Abstract

Effect pigments in coatings produce eye-catching colour and texture effects and are widely used in automotive, cosmetics, coatings, inks, flooring, textile or decoration. One of these texture effects is graininess, which is the perceived texture exhibited when the effect coating is observed under diffuse illumination. To date there is not a standard procedure to measure graininess from reflectance measurements. The objective of this work is to propose a methodology for traceable graininess measurements, similarly as it was proposed for colour in 1931. In this article, the relevant reflectance-based quantities are clearly defined, and a formal relation with data from visual experiments is given. This methodology would allow a measurement scale of graininess and a difference formula to be agreed once conclusive visual data become available.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  1. G. A. Klein, Industrial Color Physics, vol. 154 (Springer, 2010).
    [Crossref]
  2. H.-J. Streitberger and K.-F. Dossel, Automotive Paints and Coatings (Wiley-Vch, 2008).
    [Crossref]
  3. E. B. Faulkner and R. J. Schwartz, High Performance Pigments (John Wiley & Sons, 2009).
    [Crossref]
  4. F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments-past, present and future,” Prog. organic coatings 54, 150–163 (2005).
    [Crossref]
  5. P. Wißling, Metallic Effect Pigments: Fundamentals and Applications (Vincentz Network GmbH & Co KG, 2006).
  6. C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” JOSA 44, 838–850 (1954).
    [Crossref]
  7. A. Ferrero, J. Campos, A. M. Rabal, and A. Pons, “A single analytical model for sparkle and graininess patterns in texture of effect coatings,” Opt. Express 21, 26812–26819 (2013).
    [Crossref] [PubMed]
  8. S. Ershov, A. Khodulev, and K. Kolchin, Simulation of sparkles in metallic paints, in Proceedings of Graphicon (1999), pp. 121–128.
  9. E. Kirchner, G. J. van den Kieboom, L. Njo, R. Sùper, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Col. Res. Appl. 32, 256–266 (2007).
    [Crossref]
  10. M. E. Becker, “Sparkle measurement revisited: A closer look at the details,” J. Soc. for Inf. Disp. 23, 472–485 (2015).
    [Crossref]
  11. W. Richards, “Quantifying sensory channels: generalizing colorimetry to orientation and texture, touch, and tones,” Sens. Process. 3, 207–229 (1979).
  12. V. A. Billock, D. W. Cunningham, P. R. Havig, and B. H. Tsou, “Perception of spatiotemporal random fractals: an extension of colorimetric methods to the study of dynamic texture,” JOSA A 18, 2404–2413 (2001).
    [Crossref] [PubMed]
  13. A. Pentland, Fractal-based Descriptions of Surfaces (MIT Press, 1988).
  14. D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” JOSA A 4, 2379–2394 (1987).
    [Crossref]
  15. D. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229–232 (1992).
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  16. V. A. Billock, “Neural acclimation to 1/f spatial frequency spectra in natural images transduced by the human visual system,” Phys. D: Nonlinear Phenom. 137, 379–391 (2000).
    [Crossref]
  17. J. Schanda, Colorimetry: Understanding the CIE System (John Wiley & Sons, 2007).
    [Crossref]
  18. D. L. MacAdam, “Visual sensitivities to color differences in daylight,” JOSA 32, 247–274 (1942).
    [Crossref]
  19. S. Kitaguchi, M. R. Luo, E. J. Kirchner, and G.-J. van den Kieboom, “Computational model for perceptual coarseness prediction,” in “Conference on Colour in Graphics, Imaging, and Vision,” (Society for Imaging Science and Technology, 2006), pp. 278–282.
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  23. R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications, 1958).
  24. K. Tiippana, R. Näsänen, and J. Rovamo, “Contrast matching of two-dimensional compound gratings,” Vis. Res. 34, 1157–1163 (1994).
    [Crossref] [PubMed]
  25. B. Moulden, F. Kingdom, and L. F. Gatley, “The standard deviation of luminance as a metric for contrast in random-dot images,” Perception 19, 79–101 (1990).
    [Crossref] [PubMed]
  26. P. J. Bex and W. Makous, “Spatial frequency, phase, and the contrast of natural images,” JOSA A 19, 1096–1106 (2002).
    [Crossref] [PubMed]
  27. F. W. Campbell and J. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
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2018 (1)

