Abstract

In this study, we have analyzed statistical properties of the values of the first- and second-order derivatives of spectral reflectance curves. We show that values of all four tested spectral data sets have very similar statistical properties. We set outer limits that bound the clear majority of the values of the first- and second-order derivatives. These limits define smoothness of all nonfluorescent reflectance curves, and they can be used to form a new object color solid inside classical MacAdam limits, including all possible colors generated by smooth nonfluorescent reflectance spectra. We have used the CIELAB color space and filled the new object color solid with a hexagonal closest packing-point lattice to estimate that there exist about 2.5 million different colors, when viewed under the D65 standard illumination.

© 2012 Optical Society of America

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References

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  1. W. S. Stiles, G. Wyszecki, and N. Ohta, “Counting metameric object-color stimuli using frequency-limited spectral reflectance functions,” J. Opt. Soc. Am. 67, 779–784 (1977).
    [CrossRef]
  2. L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. 3, 1673–1683 (1986).
    [CrossRef]
  3. T. Jääskeläinen, J. Parkkinen, and S. Toyooka, “Vector-subspace model for color representation,” J. Opt. Soc. Am. A 7, 725–730 (1990).
    [CrossRef]
  4. C. van Trigt, “Smoothest reflactance functions. I. Definition and main results,” J. Opt. Soc. Am. 7, 1891–1904 (1990).
    [CrossRef]
  5. C. van Trigt, “Smoothest reflectance functions. II. Complete results,” J. Opt. Soc. Am. 7, 2208–2222 (1990).
    [CrossRef]
  6. M. J. Vrhel and H. J. Trussell, “Filter considerations in color correction,” IEEE Trans. Image Process. 3, 147–161 (1994).
    [CrossRef]
  7. A. García-Beltrán, J. L. Nieves, J. Hernández-Andrés, and J. Romero, “Linear bases for spectral reflectance functions of acrylic paints,” Color Res. Appl. 23, 39–45 (1998).
    [CrossRef]
  8. V. Bonnardel and L. T. Maloney, “Daylight, biochrome surfaces, and human chromatic response in the Fourier domain,” J. Opt. Soc. Am. A 17, 677–685 (2000).
    [CrossRef]
  9. O. Kohonen, J. Parkkinen, and T. Jääskeläinen, “Databases for spectral color science,” Color Res. Appl. 31, 381–390 (2006).
    [CrossRef]
  10. J. Lehtonen, J. Parkkinen, and T. Jääskeläinen, “Optimal sampling of color spectra,” J. Opt. Soc. Am. A 23, 2983–2988 (2006).
    [CrossRef]
  11. J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).
  12. J. P. S. Parkkinen, J. Hallikainen, and T. Jääskeläinen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318–322 (1989).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. D. L. MacAdam, “Maximum visual efficiency of colored materials,” J. Opt. Soc. Am. 25, 316–367 (1935).
    [CrossRef]
  18. E. B. Titchener, Outline of Psychology (Macmillan, 1896).
  19. E. G. Boring, H. S. Langfeld, and H. P. Weld, Introduction to Psychology (Wiley, 1939).
  20. D. Nickerson and S. M. Newhall, “A psychological color solid,” J. Opt. Soc. Am. 33, 419–422 (1943).
    [CrossRef]
  21. M. Biot, Ann. Soc. Sci. Bruxelles 60, 149 (1946).
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    [CrossRef]
  23. D. B. Judd and G. Wyszecki, Color in Business, Science and Industry, 3rd ed. (Wiley, 1975).
  24. M. R. Pointer and G. G. Attridge, “The number of discernible colors,” Color Res. Appl. 23, 52–54 (1998).
    [CrossRef]
  25. F. Martínez-Verdú, E. Perales, E. Chorro, D. de Fez, V. Viqueira, and E. Gilabert, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source,” J. Opt. Soc. Am. 24, 1501–1515 (2007).
    [CrossRef]
  26. J. M. M. Linhares, P. D. Pinto, and S. M. C. Nascimento, “The number of discernible colors in natural scenes,” J. Opt. Soc. Am. A 25, 2918–2924 (2008).
    [CrossRef]
  27. I. Marín-Franch and D. H. Foster, “Number of perceptually distinct surface colors in natural scenes,” J. Vis. 10(9):9, 1–7(2010).
    [CrossRef]
  28. Spectral Database, University of Eastern Finland Color Group, http://www.uef.fi/spectral/spectral-database .
  29. J. H. van Hateren, “Spatial, temporal and spectral pre-processing for colour vision,” Proc. R. Soc. Lond. B 251, 61–68(1993).
  30. M. R. Pointer, “The gamut of real surface colours,” Color Res. Appl. 5, 145–155 (1980).
    [CrossRef]
  31. M. Mahy, L. van Eycken, and A. Oosterlinck, “Evaluation of uniform color spaces developed after the adoption of CIELAB and CIELUV,” Color Res. Appl. 19, 105–121 (1994).
  32. H. R. Kang, Color Technology for Electronic Imaging Devices (SPIE, 1997).
  33. R. W. G. Hunt, Measuring Colour, 3rd ed. (Fountain, 1998).
  34. J. Y. Hardeberg, “Acquisition and reproduction of colour images: colorimetric and multispectral approaches,” Ph.D. thesis (Ecole Nationale Supérieure des Télécommunications,” 1999).
  35. Project report EUR 19552EN, “Good practice guide to surface colour measurements” (2000).

