RGB & CMY(K)-Space Conversion between CMY and CMYK

RGB & CMY(K)-Space 

•RGB = Red-Green-Blue 

Part 5: Reproduction Principles and 

Related Color Spaces 

• CMY = Cyan-Magenta-Yellow 

• CMYK = Cyan-Magenta-Yellow-Black 

RGB for reproduction on additive devices like monitors 

also used for cameras 

CMY(K) for subtractive devices like printers 

Basic color reproduction principles/Additive 

Additive Color Reproduction: 

Colors are created by adding outputs of 

three primaries (TV, Laser displays, …) 

Typical primaries: Red, Green, Blue 

Simple relation between RGB and CMY 

⎛ C ⎞ ⎛1− 

R⎞ 

⎜ ⎟ ⎜ ⎟ 

• RGB -> CMY: ⎜M 

⎟ = ⎜1−G⎟ 

⎜ ⎟ ⎜ ⎟ 

⎝ Y ⎠ ⎝1− 

B⎠ 

•CMY -> RGB: 

⎛ R⎞ 

⎛1−C 

⎞ 

⎜ ⎟ ⎜ ⎟ 

⎜G⎟ 

= ⎜1− 

M ⎟ 

⎜ ⎟ ⎜ ⎟ 

⎝ B⎠ 

⎝ 1−Y 

⎠ 

Basic color reproduction principles/Subtractive 

Conversion between CMY and CMYK 

• CMY -> CMYK: 

⎛min( 

C3, 

M 3, 

Y 

⎜ 

⎛ K ⎞ C3 

− K 

⎜ ⎟ ⎜ 

⎜ C ⎟ ⎜ − 

⎜ ⎟ 

= ⎜ M − 

K 4 1 

3 K 

M 4 

⎜ ⎟ ⎜ 1− 

⎝ Y ⎠ ⎜ Y − 

K 4 

3 K 

⎜ 

⎝ 1− 

K 

3) 

⎞ 

⎟ 

⎟ 

⎟ 

⎟ 

⎟ 

⎟ 

⎟ 

⎠ 

BUT: 

In reality this is 

much more 

complicated! 

Subtractive Color Reproduction: 

Colors are created by subtraction of 

colors from underlying white (printing,…) 

Typical primaries: Cyan, Magenta, Yellow 

• CMYK -> CMY 

⎛ C3 

⎞ ⎛ C4⋅(1 

− K) 

+ K ⎞ 

⎜ ⎟ ⎜ 

⎟ 

⎜M 

3⎟ 

= ⎜M 

4⋅(1 

− K) 

+ K⎟ 

⎜ ⎟ ⎜ 

⎟ 

⎝ Y 3 

⎠ ⎝ Y 4⋅(1− 

K) 

+ K ⎠ 

1

Device dependency 

Color Detectors (Cameras) 

Today mainly CCD cameras with: 

• one sensor array and RGB-filters 

The color represented by 

R, G, B, C, M, Y, K 

depend on the devices used, 

i.e the characteristics of the 

monitor channels, the camera or the inks 

•three sensor arrays with beam-splitter 

B 

E 

A 

M 

S 

P 

L 

I 

T 

T 

E 

R 

R 

G 

B 

Traditional photographic 

film 

(3-12+light sensitive layers) 

Conversion between RGB and 

XYZ 

Foveon 

ITU-RGB 709 is a standard describing studio cameras 

(ITU = International Telecommunications Union) 

⎛ X ⎞ ⎛41.24 

⎜ ⎟ ⎜ 

⎜ Y ⎟ = ⎜21.26 

⎜ ⎟ ⎜ 

⎝ Z ⎠ ⎝ 1.93 

35.76 

71.52 

11.92 

18.05⎞⎛ 

R⎞ 

⎟⎜ 

⎟ 

7.22 ⎟⎜G⎟ 

95.05 

⎟⎜ 

⎟ 

⎠⎝ 

B⎠ 

X,Y,Z system assumes D65 daylight 

Sony Cybershot DSC-F828 

Part 6: Some Color Measurement Devices 

RGB 

RGBE 

2

New Trends- Multispectral 

Cameras 

EU project Crisatel: 

ENST Paris, Louvre, National Gallery … 

Linear CCD 12000 pixels 

Moving frame with 30000 lines 

Multispectral filters: 13 bands 

Resolution: 16 bits/pixel 

File size: 9.4 Gb 

Product: http://www.jumboscan.com/ 

Spectroradiometers PhotoResearch 

The PR-705 SpectraScan ® SpectraRadiometer ® 

Color Detectors (Densitometers) 

Used in scanners to compare the actual (transparency, 

reflectance) 

to the ideal (transparency, reflectance) 

Often optimised to objects (inks etc.) 

