How do we see what we see?
How do we hear what we hear?
A question that has intrigued
philosophers since the beginning of
recorded history
Early Greek Philosophers
• Democritus (ca 460 B.C.) Epicurus (341-270
B.C.). Eidola or film theory of vision.
• Objects emit particles or copies of themselves
• “For particles are continually streaming off from
surfaces of bodies, though no diminution of the
bodies is observed, because other particles take
their place. And those given off for a long time
retain the position and arrangement which their
atoms had when they formed part of the solid
bodies.”
Early Greek Philosophers
Problems with Eidola theory
•
•
•
•
•
Why isn’t matter used up?
How does the image get in the eye?
Why can’t we see in the dark?
Are copies given off in all directions?
These problems led to other theories being
proposed.
Early Greek Philosophers
Scientific progress: Problems lead to new theories
• Extramission or “visual touch” theories.
• Plato (ca 427-347 B.C). Eyes emit “visual fire”
which coalesces with daylight to contact objects
and returns an impression of the object.
• Problems with “visual touch” theories.
• Exactly what is emitted?
• How does it return impressions?
• Why can’t you see in the dark?
Early Greek Philosophers
Extramission theory: Theoretical development
• Euclid’s (300 B.C.) geometric theory of vision.
Assume
• That the rectilinear rays proceeding from the eye
diverge indefinitely;
• That the figure contained by a set of visual rays is
a cone of which the vertex is at the eye and the
base at the surface of the object seen;
• That those things are seen upon which visual rays
fall and those things are not seen upon which
visual rays do not fall.
Early Greek Philosophers
Extramission theory: Theoretical development
• That things seen under a larger angle appear larger,
those under a smaller angle appear smaller, and
those under equal angles appear equal;
• That things seen by higher visual rays appear
higher, and things seen by lower rays appear lower;
• Etc.
Extramission theory: Problems led to modifications
• Galen’s answer (ca. 129-199 A.D.) as to why light
is needed.
• “When it (the air) has been illuminated by the sun,
it is already an instrument of vision of the same
description as the pneuma arriving from the brain;
but until it is illuminated it does not turn into a
sympathetic instrument in accordance with the
change effected by the outflow of pneuma into it.
After the fall of the Roman Empire
• No further developments that we know of
until;
• The work of the Islamic scholars
• Al-Kinde (9th century) took elements of
extramission theory and Euclid’s geometry
and fused them into a coherent theory of
vision.
• Alhazen (969-1039 A.D.), however, took
visual theory to a whole new level.
The Islamic Scholars: Alhazen
• Proposed a new intromission theory.
• Took Euclid and turned it around.
• Points on a body radiate light in all
directions.
• “From each point of every colored body,
illuminated by any light, issue light and
color along every straight line that can be
drawn from that point.
The Islamic Scholars: Alhazen
• Only those rays that enter the pupil of the
eye produce a visual impression.
• One problem.
• Superfluity of rays problem.
The lens is the seat of vision.
Rays from different points in space fall on same point on
the lens.
The Islamic Scholars: Alhazen
Knew about refraction.
Hypothesized only non-refracted rays penetrate the eye
One point in space corresponds to one point on the lens
Alhazen theory was not overturned until the
work of Kepler
• Kepler (1571-1630) worked out the
geometric optics of the eye.
• Light is reflected in all directions from each
point on a non-mirror surface.
• He traced the rays and proved that an
upside-down and right-left reversed image
should appear on the retina.
Thus, some 20 centuries later we
finally solved how images were
sensed by the eye
• But now we had new problems to solve.
• Images on the retina change with distance
• Images on the retina change with
orientation
• Images on the retina change with angle of
view
New problem: Superfluity of
Images
• For each object there are potentially an
infinite number of images that can be
formed.
• How does the observer recognize individual
object when the number of images is
infinite?
• Do they have an infinite number of
templates to match against the image?
To answer this problem we need
to consider how signals are
processed
• How do the eye and brain solve the
superfluity of images problem?.
• Question: How much information do we
need to characterize an image?
4

2
Cos[ ( x  y )]
4

2
Cos[ ( x  y )]

4

2
Cos[ ( x  y )]
+
+
=
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
=
Cos[ (ix  ky)]
 2 
, (i, k , odd )
 i   n k 1
ik
4
n
n
n=3
n=3
n=7
n=3
n=7
n = 15
n=3
n = 31
n=7
n = 15
n=3
n=7
n = 31
n = 61
n = 15
n=3
n=7
n = 31
n = 61
n = 15
checkerboard
Figure 4.4
The human eye, a simplified view.
Figure 4.2
The lens gets its name from Latin for lentil, referring to its shape—an
appropriate choice, as this cross section of the eye shows. The names of
other parts of the eye also refer to their appearance.
Figure 4.6
The retina lies behind the vitreous humor, which is the jelly-like substance that fills the
eyeball. Note that light does not fall directly on the rods and cones. It must first pass
through the outer layers of the retina, made up of additional nerve cells. Only about one
half of the light falling on the front of the eye reaches the rods and cones—testimony to
the eye’s amazing light sensitivity. The rods and cones are much smaller than implied
here. The smallest receptors are 1 micron (one millionth of a meter) wide. The lower left
photograph shows rods and cones as seen through an electron microscope. In the
photograph the cones are colored green and the rods blue.