2010 (1)

I. Marín-Franch and D. H. Foster, “Number of perceptually distinct surface colors in natural scenes,” J. Vis. 10(9):9, 1–7(2010).
[CrossRef]

2008 (1)

2007 (1)

F. Martínez-Verdú, E. Perales, E. Chorro, D. de Fez, V. Viqueira, and E. Gilabert, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source,” J. Opt. Soc. Am. 24, 1501–1515 (2007).
[CrossRef]

2006 (2)

O. Kohonen, J. Parkkinen, and T. Jääskeläinen, “Databases for spectral color science,” Color Res. Appl. 31, 381–390 (2006).
[CrossRef]

J. Lehtonen, J. Parkkinen, and T. Jääskeläinen, “Optimal sampling of color spectra,” J. Opt. Soc. Am. A 23, 2983–2988 (2006).
[CrossRef]

2000 (2)

1998 (2)

M. R. Pointer and G. G. Attridge, “The number of discernible colors,” Color Res. Appl. 23, 52–54 (1998).
[CrossRef]

A. García-Beltrán, J. L. Nieves, J. Hernández-Andrés, and J. Romero, “Linear bases for spectral reflectance functions of acrylic paints,” Color Res. Appl. 23, 39–45 (1998).
[CrossRef]

1994 (2)

M. J. Vrhel and H. J. Trussell, “Filter considerations in color correction,” IEEE Trans. Image Process. 3, 147–161 (1994).
[CrossRef]

M. Mahy, L. van Eycken, and A. Oosterlinck, “Evaluation of uniform color spaces developed after the adoption of CIELAB and CIELUV,” Color Res. Appl. 19, 105–121 (1994).

1993 (1)

J. H. van Hateren, “Spatial, temporal and spectral pre-processing for colour vision,” Proc. R. Soc. Lond. B 251, 61–68(1993).

1990 (3)

T. Jääskeläinen, J. Parkkinen, and S. Toyooka, “Vector-subspace model for color representation,” J. Opt. Soc. Am. A 7, 725–730 (1990).
[CrossRef]

C. van Trigt, “Smoothest reflactance functions. I. Definition and main results,” J. Opt. Soc. Am. 7, 1891–1904 (1990).
[CrossRef]

C. van Trigt, “Smoothest reflectance functions. II. Complete results,” J. Opt. Soc. Am. 7, 2208–2222 (1990).
[CrossRef]

1989 (1)

1986 (1)

L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. 3, 1673–1683 (1986).
[CrossRef]

1980 (1)

M. R. Pointer, “The gamut of real surface colours,” Color Res. Appl. 5, 145–155 (1980).
[CrossRef]

1977 (1)

1964 (1)

J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).

