Table I
Observed and computed color differences.
Pair | Tiles | Observed scale difference | Computed color difference | Error | Ratio of computed lightness difference to total difference |
---|
1 | 1 | 2 | 2.311 | 2.388 | 0.077 | 0.14 |
2 | 1 | 3 | 2.608 | 2.909 | 0.301 | 0.24 |
3 | 2 | 3 | 2.176 | 2.210 | 0.034 | 0.17 |
4 | 2 | 5 | 2.160 | 2.251 | 0.091 | 0.02 |
5 | 2 | 6 | 1.818 | 2.189 | 0.371 | 0.27 |
8 | 3 | 4 | 2.569 | 2.059 | −0.510 | 0.27 |
9 | 3 | 6 | 2.788 | 2.582 | −0.206 | 0.09 |
10 | 3 | 7 | 2.038 | 2.188 | 0.150 | 0.23 |
11 | 4 | 7 | 1.877 | 2.136 | 0.259 | 0.02 |
13 | 4 | 8 | 2.127 | 1.981 | −0.146 | 0.23 |
15 | 5 | 6 | 2.268 | 2.114 | −0.154 | 0.31 |
16 | 5 | 10 | 2.602 | 2.560 | −0.042 | 0.11 |
17 | 5 | 11 | 1.746 | 2.521 | 0.775 | 0.12 |
18 | 6 | 7 | 2.039 | 2.220 | 0.181 | 0.13 |
20 | 6 | 11 | 2.054 | 2.455 | 0.401 | 0.14 |
21 | 6 | 12 | 1.240 | 2.276 | 0.104 | 0.00 |
22 | 7 | 8 | 2.234 | 1.637 | −0.597 | 0.30 |
23 | 7 | 12 | 1.560 | 2.539 | 0.979 | 0.11 |
25 | 7 | 13 | 1.957 | 2.068 | 0.111 | 0.23 |
26 | 8 | 9 | 2.944 | 2.359 | −0.585 | 0.24 |
27 | 8 | 13 | 1.706 | 2.085 | 0.379 | 0.47 |
29 | 8 | 14 | 2.525 | 1.969 | −0.556 | 0.38 |
31 | 9 | 14 | 2.133 | 2.481 | 0.348 | 0.08 |
32 | 9 | 15 | 2.727 | 2.061 | −0.666 | 0.15 |
33 | 10 | 11 | 1.705 | 2.203 | 0.498 | 0.27 |
34 | 10 | 17 | 2.537 | 2.209 | −0.328 | 0.33 |
35 | 10 | 18 | 2.177 | 2.320 | 0.143 | 0.07 |
36 | 11 | 12 | 2.122 | 2.053 | −0.069 | 0.16 |
38 | 11 | 18 | 2.728 | 2.364 | −0.364 | 0.32 |
39 | 11 | 19 | 1.655 | 2.287 | 0.632 | 0.08 |
40 | 12 | 13 | 1.943 | 2.097 | 0.154 | 0.09 |
42 | 12 | 19 | 2.279 | 2.489 | 0.210 | 0.21 |
44 | 12 | 20 | 1.972 | 2.115 | 0.143 | 0.23 |
45 | 13 | 14 | 2.122 | 1.766 | −0.356 | 0.13 |
47 | 13 | 20 | 1.860 | 2.533 | 0.673 | 0.11 |
49 | 13 | 21 | 1.994 | 2.122 | 0.128 | 0.11 |
50 | 14 | 15 | 2.462 | 1.942 | −0.520 | 0.06 |
51 | 14 | 21 | 1.689 | 2.486 | 0.797 | 0.18 |
53 | 14 | 22 | 2.391 | 2.004 | −0.387 | 0.19 |
54 | 15 | 16 | 1.739 | 1.566 | −0.173 | 0.04 |
56 | 15 | 22 | 2.312 | 2.326 | 0.014 | 0.11 |
57 | 15 | 23 | 2.436 | 2.154 | −0.282 | 0.22 |
