Digital Video Colourmaps for

Checking the Legibility of

Displays by Dichromats

Françoise Viénot,1* Hans Brettel,2

John D. Mollon3
1
Muséum National d’Histoire Naturelle, Laboratoire de Photobiologie, 43 rue Cuvier, 75005 Paris, France

2
CNRS URA 820, Ecole Nationale Supérieure des Télécommunications, Département de Traitement du Signal et de
l’Image, 46 rue Barrault, 75013 Paris, France

3
Department of Experimental Psychology, Downing St, Cambridge CB2 3EB, UK

Received 29 May 1998; accepted 8 January 1999

Abstract: We propose replacement colourmaps that allow a METHODS

designer to check the colours seen by protanopes and deu-
teranopes. Construction of the colourmaps is based on the The method is based on the LMS system, which specifies
LMS specification of the primaries of a standard video colours in terms of the relative excitations of the longwave
monitor and has been carried out for 256 colours, including sensitive (L), the middlewave sensitive (M), and the short-
216 colours that are common to many graphics applications wave sensitive (S) cones. As dichromats lack one class of
of MS Windows and Macintosh computing environments. cone photopigment, they confuse colours that differ only in
© 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 243–252, 1999 the excitation of the missing class of photopigment. In
contrast to the case of the trichromatic observer, who re-
quires colour specifications by three components, two com-
Key words: colour; dichromacy; computer; simulation; rec- ponents are sufficient to specify colour for the dichromat.
ognition; fundamentals; colour vision deficiencies One can construct a rule to reduce any set of confused
colours to a single three-component colour specification.
Quantitative estimates of the colour perceptions typical of
protanopic and deuteranopic observers have been given for
INTRODUCTION
the whole range of colours in the Munsell colour-order
system.1 Potentialities of computer graphics systems to syn-
Digital video technologies allow us to create and modify
thesize a picture of the world as seen by dichromats have
colour images. Most often, the choice of colour is supposed
been outlined, and dichromatic versions of an image have
to enhance readability. However, for those who suffer from
been produced using (u9, v9) chromaticity transformation
colour-blindness and who represent 8% of the male popu-
for every pixel.2 A more general transformation for simu-
lation, the choice of colours may not be optimal. Colour-
lating colour-deficient vision, which circumvents the CIE
blinds confuse colours that are discriminable for the normal.
XYZ system and comprises both the dichromatic and anom-
The most severely affected people are those who have a
alous case, has been implemented in a colour editor for
dichromatic form of colour vision deficiency. It is possible
to compute colour confusions and to simulate dichromatic display design.3,4
colour vision. Here, we propose colourmaps to replace the Here, we construct colourmaps to replace a standard
“system” ones, and to allow a designer with normal colour palette of 256 colours, including 216 colours that are com-
vision to simulate the colours seen by dichromats. mon to many graphics applications of MS Windows and
Macintosh computing environments, and show how a co-
lour image would look for protanopes or for deuteranopes.
* Correspondence to: F. Viénot; e-mail: vienot@mnhn.fr In our former publications,5,6 we have given an illustra-
© 1999 John Wiley & Sons, Inc. tion and described a detailed algorithm for simulating co-

