COLOUR THEORY - UiO

0 - CMOS Image Sensors

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Main ref.: Nakamura

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COLOUR THEORY


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Rod Threshold

Rod Saturation

Cone Threshold

Retinal Damage

Moonlight

Indoor light

Sunlight

Starlight

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10-6

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ponse of the eye• The human eye has three kinds of cones S, M,

and L which is sensitive to different wavelength ranges: Blue, green, red. Colour view

• Rods has higher sensitivity but for one range only, slightly below the green range. Night vision without colour.

Ref.: www.wikipedia.org


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Ad

n.med.utah.edu/KallColor.html

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aptive and Subtractive Colour Mixing

Ref.: http://webvisio


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CoHow

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lour Matching Functions to quantify colours

• X(λ), Y(λ), and Z(λ)

• CIE 1931 standard(Commission Internationale de l'Eclairage) International Commission on Illumination

• The Colour space is associated with the colour sensitivity of the human eye.

Ref. Nakamura

Ref. Wikipedia


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Ref.: efg’a Computer Lab

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lour Matching Functions (cont.)timulus values: X, Y, Z is obtained by hting the source intensity L(λ) and the inated object’s reflectance R(λ) with the ur matching functions x(λ), y(λ) and z(λ).

(7.1)

inance: Y

minance: x, y es is represented in a 2 dimensional space.

(7.2)

verting back to X, Z

(7.3)

X L λ( )R λ( )x λ( ) λd∫=

Y L λ( )R λ( )y λ( ) λd∫=

Z L λ( )R λ( )z λ( ) λd∫=

x XX Y Z+ +-------------------------= y Y

X Y Z+ +-------------------------=

X Yy----x= Z Y

y---- 1 x– y–( )=


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CoImpstan Dev

Inde

(7.7)

where

(7.8)

(7.9)

(7.10)

b∗ 200 Yn Zn–( )=

XX0------- 0.008856>

1616

-------- XX0------- 0.008856≤

YY0------- 0.008856>

1616

-------- YY0------- 0.008856≤

ZZ0------ 0.008856>

616------ Z

Z0------ 0.008856≤

Com

u

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lour Matching Functions (cont.)roved geometric uniformity is achieved with the dard CIE 1976: L*u*v* and L*a*b*.eloped for gray background (L*=50)

x 0 represents tristimulus values for white

a∗ 500 Xn Yn–( )=

Xn

XX0------- 1 3⁄

7.787 XX0-------

1-+

=

Yn

YY0------- 1 3⁄

7.787 YY0-------

1-+

=

Zn

ZZ0------ 1 3⁄

7.787 ZZ0------ 1

1---+

=

mon L*:

(7.4)

(7.5)

where

(7.6)

L∗116 Y

Y0------- 1 3⁄

16– YY0------- 0.008856>

903.29 YY0------- Y

Y0------- 0.008856≤

=

∗ 13L∗ u' u'0–( )= v∗ 13L∗ v' v'0–( )=

u' 4XX 15Y 3Z+ +----------------------------------= v' 9Y

X 15Y 3Z+ +----------------------------------=


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L*a

ination

ination

ination

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*b* (CIE1976)

25% Illum

50% Illum

75% Illum

Ref.: efg’a Computer Lab


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L*C

L* a

Ref.: Wikipedia

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*H* (CIECAM02)

s in (7.4).

(7.11)Cab∗ a∗2

b∗2

+( )= hab180o

π----------- b∗

a∗------ atan=


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Co

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lour temperature of light sources


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trum

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lour temperature of light sources (cont.)

Equal colour temperature is not the same as equal spec

Normalised with reference to green


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CoA m

y radiation) with CRI=100.

Ave

Whe

Inde e.

Ref.: Wikipedia

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lour Rendering index (CRI)easure on a light source capability to reproduce colour.

• 100 is best, 0 is worst

• The light source is measured against a reference, a filament lamp (blackbod

• A standardized set of colours are illuminated and compared.

• The reference is daylight for colour temperatures above 5000 °K.

rage colour rendering index Ra is calculated according to formula

re ∆Ei is the colour deviation in a given colour space, e.g. 1964 L*U*V*

x i gives the colour in the standard set, index 0 represents the reference sourc

Ra18--- 100 4 6∆Ei,–( )

i 1=

8

∑=

∆Ei Li Li0–( )2 Ui Ui0–( )2 Vi Vi0–( )2+ +=


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Co

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lour Rendering index (forts.)


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CamTo gto bsens

X=cY=cZ=c

Call

Provtranspeccomcalc

Colorefle

Thefrommet

retag Macbeth colour checker

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era Colour Propertiesenerate tristimulus values unlikely, these have e a linear combination of the camera’s itivity functions:

11Sx +c12Sy +c13Sz21Sx +c22Sy +c23Sz31Sx +c32Sy +c33Sz

ed the Luther condition.

ided the reflectance has a continuous sitions in the spectrum such that the reflected trum can be decomposed into three basic ponents, an object’s tristimulus values can be ulated using any set of sensitivity functions.

ur chart for test is made to simulate the ctance of real objects.

camera colour functions can be generated the chart. Either an analytical or recursive

hod.

G


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Cam

(7.12)

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era Colour Properties (cont.)

The target:

Estimated value:

Solving for the compensation matrix:

Camera responseCompensation


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Cam

Rec

(7.13)

Whe

(7.14)

J: V

wi: C

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era Colour Properties (cont.)

ursive method to minimize colour differences:

re ∆E is the direct colour difference (e.g. L*a*b)

isible colour difference (deviation form the object’s colour)

oefficient associated to each colour on the palette.