58 | 16 | 23 | 2.315 | 2.196 | −0.119 | 0.19 |
60 | 16 | 24 | 2.538 | 1.818 | −0.720 | 0.12 |
61 | 17 | 18 | 1.709 | 1.670 | −0.039 | 0.34 |
62 | 17 | 25 | 3.399 | 2.472 | −0.927 | 0.05 |
63 | 18 | 19 | 2.247 | 2.081 | −0.166 | 0.28 |
64 | 18 | 25 | 3.345 | 2.628 | −0.717 | 0.26 |
66 | 18 | 26 | 3.223 | 2.471 | −0.752 | 0.21 |
67 | 19 | 20 | 2.342 | 1.967 | −0.375 | 0.01 |
68 | 19 | 26 | 3.019 | 2.542 | −0.477 | 0.44 |
70 | 19 | 27 | 2.588 | 2.241 | −0.347 | 0.45 |
72 | 20 | 21 | 2.257 | 1.834 | −0.423 | 0.03 |
73 | 20 | 27 | 2.459 | 2.394 | −0.065 | 0.44 |
74 | 20 | 28 | 2.387 | 1.850 | −0.537 | 0.02 |
76 | 21 | 22 | 1.599 | 1.986 | 0.387 | 0.04 |
77 | 21 | 28 | 1.792 | 2.037 | 0.245 | 0.01 |
79 | 21 | 29 | 2.358 | 2.007 | −0.351 | 0.12 |
81 | 22 | 23 | 1.409 | 1.849 | 0.440 | 0.11 |
83. | 22 | 29 | 1.643 | 2.261 | 0.618 | 0.14 |
84 | 22 | 30 | 2.160 | 1.895 | −0.265 | 0.17 |
85 | 23 | 24 | 1.846 | 1.870 | 0.024 | 0.10 |
86 | 23 | 30 | 1.872 | 2.097 | 0.225 | 0.05 |
87 | 23 | 31 | 2.507 | 2.147 | −0.360 | 0.10 |
88 | 24 | 31 | 2.907 | 2.295 | −0.612 | 0.17 |
90 | 24 | 32 | 2.974 | 2.787 | −0.187 | 0.42 |
91 | 25 | 26 | 2.232 | 1.992 | −0.240 | 0.07 |
93 | 25 | 33 | 3.389 | 2.642 | −0.747 | 0.18 |
95 | 26 | 27 | 2.126 | 2.093 | −0.033 | 0.05 |
96 | 26 | 33 | 3.001 | 2.588 | −0.413 | 0.24 |
97 | 26 | 34 | 2.740 | 2.173 | −0.567 | 0.18 |
99 | 27 | 28 | 2.000 | 2.088 | 0.088 | 0.52 |
100 | 27 | 34 | 2.734 | 2.395 | −0.339 | 0.21 |
102 | 27 | 35 | 2.513 | 1.885 | −0.628 | 0.06 |
103 | 28 | 29 | 2.014 | 2.018 | 0.004 | 0.11 |
104 | 28 | 35 | 2.730 | 2.504 | 0.226 | 0.39 |
105 | 28 | 36 | 1.957 | 1.859 | −0.098 | 0.34 |
107 | 29 | 30 | 1.369 | 1.645 | 0.276 | 0.01 |
109 | 29 | 36 | 2.071 | 2.090 | 0.019 | 0.20 |
110 | 29 | 37 | 1.496 | 1.479 | −0.017 | 0.02 |
111 | 30 | 31 | 2.052 | 2.366 | 0.314 | 0.04 |
113 | 30 | 37 | 2.483 | 1.914 | −0.569 | 0.02 |
115 | 30 | 38 | 2.039 | 2.246 | 0.207 | 0.18 |
117 | 31 | 32 | 1.218 | 1.905 | 0.687 | 0.41 |
118 | 31 | 38 | 2.519 | 2.181 | −0.338 | 0.14 |
119 | 31 | 39 | 2.487 | 2.233 | −0.254 | 0:32 |
120 | 32 | 39 | 2.564 | 2.094 | −0.470 | 0.03 |