Volume 24, Number 4, August 1999 CCC 0361-2317/99/040243-10 243

 normals. The advantage of specifying colours in the LMS
colour space rather than the XYZ colour space is that the
transformation takes into account the altered luminosity
function of dichromats, especially for protanopes.
Here we maintain this scheme of reduction, but we in-
troduce three compromises in order to achieve the practical
goal of replacement colourmaps that can be implemented on
any graphics monitor.
First, instead of requiring individual calibration of the
video display, we assume that the video display primaries
and nominal white are representative of recent standards for
Cathode Ray Tube (CRT) monitors7,8 and that its video-
transfer function is a power function with an exponent of 2.2
(“gamma”).
Second, the video display standard is specified in terms of
CIE 1931 ( x, y) chromaticity coordinates, but the best sets
of fundamentals are not derived from the CIE 1931 color-
imetric observer. The Smith and Pokorny9 set of fundamen-
tals is derived from the Judd–Vos modified colorimetric
observer,10,11 i.e., an observer slightly different from the
CIE 1931 one, with no possible linear transformation be-
FIG. 1. Representation of stimuli in LMS space. All colours tween them. Because the video display standard does not
obtainable by combination of the primaries are included in recommend a spectral power distribution for primaries but
the parallelpiped KBMRGCWY. K: Black. B: Blue primary. M: only chromaticities, we convert from ( x, y) chromaticity
Magenta. R: Red primary. G: Green primary. C: Cyan. W:
White. Y: Yellow. The replacement colours are located in the
coordinates to modified ( x9, y9) coordinates using the for-
reduced plane KBWY. QpQ is a confusion line for protanope; mula of Vos11 this formula strictly applies for spectral
all colours of QpQ line reduce to its intersection Q with the stimuli, and our second compromise consists in extending it
plane KBWY. QdQ is a confusion line for deuteranope; all to the primaries and the nominal white.
colours of QdQ line reduce to its intersection Q with the Third, in order to use as many colours as possible of the
plane KBWY.
video display gamut, we choose replacement colours on a
diagonal plane of the RGB colour space of the display
lour appearance for dichromats. We proposed to reduce all device (Fig. 1).
stimuli belonging to a confusion line, i.e., to a line parallel
to the axis of the missing photopigment in the LMS speci-
RESULTS
fication space, to a single colour and to represent the di-
chromat’s colour space by two half-planes, each of which Starting with a standard palette of 216 colours, which are
included the neutral axis and an anchor wavelength, which commonly used with MS Windows and Macintosh comput-
is the wavelength that appears similar to dichromats and ing environments, and which we have extended to 256

FIG. 2. Computational procedure giving the replacement colourmaps to simulate dichromatic vision (subscript d). Each
operation is numbered according to the successive steps described in the Methods section.

244 COLOR research and application

TABLE I. Chromaticity (x, y) of primaries and refer- 1.0271x l 2 0.00008y l 2 0.00009
ence white of the ITU-R BT.709 standard and of the x9l 5 (3)
0.03845x l 1 0.01496y l 1 1
NTSC. Modified chromaticity (x9, y9) converted from
(x, y) using Vos (1978) transformation. 0.00376x l 1 1.0072y l 1 0.00764
y9l 5 (3)
ITU-R BT.709 NTSC 0.03845x l 1 0.01496y l 1 1
standard standard
to the chromaticity ( x, y) of the red, green, and blue
x y x y primaries and nominal white of the International Telecom-
Red primary 0.64 0.33 0.67 0.33
Green primary 0.30 0.60 0.21 0.71 munication Union ITU-R BT.709 standard7 (Table I) and
Blue primary 0.15 0.06 0.14 0.08 obtain slightly modified chromaticity coordinates ( x9, y9).
Reference white D65 CIE C D93 white Then we compute the corresponding modified (X 2 , Y 2 ,
0.3127 0.3290 0.310 0.316 0.2831 0.2971 Z 2 ) tristimulus values for the primaries and get the matrix12
ITU-R BT.709

1 2 1 21 2
standard X2 R2
x9 y9 Y2 5 RGB to XYZ G2
Red primary 0.6384 0.3326
Green primary 0.3018 0.6008 Z2 B2

S DS D
Blue primary 0.1530 0.0682
Reference white D65 40.9568 35.5041 17.9167 R2
0.3157 0.3345
5 21.3389 70.6743 7.98680 G2 .
1.86297 11.4620 91.2367 B2

From Smith and Pokorny,9 we get

colours, we have constructed two replacement colourmaps

1 2 1 21 2
that illustrate protanopic and deuteranopic vision, respec-
L X2
tively.
M 5 XYZ to LMX Y2
The transformation scheme to compute the replacement
S Z2
colourmaps includes several steps (Fig. 2).

