Transcript Stereopsis

Binocular Vision Outline
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Convergence of the eye as a cue to depth
Binocular disparity as a cue to depth
Limitations on stereopsis
The computational problem of stereopsis
Binocular Convergence
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Left retinal
image
Right retinal
image
Binocular Disparity
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D=a-b
A.
B.
C.
D.
Horopter
Positive disparities =
Uncrossed disparities
Negative disparities =
Crossed disparities
Stereo fusion
• Objects are “fused” when brain interprets
disparate images in the two eyes as being
the same object and perceives the depth of
the objects
Stereo fusion
• Objects are “fused” when brain interprets
disparate images in the two eyes as being
the same object and perceives the depth of
the objects
• When disparity gets too large
– Double vision,
– or brain ignores input from one eye
Panum’s fusional area
• Range of depth’s that can be “fused”
Panum’s
fusional area
Size of Panum’s fusional area
• Disparity limit = 10 - 60 minutes of arc
Size of Panum’s fusional area
• Foveal Disparity limit = 10 - 60 minutes
– for fixation at arm’s length, depth range = five
inches or so
Size of Panum’s fusional area
• Foveal Disparity limit = 10 - 60 minutes
– for fixation at arm’s length, depth range = five
inches or so
– limit increases with “size” of texture
Size of Panum’s fusional area
• Foveal Disparity limit = 10 - 60 minutes
– for fixation at arm’s length, depth range = five
inches or so
– limit increases with “size” of texture
– limit is larger for slowly moving objects
Size of Panum’s fusional area
• Foveal Disparity limit = 10 - 60 minutes
– for fixation at arm’s length, depth range = five
inches or so
– limit increases with “size” of texture
– limit is larger for slowly moving objects
• Limit is larger in periphery than in fovea
– As large as 3 degrees
Arrangement of
wires
Fiz at ion Wire
Arrangement of
wires
Displaced Wire
Virtual
world
Fizat ion Wire
Displaced Wire
Comput er Screen
Occluder
Front view of
comput er display
Disparity acuity
• Disparity acuity in fovea - as small as .05
minutes of arc.
Disparity acuity
• Disparity acuity in fovea - as small as .05
minutes of arc
– depth resolution = .036 cm at arm’s length
Disparity acuity
• Disparity acuity in fovea - as small as .05
minutes of arc
– depth resolution = .036 cm at arm’s length
• Acuity is much better in fovea than in
periphery
Why fovea/periphery differences
• Range of disparities in natural scenes.
• Fovea - high depth acuity.
• Periphery - provides coarse information
about where to make convergence eye
movements.
Two Computational Problems of Stereopsis
• How does brain compute depth from
disparity?
• How does it know what in the left image to
match to what in the right image?
Two Computational Problems of Stereopsis
• How does brain compute depth from
disparity?
• How does it know what in the left image to
match to what in the right image?
D=a-b
∆Z
Z
D=a-b
∆Z
D = ∆Z * I / Z2
Z
I
D=a-b
∆Z
D = ∆Z * I / Z2
Z
I
D=a-b
∆Z = D * Z2 / I
• What happens to depth acuity as vergence
depth increases?
• What happens to the range of fusable depths
(Panum’s fusional area) as the vergence
depth increases?
Two Computational Problems of Stereopsis
• How does brain compute depth from
disparity?
• How does it know what in the left image to
match to what in the right image?
Midline of retinal image
Left retinal image
Right retinal image
The Correspondence Problem
- Many possible matches
for each point
The Correspondence Problem
- Why not this interpretation?
The Correspondence Problem
- Why not this interpretation?
The Correspondence Problem
- Why not this interpretation?
Solution
• Constraints on objects in the world
– objects are solid and opaque
– objects are for the most part are smooth
Solution
• Impose constraints from the world
– objects are solid
– objects are for the most part are smooth
• Matching constraints
– Uniqueness
– Ordering
The Correspondence Problem
- Why not this interpretation?
Matching Constraints
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Uniqueness
Ordering
Smoothness
Compatibility
– If no compatible parts of two images are find,
one gets binocular rivalry.
The double nail illusion
Line up two nails so that one is directly behind the other,
and you will often see three nails.
Physiology
• Many cells in V1 are disparity selective
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Tuned, zero-disparity cells
Tuned, near cells (tuned to crossed disparities)
Tuned, far cells (tuned to uncrossed disparities)
Untuned Near cells
Untuned Far cells
• Disparity tuning
– spatial offset of receptive fields for left and
right eyes.