Colour Schemes

Doc. no. : SRON/EPS/TN/09-002

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Colour Schemes Prepared by: Paul Tol

136,204,238 88CCEE

221,204,119 DDCC77

68,170,153 44AA99 51,34,136 332288

153,153,51 999933

204,102,119 CC6677

17,119,51 117733

170,68,153 AA4499

136,34,85 882255

Document Change Record Issue

Date

Changed Section

Description of Change

1.0

18 November 2009

All

Initial version

1.1

23 November 2009

Fig. 6

Improved green on grey background

2.0

17 January 2010

All

Print-friendlier schemes Added commands to simulate colour-blindness

2.1

2.2

17 August 2010

29 December 2012

Fig. 3

Different choice of 8-colour set

p. 4

Remark added on background grey

p. 5

Remark added on NEN colour set

Section 5

Added section on palette check

Section 4

Added a banded rainbow scheme


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Table of Contents 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

2

Distinct Colour Palettes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

3

Best Colour Scheme for Different Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

4

Rainbow Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

5

Colour-Scheme Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

6

Colour-Blindness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Reference Documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1

Introduction

Graphics with scientific data become clearer when the colours are chosen carefully. It is convenient to have a good default scheme ready for each type of data, with colours that are distinct for all readers, including colour-blind people. This document shows such schemes as a function of the number of colours needed, with some examples. It also gives a conversion of colour coordinates to simulate approximately how any colour is seen if you are colour-blind.

136,204,238 88CCEE

221,204,119 DDCC77

68,170,153 44AA99 51,34,136 332288

153,153,51 999933

17,119,51 117733

136,204,238 88CCEE

170,68,153 AA4499

136,34,85 882255

221,204,119 DDCC77

68,170,153 44AA99 51,34,136 332288

204,102,119 CC6677

153,153,51 999933

204,102,119 CC6677

17,119,51 117733

170,68,153 AA4499

136,34,85 882255

Figure 1: Palette I of printable websmart colours that are as distinct as possible in both normal and colour-blind vision, but also match well together. The same colours are shown on a white and a black background, marked with their decimal RGB values and hexadecimal HTML colour codes.


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Distinct Colour Palettes

Palette I in Fig. 1 consists of colours that are as distinct from each other as possible, while also: • distinct in colour-blind vision; • distinct from black and white; • distinct on computer screen and paper; • matching well together. Colour coordinates (R, G, B) are given in the RGB colour system (red R, green G and blue B), decimal at the top and hexadecimal at the bottom. Alternative palette II in Fig. 2 is more regular: colours in each row have the same shade (light, medium or dark) and in each column the same hue (azure, cyan, teal, yellow, orange, red or pink). This palette has been optimized for the medium shades, so some combinations with light or dark shades, shown in Table. 1, are best avoided. If palette I is used, colours can be chosen at random, but

119,170,221 119,204,204 136,204,170 221,221,119 221,170,119 221,119,136 204,153,187 77AADD 77CCCC 88CCAA DDDD77 DDAA77 DD7788 CC99BB

68,119,170 4477AA

68,170,170 44AAAA

68,170,119 44AA77

170,170,68 AAAA44

170,119,68 AA7744

170,68,85 AA4455

170,68,136 AA4488

17,68,119 114477

17,119,119 117777

17,119,68 117744

119,119,17 777711

119,68,17 774411

119,17,34 771122

119,17,85 771155

Figure 2: Palette II with a more regular pattern of hues (columns) and shades (rows). Table 1: Colour combinations from palette II (Fig. 2) that are least distinct in colour-blind vision. These should be avoided, especially the top two.