Spectrolino 

Amplifier 

Detector 

Probe 

Filter 

Source 

Measure with probe 

Compare to measurement without 

probe 

Characteristic of Status A densitometer 

Digital Cameras as Measurement Device 

Cheaper 

8-12M Measurements 

Needs calibration 

Expansive 

Needs experience 

Single Point Measurements 

http://www.diva-portal.org/diva/getDocument?urn_nbn_se_liu_diva-2667-1__fulltext.pdf 

Exjobb: Martin Solli: Filter characterization in digital cameras 

3

Computational Photography 

Color vocabulary 

• Hue: red-green-blue-yellow-etc 

• Brightness: how bright an object appears 

• Colorfulness: how much white is included 

• Lightness = normed brightness = 

Brightness/Brightness(White) 

• Chroma = normed 

Colorfulness=Colorfulness/Brightness(White) 

• Saturation=Colorfulness/Brightness 

• (un-)Related colors: unrelated color of an object belongs to 

an area independent of other colors 

Lightstage... 

Perception phenomena not handled by 

colorimetry 

Simultaneous contrast: 

The color of a point depends not only on its physical spectrum 

but also on the background on which it is seen 

More simultaneous contrast 

Color perception depends on the whole configuration 

Part 7: More Color Vision 

4

Crispening 

Magnitude of color difference is larger if the 

stimuli are shown on background with color similar to the stimuli 

More effects 

1. Spreading: Small stimuli are fused (half-toning). Just above the limit 

there is a region where only the colors blend but where the objects are 

perceived as different 

2. Bezold-Brücke effect: Hue depends on luminance! Viewing 

monochromatic stimuli under different luminance changes the hue 

: 

3. Abney effect: Constant hue curves are not lines! Mixing monochromatic 

light with different amounts of white light changes the hue. 

4. Helmholtz-Kohlrausch effect: Brightness increases with saturation! 

Brightness depends on luminance and chrominance. 

5. Hunt effect: Increasing luminance leads to increasing colorfulness! 

6. Stevens effect: Contrast increases with luminance! With increasing 

luminance dark becomes darker and light becomes lighter 

Depth perception of red-blue 

The human eye (again) 

Red/Blue Text 

Blue text on a red background is hard to read 

Post-detection processes 

A) Connection between retina and brain is a bottleneck 

(Many more sensors than nerves to brain) 

Therefore compression is needed! 

Red text on a blue background is easier to read 

B) All cells involved adapt to changing conditions 

Black text on a white background is best 

Continued high stimulation 

Continued low stimulation 

lower sensitivity 

increasing sensitivity 

5

Spectral processing (opponent color coding) 

L 

BW 

M 

RG 

S 

YB 

Adaptation 

Human vision system adapts, it has a tendency to go back to 

a stable state 

Examples: 

General brightness adaptation 

Lateral brightness adaptation 

Chromatic adaptation 

… 

BW = L+M+S RG = L-M YB = S-M-L 

Spatial signal processing on the retina 

Single sensor signals from a region are combined 

General brightness adaptation 

Adaptation to overall light intensity 

absolute intensity influences contrast and colorfulness 

- 

+ 

G- 

R+ 

Prints appear different in indoor and outdoor conditions even 

if the viewer is adapted to the light conditions 

Other “Detectors” 

• Oriented Edges 

• Oriented Bars 

• Input from one/two eye(s), stereo 

• Spatial frequencies 

• Temporal frequencies 

• Combination of all these features 

Lateral brightness adaptation 

Brightness at a point depends also on response from neighboring 

points 

Glowing axes, stairs, crispening …. 

Practical application: Slides on a screen in a dark room appear 

different from the same image on a screen in daylight 

6

Hermann Grid 

Mean Normalization 

Compensate such that mean is constant. 