1947 (1)

1946 (1)

M. Biot, Ann. Soc. Sci. Bruxelles 60, 149 (1946).

1943 (1)

1935 (2)

D. L. MacAdam, “The theory of the maximum visual efficiency of color materials,” J. Opt. Soc. Am. 25, 249–252 (1935).
[CrossRef]

D. L. MacAdam, “Maximum visual efficiency of colored materials,” J. Opt. Soc. Am. 25, 316–367 (1935).
[CrossRef]

Attridge, G. G.

M. R. Pointer and G. G. Attridge, “The number of discernible colors,” Color Res. Appl. 23, 52–54 (1998).
[CrossRef]

Biot, M.

M. Biot, Ann. Soc. Sci. Bruxelles 60, 149 (1946).

Bonnardel, V.

Boring, E. G.

E. G. Boring, H. S. Langfeld, and H. P. Weld, Introduction to Psychology (Wiley, 1939).

Chiao, C.-C.

Chorro, E.

F. Martínez-Verdú, E. Perales, E. Chorro, D. de Fez, V. Viqueira, and E. Gilabert, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source,” J. Opt. Soc. Am. 24, 1501–1515 (2007).
[CrossRef]

Cohen, J.

J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).

Cronin, T. W.

de Fez, D.

F. Martínez-Verdú, E. Perales, E. Chorro, D. de Fez, V. Viqueira, and E. Gilabert, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source,” J. Opt. Soc. Am. 24, 1501–1515 (2007).
[CrossRef]

Foster, D. H.

I. Marín-Franch and D. H. Foster, “Number of perceptually distinct surface colors in natural scenes,” J. Vis. 10(9):9, 1–7(2010).
[CrossRef]

García-Beltrán, A.

A. García-Beltrán, J. L. Nieves, J. Hernández-Andrés, and J. Romero, “Linear bases for spectral reflectance functions of acrylic paints,” Color Res. Appl. 23, 39–45 (1998).
[CrossRef]

Gilabert, E.

F. Martínez-Verdú, E. Perales, E. Chorro, D. de Fez, V. Viqueira, and E. Gilabert, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source,” J. Opt. Soc. Am. 24, 1501–1515 (2007).
[CrossRef]

Hallikainen, J.

Hardeberg, J. Y.

J. Y. Hardeberg, “On the spectral dimensionality of object colours,” in Proceedings of CGIV 2002: The First European Conference on Colour Graphics, Imaging, and Vision (The Society for Imaging Science and Technology, 2002), pp. 480–485.

J. Y. Hardeberg, “Acquisition and reproduction of colour images: colorimetric and multispectral approaches,” Ph.D. thesis (Ecole Nationale Supérieure des Télécommunications,” 1999).

Hernández-Andrés, J.

A. García-Beltrán, J. L. Nieves, J. Hernández-Andrés, and J. Romero, “Linear bases for spectral reflectance functions of acrylic paints,” Color Res. Appl. 23, 39–45 (1998).
[CrossRef]

Hunt, R. W. G.

R. W. G. Hunt, Measuring Colour, 3rd ed. (Fountain, 1998).

Jääskeläinen, T.

Judd, D. B.

D. B. Judd and G. Wyszecki, Color in Business, Science and Industry, 3rd ed. (Wiley, 1975).

Kang, H. R.

H. R. Kang, Color Technology for Electronic Imaging Devices (SPIE, 1997).

Kohonen, O.

O. Kohonen, J. Parkkinen, and T. Jääskeläinen, “Databases for spectral color science,” Color Res. Appl. 31, 381–390 (2006).
[CrossRef]

Langfeld, H. S.

E. G. Boring, H. S. Langfeld, and H. P. Weld, Introduction to Psychology (Wiley, 1939).

Lehtonen, J.

Linhares, J. M. M.

MacAdam, D. L.

Mahy, M.

M. Mahy, L. van Eycken, and A. Oosterlinck, “Evaluation of uniform color spaces developed after the adoption of CIELAB and CIELUV,” Color Res. Appl. 19, 105–121 (1994).

Maloney, L. T.