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68,119,170 4477AA

68,119,170 204,102,119 4477AA CC6677

68,119,170 221,204,119 204,102,119 4477AA DDCC77 CC6677

68,119,170 4477AA

17,119,51 221,204,119 204,102,119 117733 DDCC77 CC6677

51,34,136 136,204,238 17,119,51 221,204,119 204,102,119 332288 88CCEE 117733 DDCC77 CC6677

51,34,136 136,204,238 17,119,51 221,204,119 204,102,119 170,68,153 332288 88CCEE 117733 DDCC77 CC6677 AA4499

51,34,136 136,204,238 68,170,153 332288 88CCEE 44AA99

51,34,136 136,204,238 68,170,153 332288 88CCEE 44AA99

51,34,136 136,204,238 68,170,153 332288 88CCEE 44AA99

51,34,136 136,204,238 68,170,153 332288 88CCEE 44AA99

51,34,136 102,153,204 136,204,238 68,170,153 332288 6699CC 88CCEE 44AA99

51,34,136 102,153,204 136,204,238 68,170,153 332288 6699CC 88CCEE 44AA99

17,119,51 117733

17,119,51 117733

17,119,51 117733

153,153,51 221,204,119 204,102,119 170,68,153 999933 DDCC77 CC6677 AA4499

153,153,51 221,204,119 204,102,119 136,34,85 999933 DDCC77 CC6677 882255

153,153,51 221,204,119 999933 DDCC77

17,119,51 117733

17,119,51 117733

17,119,51 221,204,119 204,102,119 170,68,153 117733 DDCC77 CC6677 AA4499

102,17,0 661100

153,153,51 221,204,119 999933 DDCC77

153,153,51 221,204,119 999933 DDCC77

204,102,119 136,34,85 CC6677 882255

102,17,0 661100

102,17,0 661100

170,68,153 AA4499

170,68,153 AA4499

204,102,119 136,34,85 CC6677 882255

204,102,119 170,68,102 CC6677 AA4466

170,68,153 AA4499

136,34,85 882255

170,68,153 AA4499

Figure 3: Scheme examples for qualitative data. Each row is a scheme for a different number of colours.

even here some combinations are more distinct than others. Some of the most distinct subsets, depending on the number of colours, are given in Fig. 3. When there are more than nine colours, some extra colours outside palette I have been defined. For subsets of fewer than five colours, the dark blue has been replaced by medium azure from palette II. Data gaps can be indicated with light grey DDDDDD (221, 221, 221). The four-colour set in Fig. 3 is reasonably distinct when printed in grey, but a set optimized for this purpose is shown in Figure 4.


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Figure 4: A four-colour subset of palette I that is optimized for printing in grey scale. Tip: if used for lines, also use dashed and dotted lines.

B

A

C

T

G

S

Y

O

R

P

M

V

B

A

C

T

G

S

Y

O

R

P

M

V

Figure 5: All websmart sRGB colours with vividness 0.4 with printable colours enclosed by a black line. Initials stand for blue, azure, cyan, teal, green, spring, yellow, orange, red, pink, magenta and violet. Colours in palette I (left) and palette II (right) are indicated by white squares. Three light shades in palette II have been made less vivid (out of the plane of the figure) to put them inside the CMYK gamut, and are therefore not indicated. Geometric distance does not indicate perceptual colour distance, especially not if colour-blindness is taken into account.

The design of these palettes involved four types of calculations: • for the distance between colours the CIEDE2000 colour difference ΔE00 is used [1]; • red-blind and green-blind vision is simulated by the method described in section 6; • colours with the same product of saturation S and value V in the HSV colour system (same ‘vividness’) match well together; • colours are called ‘printable’ if they are within the CMYK gamut provided by colour profile ‘ISO Coated v2 300%’ (discussed below). To reduce the number of calculations without much loss of choice, only websmart colours were considered, meaning the hexadecimal RGB coordinates are only 00, 11, . . . , FF. The vividness was chosen to be SV = 0.4. With a smaller value colours become too grey, with a larger value there is not enough range of shades for palette II and in general there are fewer printable colours. All colours in this document are defined in sRGB colour space, the default used by most software and displays. Printers work in a different colour space that also varies from model to model. When they conform to international standard ISO 12647-2 and the exact printing conditions are not known beforehand, it is recommended to assume the CMYK colour space provided by colour profile ‘ISO Coated v2 300%’ [2]. All palette colours are taken from the overlap between this and the sRGB colour spaces. More specifically, the two colour blocks in Fig. 5 show all sRGB colours with vividness 0.4, while the colours enclosed by a black line are also in the CMYK colour space defined above and therefore printable. Pure blue of this vividness (column above B) is not printable. Magenta, green and light cyan are also problematic for printers. The palette colours are indicated by squares. They are not equally spread over the figure within the black lines, because geometric distance in this figure does not correspond to perceptual colour distance, even in normal vision. The Netherlands Standardization Institute NEN has issued a code of practice which includes a recommended palette with eight colours, three greys and white [3]. Differences between them are often much smaller than the smallest difference in palette I, two colours are not printable and they cannot be quoted without infringing copyright. This section ends on an SRON-specific topic: PowerPoint presentations on a dark grey background. In this case the light shades (top row) in palette II could be used. However, the original SRON template already


