Second-Order Processing of Visual Information
Non-Fourier (or second-order) motion stimuli, popularized by Chubb and
Sperling (JOSA, 1988), are signals whose perceived motion is not predicted
by typical energy or gradient-based models.
These stimuli include the motion of contrast envelopes (e.g., shadows),
occlusion boundaries, the motion of illusory contours, and some illusory
motions caused by aliasing.
In an attempt to provide a unifying formal account of these stimuli and
their relation to models for non-Fourier processing, Keith Langley
(University College London) and I have examined a framework that is derived,
in part, from the definition of group velocity in wave mechanics.
We showed that many non-Fourier stimuli, when viewed as multiplicative
combinations of elementary signals, have simple descriptions in the
I have also been involved in several psychophysical studies that
are directly related to these modeling efforts.
Langley, Paul Hibbard (University of Surrey), and I reported evidence
supporting the hypothesis that contrast envelopes are processed by the
visual system after orientation- and scale-specific filtering (in
visual cortex). This showed that their perception is not an artifactual
consequence of an early nonlinearity (e.g., in photo-transduction),
which had been proposed to explain these percepts.
In binocular vision, Langley and I also found evidence for a non-Fourier
process, much like that in motion analysis. In examining this issue in
greater depth, Langley, Hibbard and I showed that non-Fourier stimuli
sometimes produce a percept of transparency, distinct in its properties
from transparent percepts that arise from a superposition of two signals.
This supported the hypothesis of a non-Fourier channel in stereo depth
One of our first hypotheses was that non-Fourier stimuli are related
to distinct physical properties of natural scenes (e.g., multiplicative
transparency and occlusions), and therefore non-Fourier processing
channels may not subserve all the same visual tasks (such as egomotion)
as conventional first-order models.
However, Rick Gurnsey, Cindy Potechin (Concordia University) and I
found that non-Fourier motion can be used to induce a percept of
In this study we found a dissociation between motion-aftereffects
(non-existent with non-Fourier stimuli) and vection as the relative
amounts of Fourier and nonFourier motion
energy were varied in the stimuli.
- Langley, K., Fleet, D.J., and Hibbard, P. (1999) Stereopsis from
contrast envelopes. Vision Research (in press)
- Langley, K., Fleet, D.J., and Hibbard, P. (1998) Linear and nonlinear
transparency in binocular vision. Proceedings of the Royal Society
(London) B, 265: 1837-1845
- Gurnsey, R., Fleet, D.J. and Potechin, C. (1998) Second-order
motions contribute to vection. Vision Research, 38(18):2801-1816
- Langley, K., Fleet, D.J., and Hibbard, P. (1996) Linear filtering
precedes nonlinear processing in early vision. Current Biology,
- Langley, K. and Fleet, D.J. (1995) A model for coherent and
multiplicatively transparent plaids. Association for Research in
Vision and Ophthalmology, Fort Lauderdale
- Fleet, D.J. and Langley, K. (1994) Computational analysis of
non-Fourier motion. Vision Research, 34(22):3057-3079
- Fleet, D.J. and Langley, K. (1994) Non-Fourier channels in stereopsis
and motion. European Conference on Visual Perception, Eindhoven
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