Javier Romero, Eva Valero, Javier Hernández-Andrés, and Juan L. Nieves, "Color-signal filtering in the Fourier-frequency domain," J. Opt. Soc. Am. A 20, 1714-1724 (2003)
We have analyzed the Fourier-frequency content of spectral power distributions deriving from three types of illuminants (daylight, incandescent, and fluorescent) and the color signals from both biochrome and nonbiochrome surfaces lit by these illuminants. As far as daylight and the incandescent illuminant are concerned, after filtering the signals through parabolic (low-pass) filters in the Fourier-frequency domain and then reconstructing them, we found that most of the spectral information was contained below 0.016 c/nm. When fluorescent illuminants were involved, we were unable to recover either the original illuminants or color signals to any satisfactory degree. We also used the spectral modulation sensitivity function, which is related to the human visual system’s color discrimination thresholds, as a Fourier-frequency filter and obtained consistently less reliable results than with low-pass filtering. We provide comparative results for daylight signals recovered by three different methods. We found reconstructions based on linear models to be the most effective.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
PSE below a Frequency Limit for Color Signals Corresponding to SPDs of the Different Illuminantsa
Frequency (c/nm)
Illuminant
Daylight
Illuminant A
Commercial Fluorescent
F2
F7
F11
0.013
0.9957 [0.9952, 0.9963]
0.9924
0.8697
0.8704
0.8729
0.4382
0.016
0.9966 [0.9961, 0.9970]
0.9964
0.8719
0.8748
0.8740
0.4962
0.02
0.9973 [0.9969, 0.9981]
0.9996
0.8726
0.8751
0.8744
0.5666
0.04
0.9981 [0.9976, 0.9989]
0.9999
0.9175
0.9081
0.9052
0.7817
Values for daylight are mean values of 40 daylight SPDs; tenth and ninetieth percentiles are shown in brackets.
Table 2
CIELAB Color-Difference
Values on Comparing Original and Filtered Color Signals by Use of Parabolic Filters with Different Cutoff Frequenciesa
Frequency (c/nm)
Illuminant
Daylight
Illuminant A
Commercial Fluorescent
F2
F7
F11
0.013
3.23 [2.14, 5.11]
2.79
14.56
21.92
19.59
60.56
0.016
2.96 [2.12, 4.21]
1.27
14.36
21.70
19.47
49.54
0.02
2.37 [1.34, 3.39]
0.68
14.40
21.27
19.23
44.05
0.04
0.52 [0.37, 0.92]
0.15
12.22
19.32
16.78
29.17
Values for daylight are mean values of 40 daylight SPDs; tenth and ninetieth percentiles are shown in brackets.
Table 3
Mean Values of PSE below a Frequency Limit for 96 Biochrome Surfaces with Three Illuminantsa
Frequency (c/nm)
Illuminant
Daylight
Illuminant A
Commercial Fluorescent
0.013
0.9845 [0.9615, 0.9944]
0.9654 [0.8998, 0.9889]
0.9176 [0.8332, 0.9619]
0.016
0.9915 [0.9753, 0.9981]
0.9879 [0.9490, 0.9995]
0.9217 [0.8507, 0.9609]
0.02
0.9928 [0.9805, 0.9982]
0.9906 [0.9624, 0.9999]
0.9256 [0.8569, 0.9634]
0.04
0.9946 [0.9897, 0.9984]
0.9968 [0.9846, 0.9999]
0.9545 [0.9095, 0.9801]
The tenth and ninetieth percentiles are shown in brackets.
Table 4
Mean Values of the PSE below a Frequency Limit for 74 Nonbiochrome Surfaces with Three Illuminantsa
Frequency (c/nm)
Illuminant
Daylight
Illuminant A
Commercial Fluorescent
0.013
0.9891 [0.9761, 0.9968]
0.9871 [0.9690, 0.9919]
0.8899 [0.7784, 0.9682]
0.016
0.9926 [0.9832, 0.9976]
0.9934 [0.9775, 0.9993]
0.8910 [0.7795, 0.9711]
0.02
0.9945 [0.9874, 0.9980]
0.9972 [0.9907, 0.9999]
0.8954 [0.7898, 0.9725]
0.04
0.9963 [0.9927, 0.9985]
0.9994 [0.9885, 0.9999]
0.9343 [0.8661, 0.9626]
The tenth and ninetieth percentiles are shown in brackets.
