Three-dimensional discrimination ellipsoids are presented for a number of representative points in color space. These ellipsoids have been obtained not with the conventional split field but with flickering grating patterns. Thus our study extends the well-known results of Brown and MacAdam [
J. Opt. Soc. Am. 39,
808–
813 (
1949)] to cases in which the image is structured in space and time. As expected, we find that the discrimination ellipsoids depend on the spatiotemporal structure of the stimulus. This has potential consequences for color-difference formulas as used in industry and commerce: no single formula will do when it is important to treat patterns with different structure. We present analytical descriptions, based on the Vos–Walraven [
Vision Res. 12,
1327–
1365 (
1972)] line element augmented with spatiotemporal frequency-dependent coefficients that fit our results reasonably well. For coarse gratings (~1 cycle per degree) or slowly modulated fields (~1 Hz) our results prove to be compatable with the results of Brown and MacAdam obtained with a bipartite 2° field.
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The 16 Modulation Directions in the (dR/R, dG/G, dB/B) Space Used for the Determination of the Discrimination Ellipsoids
Direction No.
Components in the
Space
1
(1, 0, 0)
2
(0, 1, 0)
3
(0, 0, 1)
4
(1, 1, 0)
5
(1, 0, 1)
6
(0, 1, 1)
7
(1, −1, 0)
8
(1, 0, −1)
9
(0, 1, −1)
10
(1, 1, 1)
11
(1, −1, 1)
12
(−1, 1, 1)
13
(1, 1, −1)
14
(½, −1, ½)
15
(½, −1, 0)
16
(½, −1, −1)
Table 2
Parameters of the Spatial Discrimination Ellipsoids of Subject CNa
Color
Fs
a
b
c
ϕ
θ
α
χ2
f(%)
W
½
10.6
2.9
1.25
46
32
92
96
15
W
1
4.9
2.1
0.67
45
43
87
12
18
R
1
4.9
2.5
1.59
53
44
86
3
9
G
1
5.2
2.2
0.45
44
46
85
39
27
Y
1
7.0
4.0
0.52
0
89
130
12
24
B
1
5.7
2.3
0.56
39
49
100
11
13
W
2
3.8
1.60
0.42
43
82
108
2
10
W
4
6.8
0.73
0.30
10
89
147
14
18
R
4
12.0
0.89
0.53
−4
89
174
4
8
G
4
7.0
0.67
0.37
79
86
79
3
6
Y
4
11.4
0.97
0.39
13
89
146
11
17
B
4
8.6
0.73
0.41
63
88
97
9
16
W
8
36
1.34
0.37
11
90
147
38
15
W
16
40
2.5
1.41
51
90
110
12
19
Fs is the spatial frequency (in cycles per degree), a, b, and c are the lengths (in per cent) of the principal axes in the (dR/R, dG/G, dB/B) space. ϕ, θ, and α are the orientation angles (in degrees). f is the mean fractional deviation between the thresholds and the ellipsoid. For the definitions of ϕ, θ, α, χ2, and f see text.
Table 3
Parameters of the Temporal Discrimination Ellipsoids of Subjects CN and RWa
Color
Ft
a
b
c
ϕ
θ
α
χ2
f(%)
CN
W
½
11.5
1.93
0.49
43
40
94
15
12
W
½
7.0
1.61
0.39
45
37
88
18
11
W
1
5.2
1.72
0.34
46
35
90
25
8
R
1
6.0
2.3
0.72
44
30
92
6
10
G
1
5.7
1.54
0.28
45
37
92
15
10
Y
1
5.3
1.75
0.25
47
47
92
24
15
B
1
6.4
2.1
0.38
45
39
94
13
11
W
2
3.3
1.59
0.26
47
38
89
5
7
W
4
4.5
1.83
0.52
47
96
92
5
5
R
4
6.3
1.79
0.93
57
85
92
9
7
G
4
4.3
1.88
0.63
45
85
96
9
5
Y
4
5.7
1.56
0.45
17
88
125
20
11
B
4
3.5
1.97
0.51
123
88
17
8
6
W
7½
8.4
2.3
1.00
40
89
114
14
6
W
15
18.4
4.4
2.7
56
84
118
11
9
R
15
41
9.2
5.1
74
84
131
32
10
G
15
23
6.4
3.3
49
84
142
19
6
B
15
7.5
4.9
3.0
79
45
129
12
6
RW
W
½
12.1
5.5
0.68
42
33
84
32
11
W
1
11.2
3.6
0.64
45
46
91
29
9
R
1
9.2
5.6
2.0
53
63
83
13
11
Y
1
13.3
5.7
1.07
38
74
96
3
6
B
1
8.9
3.8
0.89
45
40
87
5
8
W
2
8.7
5.9
1.09
178
83
133
12
11
W
4
7.6
3.2
1.37
7
89
133
12
11
R
4
10.8
3.2
2.4
133
87
166
2
6
Y
4
32
2.8
1.41
221
84
71
29
21
B
4
5.7
3.0
2.0
146
86
23
9
13
W
7½
12.0
3.7
1.28
−74
81
77
8
7
W
15
13.8
7.6
1.55
53
83
135
6
8
R
15
28
10.1
2.5
0
86
29
34
16
B
15
7.2
4.5
1.72
105
14
111
6
9
Ft is the temporal frequency (in hertz). The meanings of a, b, c, ϕ, θ, α, χ2, and f are the same as in Table 2.