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255,255,255 FFFFFF

255,255,204 FFFFCC

255,204,102 FFCC66

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128,155,200 809BC8

100,194,4 64C204

255,102,102 FF6666

66,66,66 424242

Figure 6: SRON PowerPoint colours on a dark grey background, with the left four taken from the original template. Colours from the top row in Fig. 2 also work on this background.

defines three colours: white for titles, light yellow for normal text and orange for highlighted text. If the light blue from the footer is added, two extra hues are green and red. The complete palette optimized for projection is shown in Fig. 6. The red is rather pale, because it becomes darker on a projection screen. The green is carefully chosen so it differs from orange in red-blind vision and differs from red in green-blind vision.

3

Best Colour Scheme for Different Data Types

A colour scheme should reflect the type of data shown. There are three basic types of data: 1. Qualitative data—nominal or categorical data, where magnitude differences are not relevant. This includes text in presentations and lines in plots. Use palette I (Fig. 3) or different hues (colours from a row) in palette II (Fig. 2). 2. Sequential data—data ordered from low to high.

255,247,188 254,196,79 FFF7BC FEC44F

217,95,14 D95F0E

255,251,213 254,217,142 251,154,41 FFFBD5 FED98E FB9A29

255,251,213 254,217,142 251,154,41 FFFBD5 FED98E FB9A29

204,76,2 CC4C02

217,95,14 D95F0E

255,251,213 254,227,145 254,196,79 251,154,41 FFFBD5 FEE391 FEC44F FB9A29

153,52,4 993404

217,95,14 D95F0E

255,251,213 254,227,145 254,196,79 251,154,41 236,112,20 FFFBD5 FEE391 FEC44F FB9A29 EC7014

204,76,2 CC4C02

255,255,229 255,247,188 254,227,145 254,196,79 251,154,41 236,112,20 FFFFE5 FFF7BC FEE391 FEC44F FB9A29 EC7014

255,255,229 255,247,188 254,227,145 254,196,79 251,154,41 236,112,20 FFFFE5 FFF7BC FEE391 FEC44F FB9A29 EC7014

153,52,4 993404

140,45,4 8C2D04

204,76,2 CC4C02

204,76,2 CC4C02

140,45,4 8C2D04

153,52,4 993404

102,37,6 662506

Figure 7: Scheme for sequential data [4]. The smooth version at the bottom is produced with Eq. (1).


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153,199,236 255,250,210 245,162,117 99C7EC FFFAD2 F5A275

0,139,206 180,221,247 249,189,126 208,50,50 008BCE B4DDF7 F9BD7E D03232

0,139,206 180,221,247 255,250,210 249,189,126 208,50,50 008BCE B4DDF7 FFFAD2 F9BD7E D03232

58,137,201 153,199,236 230,245,254 255,227,170 245,162,117 210,77,62 3A89C9 99C7EC E6F5FE FFE3AA F5A275 D24D3E

58,137,201 153,199,236 230,245,254 255,250,210 255,227,170 245,162,117 210,77,62 3A89C9 99C7EC E6F5FE FFFAD2 FFE3AA F5A275 D24D3E

58,137,201 119,183,229 180,221,247 230,245,254 255,227,170 249,189,126 237,135,94 3A89C9 77B7E5 B4DDF7 E6F5FE FFE3AA F9BD7E ED875E