A. Kokka, T. Poikonen, P. Blattner, S. Jost, A. Ferrero, T. Pulli, M. Ngo, A. Thorseth, T. Gerloff, P. Dekker, and et al., “Development of white LED illuminants for colorimetry and recommendation of white LED reference spectrum for photometry,” Metrologia 55, 526 (2018).
[Crossref]

2015 (1)

M. E. Becker, “Sparkle measurement revisited: A closer look at the details,” J. Soc. for Inf. Disp. 23, 472–485 (2015).
[Crossref]

2013 (1)

2007 (1)

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Sùper, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Col. Res. Appl. 32, 256–266 (2007).
[Crossref]

2005 (1)

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments-past, present and future,” Prog. organic coatings 54, 150–163 (2005).
[Crossref]

2002 (1)

P. J. Bex and W. Makous, “Spatial frequency, phase, and the contrast of natural images,” JOSA A 19, 1096–1106 (2002).
[Crossref] [PubMed]

2001 (1)

V. A. Billock, D. W. Cunningham, P. R. Havig, and B. H. Tsou, “Perception of spatiotemporal random fractals: an extension of colorimetric methods to the study of dynamic texture,” JOSA A 18, 2404–2413 (2001).
[Crossref] [PubMed]

2000 (1)

V. A. Billock, “Neural acclimation to 1/f spatial frequency spectra in natural images transduced by the human visual system,” Phys. D: Nonlinear Phenom. 137, 379–391 (2000).
[Crossref]

1994 (1)

K. Tiippana, R. Näsänen, and J. Rovamo, “Contrast matching of two-dimensional compound gratings,” Vis. Res. 34, 1157–1163 (1994).
[Crossref] [PubMed]

1992 (1)

D. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229–232 (1992).
[Crossref] [PubMed]

1990 (1)

B. Moulden, F. Kingdom, and L. F. Gatley, “The standard deviation of luminance as a metric for contrast in random-dot images,” Perception 19, 79–101 (1990).
[Crossref] [PubMed]

1987 (1)

D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” JOSA A 4, 2379–2394 (1987).
[Crossref]

1979 (1)

W. Richards, “Quantifying sensory channels: generalizing colorimetry to orientation and texture, touch, and tones,” Sens. Process. 3, 207–229 (1979).

1968 (1)

F. W. Campbell and J. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[Crossref] [PubMed]

1954 (1)

C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” JOSA 44, 838–850 (1954).
[Crossref]

1942 (1)

D. L. MacAdam, “Visual sensitivities to color differences in daylight,” JOSA 32, 247–274 (1942).
[Crossref]

Becker, M. E.

M. E. Becker, “Sparkle measurement revisited: A closer look at the details,” J. Soc. for Inf. Disp. 23, 472–485 (2015).
[Crossref]

Bex, P. J.

P. J. Bex and W. Makous, “Spatial frequency, phase, and the contrast of natural images,” JOSA A 19, 1096–1106 (2002).
[Crossref] [PubMed]

Billock, V. A.

V. A. Billock, D. W. Cunningham, P. R. Havig, and B. H. Tsou, “Perception of spatiotemporal random fractals: an extension of colorimetric methods to the study of dynamic texture,” JOSA A 18, 2404–2413 (2001).
[Crossref] [PubMed]

V. A. Billock, “Neural acclimation to 1/f spatial frequency spectra in natural images transduced by the human visual system,” Phys. D: Nonlinear Phenom. 137, 379–391 (2000).
[Crossref]

Blackman, R. B.

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications, 1958).

Blattner, P.

A. Kokka, T. Poikonen, P. Blattner, S. Jost, A. Ferrero, T. Pulli, M. Ngo, A. Thorseth, T. Gerloff, P. Dekker, and et al., “Development of white LED illuminants for colorimetry and recommendation of white LED reference spectrum for photometry,” Metrologia 55, 526 (2018).
[Crossref]

R. Rattunde and P. Blattner, “CIE International Standard: CIE S 023/E:2013,” in “Characterization of the Performance of Illuminance Meters and Luminance Meters,” (CIE, 2013).