J wi∆E Xi Yi Zi Xi Yi Zi, , , , ,( )

i 1=

n

∑=

∆Eab∗ L1∗ L2∗–( )2

a1∗ a2∗–( )2

b1∗ b2∗–( )2

+ +=


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our-is-it-in-the-brain/

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http://neuroanthropology.net/2008/09/04/col


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Wh

Whi adjusts the sensitivity of cones to a

The

light source.

light source.

um from all part of the scene measured distribution.

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ite Balance

te act as the reference for the colours, i.e. the colour of the light source. The eye dapt to the lightning conditions.

question is: What is white in the image? There are several methods.

• Scene average. Assuming the “world is grey” and that the average colour is the colour of the

• The brightest spot is white. Assuming the light that is reflected by the brightest elements represents the

• Gamut of the scene (colour space). Assuming the total spectrum has a expected distribution, analyse the spectrand move the colours towards the highest correlation between expected and


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Whvon

Ima ound light.Con tate white = Lw1,Mw1,Sw1 Con tate white = Lw2,Mw2,Sw2

New

(7.15)

A: SB: T

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ite Balance - Chromatic adaptionKries model:

ges are viewed in a background illumination different form the recording backgre response at background illumination 1, is tristimulus values L1,M1,S1 at the se response at background illumination 2, is tristimulus values L2,M2,S2 at the s

r’ b’ g’ values is calculated from r g b by:

ensor RGB -> Tristimulus values XYZristimulus values XYZ -> cone response LMS.

L2Lw2Lw1---------- L1= M2

Mw2Mw1------------ M1= S2

Sw2Sw1---------- S1=

r'g'b'

A 1– B 1–

L'wLw-------- 0 0

0M'wMw---------- 0

0 0S'wSw--------

BArbg

= ,LMS

BArgb

=


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Suban ovaryof ospecRa (

A siada

ia.org/wiki/colour_constancy

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ite Balance - Colour constancy

jective properties of the eye ensures that bject’s colour stays nearly unchanged at ing light conditions (needed for recognition bjects). It is however required that the trum of the light has a certain width, that average colour rendering index) is high.

mple method is to use (7.15) with the ption of B to a standard light source.

http://en.wikiped


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http

://en

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iped

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ncy

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eption of colour depend on the colour of the ground

pink sheet in top image looks more like white e bottom image.


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A is

lour_constancy

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at the same grey level as B?

http://en.wikipedia.org/wiki/co


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iki/colour_constancy

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http://en.wikipedia.org/w


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CoSam

Red e directions 45° and 135°

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lour Interpolationpling of Bayer pattern CFA (Colour Filter Array)

and blue distance = 2. Green distance = √2. Nyquist frequency is 1.4x higher for green, in th


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BiliInte g points, i.e. spatial low pass filterPosi

Posi

Corr

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near Interpolationrpolation: Insert a new point with values based on averaging of the neighbourining of the data.tion 1: G(x1,y1)|R = [R(x1,y1+1) +R(x1,y1-1)]/2

G(x1,y1)|B = [B(x1+1,y1) +B(x1-1,y1)]/2

tion 2: B(x2,y2)|G = [G(x2,y2+1) +G(x2,y2-1)+G(x2+1,y2) +G(x2-1,y2)]/4 B(x2,y2)|R = [G(x2+1,y2+1) +G(x2+1,y2-1)+G(x2-1,y2+1) +G(x2-1,y2-1)]/4

esponding for red pixel.


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Co

(7.16)

The ce, directly. The osstalk.

As t tion of these is advantageous.ThisThis

The

(7.17)

Fixe

(7.18)

02007141000015

YCbCr

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lour correction

coefficients at the diagonal adjust the relation between R,G and B, white balan matrix elements outside the diagonal can be used to compensate for colour cr

he eye has lower spatial response for chrominance than for luminance, separa can be done by converting RGB to YCbCr. is especially useful in data compression.

ITU standard:

d point representation:

R'G'B'

a1 a2 a3b1 b2 b3c1 c2 c3

RGB

=

YCbCr

0.2988 0.5869 0.1143-0.1689 -0.3311 0.50000.5000 -0.4189 -0.0811

RGB

= ,RGB

1.0000 0.00000 1.41.0000 -0.34410 -0.1.0000 1.77200 -0.

=

YCbCr

306 601 117-173 -339 512512 429– -83

RGB

=


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CoMet ch colour, converting to Chro expected Chrominance values for e

Our roperties of our vision system that

The jects.

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lour Reproductionhod: Recording of Macbeth colour checker with a well defined reflectance for eaminance (and luminance using tristimulus functions. Quantifying deviation from ach colour.

perception of colour depends on the illuminance, background light, and some p are not caught by the tristimulus functions.

refore the latest adjustment is done by observing the chart plus some typical ob


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GaMus Cathode Ray Tube (CRT) has a typ a correction. Can be done in both

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mma Correction and Hue Correctiont take into account the non-linear response, the form of y=xγ. For example, the ical gamma of 0.45. The transform from one response to another is the gamm the RGB space or in the YCbCr space.

RGB YCbCr


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Ref

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erences:

NakamuraImage Sensors and Signal Processing for Digital CamerasJunichi Nakamura (editor)CRC - Taylor & Francis

Wikipediawww.wikipedia.orghttp://en.wikipedia.org/wiki/CIE_1931_color_spacehttp://en.wikipedia.org/wiki/Color_modelhttp://en.wikipedia.org/wiki/Color_Rendering_Indexhttp://en.wikipedia.org/wiki/CIE_1960_color_spacehttp://en.wikipedia.org/wiki/colour_spacehttp://en.wikipedia.org/wiki/colour_constancy

efg’s Computer Labwww.efg2.com/Lab

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