Table 4
Parameters of the Color-Matching Ellipsoids of Brown (WRJB) and MacAdam (DLM) Converted to the (dR/R, dG/G, dB/B) spacea
Color
Subject
a
b
c
ϕ
θ
α
W
WRJB
2.7
1.52
0.31
53
71
80
W
DLM
2.4
1.15
0.22
54
65
81
R
WRJB
4.6
2.7
0.85
53
46
83
R
DLM
3.1
2.4
0.98
43
25
92
G
WRJB
2.1
1.41
0.24
46
63
92
G
DLM
1.65
1.24
0.18
49
48
95
Y
WRJB
4.1
2.4
0.24
48
71
88
Y
DLM
3.3
1.75
0.30
60
79
77
B
WRJB
4.2
1.80
0.40
46
47
83
B
DLM
3.7
1.51
0.34
47
51
87
The meanings of a, b, c, ϕ, θ, and α are the same as in Tables 2 and 3.
Table 5
The Weighting Coefficients ηL, ηF, and ηS (in Inverse Trolands) for Which the Vos–Walraven Line Element for the De Vries–Rose Luminance Domain Approximates the Spatial Contrast Detection Thresholds Besta
Color
Fs
ηL
ηF
ηS
f(%)
W
½
0.85
48
326
14
W
1
4.4
167
723
17
R
1
5.2
47
982
13
G
1
4.5
312
737
25
Y
1
4.4
299
399
24
B
1
4.5
278
158
13
W
2
50
445
419
17
W
4
262
721
122
20
R
4
156
285
71
7
G
4
214
417
126
14
Y
4
146
390
176
21
B
4
189
342
11.0
19
W
8
113
514
3.7
21
W
16
14.3
24
2.8
18
Subject CN. Fs is the spatial frequency (in cycles per degree). f is the mean fractional deviation between the thresholds and the line element.
Table 6
The Weighting Coefficients ηL, ηF, and ηS (in Inverse Trolands) for Which the Vos–Walraven Line Element for the De Vries–Rose Luminance Domain Approximates the Temporal Contrast Detection Thresholds Besta
Color
Ft
ηL
ηF
ηS
f(%)
CN
W
½
1.25
307
951
15
W
½
2.0
500
1280
10
W
1
3.3
652
964
8
R
1
3.0
237
1280
11
G
1
2.9
889
1420
9
Y
1
4.4
1240
4720
15
B
1
2.4
505
217
12
W
2
8.3
1120
1290
8
W
4
21
265
265
8
R
4
28
122
274
6
G
4
19.2
174
252
7
Y
4
32
340
653
12
B
4
17.9
276
95
8
W
7½
20
57
68
8
W
15
5.8
6.4
16.6
10
R
15
2.7
1.71
7.9
21
G
15
4.2
2.2
11.2
12
B
15
3.6
2.9
55
7
RW
W
½
8.6
120
259
12
W
1
1.26
157
279
9
R
1
2.1
31
156
12
Y
1
2.0
55
164
7
B
1
1.50
80
59
9
W
2
2.3
50
89
12
W
4
8.2
32
85
10
R
4
5.4
18.5
81
15
Y
4
12.0
27
51
19
B
4
10.4
9.5
32
17
W
7½
33
8.8
44
11
W
15
24
2.1
42
19
R
15
7.6
1.9
2.1
37
B
15
13
1.35
105
18
Ft is the temporal frequency (in hertz). f is the mean fractional deviation between the thresholds and the line element.