1 21 2
0.15514 0.54312 2 0.03286 X2
1. Given (I, J, K) as the 8-bit DAC values for each of the 2 0.15514 0.45684
5 0.03286 Y2 .
(R, G, B) video channels, we compute the relative 0 0 0.01608 Z2
photometric quantities R, G, B:
R 5 ~I/ 255!^2.2 (1) The RGB to LMS matrix is the product of two matrices:

G 5 ~ J/ 255!^2.2

B 5 ~K/ 255!^2.2.
(1)

(1)
S D
L
M
S
5 ~ XYZ to LMS !~ RGB to XYZ ! S D R2
G2
B2

2. In order to produce reduced colours that are included in

the colour gamut of the monitor, we slightly reduce the
colour domain of the initial palette. This is achieved by
S D
L
M
S
5 ~ RGB to LMS ! S D
R2
G2
B2

S D
appropriate scaling of the relative photometric quantities. 17.8824 43.5161 4.11935
For protanopes: 5 3.45565 27.1554 3.86714
R 2 5 0.992052 R 1 0.003974 (2) 0.0299566 0.184309 1.46709

G 2 5 0.992052 G 1 0.003974

B 2 5 0.992052 B 1 0.003974.
(2)

(2)
3 S D
R2
G2
B2
. (4)

For deuteranopes:
4. The reduced colour domain is the plane including the
R 2 5 0.957237 R 1 0.0213814 (2) origin, the white point, and the blue primary. Solving the
plane equation for the origin (0, 0, 0), the blue primary
G 2 5 0.957237 G 1 0.0213814 (2) stimulus (L B , M B , S B ) and the white stimulus (L W , M W ,
S W ) gives the equation of the reduced plane
B 2 5 0.957237 B 1 0.0213814. (2)
aL 1 bM 1 gS 5 0
3. The LMS specification of each colour is obtained from
the CIE 1931 ( x, y) specifications of the CRT display by with
the following procedure. We first apply the Judd–Vos
colorimetric modification10,11 a 5 M WS B 2 M BS W

Volume 24, Number 4, August 1999 245

 TABLE II. DAC values of replacement colourmaps, which allow a designer to check the readability of colour images by protanopes and deuteranopes. As

246
the plane of reduced stimuli is a diagonal plane of the RGB colour space of the video display, DAC values for red and green primaries are equal.
Protan Deutan Protan Deutan Protan Deutan Protan Deutan
Standard replacement replacement Standard replacement replacement Standard replacement replacement Standard replacement replacement
DAC values values values DAC values values values DAC values values values DAC values values values
I J K Ip, Jp Kp Id, Jd Kd I J K Ip, Jp Kp Id, Jd Kd I J K I p , Jp Kp Id, Jd Kd I J K Ip, Jp Kp Id, Jd Kd

