the human visual system - university of...
TRANSCRIPT
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The Human Visual System
Lecture 1 The Human Visual System
Retina
Optic Nerve
Optic Chiasm
LateralGeniculateNucleus (LGN)
Visual Cortex
Optic NerveFovea
Vitreous
Optic Disc
Lens
Pupil
Cornea
Ocular MuscleRetina
Humor
Iris
The Human Eye
light
rods cones
horizontal
amacrine
bipolar
ganglion
The Human Retina
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Light
OS
GCL
INL
ONL
Inner
Outer
Cross-section of Human Retina Retinal Photoreceptors
rods
cone
10 µm
X 1000
Receptor Models
Retinal PhotoreceptorsRods -
Distribution of rod and cone photoreceptors
Cones - • High illumination levels (Photopic vision)• Less sensitive than rods.• 5 million cones in each eye.• Only cones in fovea (aprox. 50,000).• Density decreases with distance from fovea.
• Low illumination levels (Scotopic vision).• Highly sensitive (respond to a single photon).• 100 million rods in each eye.• No rods in fovea.
Degrees of Visual Angle
Rec
epto
rs p
er s
quar
e m
m
-60 -40 -20 0 20 40 60
2
6
10
14
18x 104
rodscones
2.3 µ − width2.5 µ − inter-cone distance0.5‘− field of view
θθ
17mm
2.5µ
tan(θ) = 2.5 x 101.7 x 10
= 1.47 x 10-6
-2-4
= 0.0084 deg = 0.5 (arcmin)~ '
Cones -
Calculating the viewing angle of a single cone in the fovea:
θ
-
Cone Mosaic
Cone Mosaic at Fovea
Cone Mosaic in periphery
Rods
Cones
10 µm
Cones - • High illumination levels (Photopic vision)• Less sensitive than rods.• 5 million cones in each eye.• Only cones in fovea (aprox. 50,000).• Density decreases with distance from fovea.• 3 cone types differing in their spectral
sensitivity: L , M, and S cones.
Retinal Photoreceptors
Wavelength (nm)
Rel
ativ
e se
nsiti
vity
Cone Spectral Sensitivity
400 500 600 7000
0.25
0.5
0.75
1ML
SM
Cone Receptor Mosaic(Roorda and Williams, 1999)
L-cones M-cones S-cones
S cone Sampling Mosaic
rodsS - Cones
L/M - Cones
Foveal Periphery
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Human Image Formation
What is the quality of the opticsof the human eye?
scene film
Put a piece of film in front of an object.
source: Yung-Yu Chuang
Image Formation - Optics
scene film
Add a barrier to block off most of the rays.
• It reduces blurring• The pinhole is known as the aperture• The image is inverted
barrier
pinhole camera
source: Yung-Yu Chuang
Image Formation - Optics Image Formation - Optics
Shrinking the aperture
Why not create the aperture as small as possible?
• Less light gets through
• Diffraction effect
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Image Formation - Optics
Shrinking the apertureImage Formation - Optics
Adding a Lens
scene film
Image Formation - OpticsAdding a Lens
scene filmlens
“circle of confusion”
Lens Design: Snell’s Law
)'sin(')sin( φφ nn =
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Lensmaker’s Equation
lengthfocalfdistimageddistsourced
i
s
===
obje
ct
imag
e
ds di
fdd is111 =+
Optical power and object distance
Encoding Characteristics - Line spread
Line spread defines the optical quality of the eye
Light Scattered From From The Retina Is Used To Estimate Optical Quality
(e.g., Campbell and Gubisch)
Double Pass Method
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Campell and Gubisch 1966
Inte
nsity
of l
ight
refle
cted
from
the
eye
Visual Angle (minutes of arc)
6.6
5.8
4.9
3.8
3.0
2.4
2.0
1.5
1.0
Measurements of light reflected from the retina (Linespread) at various pupil diameters
a/22aa
bb/2
2b
Homogeneity:
Additivity:
a
b b’
a’ a a’
b b’
monitor image
retinal image
monitor image
retinal image
Image formation satisfies :
Image formation is a linear system
Image Formation is a Linear System
A system is Linear if it satisfies superposition:
A finite dimensional linear system can be writtenas a matrix equation:
where R is the system matrix.