“Rotating Snake” 

Max Normalization 

Compensate such that the point with maximum intensity is white 

by Akiyoshi Kitaoka 

Chromatic adaptation 

Mean Result 

Longer stimulation of a channels decreases its sensitivity 

Demonstrated by different versions of the afterimage 

Von Kries adaptation = different scaling for different 

channels 

7

Scaling 

Compensation Scene 6 

mean-Kries 

white-Kries 

Multispectral Simulation 

RGB Compensation 

Some recent results 

Simulation Scene 8 

Input: Multi-spectral image with 31 channels 

Illumination: Planck Spectra 

Camera: Canon Calibrated 

Experiment 1: Find RGB transforms that stabilize the image 

Application Industrial Inspection 

Experiment 2: Find RGB transform that predicts the image 

Application Movie industry-Relighting 


RGB Simulation 

Other visual mechanism relevant for human 

vision 

• Memory color: We “KNOW” the color of many objects 

• Color constancy: We know that objects usually don’t 

change colors (involves memory color and chromatic 

adaptation) 

• Discounting the illuminant: May often know the 

characteristics of the illuminant 

• Object recognition: Filling-in, induction, memory, 

learning etc. 

Compensation 


RGB Compensation 

8

Simulation 

Intelligent 

Color 

Correction (1) 


RGB Simulation 

Segment image in 

Object and 

background 

Application: Automatic Color Correction 

Intelligent 

Color 

Correction (2) 

Bad example 

Application: Automatic Color 

Correction 

Part 8: Color in Matlab 

Sorted 

9

Color Spaces 

Part 9: Color Management Systems 

How it works 

I_rgb = imread('peppers.png'); 

Create a color transformation structure. A color transformation structure defines the 

conversion between two color spaces. You use the makecform function to create the 

structure, specifying a transformation type string as an argument. This example creates 

a color transformation structure that defines a conversion from RGB color data to XYZ 

color data. 

C = makecform('srgb2xyz'); 

Perform the conversion. You use the applycform function to perform the conversion, 

specifying as arguments the color data you want to convert and the color transformation 

structure that defines the conversion. The applycform function returns the converted 

data. 

I_xyz = applycform(I_rgb,C); 

C 1x1 7744 struct array 

I_xyz 384x512x3 1179648 uint16 array 

I_rgb 384x512x3 589824 uint8 array 

Typical color image handling: 

• Take slide with camera 

• Scan the slide store on 

file 

• Edit file on the monitor 

• Convert file and print 

Why Color Management? 

Some factors which influence the result: 

• Illumination conditions 

• Camera 

• Film-type 

• Chemical processing of film 

• Scanner characteristics 

• Monitor characteristics 

• Software implementations 

• Printer characteristics 

• Ink properties 

• Paper type 

Data Types 

Basic strategies/Practical problems 

• Try to produce an output which is colorimetric as similar to the input as 

possible 

• Try to convert all images involved to a common set of colors 

(for example printer colors) 

• Try to keep as much information about each module as possible 

Practical problems 

• Each device has a color set it can handle (Color gamut) 

• File formats 

• Data compression 

• Color co-ordinates 

• ... 

10

ICC = International Color Consortium 

ICC was founded 1993 by companies from Computer, Printer and Software 

business 

Treatment of color is done by Operating System 

Devices are characterized by profiles 

Tables, programs etc. which describe the device 

Several color spaces are supported as standard (CIEXYZ, 

CIELAB) 

Profiles describe 

• Input devices 

• Output devices 

• Display devices 

• Color space conversions 

• Other profiles 

Characterization of input and output devices 

There are two main strategies to describe input/output devices 

• Look-up-tables (LUT) describing input-output relations by a 

table 

• Analytical descriptions: 

White point and 

Gamma value and 

Black point 

Example: 

output = a * exp(c*x) + b 

Basic Color Management Systems 

Generating Profiles 

Generation of a profile for a scanner is done by 

Scanning in a test image 

Mapping result into common color space (Profile Connection Space, PCS) 

and 

Comparison of measured an reference values 

Generation of printer profiles is done by printing standard patches and 

measuring the resulting images 

A basic color management system connects input and output profiles by 

converting color information from input to output device 

Several samples should be measured and averaged to get reliable results 

Advanced Color Management Module 

Gamut mapping 

Important problem in color management: 

Different devices have different gamuts, i.e sets of colors they 

can 

produce 

Moving color images between different devices needs decision 

what to 

do with non-existing colors. 

Take into account input/output viewing conditions ……. 

11

Gamuts for different systems 

ITN: Color Related Research 

Scene=objects+illuminations 

Digital camera 

Estimation of 

camera sensitivity 

Illumination + 

Camera 

Modelling: 

Cameras 

Illuminations 

Interactions 

Image 

Temperature Parameter 

Example 

Planck 

Spectrum 

Small continuous changes 

are hardly visible 

Color Constancy 

12

RGB & CMY(K)-Space Conversion between CMY and CMYK

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