255 255 255 255 255 253 253 255 255 153 255 153 253 155 255 255 51 255 54 253 65 238 0 0 89 27 139 18
204 255 255 249 254 239 253 204 255 153 249 153 239 156 204 255 51 249 53 239 70 221 0 0 83 27 130 24
153 255 255 246 254 229 254 153 255 153 246 153 229 158 153 255 51 246 52 229 73 187 0 0 71 25 112 32
102 255 255 243 254 222 255 102 255 153 243 153 222 158 102 255 51 243 51 222 75 170 0 0 65 24 103 35
51 255 255 242 254 218 255 51 255 153 242 152 218 159 51 255 51 242 51 218 76 136 0 0 53 23 86 39
0 255 255 241 254 217 255 0 255 153 241 152 217 159 0 255 51 241 51 217 76 119 0 0 48 22 78 40
255 204 255 210 255 219 252 255 204 153 210 154 219 153 255 204 51 210 55 219 60 85 0 0 37 21 63 43
204 204 255 204 255 203 253 204 204 153 204 153 203 155 204 204 51 204 54 203 65 68 0 0 32 21 57 43
153 204 255 199 254 191 253 153 204 153 199 153 191 156 153 204 51 199 53 191 68 34 0 0 24 21 47 44
102 204 255 196 254 181 254 102 204 153 196 153 181 157 102 204 51 196 52 181 71 17 0 0 21 21 45 44
51 204 255 194 254 176 254 51 204 153 194 153 176 157 51 204 51 194 52 176 72 0 238 0 225 8 203 59
0 204 255 193 254 175 254 0 204 153 193 153 175 157 0 204 51 193 52 175 72 0 221 0 209 11 189 57
255 153 255 168 255 190 251 255 153 153 168 154 190 152 255 153 51 168 56 190 55 0 187 0 177 15 161 53
204 153 255 160 255 171 252 204 153 153 160 154 171 153 204 153 51 160 55 171 61 0 170 0 161 16 147 52
153 153 255 153 255 155 253 153 153 153 153 153 155 155 153 153 51 153 54 155 65 0 136 0 129 18 120 49
102 153 255 149 254 143 253 102 153 153 149 153 143 155 102 153 51 149 53 143 67 0 119 0 114 19 107 48
51 153 255 146 254 136 253 51 153 153 146 153 136 156 51 153 51 146 53 136 68 0 85 0 82 20 82 46
0 153 255 145 254 134 253 0 153 153 145 153 134 156 0 153 51 145 53 134 69 0 68 0 67 20 70 45
255 102 255 131 255 167 250 255 102 153 131 154 167 151 255 102 51 131 56 167 52 0 34 0 37 21 51 45
204 102 255 120 255 144 251 204 102 153 120 154 144 152 204 102 51 120 55 144 58 0 17 0 25 21 46 44
153 102 255 110 255 123 252 153 102 153 110 153 123 154 153 102 51 110 54 123 62 0 0 238 21 238 44 236
102 102 255 103 255 107 253 102 102 153 103 153 107 155 102 102 51 103 54 107 65 0 0 221 21 221 44 220
51 102 255 99 254 97 253 51 102 153 99 153 97 155 51 102 51 99 54 97 66 0 0 187 21 187 44 187
0 102 255 98 254 94 253 0 102 153 98 153 94 155 0 102 51 98 53 94 67 0 0 170 21 170 44 171
255 51 255 105 255 152 250 255 51 153 105 154 152 150 255 51 51 105 57 152 51 0 0 136 21 136 44 139
204 51 255 89 255 126 251 204 51 153 89 154 126 152 204 51 51 89 56 126 57 0 0 119 21 120 44 123
153 51 255 74 255 102 252 153 51 153 74 154 102 153 153 51 51 74 55 102 61 0 0 85 21 86 44 92
102 51 255 62 255 80 252 102 51 153 62 153 80 154 102 51 51 62 54 80 63 0 0 68 21 70 44 78
51 51 255 54 255 65 253 51 51 153 54 153 65 155 51 51 51 54 54 65 65 0 0 34 21 39 44 54
0 51 255 51 255 60 253 0 51 153 51 153 60 155 0 51 51 51 54 60 65 0 0 17 21 26 44 47
255 0 255 96 255 148 250 255 0 153 96 154 148 150 255 0 51 96 57 148 50 238 238 238 238 238 236 236
204 0 255 77 255 121 251 204 0 153 77 154 121 152 204 0 51 77 56 121 56 221 221 221 221 221 220 220
153 0 255 59 255 94 252 153 0 153 59 154 94 153 153 0 51 59 55 94 60 187 187 187 187 187 187 187
102 0 255 42 255 70 252 102 0 153 42 153 70 154 102 0 51 42 54 70 63 170 170 170 170 170 171 171
51 0 255 27 255 51 252 51 0 153 27 153 51 154 51 0 51 27 54 51 64 136 136 136 136 136 139 139
0 0 255 21 255 44 253 0 0 153 21 153 44 155 0 0 51 21 54 44 65 119 119 119 120 120 123 123

COLOR research and application

 TABLE II. (Continued)
Protan Deutan Protan Deutan Protan Deutan Protan Deutan
Standard replacement replacement Standard replacement replacement Standard replacement replacement Standard replacement replacement
DAC values values values DAC values values values DAC values values values DAC values values values
I J K Ip, Jp Kp Id, Jd Kd I J K Ip, Jp Kp Id, Jd Kd I J K I p , Jp Kp Id, Jd Kd I J K Ip, Jp Kp Id, Jd Kd