Table 7
The Metrical Coefficients gij in the (dx, dy, dl) Space Used by Brown and MacAdama
The 16 Modulation Directions in the (dR/R, dG/G, dB/B) Space Used for the Determination of the Discrimination Ellipsoids
Direction No.
Components in the
Space
1
(1, 0, 0)
2
(0, 1, 0)
3
(0, 0, 1)
4
(1, 1, 0)
5
(1, 0, 1)
6
(0, 1, 1)
7
(1, −1, 0)
8
(1, 0, −1)
9
(0, 1, −1)
10
(1, 1, 1)
11
(1, −1, 1)
12
(−1, 1, 1)
13
(1, 1, −1)
14
(½, −1, ½)
15
(½, −1, 0)
16
(½, −1, −1)
Table 2
Parameters of the Spatial Discrimination Ellipsoids of Subject CNa
Color
Fs
a
b
c
ϕ
θ
α
χ2
f(%)
W
½
10.6
2.9
1.25
46
32
92
96
15
W
1
4.9
2.1
0.67
45
43
87
12
18
R
1
4.9
2.5
1.59
53
44
86
3
9
G
1
5.2
2.2
0.45
44
46
85
39
27
Y
1
7.0
4.0
0.52
0
89
130
12
24
B
1
5.7
2.3
0.56
39
49
100
11
13
W
2
3.8
1.60
0.42
43
82
108
2
10
W
4
6.8
0.73
0.30
10
89
147
14
18
R
4
12.0
0.89
0.53
−4
89
174
4
8
G
4
7.0
0.67
0.37
79
86
79
3
6
Y
4
11.4
0.97
0.39
13
89
146
11
17
B
4
8.6
0.73
0.41
63
88
97
9
16
W
8
36
1.34
0.37
11
90
147
38
15
W
16
40
2.5
1.41
51
90
110
12
19
Fs is the spatial frequency (in cycles per degree), a, b, and c are the lengths (in per cent) of the principal axes in the (dR/R, dG/G, dB/B) space. ϕ, θ, and α are the orientation angles (in degrees). f is the mean fractional deviation between the thresholds and the ellipsoid. For the definitions of ϕ, θ, α, χ2, and f see text.
Table 3
Parameters of the Temporal Discrimination Ellipsoids of Subjects CN and RWa
Color
Ft
a
b
c
ϕ
θ
α
χ2
f(%)
CN
W
½
11.5
1.93
0.49
43
40
94
15
12
W
½
7.0
1.61
0.39
45
37
88
18
11
W
1
5.2
1.72
0.34
46
35
90
25
8
R
1
6.0
2.3
0.72
44
30
92
6
10
G
1
5.7
1.54
0.28
45
37
92
15
10
Y
1
5.3
1.75
0.25
47
47
92
24
15
B
1
6.4
2.1
0.38
45
39
94
13
11
W
2
3.3
1.59
0.26
47
38
89
5
7
W
4
4.5
1.83
0.52
47
96
92
5
5
R
4
6.3
1.79
0.93
57
85
92
9
7
G
4
4.3
1.88
0.63
45
85
96
9
5
Y
4
5.7
1.56
0.45
17
88
125
20
11
B
4
3.5
1.97
0.51
123
88
17
8
6
W
7½
8.4
2.3
1.00
40
89
114
14
6
W
15
18.4
4.4
2.7
56
84
118
11
9
R
15
41
9.2
5.1
74
84
131
32
10
G
15
23
6.4
3.3
49
84
142
19
6
B
15
7.5
4.9
3.0
79
45
129
12
6
RW
W
½
12.1
5.5
0.68
42
33
84
32
11
W
1
11.2
3.6
0.64
45
46
91
29
9
R
1
9.2
5.6
2.0
53
63
83
13
11
Y
1
13.3
5.7
1.07
38
74
96
3
6
B
1
8.9
3.8
0.89
45
40
87
5
8
W
2
8.7
5.9
1.09
178
83
133
12
11
W
4
7.6
3.2
1.37
7
89
133
12
11
R
4
10.8
3.2
2.4
133
87
166
2
6
Y
4
32
2.8
1.41
221
84
71
29
21
B
4
5.7
3.0
2.0
146
86
23
9
13
W
7½
12.0
3.7
1.28
−74
81
77
8
7
W
15
13.8
7.6
1.55
53
83
135
6
8
R
15
28
10.1
2.5
0
86
29
34
16
B
15
7.2
4.5
1.72
105
14
111
6
9
Ft is the temporal frequency (in hertz). The meanings of a, b, c, ϕ, θ, α, χ2, and f are the same as in Table 2.