V. Bonnardel and L. T. Maloney, “Daylight, biochrome surfaces, and human chromatic response in the Fourier domain,” J. Opt. Soc. Am. A 17, 677–685 (2000).
[CrossRef]

L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. 3, 1673–1683 (1986).
[CrossRef]

Marín-Franch, I.

I. Marín-Franch and D. H. Foster, “Number of perceptually distinct surface colors in natural scenes,” J. Vis. 10(9):9, 1–7(2010).
[CrossRef]

Martínez-Verdú, F.

F. Martínez-Verdú, E. Perales, E. Chorro, D. de Fez, V. Viqueira, and E. Gilabert, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source,” J. Opt. Soc. Am. 24, 1501–1515 (2007).
[CrossRef]

Nascimento, S. M. C.

Nassau, K.

K. Nassau, The Physics and Chemistry of Color: The Fifteen Causes of Color, 2nd ed. (Wiley, 2001).

Newhall, S. M.

Nickerson, D.

Nieves, J. L.

A. García-Beltrán, J. L. Nieves, J. Hernández-Andrés, and J. Romero, “Linear bases for spectral reflectance functions of acrylic paints,” Color Res. Appl. 23, 39–45 (1998).
[CrossRef]

Ohta, N.

Oosterlinck, A.

M. Mahy, L. van Eycken, and A. Oosterlinck, “Evaluation of uniform color spaces developed after the adoption of CIELAB and CIELUV,” Color Res. Appl. 19, 105–121 (1994).

Osorio, D.

Parkkinen, J.

Parkkinen, J. P. S.

Perales, E.

F. Martínez-Verdú, E. Perales, E. Chorro, D. de Fez, V. Viqueira, and E. Gilabert, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source,” J. Opt. Soc. Am. 24, 1501–1515 (2007).
[CrossRef]

Pinto, P. D.

Pointer, M. R.

M. R. Pointer and G. G. Attridge, “The number of discernible colors,” Color Res. Appl. 23, 52–54 (1998).
[CrossRef]

M. R. Pointer, “The gamut of real surface colours,” Color Res. Appl. 5, 145–155 (1980).
[CrossRef]

Romero, J.

A. García-Beltrán, J. L. Nieves, J. Hernández-Andrés, and J. Romero, “Linear bases for spectral reflectance functions of acrylic paints,” Color Res. Appl. 23, 39–45 (1998).
[CrossRef]

Stiles, W. S.

Titchener, E. B.

E. B. Titchener, Outline of Psychology (Macmillan, 1896).

Toyooka, S.

Trussell, H. J.

M. J. Vrhel and H. J. Trussell, “Filter considerations in color correction,” IEEE Trans. Image Process. 3, 147–161 (1994).
[CrossRef]

van Eycken, L.

M. Mahy, L. van Eycken, and A. Oosterlinck, “Evaluation of uniform color spaces developed after the adoption of CIELAB and CIELUV,” Color Res. Appl. 19, 105–121 (1994).

van Hateren, J. H.

J. H. van Hateren, “Spatial, temporal and spectral pre-processing for colour vision,” Proc. R. Soc. Lond. B 251, 61–68(1993).

van Trigt, C.

C. van Trigt, “Smoothest reflactance functions. I. Definition and main results,” J. Opt. Soc. Am. 7, 1891–1904 (1990).
[CrossRef]

C. van Trigt, “Smoothest reflectance functions. II. Complete results,” J. Opt. Soc. Am. 7, 2208–2222 (1990).
[CrossRef]

Viqueira, V.

F. Martínez-Verdú, E. Perales, E. Chorro, D. de Fez, V. Viqueira, and E. Gilabert, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source,” J. Opt. Soc. Am. 24, 1501–1515 (2007).
[CrossRef]

Vrhel, M. J.

M. J. Vrhel and H. J. Trussell, “Filter considerations in color correction,” IEEE Trans. Image Process. 3, 147–161 (1994).
[CrossRef]

Weld, H. P.

E. G. Boring, H. S. Langfeld, and H. P. Weld, Introduction to Psychology (Wiley, 1939).

Wyszecki, G.