122 | 33 | 34 | 2.709 | 1.979 | −0.730 | 0.11 |
124 | 34 | 35 | 1.805 | 1.792 | −0.013 | 0.34 |
125 | 34 | 40 | 2.435 | 2.563 | 0.128 | 0.00 |
127 | 35 | 36 | 1.889 | 1.916 | 0.027 | 0.18 |
128 | 35 | 40 | 2.150 | 2.643 | 0.493 | 0.23 |
129 | 35 | 41 | 2.372 | 2.694 | 0.322 | 0.07 |
131 | 36 | 37 | 1.915 | 1.916 | 0.001 | 0.20 |
133 | 36 | 41 | 2.853 | 2.775 | −0.078 | 0.20 |
134 | 36 | 42 | 2.024 | 3.296 | 1.272 | 0.15 |
135 | 37 | 38 | 1.489 | 2.253 | 0.764 | 0.17 |
137 | 37 | 42 | 2.436 | 3.057 | 0.621 | 0.29 |
138 | 37 | 43 | 2.525 | 3.294 | 0.769 | 0.21 |
139 | 38 | 39 | 1.457 | 2.002 | 0.545 | 0.20 |
141 | 38 | 43 | 2.945 | 2.795 | −0.150 | 0.11 |
143 | 40 | 41 | 2.242 | 1.840 | −0.402 | 0.22 |
144 | 41 | 42 | 2.093 | 2.236 | 0.143 | 0.02 |
147 | 42 | 43 | 1.275 | 1.386 | 0.111 | 0.14 |
151 | R1 | R2 | 1.611 | 1.431 | −0.180 | 0.25 |
152 | R1 | R3 | 3.497 | 2.952 | −0.545 | 0.82 |
153 | R1 | R4 | 3.150 | 2.732 | −0.418 | 0.75 |
154 | R2 | R3 | 3.538 | 3.422 | −0.116 | 0.82 |
155 | R2 | R4 | 2.590 | 2.728 | 0.138 | 0.89 |
156 | R3 | R4 | 3.253 | 3.090 | −0.163 | 0.12 |
157 | Y1 | Y2 | 2.498 | 2.263 | −0.235 | 0.04 |
158 | Y1 | Y3 | 3.365 | 3.262 | −0.103 | 0.83 |
159 | Y1 | Y4 | 3.701 | 3.302 | −0.399 | 0.82 |
160 | Y2 | Y3 | 2.773 | 2.808 | 0.035 | 0.93 |
161 | Y2 | Y4 | 2.610 | 2.700 | 0.090 | 0.97 |
162 | Y3 | Y4 | 2.253 | 1.395 | −0.858 | 0.00 |
163 | G1 | G2 | 1.733 | 2.155 | 0.422 | 0.31 |
164 | G1 | G3 | 3.375 | 3.262 | −0.113 | 0.88 |
165 | G1 | G4 | 2.804 | 2.975 | 0.171 | 0.85 |
166 | G2 | G3 | 3.803 | 3.814 | 0.011 | 0.93 |
167 | G2 | G4 | 3.375 | 3.429 | 0.054 | 0.93 |
168 | G3 | G4 | 2.508 | 2.088 | −0.420 | 0.17 |
169 | B1 | B2 | 1.835 | 2.686 | 0.851 | 0.22 |
170 | B1 | B3 | 2.467 | 2.981 | 0.514 | 0.74 |
171 | B1 | B4 | 3.151 | 3.026 | −0.125 | 0.65 |
172 | B2 | B3 | 2.641 | 3.203 | 0.562 | 0.88 |
173 | B2 | B4 | 2.936 | 3.057 | 0.121 | 0.84 |
174 | B3 | B4 | 3.008 | 2.654 | −0.354 | 0.09 |
Weighted means | 2.483 | 2.453 | | |
rms error | | | 0.421 | |
Table II
Colorimetric specifications of tiles (diffuse) D65, CIE 1964 supplementary 10° observer.