Table 5
Mean CIELAB Color-Difference
Values on Comparing Original and Filtered Color Signals by Use of Parabolic Filters with Different Cutoff Frequencies for 96 Biochrome Surfaces with Three Illuminantsa
Frequency (c/nm)
Illuminant
Daylight
Illuminant A
Commercial Fluorescent
0.013
2.44 [1.08, 3.97]
3.00 [1.63, 4.31]
7.83 [1.76, 17.63]
0.016
1.39 [0.49, 2.69]
2.39 [1.29, 3.40]
7.72 [1.33, 17.42]
0.02
1.00 [0.26, 2.02]
2.21 [1.25, 3.04]
7.45 [0.97, 19.10]
0.04
0.42 [0.05, 1.04]
0.67 [0.38, 0.94]
6.21 [0.57, 14.62]
The tenth and ninetieth percentiles are shown in brackets.
Table 6
Mean CIELAB Color-Difference
Values on Comparing Original and Filtered Color Signals by Use of Parabolic Filters with Different Cutoff Frequencies for 74 Nonbiochrome Surfaces with Three Illuminantsa
Frequency (c/nm)
Illuminant
Daylight
Illuminant A
Commercial Fluorescent
0.013
3.27 [1.17, 6.15]
3.09 [1.16, 5.23]
7.92 [3.00, 18.09]
0.016
1.80 [0.50, 3.89]
2.41 [1.01, 3.86]
7.83 [2.41, 17.84]
0.02
1.28 [0.24, 2.62]
2.22 [1.04, 3.48]
7.63 [2.27, 18.78]
0.04
0.48 [0.05, 1.22]
0.67 [0.32, 0.98]
6.27 [0.60, 16.10]
The tenth and ninetieth percentiles are shown in brackets.
Table 7
PSE on Comparing Original and Filtered Color Signals by Use of SMSF Filtera
Signal
PSE
Illuminant
Daylight
0.9864 [0.9849, 0.9896]
Illuminant A
0.9735
Com. Fluor.
0.8650
F2
0.8719
F7
0.8701
F11
0.5137
Biochrome surface
Daylight
0.9735 [0.9555, 0.9836]
Illuminant A
0.9328 [0.8668, 0.9731]
Com. Fluor.
0.9409 [0.9120, 0.9641]
Nonbiochrome Surface
Daylight
0.9791 [0.9658, 0.9885]
Illuminant A
0.9568 [0.9282, 0.9740]
Com. Fluor.
0.8942 [0.7587, 0.9641]
Color signals correspond to SPDs of the illuminants and color signals from 96 biochrome and 74 nonbiochrome surfaces with three different illuminants. Values for daylight are mean values of 40 daylight SPDs. The tenth and ninetieth percentiles are shown in brackets. Com. Fluor. stands for commercial fluorescent.
Tables (7)
Table 1
PSE below a Frequency Limit for Color Signals Corresponding to SPDs of the Different Illuminantsa
Frequency (c/nm)
Illuminant
Daylight
Illuminant A
Commercial Fluorescent
F2
F7
F11
0.013
0.9957 [0.9952, 0.9963]
0.9924
0.8697
0.8704
0.8729
0.4382
0.016
0.9966 [0.9961, 0.9970]
0.9964
0.8719
0.8748
0.8740
0.4962
0.02
0.9973 [0.9969, 0.9981]
0.9996
0.8726
0.8751
0.8744
0.5666
0.04
0.9981 [0.9976, 0.9989]
0.9999
0.9175
0.9081
0.9052
0.7817
Values for daylight are mean values of 40 daylight SPDs; tenth and ninetieth percentiles are shown in brackets.
Table 2
CIELAB Color-Difference
Values on Comparing Original and Filtered Color Signals by Use of Parabolic Filters with Different Cutoff Frequenciesa
Frequency (c/nm)
Illuminant
Daylight
Illuminant A
Commercial Fluorescent
F2
F7
F11
0.013
3.23 [2.14, 5.11]
2.79
14.56
21.92
19.59
60.56
0.016
2.96 [2.12, 4.21]
1.27
14.36
21.70
19.47
49.54
0.02
2.37 [1.34, 3.39]
0.68
14.40
21.27
19.23
44.05
0.04
0.52 [0.37, 0.92]
0.15
12.22
19.32
16.78
29.17
Values for daylight are mean values of 40 daylight SPDs; tenth and ninetieth percentiles are shown in brackets.