Ann. Soc. Sci. Bruxelles (1)

M. Biot, Ann. Soc. Sci. Bruxelles 60, 149 (1946).

Color Res. Appl. (5)

M. R. Pointer and G. G. Attridge, “The number of discernible colors,” Color Res. Appl. 23, 52–54 (1998).
[CrossRef]

M. R. Pointer, “The gamut of real surface colours,” Color Res. Appl. 5, 145–155 (1980).
[CrossRef]

M. Mahy, L. van Eycken, and A. Oosterlinck, “Evaluation of uniform color spaces developed after the adoption of CIELAB and CIELUV,” Color Res. Appl. 19, 105–121 (1994).

A. García-Beltrán, J. L. Nieves, J. Hernández-Andrés, and J. Romero, “Linear bases for spectral reflectance functions of acrylic paints,” Color Res. Appl. 23, 39–45 (1998).
[CrossRef]

O. Kohonen, J. Parkkinen, and T. Jääskeläinen, “Databases for spectral color science,” Color Res. Appl. 31, 381–390 (2006).
[CrossRef]

IEEE Trans. Image Process. (1)

M. J. Vrhel and H. J. Trussell, “Filter considerations in color correction,” IEEE Trans. Image Process. 3, 147–161 (1994).
[CrossRef]

J. Opt. Soc. Am. (9)

D. Nickerson and S. M. Newhall, “A psychological color solid,” J. Opt. Soc. Am. 33, 419–422 (1943).
[CrossRef]

D. L. MacAdam, “Note on the number of distinct chromaticities,” J. Opt. Soc. Am. 37, 308–309 (1947).
[CrossRef]

F. Martínez-Verdú, E. Perales, E. Chorro, D. de Fez, V. Viqueira, and E. Gilabert, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source,” J. Opt. Soc. Am. 24, 1501–1515 (2007).
[CrossRef]

W. S. Stiles, G. Wyszecki, and N. Ohta, “Counting metameric object-color stimuli using frequency-limited spectral reflectance functions,” J. Opt. Soc. Am. 67, 779–784 (1977).
[CrossRef]

L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. 3, 1673–1683 (1986).
[CrossRef]

C. van Trigt, “Smoothest reflactance functions. I. Definition and main results,” J. Opt. Soc. Am. 7, 1891–1904 (1990).
[CrossRef]

C. van Trigt, “Smoothest reflectance functions. II. Complete results,” J. Opt. Soc. Am. 7, 2208–2222 (1990).
[CrossRef]

D. L. MacAdam, “The theory of the maximum visual efficiency of color materials,” J. Opt. Soc. Am. 25, 249–252 (1935).
[CrossRef]

D. L. MacAdam, “Maximum visual efficiency of colored materials,” J. Opt. Soc. Am. 25, 316–367 (1935).
[CrossRef]

J. Opt. Soc. Am. A (6)

J. Vis. (1)

I. Marín-Franch and D. H. Foster, “Number of perceptually distinct surface colors in natural scenes,” J. Vis. 10(9):9, 1–7(2010).
[CrossRef]

Proc. R. Soc. Lond. B (1)

J. H. van Hateren, “Spatial, temporal and spectral pre-processing for colour vision,” Proc. R. Soc. Lond. B 251, 61–68(1993).

Psychon. Sci. (1)

J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).

Other (10)

J. Y. Hardeberg, “On the spectral dimensionality of object colours,” in Proceedings of CGIV 2002: The First European Conference on Colour Graphics, Imaging, and Vision (The Society for Imaging Science and Technology, 2002), pp. 480–485.

K. Nassau, The Physics and Chemistry of Color: The Fifteen Causes of Color, 2nd ed. (Wiley, 2001).

E. B. Titchener, Outline of Psychology (Macmillan, 1896).

E. G. Boring, H. S. Langfeld, and H. P. Weld, Introduction to Psychology (Wiley, 1939).

H. R. Kang, Color Technology for Electronic Imaging Devices (SPIE, 1997).

R. W. G. Hunt, Measuring Colour, 3rd ed. (Fountain, 1998).

J. Y. Hardeberg, “Acquisition and reproduction of colour images: colorimetric and multispectral approaches,” Ph.D. thesis (Ecole Nationale Supérieure des Télécommunications,” 1999).