255 255 204 255 204 253 203 255 255 102 255 103 253 107 255 255 0 255 21 253 44 85 85 85 86 86 92 92
204 255 204 249 204 239 205 204 255 102 249 102 239 110 204 255 0 249 17 239 52 68 68 68 70 70 78 78
153 255 204 246 203 229 205 153 255 102 246 102 229 112 153 255 0 246 12 229 56 34 34 34 39 39 54 54

Volume 24, Number 4, August 1999

102 255 204 243 203 222 206 102 255 102 243 102 222 113 102 255 0 243 8 222 59 17 17 17 26 26 47 47
51 255 204 242 203 218 206 51 255 102 242 102 218 114 51 255 0 242 4 218 60
0 255 204 241 203 217 206 0 255 102 241 102 217 114 0 255 0 241 0 217 61
255 204 204 210 204 219 202 255 204 102 210 104 219 105 255 204 0 210 24 219 36
204 204 204 204 204 203 203 204 204 102 204 103 203 107 204 204 0 204 21 203 44
153 204 204 199 204 191 204 153 204 102 199 103 191 109 153 204 0 199 18 191 50
102 204 204 196 204 181 205 102 204 102 196 102 181 111 102 204 0 196 15 181 53
51 204 204 194 204 176 205 51 204 102 194 102 176 111 51 204 0 194 14 176 55
0 204 204 193 203 175 205 0 204 102 193 102 175 111 0 204 0 193 13 175 55
255 153 204 168 204 190 201 255 153 102 168 104 190 102 255 153 0 168 26 190 27
204 153 204 160 204 171 202 204 153 102 160 103 171 105 204 153 0 160 23 171 38
153 153 204 153 204 155 203 153 153 102 153 103 155 107 153 153 0 153 21 155 44
102 153 204 149 204 143 204 102 153 102 149 103 143 109 102 153 0 149 19 143 48
51 153 204 146 204 136 204 51 153 102 146 103 136 109 51 153 0 146 18 136 50
0 153 204 145 204 134 204 0 153 102 145 103 134 110 0 153 0 145 17 134 50
255 102 204 131 204 167 200 255 102 102 131 104 167 101 255 102 0 131 27 167 18
204 102 204 120 204 144 202 204 102 102 120 104 144 104 204 102 0 120 25 144 33
153 102 204 110 204 123 203 153 102 102 110 103 123 106 153 102 0 110 22 123 40
102 102 204 103 204 107 203 102 102 102 103 103 107 107 102 102 0 103 21 107 44
51 102 204 99 204 97 204 51 102 102 99 103 97 108 51 102 0 99 20 97 46
0 102 204 98 204 94 204 0 102 102 98 103 94 108 0 102 0 98 19 94 47
255 51 204 105 204 152 200 255 51 102 105 104 152 100 255 51 0 105 28 152 9
204 51 204 89 204 126 201 204 51 102 89 104 126 103 204 51 0 89 25 126 30
153 51 204 74 204 102 202 153 51 102 74 103 102 105 153 51 0 74 23 102 38
102 51 204 62 204 80 203 102 51 102 62 103 80 107 102 51 0 62 22 80 42
51 51 204 54 204 65 203 51 51 102 54 103 65 107 51 51 0 54 21 65 44
0 51 204 51 204 60 203 0 51 102 51 103 60 107 0 51 0 51 20 60 45
255 0 204 96 204 148 200 255 0 102 96 104 148 100 255 0 0 96 28 148 0
204 0 204 77 204 121 201 204 0 102 77 104 121 103 204 0 0 77 26 121 29
153 0 204 59 204 94 202 153 0 102 59 103 94 105 153 0 0 59 23 94 37
102 0 204 42 204 70 203 102 0 102 42 103 70 106 102 0 0 42 22 70 42
51 0 204 27 204 51 203 51 0 102 27 103 51 107 51 0 0 27 21 51 44
0 0 204 21 204 44 203 0 0 102 21 103 44 107 0 0 0 21 21 44 44

247
 b 5 S WL B 2 S BL W

g 5 L WM B 2 L BM W.

