuronal Responses in Visual Area MT.
Vision Research, 38(5), pp 743-761, 1998.
Abstract
/
Reprint (1.9M, pdf)
/
Manuscript (444k, ps.gz)
- E P Simoncelli, W D Bair, J R Cavanaugh, and J A Movshon.
Testing and Refining a Computational Model of Neural
Responses in Area MT. ARVO, 1996.
Abstract
/
Presentation slides (pdf)
- D J Heeger, E P Simoncelli, and J A Movshon.
Computational Models of Cortical Visual Processing
Proc. National Academy of Science.
93:623-627. January, 1996.
Abstract
/
Reprint (158k, pdf)
/
TextOnly PostScript (70k)
- E P Simoncelli and D J Heeger.
A Velocity-representation Model for MT Cells. ARVO, 1994.
Abstract
- Eero P Simoncelli.
Distributed Analysis and Representation of Visual Motion.
PhD thesis, Massachusetts Institute of Technology, Department of
Electrical Engineering and Computer Science,
Cambridge MA, January 1993.
Abstract /
Full PostScript (1.7M)
- E P Simoncelli and D J Heeger.
A Computational Model for Representation of Image Velocities.
ARVO, 1993.
Abstract
Related Computational Motion Models
- Y Weiss, E P Simoncelli and E H Adelson
Motion illusions as optimal percepts.
Nature:Neuroscience, 5(6): 598-604, June 2002,
[abstract/reprint]
- Y Weiss and E H Adelson.
Slow and smooth: a Bayesian theory for the combination of
local motion signals in human vision.
MIT A.I. Lab Memo No. 1624, C.B.C.L. Paper No. 158, February 1998.
- S J Nowlan and T J Sejnowski.
A Selection Model for Motion Processing in Area MT of
Primates.
Journal of Neuroscience, vol 15, pp 1195-1214, 1995.
- D J Heeger and E P Simoncelli.
Model of Visual Motion Sensing.
Chapter 19 in Spatial Vision in Humans and Robots, ed
L Harris and M Jenkin. Cambridge University Press, 1994,
[abstract/reprint]
- J A Smith and N M Grzywacz.
A Local Model for Transparent Motion Based on Spatio-temporal
Filtering.
Computation and Neural Systems, ed. F H Eeckman and J M Bower.
Kluwer Academic Press, 1993.
- M E Sereno.
Neural Computation of Pattern Motion: Modeling Stages of
Motion Anaysis in the Primate Visual Cortex.
MIT Press, 1993.
- E P Simoncelli and D J Heeger.
A computational Model for Perception of
Two-dimensional Pattern Velocities.
ARVO, 1992.
[abstract/reprint]
- H R Wilson and V P Ferrara and C Yo.
A Psychophysically Motivated Model for Two-dimensional Motion
Perception.
Visual Neuroscience, vol 9, pp 79-97, 1992.
- N M Grzywacz and A L Yuille.
A Model for the Estimate of Local Image Velocity by Cells in
the Visual Cortex.
Proc. Royal Society of London A, vol 239, pp 129-161, 1990.
- D J Heeger.
Model for the Extraction of Image Flow.
Journal Optical Society of America, vol 4, pp 1455-1471, 1987.
- E H Adelson and J R Bergen.
Spatiotemporal Energy Models for the Perception of Motion.
Journal Optical Society of America, vol 2, pp 284-299, 1985.