The Apparatus
Seeing
Seeing in
in
Stereo
Stereo
Seeing in Stereo
It’s
It’svery
veryhard
hardtotoread
readwords
wordsififthere
there
are
aremultiple
multipleimages
imageson
onyour
yourretina
retina
Seeing in Stereo
It’s
It’svery
veryhard
hardtotoread
readwords
wordsififthere
there
are
aremultiple
multipleimages
imageson
onyour
yourretina
retina
But how many images are there on your
retinae?
Binocular Disparity
• Your eyes have a different image on each
retina
– hold pen at arms length and fixate the spot
– how many pens do you see?
– which pen matches which eye?
Binocular Disparity
• Your eyes have a different image on each
retina
– now fixate the pen
– how many spots do you see?
– which spot matches which eye?
Binocular Disparity
• Binocular disparity is the difference
between the two images
Binocular Disparity
• Binocular disparity is the difference
between the two images
• Disparity depends on where the
object is relative to the fixation point:
– objects closer than fixation project
images that “cross”
– objects farther than fixation project
images that do not “cross”
Binocular Disparity
• Corresponding retinal points
Binocular Disparity
• Points in space that have corresponding
retinal points define a plane called the
horopter
The Horopter
Binocular Disparity
• Points not on the horopter will be
disparate on the retina (they project
images onto non-corresponding
points)
Binocular Disparity
• Points not on the horopter will be
disparate on the retina (they project
images onto non-corresponding
points)
• The nature of the disparity depends
on where they are relative to the
horopter
Binocular Disparity
• points nearer than
horopter have crossed
disparity
• points farther than
horopter have
uncrossed disparity
The Horopter
Binocular Disparity
• Why don’t we see double vision?
Binocular Disparity
• Why don’t we see double vision?
• Images with a small enough disparity
are fused into a single image
• The region over which these are
fused is called Panum’s Area
Now on to Magic Eye
Stereograms
Stereoscopes
•
seeing depth requires “only” two
different images on the retina
•
this could be accomplished by an optical
device that projects separate images
into the two eyes
Stereoscopes
•
seeing depth requires “only” two
different images on the retina
•
this could be accomplished by an optical
device that projects separate images
into the two eyes
•
Note that some of you can’t see in
stereo because you have amblyopia
–
•
Brain failed to learn to use one eye’s image
during development
You might have amblyopia if:
–
–
–
you had a strabismus or “lazy eye”
you had poor vision in one eye as a child
you had to wear a patch over one eye when
you were a child
Stereoscopes
•
3D movies are just tricky stereoscopes in that the
lenses allow one image to enter one eye and the
other image to enter the other eye
•
Difference is that images are superposed on the
screen
Stereoscopes
Divider
Left Eye
Right Eye
•Right eye sees face to the
right; left eye sees face to the
left therefore:
uncrossed disparity
•Face appears behind the
square
Stereoscopes
Divider
Left Eye
Right Eye
What would you see?
Stereoscopes
Divider
Left Eye
Right Eye
•Right eye sees face to the
left; left eye sees face to the
right therefore:
crossed disparity
•Face appears in front of
square
Autostereograms
• Optically separate images aren’t
needed
Autostereograms
• Optically separate images aren’t
needed
• It’s possible to create disparity by
misadjusting the vergence of your eyes
Autostereograms
• WARNING! Tricky stuff coming in the
next slides
• Keep definitions of crossed/uncrossed
disparity and crossed/uncrossed
convergence separate in your mind!
Autostereograms
What would happen if you remove the
divider of a stereoscope?
•Convergence is on a point
at the same distance as the
images
•Boxes and faces are on the
horopter
•How many boxes would you
see?
boxes and faces are on the horopter
Autostereograms
Now cross your eyes:
•right-eye line of sight crosses lefteye line of sight in front of image
(crossed convergence)
•each retina is now pointed at the
opposite box
•How many boxes would you see?
crossed convergence
•What would happen to the face?
Autostereograms
Now cross your eyes:
•right-eye line of sight crosses lefteye line of sight in front of image
(crossed convergence)
•each retina is now pointed at the
opposite box
•How many boxes would you see?
crossed convergence
•What would happen to the face?
Note the difference between
convergence and disparity
Autostereograms
This is what your brain would
get from your eyes:
Autostereograms
•There would be three boxes
•middle box: right eye sees face
shifted to right; left eye sees face
shifted to left therefore:
uncrossed disparity
•Face in the middle box appears
behind square
crossed convergence
Autostereograms
What would happen if the convergence was
uncrossed?
Autostereograms
What would happen if the faces were switched relative
to the boxes?
Autostereograms
• Switching your convergence will switch the
direction of depth (in/out)
• Switching the elements of the image left/right
will switch the direction of depth (in/out)
• Notice the disconnection between
convergence and disparity!
Autostereograms
• one doesn’t even need two different
images!
Autostereograms
RIGHT EYE
LEFT EYE
Faces fuse
Convergence tells your brain that the plane of the image
is farther away than it really is
Autostereograms
• Uneven spacing between identical
objects in a single picture can appear as
disparity if the angle of convergence is
inappropriate
Autostereograms
• Uneven spacing between identical
objects in a single picture can appear as
disparity if the angle of convergence is
inappropriate
• TRICK: Seeing depth in
autostereograms requires you to
suppress the reflexive coordination
between convergence and
accommodation
Autostereograms
Any repeating objects that have a spacing different from the background will
have either crossed or uncrossed disparity
RIGHT EYE
LEFT EYE
If you uncross convergence, your right eye gets these faces
shifted slightly to left, left eye gets them shifted to right =
CROSSED DISPARITY
What would you see?
Autostereograms
Any repeating objects that have a spacing difference from the background
will have either crossed or uncrossed disparity
RIGHT EYE
LEFT EYE
If you uncross convergence, right eye gets these faces shifted
slightly to right, left eye gets them shifted to left =
UNCROSSED DISPARITY
What would you see?
Autostereograms
• by adjusting the disparity at different parts of
the image (with a computer usually) one can
make shapes that emerge or recede in depth
“Magic Eye” Stereograms
• Usually viewed with uncrossed convergence
• Imagine gazing farther than the surface (let your eyes
“relax”)
• Now try to notice objects or forms in the blurriness
• As you become aware of shapes, try to focus
(accommodate) the plane of the image without
converging your eyes
Autostereograms
Autostereograms
Autostereograms