Tile | x | y | Y | g | j | L |
---|
1 | 0.3120 | 0.5412 | 30.50 | 6.859 | 7.125 | −0.24 |
2 | 0.2952 | 0.4786 | 29.96 | 5.934 | 4.948 | −0.47 |
3 | 0.3466 | 0.4899 | 29.28 | 4.177 | 6.237 | −0.73 |
4 | 0.3949 | 0.4897 | 27.15 | 2.385 | 7.089 | −1.12 |
5 | 0.2627 | 0.4254 | 29.58 | 6.027 | 2.700 | −0.43 |
6 | 0.3039 | 0.4358 | 27.84 | 4.261 | 3.666 | −0.89 |
7 | 0.3550 | 0.4477 | 27.16 | 2.477 | 4.955 | −1.09 |
8 | 0.3933 | 0.4506 | 25.06 | 1.085 | 5.662 | −1.44 |
9 | 0.4469 | 0.4595 | 26.79 | −0.423 | 7.389 | −1.04 |
10 | 0.2376 | 0.3652 | 29.51 | 5.810 | 0.164 | −0.32 |
11 | 0.2747 | 0.3785 | 28.26 | 3.989 | 1.249 | −0.65 |
12 | 0.3159 | 0.3928 | 27.56 | 2.346 | 2.436 | −0.89 |
13 | 0.3616 | 0.4073 | 28.68 | 0.803 | 3.842 | −0.75 |
14 | 0.4025 | 0.4161 | 27.55 | −0.577 | 4.920 | −0.91 |
15 | 0.4475 | 0.4224 | 27.30 | −2.058 | 6.172 | −0.83 |
16 | 0.4833 | 0.4221 | 26.54 | −3.358 | 7.043 | −0.79 |
17 | 0.2305 | 0.3215 | 30.03 | 5.136 | −1.809 | 0.29 |
18 | 0.2531 | 0.3311 | 29.53 | 3.801 | −0.980 | −0.11 |
19 | 0.2863 | 0.3418 | 28.39 | 2.070 | 0.016 | −0.52 |
20 | 0.3247 | 0.3584 | 28.84 | 0.608 | 1.333 | −0.54 |
21 | 0.3627 | 0.3704 | 28.75 | −0.815 | 2.488 | −0.59 |
22 | 0.4068 | 0.3840 | 28.21 | −2.241 | 3.868 | −0.64 |
23 | 0.4459 | 0.3884 | 28.23 | −3.747 | 4.921 | −0.50 |
24 | 0.4916 | 0.3973 | 26.38 | −5.000 | 6.294 | −0.64 |
25 | 0.2368 | 0.2855 | 29.58 | 3.309 | −3.470 | 0.37 |
26 | 0.2661 | 0.3005 | 29.83 | 1.745 | −2.245 | 0.26 |
27 | 0.3007 | 0.3189 | 30.26 | 0.244 | −0.790 | 0.20 |
28 | 0.3342 | 0.3340 | 27.95 | −1.024 | 0.462 | −0.57 |
29 | 0.3738 | 0.3455 | 28.77 | −2.629 | 1.664 | −0.41 |
30 | 0.4090 | 0.3570 | 28.49 | −3.793 | 2.827 | −0.42 |
31 | 0.4588 | 0.3637 | 27.72 | −5.744 | 4.161 | −0.35 |
32 | 0.4869 | 0.3649 | 28.29 | −7.218 | 5.085 | 0.20 |
33 | 0.2519 | 0.2619 | 30.72 | 0.987 | −4.642 | 0.70 |
34 | 0.2797 | 0.2814 | 30.73 | −0.218 | −3.087 | 0.55 |
35 | 0.3064 | 0.2960 | 29.14 | −1.331 | −1.820 | 0.12 |
36 | 0.3406 | 0.3133 | 29.18 | −2.552 | −0.384 | −0.12 |
37 | 0.3787 | 0.3272 | 28.12 | −3.905 | 0.917 | −0.40 |
38 | 0.4199 | 0.3336 | 28.50 | −5.843 | 2.004 | −0.13 |
39 | 0.4555 | 0.3383 | 28.14 | −7.523 | 3.015 | 0.15 |
40 | 0.2938 | 0.2605 | 29.86 | −2.586 | −4.066 | 0.55 |