210,77,62 D24D3E

58,137,201 119,183,229 180,221,247 230,245,254 255,250,210 255,227,170 249,189,126 237,135,94 3A89C9 77B7E5 B4DDF7 E6F5FE FFFAD2 FFE3AA F9BD7E ED875E

61,82,161 3D52A1

61,82,161 3D52A1

58,137,201 119,183,229 180,221,247 230,245,254 255,227,170 249,189,126 237,135,94 3A89C9 77B7E5 B4DDF7 E6F5FE FFE3AA F9BD7E ED875E

210,77,62 D24D3E

210,77,62 D24D3E

58,137,201 119,183,229 180,221,247 230,245,254 255,250,210 255,227,170 249,189,126 237,135,94 3A89C9 77B7E5 B4DDF7 E6F5FE FFFAD2 FFE3AA F9BD7E ED875E

174,28,62 AE1C3E

210,77,62 D24D3E

174,28,62 AE1C3E

Figure 8: Scheme for diverging data [4]. The smooth version at the bottom is produced with Eq. (2).

(a) If there are two or three classes, it is possible to use different intensities of the same hue (colours from a column) in palette II (Fig. 2). (b) For three or more classes, use a scheme as given in Fig. 7. 3. Diverging data—data ordered between two extremes where the midpoint is important, e.g. positive and negative deviations from zero or a mean. Use a scheme as given in Fig. 8. Plot examples of qualitative data, sequential data and a combination are given in Figs. 9, 10 and 11, respectively. An example of diverging data is shown in Fig. 12.

The smooth version of the yellow-orange-brown

scheme in Fig. 7 is produced by R/ 255 = 1 − 0.392(1 + erf[( − 0.869)/ 0.255]) ,

(1a)

G/ 255 = 1.021 − 0.456(1 + erf[( − 0.527)/ 0.376]) ,

(1b)

B/ 255 = 1 − 0.493(1 + erf[( − 0.272)/ 0.309]) ,

(1c)


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blue yellow red

0.5

0.0

-0.5

green

-1.0 -1.0

-0.5

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1.0

Figure 9: A qualitative colour scheme: distinct colour hues with modest intensity differences for data where magnitude differences are not relevant. Left: four curves and labels that are distinguishable from each other and clear on a white background. Right: members (red), associate members (green), observers (blue) and associate partners (yellow) of the Western European Union. The four-colour set from Fig. 3 is used. 400

300 250 200 150 100

population density @km-2 D

350

50 0

Figure 10: A sequential colour scheme: variation of colour intensity for data that are ordered from low to high, in this case the population density. The hue can also vary to some extent, as long as the intensity differences dominate. (On this map there are no countries in the class 250–300 km−2 .)

Figure 11: A combination of a qualitative and a sequential colour scheme. As in Fig. 9, different categories have different hues: European Football Championship winners are red. As in Fig. 10, within each category, data are ordered from low to high by different intensities: the suicide rate per 100,000 is < 10 (light), 10–15 (medium) or > 15 (dark). Three shades of two hues from Fig. 2 are used.


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Figure 12: A diverging colour scheme: the middle of the legend is emphasized with light colours and low and high extremes are emphasized with dark colours that have contrasting hues. Distance between the WGS84 ellipsoid and the geoid calculated with the EGM96 gravity model.

with 0 ≤  ≤ 1 and error function erf. The smooth blue-yellow-red scheme in Fig. 8 is given by: R/ 255 = 0.237 − 2.13 + 26.922 − 65.53 + 63.54 − 22.365 , !2 0.572 + 1.524 − 1.8112 G/ 255 = , 1 − 0.291 + 0.15742 B/ 255 = 1 1.579 − 4.03 + 12.922 − 31.43 + 48.64 − 23.365 .

(2a) (2b) (2c)

The quantitative (sequential and diverging) schemes in Fig. 7 and 8 were taken from the ColorBrewer website [4], where many others can be found. The qualitative schemes there do not have the characteristics of palettes I and II, which was the reason I designed these two.

