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Vision & Perception

• Simple model:

simple reflectance/illumination model

image: x(n1,n2)=i(n1,n2)r(n1,n2)

where 0 < i(n1,n2) <

0 < r(n1,n2) < 1

Eye

illumination source i(n1,n2)

reflectance term r(n1,n2)

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Vision & Perception

• Imaging on the retina (back of eye consisting of photoreceptors)

17mm

20mm 100m

2m

Focal point

of lens Eye

Retinal

image

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Vision & Perception

• Visible range of electromagnetic spectrum is 350 nm to 780 nm.

rays x rays ultraviolet visible infrared microwaves radio

380nm 780nm

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• Simple model for HVS

NOTE: The HVS is really a non-linear system.

Vision & Perception

optic nerve

eye brain

HVS

HVS

Primarily a BPF/LPF

Input (spatial pulse)

What we see

Output

What we think we see

Approximate HVS with a LTI system

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Vision & Perception

• Light: electromagnetic radiation that stimulates our visual

response

expressed as a spectral energy distribution

C( ); 380nm 780nm – wavelength in visible spectrum

Spectral distribution of a colored light

C( ) represents amount of energy present at each frequency wavelength

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Vision & Perception

• Color vision model (3 receptor absorption model)

3 types of cones: each has a different peak absorption frequency

Typical absorption spectra (also called sensitivity curves) for the three cones

(not to scale)

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Vision & Perception

• Let C(): spectral energy distribution of a “colored” light source

C()

max max min

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• Color sensation described by

i[C()], i=1,2,3, called spectral responses

If C1() and C2() produce responses such that

i[C1()]=i[C2()] for i = 1,2,3 C1() and C2() perceived to be identical

• Color sensation – perceptual attributes

1. Brightness – perceived Luminance

2. Hue – color

3. Saturation – amount of white light diluting the color

Vision & Perception

3,2,1,max

min

idCSC ii

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Vision & Perception

• The following curves show the relative spectral response

functions of each of the 3 types of cones:

Eye’s response to Blue light is much less strong than is its

response to Red or Green

400 700 550 (nm) 0

0.2 R G

B

0.01

Fra

cti

on

of

lig

ht

ab

so

rbed

by e

ach

typ

e o

f co

ne

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Vision & Perception

• Luminance and Brightness

The luminance or intensity of an object with light spectral

distribution I(x,y, ) is

where V( ) is the “relative luminous efficiency function” of the HVS

Bell-shaped curve = sum of 3 previous curves.

0

),,(, dVyxIyxL

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Vision & Perception

• Luminance versus Brightness

Brightness:

subjective perceptual measure (depends on observer’s judgment)

perceived Luminance

depends on luminance of the surround (lateral inhibition, contrast)

Luminance:

objective quantitative measure (Unit: watts/m2 or watts/steradians)

independent of the luminances of the surrounding objects

Note: the illumination (Luminance) range over which HVS can operate

is roughly 1010 (normalized unit, e.g. milli-luminance = milli-unit of

luminance) or 10 orders of magnitude on log scale.

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Vision & Perception

• Scotopic vision mediated thru rods at the lower part of the

range

• Photopic vision mediated thru cones at the higher 5 to 6 order

of magnitude of interest here, computer screens are bright

• Our perception is sensitive to luminance contrast rather then

the absolute luminance value.

• Brightness is log related to luminance

103 milli-luminance (power)

Glare limit

10-1 10-6

Scotopic threshold

scotopic

photopic

Brightness (log scale)

Brightness is approximately

linear on the log scale

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Vision & Perception

• Concept of just-noticeable difference (contrast sensitivity)

Experiment: Human observer views background L and a spot with

intensity L+L. As we change L, dot becomes visible. The L for

which dot is visible is the just-noticeable difference.

L/L is the Weber ratio

Weber’s law: L/L= C (constant) = 0.02

d(logL) = constant C

equal increments in log L should be perceived to be equally

different ( linear relation between Brightness and log L)

log L is proportional to C, the change in contrast

L

L+L

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Vision & Perception

milli-luminance 10-1 103

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Vision & Perception

• Exploit this brightness property to derive contrast models:

c = a1 + a2 log f – logarithmic law

c = f1/n – root law

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Vision & Perception

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Vision & Perception

• Visual Acuity

Ability to detect spatial details; spatial frequency sensitivity of the eye

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Vision & Perception

• Retinal arc

Divide the eye into degrees

Images are projected onto rods and cones by retinal arc. We can

unwrap the retina:

10o 0o 10o

30o 30o

17mm 20mm

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Vision & Perception

• Spatial frequency

is not related to the wavelength of the light

is the number of oscillations in a given space

10o

0o

10o

30o

30o

0o 1o

4 cycles/retinal arc

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Color Models

• RGB CIE spectral primary sources; CRT monitors

• CMY Printers; ink-based devices

Traditionally, RGB primary colors, CMY complements of RGB

C = W - R

M = W - G = R + B

Y = W – B = R + G

• RNGNBN NTSC receiver primaries; standard for

television receivers; three phosphor primaries that glow in the

red, green, and blue regions of the visible spectrum

• YIQ NTSC transmission standard; compatible with

B/W TV broadcast; more efficient transmission than RGB

• HSV or HSB User-oriented, based on intuitive or

perceptual measure

• Note: NTSC stands for National Television Systems Committee

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TG(

)