41 | 0.3225 | 0.2740 | 28.77 | −3.839 | −2.781 | 0.26 |
42 | 0.3609 | 0.2870 | 28.65 | −5.633 | −1.447 | 0.23 |
43 | 0.3866 | 0.2940 | 27.92 | −6.733 | −0.627 | 0.09 |
R1 | 0.5150 | 0.3380 | 10.60 | −7.078 | 2.959 | −3.78 |
R2 | 0.4916 | 0.3477 | 10.30 | −5.697 | 2.854 | −4.03 |
R3 | 0.4424 | 0.3160 | 18.10 | −6.914 | 1.289 | −2.06 |
R4 | 0.4874 | 0.3661 | 17.27 | −5.702 | 4.107 | −2.32 |
Y1 | 0.3708 | 0.4040 | 79.95 | 0.396 | 5.877 | 5.22 |
Y2 | 0.3896 | 0.4340 | 80.15 | 1.001 | 8.055 | 5.15 |
Y3 | 0.4054 | 0.4334 | 58.27 | 0.023 | 7.667 | 3.31 |
Y4 | 0.3868 | 0.4409 | 58.85 | 1.406 | 7.480 | 3.30 |
G1 | 0.2674 | 0.3504 | 28.85 | 3.515 | 0.064 | −0.44 |
G2 | 0.2434 | 0.3636 | 30.07 | 5.561 | 0.202 | −0.03 |
G3 | 0.2560 | 0.3926 | 18.37 | 4.549 | 1.218 | −2.47 |
G4 | 0.2265 | 0.3406 | 18.70 | 4.819 | −0.823 | −2.22 |
B1 | 0.1930 | 0.1766 | 6.48 | 1.404 | −6.289 | −5.10 |
B2 | 0.2248 | 0.2276 | 6.04 | 0.865 | −3.726 | −5.52 |
B3 | 0.2136 | 0.2379 | 11.74 | 2.226 | −4.461 | −3.54 |
B4 | 0.2432 | 0.2212 | 10.98 | −0.389 | −4.838 | −3.72 |
Table III
Observed and computed lightness differences.
Pair | Computed lightness difference | Number of observers who picked the lightness in accord with computation |
---|
27 | 1.0 | 8 |
67 | 0.04 | 4 |
68 | 1.0 | 8 |
70 | 1.0 | 6 |
73 | 1.0 | 8 |
88 | 0.4 | 5 |
90 | 1.1 | 8 |
95 | 0.1 | 8 |
99 | 1.1 | 10 |
117 | 0.8 | 6 |
Table IV
Numbers, N, of lattice points at various distances S = √2n from any reference point in the lattice, for indicated combinations of ΔL, Δg, Δj. Lattice points specified by interchanging the indicated increments of Δg and Δj are included in the numbers given. Rows in which the column headed n is empty are continuations of immediately preceding rows, for the same value of n.
n | ΔL | Δg | Δj | ΔN |
|
|
|
---|
1 | ±1 | ±1 | ±1 | 8 | | | 2.000 |
| 0 | ±2 | 0 | 4 | 12 | 12 | |
2 | ±2 | 0 | 0 | 2 | | | 2.38 |
| 0 | ±2 | ±2 | 4 | 6 | 18 | |
3 | ±2 | ±2 | 0 | 8 | | | 2.63 |
| ±1 | ±3 | ±1 | 16 | 24 | 42 | |
4 | ±2 | ±2 | ±2 | 8 | | | 2.83 |
| 0 | ±4 | 0 | 4 | 12 | 54 | |
5 | ±3 | ±1 | ±1 | 8 | | | 2.99 |
| ±1 | ±3 | ±3 | 8 | | | |
| 0 | ±4 | ±2 | 8 | 24 | 78 | |
6 | ±2 | ±4 | 0 | 8 | 8 | 86 | 3.13 |
7 | ±3 | ±3 | ±1 | 16 | | | 3.25 |