4

Rainbow Schemes

Quantitative data should not be shown with a rainbow scheme, because the spectral order of visible light carries no inherent magnitude message. In addition, most rainbow schemes contain bands of almost constant hue with sharp transitions in-between, which are perceived as jumps in the data. Finally, colour-blind people have difficulty distinguishing some colours of the rainbow. However, if you have tried schemes as discussed in the previous section and still want a rainbow, Fig. 13 shows such a scheme that is continuous and reasonably clear in colour-blind vision. The colours in each row are equidistant in normal vision using the CIEDE2000 colour difference [1] as a distance measure. The smooth


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64,64,150 404096

64,64,150 404096

64,64,150 404096

120,28,129 781C81

120,28,129 781C81

120,28,129 781C81

120,28,129 781C81

120,28,129 781C81

120,28,129 781C81

63,71,155 3F479B

64,64,150 404096

65,59,147 413B93

63,78,161 3F4EA1

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217,33,32 D92120

82,157,183 125,184,116 227,156,55 529DB7 7DB874 E39C37

217,33,32 D92120

73,140,194 99,173,153 190,188,72 230,139,51 498CC2 63AD99 BEBC48 E68B33

63,96,174 3F60AE

63,86,167 3F56A7

87,163,173 222,167,58 57A3AD DEA73A

Issue

217,33,32 D92120

83,158,182 109,179,136 202,184,67 231,133,50 539EB6 6DB388 CAB843 E78532

217,33,32 D92120

75,145,192 95,170,159 145,189,97 216,175,61 231,124,48 4B91C0 5FAA9F 91BD61 D8AF3D E77C30

217,33,32 D92120

70,131,193 87,163,173 109,179,136 177,190,78 223,165,58 231,116,47 4683C1 57A3AD 6DB388 B1BE4E DFA53A E7742F

217,33,32 D92120

66,119,189 82,157,183 98,172,155 134,187,106 199,185,68 227,156,55 231,109,46 4277BD 529DB7 62AC9B 86BB6A C7B944 E39C37 E76D2E

217,33,32 D92120

65,108,183 77,149,190 91,167,167 110,179,135 161,190,86 211,179,63 229,148,53 230,104,45 416CB7 4D95BE 5BA7A7 6EB387 A1BE56 D3B33F E59435 E6682D

217,33,32 D92120

64,101,177 72,139,194 85,161,177 99,173,153 127,185,114 181,189,76 217,173,60 230,142,52 230,100,44 4065B1 488BC2 55A1B1 63AD99 7FB972 B5BD4C D9AD3C E68E34 E6642C

217,33,32 D92120

Figure 13: Continuous rainbow scheme. The smooth version at the bottom is produced with Eq. (3).

136,46,114 177,120,166 214,193,222 25,101,176 82,137,199 123,175,222 78,178,101 144,201,135 202,224,171 247,238,85 246,193,65 241,147,45 882E72 B178A6 D6C1DE 1965B0 5289C7 7BAFDE 4EB265 90C987 CAE0AB F7EE55 F6C141 F1932D

17,68,119 114477

119,17,85 771155

119,17,85 771155

68,119,170 119,170,221 17,119,85 4477AA 77AADD 117755

170,68,136 204,153,187 17,68,119 AA4488 CC99BB 114477

170,68,136 204,153,187 17,68,119 AA4488 CC99BB 114477

68,170,136 153,204,187 119,119,17 170,170,68 221,221,119 119,17,17 44AA88 99CCBB 777711 AAAA44 DDDD77 771111

170,68,68 221,119,119 119,17,68 AA4444 DD7777 771144

68,119,170 119,170,221 17,119,119 68,170,170 119,204,204 119,119,17 170,170,68 221,221,119 119,68,17 4477AA 77AADD 117777 44AAAA 77CCCC 777711 AAAA44 DDDD77 774411

68,119,170 119,170,221 17,119,119 68,170,170 119,204,204 17,119,68 4477AA 77AADD 117777 44AAAA 77CCCC 117744

232,96,28 E8601C

170,68,119 221,119,170 AA4477 DD77AA

170,119,68 221,170,119 119,17,34 AA7744 DDAA77 771122

68,170,119 136,204,170 119,119,17 170,170,68 221,221,119 119,68,17 44AA77 88CCAA 777711 AAAA44 DDDD77 774411

220,5,12 DC050C

170,68,85 221,119,136 AA4455 DD7788

170,119,68 221,170,119 119,17,34 AA7744 DDAA77 771122

170,68,85 221,119,136 AA4455 DD7788

Figure 14: Banded rainbow schemes with a large number of steps. It is better to use all colours in a smaller scheme than to pick colours from a larger scheme.