Systemf
in outa f(a) = b
homogeneity f(ka) = kf(a) = kb
additivity f(a1+a2) = f(a1) + f(a2) = b1 + b2
b = Ra
Image formation is a Shift Invariant linear system
A shifted input produces a shifted output:
a
b b’
a’ monitor image
retinal image
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Scene:
Retinal Image:
Visual angle (arc mins)
Rel
ativ
e In
tens
ity
-4 -2 2 40
1.0
0.8
0.6
0.4
0.2
0.0
Modeling Image Formation(Westheimer)
Visual angle (arc mins)
Rel
ativ
e In
tens
ity
-4 -2 2 40
1.0
0.8
0.6
0.4
0.2
0.0
The Human Linespread Function
10 3020 40 50 60Spatial Frequency (cpd)
Sca
le fa
ctor
0.5
1.0
0.0
The Human Modulation Transfer Function
The Pointspread Function
The pointspread function is a generalizationof the linespread function.
Monitor Image
Retinal Image
Astigmatism Measures the Assymmetry andOrientation of the Pointspread Function
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Visual Acuity
Cones at fovea are 2.5µ apart corresponding to 0.5’ (arc min).
Typical acuity targets:
VernierAcuity
Landolt C Resolutionacuity
Gratingacuity
SnellenLetter
Expected acuity is size of cone or visual angle of cone.
receptors
light stimulus
Actual acuity ~ 5’’ (arc seconds) = Hyperacuity~
PhotopicScotopic
0.4
0.0
0.6
0.2
1.0
0.8
0-1-2-3-4 1 2 3 4
0.4
0.0
0.6
0.2
1.0
0.8
0-20-40 20 40
Blind spot
Fovea TemporalNasalVisual angle
Do to linespread, movement of stimulus by less than receptor width causes change in receptor response:
receptorpositions
reseptorresponses
stimuli
Acuity is affected by retinal position and illumination:
Rel
ativ
e vi
sual
acu
ity
Log illumination (trolands)
Visual Acuity
K+50
B+40
X+30
M+20
P+10
A+5
S+0
Visual Acuity Test Electromagnetic Radiation -Spectrum
Gamma X rays Infrared Radar FM TV AMUltra-violet
10-12
10-8
10-4
104
1 108
electricityACShort-
wave
400 nm 500 nm 600 nm 700 nmWavelength in nanometers (1nm=10-9 m)
Wavelength in meters (m)
Visible light
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The Spectral Power Distribution (SPD) of a light is a function f(l) which defines the energy at each wavelength.
Wavelength (λ)
400 500 600 7000
0.5
1
Rel
ativ
e P
ower
Spectral Power Distribution Examples of Spectral power Distributions
Blue Skylight Tungsten bulb
Red monitor phosphor Monochromatic light
400 500 600 7000
0.5
1
400 500 600 7000
0.5
1
400 500 600 7000
0.5
1
400 500 600 7000
0.5
1
400 nm 500 nm 600 nm 700 nm
Multispectral Images
400 500 600 7000
Chromatic Aberration
Different wavelengths bending at lens, focus at different distances.
Wavelength (nm)
Pow
er o
f Len
s (d
iopt
ers)
400 500 600 700
1.0
0.0
-1.0
-2.0
-3.0
* Wald and Griffin (1947)Bedford and Wyszecki (1957)Thibos et al. (1992)
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Chromatic Aberration Measures Differencesin Optical Focus Across Wavelength
Chromatic Aberration
A B C D E F G
A B C D E F G
A B C D E F G
A B C D E F G
A B C D E F G
Chromatic Aberration affects the MTF
Chromatic Modulation Transfer Function
1
0.8
0.6
0.4
0.2
0
Spatial Frequency0 10 20 30
Atte
nuat
ion
Fact
or
Blue vs Green Modulation Transfer Function
Sampling rate of Blue vs Green is in accord with Nyquist Theorem
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Wavel
ength (
nm)
Spatial position (deg)
Chromatic Linespread Function
Some Animals Have Non-Circular Pupils
Cat Eye