Sensory InformationProcessing

Color space

Perception and reproduction of color

Light and Color

• Light : physical– Light is a electromagnetic wave– Physically, there is no concept of “color”

(distribution with respect to the wavelength)

• color ： psychological– One aspect of perception of the light– Relative intensity of three ranges of

wavelength

To learn about color, we must learn about human

eyeball• diameter

24mm

• Flexible lens (crystalline)

• Iris = aperture

• Focal length = 17mm

• Retina : film or CCD

Fovea

Fovea

• Center of the image– Highest resolution

Retina

• Two types of photo receptor– Rod :

monochromatic, high response, work in dark environment

– Cone : three types (L, M, S) : colorlow response, work only at bright environment

Spectral sensitivity of cones

measured neurophysiology

How to identify the color perception?

How to measure the relationships between wavelength and color perception

• Measuring signals of neurons– Not easy– Perception is not directly related to signal

• Subjective tests– Comparing very single spectral light with

additive color mixture– Ambiguity of coordinate transform remains

Color matching experiment(1)

• Adjust the levels of R, G, B so as to match to monochromatic light– R : 700nm 　 G : 546.1nm 　 B : 435.8nm

Negative response

Color matching (2)

• Negative value means the light at opposite side

All in positive ith negative values

Why we have “negative values”?

• No negative response at our retina

wavelength

sensitivity

wavelength

intensity

L(λ)M(λ)S(λ)

change

i(λ)

×L

S=∫S(λ) ・ i(λ)dλ

Mλ

Smooth curve in positive region

Actual spectral response(unknown)

Sample stimulus

• R>0, G=B=0 when i = 700nm(R)– RGB space is smaller than the original space

with our actual sensitivity. Therefore, between the wavelength of B and G, R should be negative

L

S

Mλi

i=B

i=G

i=R

B

G

R

Why we have “negative values”?

rg chromaticity coordinate

• rg : chromaticity : Relative values of RGBr = R/(R+G+B), g = G/(R+G+B)

Single wavelength passes three points (r,g)=(0,0), (0,1), (1,0)

L

S

Mλ

i=B

i=G

i=R

B

G

R

R

B

G

rg

Linear trransform

rg chromaticity and RGB color matching curve

• All three values have negative regions

XYZ color space• To avoid the negative

values of RGB color space

New coordinate system which includes the spectral curve in positive areaThree points, X, Y, Z, is outside of spectral curve, so, it does not physically exist called as”imaginary color”

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G

R

Z

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X

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XYZ color matching function

0

0.5

1

1.5

2

380410440470500530560590620650680710740770Wavelength　(nm)

x_bar(l)y_bar(l)z_bar(l)

CIE1931　XYZ　color　matching　function

xy chromaticity• Relative value

of XYZ• x = X/(X+Y+Z),

y = Y/(X+Y+Z)• Black curve :

black body radiation (related to the color temperature)

xy chromaticity and brightness

• Reflectance is limited to 1.0 or below– White is brightest– Intensity of the boundary

of spectral curve is 0– Called MacAdam limit

White light source

intensity

Object with various color

Color reproduction and gamut (1)

• Range of additive color is limited in the triangle which verteces are primal colors

• Called gamut• left figure indicates

the range of RGB tristimulus

Display and color reproduction

s

• Range of the color depends on the primal colors

• “RGB” of PC is not CIE RGB

• Wrong use of color space causes the color mismatch

examples

• Color space of digital camera

• Adobe Photoshop

• Apple ColorSync

• Display

Printing and color

• Printing is subtractive color (CMY)

• Inside the convex hull which defined by 6 points of C, M, Y, CM,CY, MY

• RGB and CMY have different gamut

print

• Convex hull of 6 primal colors

White material (paper)

cyan=G+B

magenta=R+B

yellow=R+G yellow=R+G

cyan green black blue magenta red yerrow white

・ spectral reflectance of green yellow ≒ ・　 cyan　 → spectral reflectance of green is linearly independentfrom yellow and cyan

・ represented by halftone dot　 → mixture of 8 colors above

Halftone dot

Color space matched for perception

• HSB color space– Polar coordinate– HSB (Hue, Saturation,

Brightness)

• xy color space– Perceptually not

uniform– MacAdam ellipse

L*a*b* color space

• Perceptually uniform color space by nonlinear transform ⎥

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nnnn

n

Z

Z

Y

Yb

Y

Y

X

Xa

Y

YL

`erception R

`erception G

Perception B

Metamerism

• Visually same color but different spectral curve

• Depends on not only the object but also the light source

Light 1 Object 1× Perception R

Perception G

Perception BLight 2 Object 2×

same

same

same

Spectral sensitivity and evaluation of color

• If the spectral sensitivity of the sensor is different from the human beings, color matching fails

• If the spectral curve of light source is special, color matching fails (object with different colors seems same)

• （ fluorescent light is not good as light bulb)

Psychology vs. Physics

• Psychology– System which works as same as human

• Color quality control

• physical– Color marker (distinguish objects with color)– Recognition of material using color

• Marginal– QC of papers using color (visual, or other?)– QC of agricultural products