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latitude @degreesD

20

0

-20

-40 -60 -100

0.6

0

-50

0.8

1.0

1.2

1.4

50 longitude @degreesD

1.6

1.8

2.0

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2.2

2.4

2.6

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2.8

3.0

1018 moleculescm2

Figure 15: The smooth, continuous rainbow scheme from Fig. 13 used for sequential data. SCIAMACHY CO total column in October 2004 [5].

latitude @degreesD

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-40 -60 -100

0.6

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0.8

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50 longitude @degreesD

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1.8 18

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Figure 16: Top banded rainbow scheme from Fig. 14 used for the same sequential data as in Fig. 15.

version at the bottom is given by: R/ 255 =

0.472 − 0.567 + 4.052 1 + 8.72 − 19.172 + 14.13

,

G/ 255 = 0.108932 − 1.22635 + 27.2842 − 98.5773 + 163.34 − 131.3955 + 40.6346 , B/ 255 = 1 1.97 + 3.54 − 68.52 + 2433 − 2974 + 1255 .

(3a) (3b) (3c)

If more than 10 steps are needed, the colours become difficult to discern. In that case consider using the smooth version or (part of) one of the banded schemes in Fig. 14. The top banded scheme is based on the temperature map of the weather forecast in newspaper de Volkskrant, tweaked to make the colours more distinct. The other banded schemes are based on distinct colour palette II and a reoptimization with 15 colours. Examples of all types are shown in Figs. 15, 16 and 17. Figure 15 shows an advantage of the continuous rainbow scheme over the earlier quantitative schemes when data is missing: because the whole range of colours is equally saturated, there is a clear distinction between data and non-data. The other schemes have pale colours at the low end or middle of the range. With a banded scheme as in Fig. 16, it is easier to determine the value at a particular location.


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Figure 17: Bottom banded scheme from Fig. 14 used for sequential data. Albedo of snow- and cloud-free land at 2.1 µm at a resolution of 7.5 km, using MODIS data from 4–19 July 2007.

5

Colour-Scheme Robustness

Figure 18 shows most schemes defined in this document used in a variation of the diagnostic map used by the ColorBrewer website [4]. A scheme works if the following can be done without much effort: • in the random section at the left, distinguish every colour; • in each section with one main colour, find the outliers (one per colour) and distinguish them from each other. All schemes are shown with nine colours; in cases where fewer colours are used, the data will be clearer.

6

Colour-Blindness

People usually find out at an early age whether they are colour-blind. However, there are subtle variants of colour-vision deficiency. The two main types are: • Green-blindness – the cone cells in the retina that are sensitive to medium wavelengths are absent or have their response shifted to the red (6% of men, 0.4% of women);


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Figure 18: Check for colour-scheme robustness: can all colours be distinguished in a random pattern and when surrounded by another colour.


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Figure 19: The readable text in this image is the colour-vision diagnosis of the reader. It is not a puzzle: there is no hidden message that requires much effort to see. The clarity of the text is not important, only whether it is readable at all. Please do not make life-changing decisions based only on this test.

