lecture 1 the human visual system - university of...

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

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

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

Image Formation - Optics

Shrinking the aperture

Image Formation - OpticsAdding a Lens

scene film

Image Formation - OpticsAdding a Lens

scene filmlens

“circle of confusion”

Lens Design: Snell’s Law

)'sin(')sin( φφ nn =

Lensmaker’s Equation

lengthfocalfdistimageddistsourced

i

s

===

obje

ct

imag

e

ds di

fdd is

111 =+

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

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

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

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

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)

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

Wavelength (nm)

Spatial position (deg)

Chromatic Linespread Function

Some Animals Have Non-Circular Pupils

Cat Eye