Campbell, F. W.

F. W. Campbell and J. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[Crossref] [PubMed]

Campos, J.

Chao, T.

D. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229–232 (1992).
[Crossref] [PubMed]

Cox, C.

C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” JOSA 44, 838–850 (1954).
[Crossref]

Cunningham, D. W.

V. A. Billock, D. W. Cunningham, P. R. Havig, and B. H. Tsou, “Perception of spatiotemporal random fractals: an extension of colorimetric methods to the study of dynamic texture,” JOSA A 18, 2404–2413 (2001).
[Crossref] [PubMed]

Dekker, P.

A. Kokka, T. Poikonen, P. Blattner, S. Jost, A. Ferrero, T. Pulli, M. Ngo, A. Thorseth, T. Gerloff, P. Dekker, and et al., “Development of white LED illuminants for colorimetry and recommendation of white LED reference spectrum for photometry,” Metrologia 55, 526 (2018).
[Crossref]

Dossel, K.-F.

H.-J. Streitberger and K.-F. Dossel, Automotive Paints and Coatings (Wiley-Vch, 2008).
[Crossref]

Ershov, S.

S. Ershov, A. Khodulev, and K. Kolchin, Simulation of sparkles in metallic paints, in Proceedings of Graphicon (1999), pp. 121–128.

Faulkner, E. B.

E. B. Faulkner and R. J. Schwartz, High Performance Pigments (John Wiley & Sons, 2009).
[Crossref]

Ferrero, A.

A. Kokka, T. Poikonen, P. Blattner, S. Jost, A. Ferrero, T. Pulli, M. Ngo, A. Thorseth, T. Gerloff, P. Dekker, and et al., “Development of white LED illuminants for colorimetry and recommendation of white LED reference spectrum for photometry,” Metrologia 55, 526 (2018).
[Crossref]

A. Ferrero, J. Campos, A. M. Rabal, and A. Pons, “A single analytical model for sparkle and graininess patterns in texture of effect coatings,” Opt. Express 21, 26812–26819 (2013).
[Crossref] [PubMed]

Field, D. J.

D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” JOSA A 4, 2379–2394 (1987).
[Crossref]

Gatley, L. F.

B. Moulden, F. Kingdom, and L. F. Gatley, “The standard deviation of luminance as a metric for contrast in random-dot images,” Perception 19, 79–101 (1990).
[Crossref] [PubMed]

Gerloff, T.

A. Kokka, T. Poikonen, P. Blattner, S. Jost, A. Ferrero, T. Pulli, M. Ngo, A. Thorseth, T. Gerloff, P. Dekker, and et al., “Development of white LED illuminants for colorimetry and recommendation of white LED reference spectrum for photometry,” Metrologia 55, 526 (2018).
[Crossref]

Gottenbos, R.

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Sùper, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Col. Res. Appl. 32, 256–266 (2007).
[Crossref]

Havig, P. R.

V. A. Billock, D. W. Cunningham, P. R. Havig, and B. H. Tsou, “Perception of spatiotemporal random fractals: an extension of colorimetric methods to the study of dynamic texture,” JOSA A 18, 2404–2413 (2001).
[Crossref] [PubMed]

Jost, S.

A. Kokka, T. Poikonen, P. Blattner, S. Jost, A. Ferrero, T. Pulli, M. Ngo, A. Thorseth, T. Gerloff, P. Dekker, and et al., “Development of white LED illuminants for colorimetry and recommendation of white LED reference spectrum for photometry,” Metrologia 55, 526 (2018).
[Crossref]

Khodulev, A.

S. Ershov, A. Khodulev, and K. Kolchin, Simulation of sparkles in metallic paints, in Proceedings of Graphicon (1999), pp. 121–128.

Kingdom, F.

