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0 - CMOS Image Sensors
AO 7.1
Col
Main ref.: Nakamura
INF 544
10V
our Theory
COLOUR THEORY
0 - CMOS Image Sensors
AO 7.2
Col
Res
Rod Threshold
Rod Saturation
Cone Threshold
Retinal Damage
Moonlight
Indoor light
Sunlight
Starlight
108
106
104
102
1
10-2
10-4
10-6
INF 544
10V
our Theory
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
0 - CMOS Image Sensors
AO 7.3
Col
Ad
n.med.utah.edu/KallColor.html
INF 544
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our Theory
aptive and Subtractive Colour Mixing
Ref.: http://webvisio
0 - CMOS Image Sensors
AO 7.4
Col
CoHow
INF 544
10V
our Theory
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
0 - CMOS Image Sensors
AO 7.5
Col
CoTrisweigillumcolo
Lum
Chrovalu
Con
Ref.: efg’a Computer Lab
INF 544
10V
our Theory
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–( )=
0 - CMOS Image Sensors
AO 7.6
Col
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
INF 544
10V
our Theory
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+ +----------------------------------=
0 - CMOS Image Sensors
AO 7.7
Col
L*a
ination
ination
ination
INF 544
10V
our Theory
*b* (CIE1976)
25% Illum
50% Illum
75% Illum
Ref.: efg’a Computer Lab
0 - CMOS Image Sensors
AO 7.8
Col
L*C
L* a
Ref.: Wikipedia
INF 544
10V
our Theory
*H* (CIECAM02)
s in (7.4).
(7.11)Cab∗ a∗2
b∗2
+( )= hab180o
π----------- b∗
a∗------ atan=
0 - CMOS Image Sensors
AO 7.9
Col
Co
INF 544
10V
our Theory
lour temperature of light sources
0 - CMOS Image Sensors
AO 7.10
Col
Co
trum
INF 544
10V
our Theory
lour temperature of light sources (cont.)
Equal colour temperature is not the same as equal spec
Normalised with reference to green
0 - CMOS Image Sensors
AO 7.11
Col
CoA m
y radiation) with CRI=100.
Ave
Whe
Inde e.
Ref.: Wikipedia
INF 544
10V
our Theory
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+ +=
0 - CMOS Image Sensors
AO 7.12
Col
Co
INF 544
10V
our Theory
lour Rendering index (forts.)
0 - CMOS Image Sensors
AO 7.13
Col
CamTo gto bsens
X=cY=cZ=c
Call
Provtranspeccomcalc
Colorefle
Thefrommet
retag Macbeth colour checker
INF 544
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our Theory
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
0 - CMOS Image Sensors
AO 7.14
Col
Cam
(7.12)
INF 544
10V
our Theory
era Colour Properties (cont.)
The target:
Estimated value:
Solving for the compensation matrix:
Camera responseCompensation
0 - CMOS Image Sensors
AO 7.15
Col
Cam
Rec
(7.13)
Whe
(7.14)
J: V
wi: C
INF 544
10V
our Theory
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
+ +=
0 - CMOS Image Sensors
AO 7.16
Col
INF 54410V
our Theory
0 - CMOS Image Sensors
AO 7.17
Col
our-is-it-in-the-brain/
INF 544
10V
our Theory
http://neuroanthropology.net/2008/09/04/col
0 - CMOS Image Sensors
AO 7.18
Col
Wh
Whi adjusts the sensitivity of cones to a
The
light source.
light source.
um from all part of the scene measured distribution.
INF 544
10V
our Theory
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
0 - CMOS Image Sensors
AO 7.19
Col
Whvon
Ima ound light.Con tate white = Lw1,Mw1,Sw1 Con tate white = Lw2,Mw2,Sw2
New
(7.15)
A: SB: T
INF 544
10V
our Theory
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
=
0 - CMOS Image Sensors
AO 7.20
Col
Wh
Suban ovaryof ospecRa (
A siada
ia.org/wiki/colour_constancy
INF 544
10V
our Theory
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
0 - CMOS Image Sensors
AO 7.21
Col
Percback
Thein th
http
://en
.wik
iped
ia.o
rg/w
iki/c
olou
r_co
nsta
ncy
INF 544
10V
our Theory
eption of colour depend on the colour of the ground
pink sheet in top image looks more like white e bottom image.
0 - CMOS Image Sensors
AO 7.22
Col
A is
lour_constancy
INF 544
10V
our Theory
at the same grey level as B?
http://en.wikipedia.org/wiki/co
0 - CMOS Image Sensors
AO 7.23
Col
iki/colour_constancy
INF 544
10V
our Theory
http://en.wikipedia.org/w
0 - CMOS Image Sensors
AO 7.24
Col
CoSam
Red e directions 45° and 135°
INF 544
10V
our Theory
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
0 - CMOS Image Sensors
AO 7.25
Col
BiliInte g points, i.e. spatial low pass filterPosi
Posi
Corr
INF 544
10V
our Theory
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.
0 - CMOS Image Sensors
AO 7.26
Col
Co
(7.16)
The ce, directly. The osstalk.
As t tion of these is advantageous.ThisThis
The
(7.17)
Fixe
(7.18)
02007141000015
YCbCr
INF 544
10V
our Theory
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
=
0 - CMOS Image Sensors
AO 7.27
Col
CoMet ch colour, converting to Chro expected Chrominance values for e
Our roperties of our vision system that
The jects.
INF 544
10V
our Theory
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
0 - CMOS Image Sensors
AO 7.28
Col
GaMus Cathode Ray Tube (CRT) has a typ a correction. Can be done in both
INF 544
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our Theory
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
0 - CMOS Image Sensors
AO 7.29
Col
Ref
INF 544
10V
our Theory
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