TB( ) TR( )

• RGB (CIE primaries) color matching functions

• The tristimulus values (weights) of an arbitrary color C( ):

Color Models

max

min

)(

dTCt kk BGRk ,,

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Color Models

• CIE Chromaticity Diagram

CIE defined 3 standard (hypothetical) primary sources called

X, Y and Z to replace R,G and B. These new primaries can match

all visible color with positive weights (positive matching functions)

Y color matching function matches the luminous efficiency

function of the eye

(nm) 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

380

410

440

470

500

530

560

590

620

650

680

710

740

770

nxny

nz

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Color Models

• Let

Then

will produce the same color but with a different intensity; i.e.,

same Hue and Saturation, but different Brightness

Normalize by setting

where

zyx

zz

zyx

yy

zyx

xx nnn

;;

zZyYxXC

azZayYaxXC '

zyxa

ZzYyXxC nnnn

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Color Models

•Note: (Unit Plane)

out of the 3 normalized weights, only 2 have to be specified

only 2 primaries needed to define color

CIE diagram = projection of Unit Plane into (X,Y) plane

•The three values , and define hue and saturation but give no

info about the brightness since they are relative components

An extra value is required to determine the intensity (Brightness) and

the value of Y is chosen, In practice, any absolute intensity value

(x, y or z) may be specified to determine the brightness.

1 nnn zyx

nnn yxz 1

nznynx

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Curve (Horse-shoe) boundary

corresponds to 100% pure colors

All possible colors (of normalized

intensity) are displayed on CIE

diagram

The (MacAdam) ellipses are the

just noticeable color difference

ellipses.

Color Models

• CIE Chromaticity Diagram

White: xn = yn = 0.333

zn = 1 – xn – yn = 0.333

Yellow

0.333

G

R

B

White

xn

yn

700nm

435.8nm

546.1nm

0.333

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• YIQ:

NTSC transmission standard

Y = Luminance (same as CIE Y primary); color matching function

identical to luminous efficiency function V( )

I and Q: chrominance components (give hue and saturation)

Recoding of RNGNBN for transmission efficiency

Transmission efficiency: Bandwidth of I or Q < half bandwidth of Y

NTSC encoding of YIQ into a broadcast signal assigns:

4 MHz to Y

1.5 MHz to I

0.6 MHz to Q

I and Q components contain less information

less samples (more than 50%less) used to represent I and Q

Downward compatibility with B/W TV receivers (Y component)

Color Models

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Color Models

• Converting RNGNBN to YIQ:

Recall:

C( ) consists of only three components of weights RN at R,

GN at G and BN at B

C( ) = RN ( - R) + GN ( - G) + BN ( - G)

becomes a summation weighted by the corresponding V( R),

V( G) and V( B)

Y = L() = V( R) C( R) + V( G) C( G) + V( B) C( B)

= 0.30 RN + 0.59 GN + 0.11 BN

N

N

N

B

G

R

Q

I

Y

312.0523.0211.0

322.0274.0596.0

114.0587.0299.0BGRY 11.059.030.0

R G B

C()

BN GN RN

max

min

)(

dVCL

Colored light distribution

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Color Models

• Some useful transformations between color coordinate systems

RGB to XYZ

RNGNBN to XYZ

B

G

R

Z

Y

X

990.0010.0000.0

011.0813.0177.0

200.0310.0490.0

Z

Y

X

B

G

R

N

N

N

896.0118.0058.0

028.0000.2985.0

288.0533.0910.1

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Temporal Properties of Vision

• Important for processing motion images (video) and in the

design of image displays for stationary images

• Main properties:

Bloch’s law

If we expose an observer to flashing light where flashes have

different durations but same energy these durations became

indistinguishable below a critical duration threshold

This threshold was found to be about 30 ms when eye adapted

at moderate illumination level

The more the eye is adapted to dark, the longer the critical

duration

d1 d2

Flash 1 duration Flash 2 duration

d1 indistinguishable of d2 if d1 dc and d2 dc

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Temporal Properties of Vision

Critical Fusion Frequency (CFF)

If flashing rate of light > CFF individual flashes are

indistinguishable; i.e., flashes are indistinguishable from a

steady light at the same average intensity

CFF does not generally exceed 50 to 60 Hz

Basis for TV raster scanning cameras and displays

Interlaced image fields sampled and displayed at rates of 50 or

60 Hz

Modern displays are refreshed at 60 frames/sec to avoid

flicker perception

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Temporal Properties of Vision

• Spatial versus Temporal effects:

Eye more sensitive to flickering of high spatial frequencies (i.e.

flickering edges) than low spatial frequencies

Useful in coding of motion video where moving areas are

subsampled except at the edges (low spatial areas represented by

less samples)