| ±2 | ±4 | ±2 | 16 | | | |
| ±1 | ±5 | ±1 | 16 | 48 | 134 | |
8 | ±4 | 0 | 0 | 2 | | | 3.36 |
| 0 | ±4 | ±4 | 4 | 6 | 140 | |
9 | ±4 | ±2 | 0 | 8 | | | 3.46 |
| ±3 | ±3 | ±3 | 8 | | | |
| ±1 | ±5 | ±3 | 16 | | | |
| 0 | ±6 | 0 | 4 | 36 | 176 | |
10 | ±4 | ±2 | ±2 | 8 | | | 3.56 |
| ±2 | ±4 | ±4 | 8 | | | |
| 0 | ±6 | ±2 | 8 | 24 | 200 | |
11 | ±3 | ±5 | ±1 | 16 | | | 3.64 |
| ±2 | ±6 | 0 | 8 | 24 | 224 | |
12 | ±4 | ±4 | 0 | 8 | | | 3.72 |
| ±2 | ±6 | ±2 | 16 | 24 | 248 | |
13 | ±5 | ±1 | ±1 | 8 | | | 3.80 |
| ±4 | ±4 | ±2 | 16 | | | |
| ±3 | ±5 | ±3 | 16 | | | |
| ±1 | ±5 | ±5 | 8 | | | |
| ±1 | ±7 | ±1 | 16 | | | |
| 0 | ±6 | ±4 | 8 | 72 | 320 | |
14 | | | | 0 | 0 | 320 | 3.87 |
15 | ±5 | ±3 | ±1 | 16 | | | 3.94 |
| ±2 | ±6 | ±4 | 16 | | | |
| ±1 | ±7 | ±3 | 16 | 48 | 368 | |
16 | ±4 | ±4 | ±4 | 8 | | | 4.000 |
| 0 | ±8 | 0 | 4 | 12 | 380 | |
17 | ±5 | ±3 | ±3 | 8 | | | 4.06 |
| ±4 | ±6 | 0 | 8 | | | |
| ±3 | ±5 | ±5 | 8 | | | |
| ±3 | ±7 | ±1 | 16 | | | |
| 0 | ±8 | ±2 | 8 | 48 | 428 | |
18 | ±6 | 0 | 0 | 2 | | | 4.12 |
| ±4 | ±6 | ±2 | 16 | | | |
| ±2 | ±8 | 0 | 8 | | | |
| 0 | ±6 | ±6 | 4 | 30 | 458 | |
19 | ±6 | ±2 | 0 | 8 | | | 4.18 |
| ±5 | ±5 | ±1 | 16 | | | |
| ±3 | ±7 | ±3 | 16 | | | |
| ±2 | ±8 | ±2 | 16 | | | |
| ±1 | ±7 | ±5 | 16 | 72 | 530 | |
20 | ±6 | ±2 | ±2 | 8 | | | 4.23 |
| ±2 | ±6 | ±6 | 8 | | | |
| 0 | ±8 | ±4 | 8 | 24 | 554 | |
21 | ±5 | ±5 | ±3 | 16 | | | 4.28 |
| ±4 | ±6 | ±4 | 16 | | | |
| ±1 | ±9 | ±1 | 16 | 48 | 602 | |
22 | ±6 | ±4 | 0 | 8 | | | 4.33 |
| ±2 | ±8 | ±4 | 16 | 24 | 626 | |
23 | ±6 | ±4 | ±2 | 16 | | | 4.38 |
| ±3 | ±7 | ±5 | 16 | | | |
| ±1 | ±9 | ±3 | 16 | 48 | 674 | |
24 | ±4 | ±8 | 0 | 8 | 8 | 682 | 4.43 |
25 | ±7 | ±1 | ±1 | 8 | | | 4.47 |
| ±5 | ±7 | ±1 | 16 | | | |
| ±5 | ±5 | ±5 | 8 | | | |
| ±4 | ±8 | ±2 | 16 | | | |
| ±3 | ±9 | ±1 | 16 | | | |
| ±1 | ±7 | ±7 | 8 | | | |
| 0 | ±8 | ±6 | 8 | | | |
| 0 | +10 | 0 | 4 | 84 | 766 | |
Table V
Number NL,10 of lattice points in a plane at the indicated increment ΔL of lightness above or below a reference lattice point, and within or at the distance S = 10, i.e., n = 25 from the reference point.
ΔL | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 or more |
---|
NL,10 | 80 | 80 | 69 | 68 | 57 | 44 | 21 | 4 | 0 |