Project report EUR 19552EN, “Good practice guide to surface colour measurements” (2000).

Spectral Database, University of Eastern Finland Color Group, http://www.uef.fi/spectral/spectral-database .

D. B. Judd and G. Wyszecki, Color in Business, Science and Industry, 3rd ed. (Wiley, 1975).

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Figures (8)

Fig. 1.
Fig. 1.

Example of the noise-removal process. (a) shows one spectrum before and after noise filtering, marked with red (noisy) and black (smooth) curves, respectively. The copy of black smooth curve is shifted upward to visualize the difference more efficiently. (b) shows envelopes of three different histograms based on the values of the first-order derivatives (the unit of the values in the x-axis is change of reflectance per one nanometer). The black curve is formed by using the original virtually noiseless acrylic paints data. The red flat curve represents the same data with added Gaussian noise. The blue curve is the histogram corresponding to the filtered data. It has almost the same shape as the original histogram (black curve), which means the filtering process removes all added noise without changing the original features of the spectra.

Fig. 2.
Fig. 2.

Distribution of the values of the first-order derivatives of spectra in spectral sample sets.

Fig. 3.
Fig. 3.

Distribution of the values of the second-order derivatives of spectra in spectral sample sets.

Fig. 4.
Fig. 4.

Structure of generated spectrum. The spectrum (blue smooth curve) is constructed from six parts and each part has specific rules for values of the first- and second-order derivatives (green curve and red jagged curve, respectively), as shown in figure.

Fig. 5.
Fig. 5.

Different types of generated spectra. Values of spectral reflectance may increase from zero level as in case (a), or they may decrease from maximum level as in case (b). If maximum value of the height parameter h is higher than 1, the spectrum appears as the red-colored spectra (middle). If h is considerably higher than 1, the spectrum appears as the green-colored spectra (right).

Fig. 6.
Fig. 6.

Outer boundary of the natural (black curve) and MacAdam (blue outermost curve) color solids plotted in planes of constant CIE lightness L* with respect to the CIE standard illuminant D65. Real sample points belonging to each plane of constant lightness are marked with red crosses. In (a)–(e) the Natural color solid covers 82%, 78%, 77%, 76%, and 72% of the area of the MacAdam color solid, respectively. Orange innermost curves represent Pointer’s limits for real surface colors calculated by using the CIE standard illuminant C.

Fig. 7.
Fig. 7.

Each point of the HCP lattice is surrounded by 12 nearest neighbors, each at the same distance. Six points are in the planar hexagonal array, and three in the layer below and three in the layer above.

Fig. 8.
Fig. 8.

Two different layers of the HCP lattice plotted onto the a*b* axes with the cross sections of a color solid. Coordinate points of the edge line corresponding to the color solid are marked with red crosses. In this example picture the number of edges and lattice points is only a fraction of their real numbers. The edge line can be divided into upper and lower edges, marked with dark blue and light green colors, respectively. The total number of the lattice points between the lower and upper edge lines can be defined by going through the separate vertical lines of the lattice points. One such line is marked with red color.

Tables (3)

Tables Icon

Table 1. Boundary Limits between Which 99.9% of the Values of the First- and Second-Order Derivatives Are Located for Different Data Sets and the Combination of Setsa

Tables Icon

Table 2. CIE 1931 (x,y)-Chromaticity Coordinates of the Maximum Gamut of Colors Generated by Smooth Nonfluorescent Reflectance Spectra under the CIE Standard Illuminant D65a

Tables Icon

Table 3. CIE 1976 a*, b* Color Coordinates of the Maximum Gamut of Colors Generated by Smooth Nonfluorescent Reflectance Spectra under the CIE Standard Illuminant D65a

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

ρ(λ)=d12d2sin(d2d1λ).
f=300d22πd1.
Number of lattice points=floor(bmax*JNDs)ceil(bmin*JNDs)+1,
Number of colors=2.48·106JND3.

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