and
the Ponzo illusion
. In each case, one portion of the figure
appears
larger than its partner, even though they are both identical in size.
Almost everyone experiences these size illusions and always in the same
way. For over a century, psychologists have been fascinated by these
illusions and have focused a great deal of research on testing
various theories concerning their origins (A good summary of
these theories is Coren and Girgus, 1978). The most
popular theory of size illusions attributes errors in perceived size to the
operation of monocular cues (Gregory 1970).
Let's call this the depth theory.
Consider the Muller-Lyer illusion,
according to the depth theory, the arrowheads on the ends of the horizontal
lines can be seen as angles formed by two intersecting surfaces. The
horizontal line represents the point of intersection, or the corner formed by
two surfaces. When the arrowheads point outward, the two surfaces are seen
as slanted toward you; when they point inward, the surfaces are seen as
receding away from you. According to the depth theory, because of the
perspective cues supplied by the arrowheads, the receding corner appears
farther away than the approaching corner. At the same time, the retinal
images of the two corners are identical in size. Now there is only one way
objects at different distances can cast
images of equal size: the farther
object must be larger. The depth theory attributes size illusion to errors
in perceived distance (Gregory 1970). The theory
is based on the observation that perceived size remains constant despite
differences in distance from the viewer and, hence, changes in the size of
the retinal image cast. In other words, perceived size is scaled in terms
of perceived distance, a process known as size
constancy. We call size constancy a scaling process
because one unit of measure (retinal image size) is
converted, or scaled, into another (perceived size).
Because the retina of the eye is mapped onto the visual cortex in a
distorted manner; the number of cortical cells devoted to a given region of
the retina varies with retinal eccentricity. The central retinal area,
especially the fovea, commands a disproportionately large number of
cortical cells. This means, for instance, that a vertical line of
constant length engages fewer and fewer cortical cells as it is imaged
farther and farther into the periphery of the retina. This relation
between retinal eccentricity and number of affected cortical cells defines
cortical magnification, which plays a key role in size constancy. For
example, Road maps typically include scales that transform centimeters into
kilometers; similarly, the visual system contains a mechanism that scales image
size
into object size. Without size scaling, one would always be confused about
the height of people, the width of doorways, the size of cars, and so on.
Size constancy seems to occur automatically. This is evidenced by the fact
that people are rarely aware of the size of their retinal image. At
present, it can only be guessed how the visual system actually performs
this scaling process of size constancy. Visual neurons, don't exhibit the
properties required of such a process. These neurons do encode size
information, by virtue of the limited spatial extent of their receptive
fields. But this information refers to the size of the retina, not the
invariant size of the object itself. If at all involved in size
perception, the activity of these neurons must somehow be integrated with
depth information before size constancy can be realized. At best,
the connection between illusion and size constancy may involve a more
global, or widespread, neuronal operation that transcends individual
neurons.
References Coren, S and Girgus, J.S (1978) Visual Illusion Handbook of Sensory
physiology Gregory, R. L. (1970) The intelligent
eye Schwartz, E. L. (1980) Computational anatomy and functional
architecture of striate cortex. Vision
Research