• Red-blindness – the cone cells in the retina that are sensitive to long wavelengths are absent or have their response shifted to the green (2.5% of men). Figure 19 is a test on these types. It works on a computer screen (when looking straight at it), projected with a beamer and sometimes even in unfaded print, although this will depend on the quality of the equipment. To simulate green-blindness [6, 7], all RGB colours in an image are converted to R’G’B’ colours with 1/ 2.2 , (4a) R0 = 4211 + 0.677G2.2 + 0.2802R2.2 1/ 2.2 G0 = 4211 + 0.677G2.2 + 0.2802R2.2 , (4b) 1/ 2.2 B0 = 4211 + 0.95724B2.2 + 0.02138G2.2 − 0.02138R2.2 , (4c) with parameters R, G and B in the range 0–255 and the output values rounded. To simulate red-blindness, colours are shifted as follows: 1/ 2.2 , R0 = 782.7 + 0.8806G2.2 + 0.1115R2.2 1/ 2.2 G0 = 782.7 + 0.8806G2.2 + 0.1115R2.2 , 1/ 2.2 B0 = 782.7 + 0.992052B2.2 − 0.003974G2.2 + 0.003974R2.2 .

(5a) (5b) (5c)

These conversions should be applied in sRGB colour space, i.e. they work on a standard video display, but not necessarily on paper. The conversion can be performed with the free software suite ImageMagick. The following two commands make green-blind and red-blind versions of original image original.png, respectively:1 convert original.png \( +clone -channel RG -fx "(0.02138+0.6770*G^2.2+0.2802*R^2.2)^(1/2.2)" \) \ +swap -channel B -fx "(0.02138(1+v.G^2.2-v.R^2.2)+0.9572*v.B^2.2)^(1/2.2)" greenblind.png convert original.png \( +clone -channel RG -fx "(0.003974+0.8806*G^2.2+0.1115*R^2.2)^(1/2.2)" \) \ +swap -channel B -fx "(0.003974(1-v.G^2.2+v.R^2.2)+0.9921*v.B^2.2)^(1/2.2)" redblind.png

Figure 20 shows the result when they are applied to a triangle of normal colours (top): the green-blind simulation is at bottom left, the red-blind simulation at bottom right. Contrary to popular belief, pure red and green 1 These

are Unix-style commands, for Windows replace \( and \) by ( and ), and use a caret (ˆ) instead of a backslash to end the first line.


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Figure 20: Colour scale in normal vision (top), green-blind vision (bottom left) and red-blind vision (bottom right). These conversions are only approximate and are designed for a computer screen. Table 2: Colours in Fig. 1 as seen in normal and colour-blind vision. Palette I in normal vision.

Approximate green-blind simulation of palette I.

Approximate red-blind simulation of palette I.

can be distinguished. Instead, yellow/green and purple/blue combinations are problematic. However, there are more unexpected pairs of colours that look the same, as used in Fig. 19. Table 2 shows colour-blind vision simulations of distinct colour palette I.


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Reference Documents [1] Gaurav Sharma, Wencheng Wu, and Edul N. Dalal. The CIEDE2000 color-difference formula: implementation notes, supplementary test data, and mathematical observations. Color Research and Application, 30:21–30, 2005. http://www.ece.rochester.edu/~gsharma/ciede2000/ciede2000noteCRNA.pdf. [2] Olaf Drümmer. ECI offset profiles, 2009. http://www.eci.org/doku.php?id=en:colorstandards:offset. [3] Normcommissie ‘Ergonomie van de fysische werkomgeving’ with Buro Blind Color. Functional use of colour—accommodating colour vision disorders. Code of practice NPR 7022, Netherlands Standardization Institute, Delft, April 2006. [4] Cynthia A. Brewer. ColorBrewer, a web tool for selecting colors for maps, 2009. http://colorbrewer2.org. [5] A.M.S. Gloudemans, M.C. Krol, J.F. Meirink, A.T.J. de Laat, G.R. van der Werf, H. Schrijver, M.M.P. van den Broek, and I. Aben. Evidence for long-range transport of carbon monoxide in the southern hemisphere from SCIAMACHY observations. Geophysical Research Letters, 33:L16807, 2006. [6] Françoise Viénot, Hans Brettel, and John D. Mollon. Digital video colourmaps for checking the legibility of displays by dichromats. Color Research and Application, 24:243–252, 1999. [7] Hans Brettel, Françoise Viénot, and John D. Mollon. Computerized simulation of color appearance for dichromats. Journal of the Optical Society of America A, 14:2647–2655, 1997.