Table 4
Parameters of the Color-Matching Ellipsoids of Brown (WRJB) and MacAdam (DLM) Converted to the (dR/R, dG/G, dB/B) spacea
Color
Subject
a
b
c
ϕ
θ
α
W
WRJB
2.7
1.52
0.31
53
71
80
W
DLM
2.4
1.15
0.22
54
65
81
R
WRJB
4.6
2.7
0.85
53
46
83
R
DLM
3.1
2.4
0.98
43
25
92
G
WRJB
2.1
1.41
0.24
46
63
92
G
DLM
1.65
1.24
0.18
49
48
95
Y
WRJB
4.1
2.4
0.24
48
71
88
Y
DLM
3.3
1.75
0.30
60
79
77
B
WRJB
4.2
1.80
0.40
46
47
83
B
DLM
3.7
1.51
0.34
47
51
87
The meanings of a, b, c, ϕ, θ, and α are the same as in Tables 2 and 3.
Table 5
The Weighting Coefficients ηL, ηF, and ηS (in Inverse Trolands) for Which the Vos–Walraven Line Element for the De Vries–Rose Luminance Domain Approximates the Spatial Contrast Detection Thresholds Besta
Color
Fs
ηL
ηF
ηS
f(%)
W
½
0.85
48
326
14
W
1
4.4
167
723
17
R
1
5.2
47
982
13
G
1
4.5
312
737
25
Y
1
4.4
299
399
24
B
1
4.5
278
158
13
W
2
50
445
419
17
W
4
262
721
122
20
R
4
156
285
71
7
G
4
214
417
126
14
Y
4
146
390
176
21
B
4
189
342
11.0
19
W
8
113
514
3.7
21
W
16
14.3
24
2.8
18
Subject CN. Fs is the spatial frequency (in cycles per degree). f is the mean fractional deviation between the thresholds and the line element.
Table 6
The Weighting Coefficients ηL, ηF, and ηS (in Inverse Trolands) for Which the Vos–Walraven Line Element for the De Vries–Rose Luminance Domain Approximates the Temporal Contrast Detection Thresholds Besta
Color
Ft
ηL
ηF
ηS
f(%)
CN
W
½
1.25
307
951
15
W
½
2.0
500
1280
10
W
1
3.3
652
964
8
R
1
3.0
237
1280
11
G
1
2.9
889
1420
9
Y
1
4.4
1240
4720
15
B
1
2.4
505
217
12
W
2
8.3
1120
1290
8
W
4
21
265
265
8
R
4
28
122
274
6
G
4
19.2
174
252
7
Y
4
32
340
653
12
B
4
17.9
276
95
8
W
7½
20
57
68
8
W
15
5.8
6.4
16.6
10
R
15
2.7
1.71
7.9
21
G
15
4.2
2.2
11.2
12
B
15
3.6
2.9
55
7
RW
W
½
8.6
120
259
12
W
1
1.26
157
279
9
R
1
2.1
31
156
12
Y
1
2.0
55
164
7
B
1
1.50
80
59
9
W
2
2.3
50
89
12
W
4
8.2
32
85
10
R
4
5.4
18.5
81
15
Y
4
12.0
27
51
19
B
4
10.4
9.5
32
17
W
7½
33
8.8
44
11
W
15
24
2.1
42
19
R
15
7.6
1.9
2.1
37
B
15
13
1.35
105
18
Ft is the temporal frequency (in hertz). f is the mean fractional deviation between the thresholds and the line element.
Table 7
The Metrical Coefficients gij in the (dx, dy, dl) Space Used by Brown and MacAdama
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