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M.I. Suero, P.J. Pardo, A.L. Pérez |
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Table 4. Total variance explained for Observer 3.
Component |
Initial eigenvalues |
|
Sums of the squares of the saturations |
|||
|
Total |
% Variance |
Cumulative % |
Total |
% Variance |
Cumulative % |
1 |
2.156 |
71.878 |
71.878 |
2.156 |
71.878 |
71.878 |
2 |
0.542 |
18.057 |
89.935 |
0.542 |
18.057 |
89.935 |
3 |
0.302 |
10.065 |
100.000 |
0.302 |
10.065 |
100.000 |
Extraction method: Principal component analysis
In the component matrix (Table 5), it could be seen for the three observers that Component 1 accounts for the contributions of L and M, from which is subtracted the variable S. This coincides with the usual treatment of the channel D in neural models. Component 2 has the form of an opponent channel of type T, with the contribution of the variable M being subtracted from that of the variable L, and an almost negligible contribution of the variable S. Component 3 is a sum of contributions of the three variables L, M, and S with small weights, and may correspond to variations in the achromatic channel A in the determination of the isobrightness curve.
It should be emphasized that Components 2 and 3, which resemble channels T and A, respectively, arose solely from the statistical treatment applied to the experimental data.
Table 5. Component matrix for Observer 1.
|
Ob1’s components |
|
Ob2’s components |
|
Ob3’s components |
|
|||
|
1 |
2 |
3 |
1 |
2 |
3 |
1 |
2 |
3 |
L |
0.827 |
0.534 |
0.176 |
0.821 |
0.525 |
0.226 |
0.803 |
0.570 |
0.176 |
M |
0.837 |
-0.513 |
0.191 |
0.822 |
-0.522 |
0.228 |
0.839 |
-0.459 |
0.293 |
S |
-0.946 |
0.013 |
0.323 |
-0.913 |
0.002 |
0.408 |
-0.899 |
0.080 |
0.430 |
4. CONCLUSION
The statistical results of the previous section show an underlying structure of the experimental data that is common to all three observers, and coincident with the channels into which neural models of colour vision are usually divided.
The first component reflects the behaviour of a blue/yellow or type D channel in Guth's terminology, in all cases accounting for over 70% of the variance. The second component corresponds to the behaviour of a red/green or type T channel, accounting for 18% of the variance for the three observers. Finally, the third component would correspond to the behaviour of a luminance or achromatic channel accounting for the remainder of the variance, but with certain differences.
These differences bring out the particularities of each observer's colour perception, not only in the physical but also in the perceptive aspect, since this last experiment included a correction for the differences in the optical density of the macular pigment and lenses.
The principal component analysis yielded completely uncorrelated linear combinations of the original variables, which explained 100% of the initial variance in a three-dimensional vector space. Independently of the normalization applied to the principal components which indicates their different weights in the total variance, these principal components indicate the
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directions in the three-dimensional vector space into which the original variance is mapped. Expressing these components by means of the angles corresponding to their direction cosines is a way of representing them that is independent of the particular weight that they each have in accounting for the total variance.
Thus, for Component 1 or channel D, for Component 2 or channel T and, for Component 3 or channel A one has the angles expressed in the tables 6-8.
Table 6. Direction angles of Principal Component 1.
Component 1 |
θL |
θM |
θS |
Observer 1 |
56.79 |
56.34 |
128.79 |
Observer 2 |
56.24 |
56.20 |
128.17 |
Observer 3 |
56.85 |
55.15 |
127.75 |
Table 7. Direction angles of Principal Component 2.
Component 2 |
θL |
θM |
θS |
Observer 1 |
43.83 |
133.87 |
88.99 |
Observer 2 |
44.83 |
134.84 |
89.84 |
Observer 3 |
39.26 |
128.57 |
83.76 |
Table 8. Direction angles of Principal Component 3.
Component 2 |
θL |
θM |
θS |
Observer 1 |
64.89 |
62.58 |
38.85 |
Observer 2 |
64.22 |
63.97 |
38.26 |
Observer 3 |
71.32 |
57.78 |
38.51 |
This allows one to better appreciate the consistency of the results for Component 1 (channel D) between all three observers, and the small variations, especially for Observer 3, in Component 2 (channel T) and in Component 3 (channel A).
Therefore, the next step in colorimetry should be to provide coverage for all these individual differences [65] which also have great importance for the preservation of metameric matches in digital devices (LCDs, printers, etc.) [66]. To attain this goal, it is essential to develop a straightforward chromatic characterization of observers so that these colorimetric transformations can subsequently be implemented in digital devices. The authors' group has been working on this topic for several years, and is currently carrying out a research project entitled "Intelligent System for the Chromatic Characterization of Observers" which is hoped soon to yield relevant results.
ACKNOWLEDGMENTS
Thanks are due to Prof. Françoise Viénot of the Natural History Museum of Paris and to the Department of Optics of the University of Granada, and in particular to Prof. Enrique Hita
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Villaverde for his constant support. This work was supported by the Spanish Ministry of Science and Innovation through the Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica (I+D+I) and the FEDER program of the European Union, grant FIS2006-06110 and by the Consejería de Economía, Comercio e Innovación of the Junta de Extremadura.
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