Table 3
Mean Values of PSE below a Frequency Limit for 96 Biochrome Surfaces with Three Illuminantsa
Frequency (c/nm)
Illuminant
Daylight
Illuminant A
Commercial Fluorescent
0.013
0.9845 [0.9615, 0.9944]
0.9654 [0.8998, 0.9889]
0.9176 [0.8332, 0.9619]
0.016
0.9915 [0.9753, 0.9981]
0.9879 [0.9490, 0.9995]
0.9217 [0.8507, 0.9609]
0.02
0.9928 [0.9805, 0.9982]
0.9906 [0.9624, 0.9999]
0.9256 [0.8569, 0.9634]
0.04
0.9946 [0.9897, 0.9984]
0.9968 [0.9846, 0.9999]
0.9545 [0.9095, 0.9801]
The tenth and ninetieth percentiles are shown in brackets.
Table 4
Mean Values of the PSE below a Frequency Limit for 74 Nonbiochrome Surfaces with Three Illuminantsa
Frequency (c/nm)
Illuminant
Daylight
Illuminant A
Commercial Fluorescent
0.013
0.9891 [0.9761, 0.9968]
0.9871 [0.9690, 0.9919]
0.8899 [0.7784, 0.9682]
0.016
0.9926 [0.9832, 0.9976]
0.9934 [0.9775, 0.9993]
0.8910 [0.7795, 0.9711]
0.02
0.9945 [0.9874, 0.9980]
0.9972 [0.9907, 0.9999]
0.8954 [0.7898, 0.9725]
0.04
0.9963 [0.9927, 0.9985]
0.9994 [0.9885, 0.9999]
0.9343 [0.8661, 0.9626]
The tenth and ninetieth percentiles are shown in brackets.
Table 5
Mean CIELAB Color-Difference
Values on Comparing Original and Filtered Color Signals by Use of Parabolic Filters with Different Cutoff Frequencies for 96 Biochrome Surfaces with Three Illuminantsa
Frequency (c/nm)
Illuminant
Daylight
Illuminant A
Commercial Fluorescent
0.013
2.44 [1.08, 3.97]
3.00 [1.63, 4.31]
7.83 [1.76, 17.63]
0.016
1.39 [0.49, 2.69]
2.39 [1.29, 3.40]
7.72 [1.33, 17.42]
0.02
1.00 [0.26, 2.02]
2.21 [1.25, 3.04]
7.45 [0.97, 19.10]
0.04
0.42 [0.05, 1.04]
0.67 [0.38, 0.94]
6.21 [0.57, 14.62]
The tenth and ninetieth percentiles are shown in brackets.
Table 6
Mean CIELAB Color-Difference
Values on Comparing Original and Filtered Color Signals by Use of Parabolic Filters with Different Cutoff Frequencies for 74 Nonbiochrome Surfaces with Three Illuminantsa
Frequency (c/nm)
Illuminant
Daylight
Illuminant A
Commercial Fluorescent
0.013
3.27 [1.17, 6.15]
3.09 [1.16, 5.23]
7.92 [3.00, 18.09]
0.016
1.80 [0.50, 3.89]
2.41 [1.01, 3.86]
7.83 [2.41, 17.84]
0.02
1.28 [0.24, 2.62]
2.22 [1.04, 3.48]
7.63 [2.27, 18.78]
0.04
0.48 [0.05, 1.22]
0.67 [0.32, 0.98]
6.27 [0.60, 16.10]
The tenth and ninetieth percentiles are shown in brackets.
Table 7
PSE on Comparing Original and Filtered Color Signals by Use of SMSF Filtera
Signal
PSE
Illuminant
Daylight
0.9864 [0.9849, 0.9896]
Illuminant A
0.9735
Com. Fluor.
0.8650
F2
0.8719
F7
0.8701
F11
0.5137
Biochrome surface
Daylight
0.9735 [0.9555, 0.9836]
Illuminant A
0.9328 [0.8668, 0.9731]
Com. Fluor.
0.9409 [0.9120, 0.9641]
Nonbiochrome Surface
Daylight
0.9791 [0.9658, 0.9885]
Illuminant A
0.9568 [0.9282, 0.9740]
Com. Fluor.
0.8942 [0.7587, 0.9641]
Color signals correspond to SPDs of the illuminants and color signals from 96 biochrome and 74 nonbiochrome surfaces with three different illuminants. Values for daylight are mean values of 40 daylight SPDs. The tenth and ninetieth percentiles are shown in brackets. Com. Fluor. stands for commercial fluorescent.