The reduction of the normal colour domain to the dichro-

matic colour domain maintains the fundamental values cor-
responding to the existing photopigments, S and M for the
protanope, and S and L for the deuteranope.
The replacement tristimulus value corresponding to the
missing photopigment is, for the protanope,
L p 5 2~ b M 1 g S!/ a ;
and, for the deuteranope,
M d 5 2~ a L 1 g S!/ b .
This results in the following linear transformations for re-
ducing the normal colour domain to the dichromat colour
domain, for protanopes:

S DS Lp
Mp
Sp
5
0 2.02344
0
0
1
0
2 2.52581
0
1
DS D L
M
S
(5)

and for deuteranopes:

S DS Ld
Md
Sd
5
1 0 0
0.494207 0 1.24827
0 0 1
DS D L
M
S
. (5)

5. Transformation of L d M d S d or L p M p S p to RGB is ob-

tained using the inverse matrix of matrix (4) in step 3):

S D
Rd
Gd
Bd
5 ~ RGB to LMS ! 21 S D Ld
Md
Sd
FIG. 3. Colour illustration of the 256 colour palettes spec-
ified in Table II. Within each block, the first column illustrates
the original colour of the normal colourmap, the second and

S D
third columns illustrate its appearance in the protan and
Rd deutan transformation. The vertical sequence of samples is
Gd as in Table II.
Bd

5S 0.080944
2 0.0102485
2 0.000365294
2 0.130504
0.0540194
2 0.00412163
0.116721
2 0.113615
0.693513
D Figure 3 illustrates side-by-side every sample of the
256 colour palette of Table II in its normal, protan, and
deutan version, in the same order as in the table. It can be

S D
seen that samples of the colourful left column are re-
Ld
placed by yellow or blue shades, in various lightnesses
3 Md . (6)
or saturations. It can be seen also that the protan and
Sd
the deutan transformation yield colours of different
lightnesses.
6. DAC-values of the replacement colourmaps are obtained
Figure 4 shows an example where the normal, protan,
using the inverse of the relationship described in step (1):
and deutan versions of an RATP-RER transportation map
I d 5 255 R d^~1/ 2.2! (7) of Paris (France) are presented in colour. The Réseau
Express Régional (RER) of Régie Autonome des Trans-
J d 5 255 G d^~1/ 2.2! (7) ports Parisiens (RATP, Paris, France) is the underground
and train network, which operates between Paris and its
K d 5 255 B d^~1/ 2.2!. (7)
outskirts. All colours of the transportation map that have
Table II shows the DAC values of the resulting replacement been originally used by the designer are part of Table II.
colourmaps. The protan and deutan versions result from replacing the
Because the plane of reduced stimuli is a diagonal plane normal colourmap by the protan or by the deutan colour-
of the RGB colour space of the video display, DAC values map. Although our algorithm was not available by the
for red and green primaries are equal. time the map was designed, the various transportation

248 COLOR research and application

FIG. 4. Normal, protan, and deutan versions of the trans-
portation map of the RATP-RER (Paris, France). The original
image has been produced using a high-resolution version of
the map provided by RATP (by courtesy of RATP). Every
colour has been adjusted in order to comply with the Web
version accessible at: http://www.ratp.fr/Transpor/Reseaux/
planrer.htm. All colours are part of Table II. The protan and
deutan versions result from the replacement of the normal
colourmap by the protan or by the deutan colourmap. The
original red transportation line is transformed in a darker
shade in the protan version than in the deutan version. Left:
normal version. Upper-right: protan version. Lower-right:
deutan version.

lines are still identifiable. Now that it is available, guid- Colorimetric Accuracy
ance on the choice of colours can be obtained simply by
When proper calibration of the user’s video display is not
substituting the colourmaps.
available, the lack of conformity with the ITU standard may
be a source of discrepancy. We have computed the errors of
confused colours originating from poor calibration taking as
DISCUSSION a model the most common shifts of CRT parameters. In
Table III, we indicate the errors in terms of DAC values for
Although the colourmaps we propose have been constructed a few samples of the protan replacement palette:
along the same lines as those used in the full “TrueColour”
representation,6 we should evaluate how far the simulation if the primaries and reference white have the chromaticity
of dichromatic vision is affected by the simplification of the recommended by the National Television Systems Com-
algorithm that we have adopted here. mittee12 instead of those recommended by ITU (Table I),

