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Depth from
rotation? (movie here) This illusion requires
observers with two eyes, stereo vision, and the ability to free-fuse. If you’re such an observer, run the
movie (in ‘loop’ mode), fuse the images (convergently
or divergently; it doesn’t matter), and fixate either the grating in
the middle or the plaid annulus. What
do you see? What you should see is that
the grating rotates to and fro. That
much is obvious. More subtly, the
grating also moves forward and back in depth.
You’ll see the grating in front of the annulus, then behind it,
in phase with the rotation. (If you
can’t see this, it’s probably because the plaid is diplopic when
you fixate the grating; try fixating the plaid instead of the grating and attend
to the grating as it rotates. Also,
change your distance from the screen.) So, what’s the
deal? Why is this an
illusion? It’s because, despite
all appearances, despite what you see in front of your very eyes, despite
everything logic demands you to believe, there’s nothing moving in this
movie! Just kidding! Ha, ha. But there is, cross my
heart, no change in disparity in this movie.
The depth modulation is a stereo effect; you won’t see it monocularly. And
it depends on relative disparity. And
the effect is a change in perceived depth over time. But there is no change in disparity
anywhere in the display. So, why do you see depth
changes? The plaid’s two
components, oriented at 45° and 135°, have different disparities (nominally,
one has positive disparity and the other negative disparity; this is the case
when you fixate on the central grating, whose disparity is zero). But the components of a stereo plaid, like
those of a moving plaid, cohere. They
cohere in depth, forming a plaid that inhabits a single depth plane (though
its components, presented separately, are seen in very different
planes). The plaid’s disparity
is given by the intersection-of-constraints calculation (its direction here
is vertical). Now, when the central
grating is at the ends of its rotational excursion, it’s parallel to
either the 45° component or the 135° component. And it turns out that this matters—it
makes the illusion go—because relative disparity is orientation
specific. We cannot compute the
relative disparity between stimuli with very different orientations, only
that between stimuli of similar orientations.
So, when the central grating, with a disparity of zero, is parallel to
the plaid’s component that has positive disparity, the relative
disparity between them tells us that the grating is on the near side of the
plaid. When the grating completes its
rotation and is parallel to the plaid’s component with negative
disparity, its disparity is relatively positive and it’s seen on the
far side of the plaid. The other,
non-parallel, component doesn’t matter, regardless of its disparity,
because its orientation is very different from the orientation of the
grating. What does this tell us
about our visual systems? It tells us
something about the fine structure of the stereo computation. It tells us that our visual system computes
relative disparity within orientation channels. And the relative disparities that matter
are those of patterns’ one-dimensional components. For further details, see: Farell, B. (2006). Orientation-specific computation in
stereoscopic vision. J. Neurosci., 26(36), 9098-9106. |