Volume 24, Number 4, August 1999 249

TABLE III. Computed DAC values, IpJpKp for the protan replacement colourmap, considering different CRT
primaries, reference white, and transfer functions. First column: I J K refer to a few DAC values selected from the
original colourmap. Following columns: IpJpKp are obtained by performing steps 1–7 of the computation as
indicated in the block diagram in Fig. 2. Last line gives the scaling factor used to compute the replacement DAC
values in each case, which at the same time is the maximum achievable scaling factor enabling the reduction of
the entire colour gamut within the real colour gamut of the monitor.
DAC values for the protan replacement map
ITU-R BT.709 ITU-R BT.709
ITU standard NTSC standard primaries primaries
DAC values of the original D65 white CIE C white D93 white D65 white
colourmap Gamma 2.2 Gamma 2.2 Gamma 2.2 Gamma 1.8
I J K Ip, Jp Kp I9p, J9p K9p I0p, J0p K0p I-p, J-p K-p

255 255 255 255 255 254 254 255 255 254 254
0 255 255 241 254 235 255 243 254 238 254
255 0 255 96 255 112 253 89 255 77 255
0 0 255 21 255 30 254 17 255 12 254
255 255 0 255 21 254 30 255 17 254 12
0 255 0 241 0 235 41 243 0 238 0
255 0 0 96 28 112 0 89 23 77 17
0 0 0 21 21 30 30 17 17 12 12
170 0 0 65 24 77 24 60 20 52 15
85 0 0 37 21 46 29 33 18 29 13
0 170 0 161 16 158 35 163 13 159 8
0 85 0 82 20 82 31 82 16 81 11
0 0 170 21 170 30 170 17 170 12 170
0 0 85 21 86 30 88 17 86 12 86
Scaling factor 0.992052 0.982004 0.994881 0.992052

if D93 reference illuminant13 is used as the nominal white are indiscriminable by a dichromatic observer of the same
instead of D65, type.
if the gamma value is 1.8 instead of 2.2. In the absence of an officially recommended set of cone
fundamentals, either those of Smith and Pokorny9 or those
This gives a figure of merit of the replacement colourmaps. of Stockman, MacLeod, and Johnson14 are currently em-
It shows that significant discrepancies could arise from ployed in research. We assume that both come close to the
changing either the primaries or the video transfer function; average normal observer.
the former should not occur, since all ITU members have Strictly, the Smith and Pokorny transformation applies to
agreed on a unique recommendation that is gaining accep- modified tristimulus values obtained from the spectral
tance for CRT based applications,8 but the latter is easily power distribution of the stimulus and the colour-matching
encountered in practice. However, changing the nominal functions modified by Judd and Vos.11 Because the ITU
white would have minimal effect on the palette. video display standard does not specify the primaries in
terms of spectral power distribution but in terms of CIE
1931 chromaticity coordinates, we have extended the appli-
Simplification of the Reduction Scheme
cation of the Vos formula to the chromaticity coordinates of
We propose replacement colourmaps for simulating protan- the primaries and nominal white. In order to evaluate the
opic vision and deuteranopic vision, which are the most error introduced by this procedure, we have compared the
severe cases of colour deficiency. Anomalous trichromatic results with those obtained by a rigorous calculation for an
observers do not confuse all colours of a colour confusion actual video display.
line, so they would be able to discriminate the colours that First, we have measured the ( x, y) chromaticity coordi-

TABLE IV. Comparison between measurements and calculations for an actual CRT video display (IIYAMA
MF-8617A 1995). Columns 2– 4: ( x, y) chromaticity coordinates and (Y) luminance (normalized to 100) in the CIE
1931 colorimetric system. Column 5–7: (x9, y9) chromaticity coordinates and (Ym) luminance obtained using the
Judd–Vos modified colour-matching functions. Column 8 –9: (x9, y9) chromaticity coordinates obtained applying
the Vos formula to (x, y) CIE 1931 chromaticity coordinates.
Measurements Results obtained using Vos cmfs x9 y9 converted from x y
x y Y x9 y9 Ym x9 y9

RED 0.6254 0.3370 24.4929 0.6242 0.3406 24.5046 0.6241 0.3396

GREEN 0.2818 0.6006 67.8719 0.2838 0.6052 67.8903 0.2837 0.6017
BLUE 0.1500 0.0646 7.6353 0.1545 0.0727 8.1588 0.1530 0.0727
WHITE 0.3127 0.3290 100 0.3175 0.3394 100.55 0.3157 0.3345

250 COLOR research and application

 described in the methods section) to the CIE 1931 ( x, y)
chromaticity coordinates of the measured video display. It
appears that the values differ only on the third digit. Then
we have computed the full palette for this actual monitor
using the procedure described in the Methods section, and
the full palette for the same monitor starting the transfor-
mation with the ( x9, y9) modified chromaticity coordinates
directly obtained from the absolute spectral power distribu-
tion of the primaries and the white. For every element of the
256 colour palette, the difference in DAC-value is never
larger than one (Table V). This leads us to conclude that, for
our particular application, extending the Vos formula to the
primaries and the white of a CRT video display is satisfac-
tory.
We are aware that several sources of inter-observer vari-
ability15 such as lens pigmentation, macular pigmentation,
cone effective optical density, and spectral sensitivity of the
visual photopigments are also ignored in this simplified
FIG. 5. Relative spectral power distribution of the primaries
scheme for illustrating the losses of dichromatic colour
of a CRT video display (IIYAMA MF-8617A 1995) adjusted to
give a metamer of D65 as the nominal white. vision.
Finally, by adopting the diagonal plane on which to
project the confused colours, we slightly distort the colour
nates of four CRT video displays and selected the one appearance of the simulated dichromatic image, compared
(IIYAMA MF-8617A 1995) that best conformed to the ITU to our previous simulation. In terms of dominant wave-
standard (Table IV). Then we have measured the spectral lengths, this corresponds to a shift from 475 to 464 nm for
power distribution of its primaries every 5 nm using a the blue anchor wavelength, and to a shift from 575 to 571
calibrated telespectrophotometer (Minolta CS-1000), and nm for the yellow anchor wavelength.
we have computed the absolute spectral power distribution
(Fig. 5) and the (Y) luminance of the primaries that gives a
CONCLUSION
metamer of D65 as the nominal white (Table IV). Knowing
the absolute spectral power distribution of the primaries, it In conclusion, replacing a normal palette by a reduced
is possible to calculate the (X9, Y9, Z9) modified tristimulus palette allows the designer to check the readability of
values and the ( x9, y9) modified chromaticity coordinates of colour information by dichromatic observers in any dis-
the primaries and the white for the Judd–Vos modified played image. Although an accurate simulation of dichro-
colorimetric observer, using the modified colour-matching matic vision would require a careful calibration of the
functions given by Vos.11 We have also computed the result video display, our colourmaps provide an immediate and
of applying the Vos modification11 (step 3 of the procedure efficient warning of possible losses of readability by

TABLE V. DAC values, IpJpKp, for the protan replacement colourmap computed for the actual CRT video display
(IIYAMA MF-8617A 1995), obtained using the Judd–Vos modified colour-matching functions with the spectral
distribution of the primaries, or obtained applying the Vos formula to (x, y) CIE 1931 chromaticity coordinates.
DAC values obtained using DAC values obtained
DAC values of the original colourmap Vos cmfs applying Vos formula
I J K Ip, Jp Kp I9p, J9p K9p

255 255 255 254 254 254 254

0 255 255 238 254 238 254
255 0 255 105 255 106 255
0 0 255 23 254 23 254
255 255 0 254 23 254 23
0 255 0 238 0 238 0
255 0 0 105 32 106 32
0 0 0 23 23 23 23
170 0 0 72 27 72 27
85 0 0 40 24 41 24
0 170 0 159 18 159 18
0 85 0 81 22 81 22
0 0 170 23 170 23 170
0 0 85 23 87 23 87
Scaling factor 0.989729 0.989725

Volume 24, Number 4, August 1999 251

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252 COLOR research and application