B. Moulden, F. Kingdom, and L. F. Gatley, “The standard deviation of luminance as a metric for contrast in random-dot images,” Perception 19, 79–101 (1990).
[Crossref] [PubMed]

Kirchner, E.

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Sùper, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Col. Res. Appl. 32, 256–266 (2007).
[Crossref]

Kirchner, E. J.

S. Kitaguchi, M. R. Luo, E. J. Kirchner, and G.-J. van den Kieboom, “Computational model for perceptual coarseness prediction,” in “Conference on Colour in Graphics, Imaging, and Vision,” (Society for Imaging Science and Technology, 2006), pp. 278–282.

Kitaguchi, S.

S. Kitaguchi, M. R. Luo, E. J. Kirchner, and G.-J. van den Kieboom, “Computational model for perceptual coarseness prediction,” in “Conference on Colour in Graphics, Imaging, and Vision,” (Society for Imaging Science and Technology, 2006), pp. 278–282.

Klein, G. A.

G. A. Klein, Industrial Color Physics, vol. 154 (Springer, 2010).
[Crossref]

Kokka, A.

A. Kokka, T. Poikonen, P. Blattner, S. Jost, A. Ferrero, T. Pulli, M. Ngo, A. Thorseth, T. Gerloff, P. Dekker, and et al., “Development of white LED illuminants for colorimetry and recommendation of white LED reference spectrum for photometry,” Metrologia 55, 526 (2018).
[Crossref]

Kolchin, K.

S. Ershov, A. Khodulev, and K. Kolchin, Simulation of sparkles in metallic paints, in Proceedings of Graphicon (1999), pp. 121–128.

Luo, M. R.

S. Kitaguchi, M. R. Luo, E. J. Kirchner, and G.-J. van den Kieboom, “Computational model for perceptual coarseness prediction,” in “Conference on Colour in Graphics, Imaging, and Vision,” (Society for Imaging Science and Technology, 2006), pp. 278–282.

MacAdam, D. L.

D. L. MacAdam, “Visual sensitivities to color differences in daylight,” JOSA 32, 247–274 (1942).
[Crossref]

Maile, F. J.

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments-past, present and future,” Prog. organic coatings 54, 150–163 (2005).
[Crossref]

Makous, W.

P. J. Bex and W. Makous, “Spatial frequency, phase, and the contrast of natural images,” JOSA A 19, 1096–1106 (2002).
[Crossref] [PubMed]

Moulden, B.

B. Moulden, F. Kingdom, and L. F. Gatley, “The standard deviation of luminance as a metric for contrast in random-dot images,” Perception 19, 79–101 (1990).
[Crossref] [PubMed]

Munk, W.

C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” JOSA 44, 838–850 (1954).
[Crossref]

Näsänen, R.

K. Tiippana, R. Näsänen, and J. Rovamo, “Contrast matching of two-dimensional compound gratings,” Vis. Res. 34, 1157–1163 (1994).
[Crossref] [PubMed]

Ngo, M.

A. Kokka, T. Poikonen, P. Blattner, S. Jost, A. Ferrero, T. Pulli, M. Ngo, A. Thorseth, T. Gerloff, P. Dekker, and et al., “Development of white LED illuminants for colorimetry and recommendation of white LED reference spectrum for photometry,” Metrologia 55, 526 (2018).
[Crossref]

Njo, L.

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Sùper, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Col. Res. Appl. 32, 256–266 (2007).
[Crossref]

Pentland, A.

A. Pentland, Fractal-based Descriptions of Surfaces (MIT Press, 1988).

Pfaff, G.

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments-past, present and future,” Prog. organic coatings 54, 150–163 (2005).
[Crossref]

Poikonen, T.

A. Kokka, T. Poikonen, P. Blattner, S. Jost, A. Ferrero, T. Pulli, M. Ngo, A. Thorseth, T. Gerloff, P. Dekker, and et al., “Development of white LED illuminants for colorimetry and recommendation of white LED reference spectrum for photometry,” Metrologia 55, 526 (2018).
[Crossref]

Pons, A.

Pulli, T.

A. Kokka, T. Poikonen, P. Blattner, S. Jost, A. Ferrero, T. Pulli, M. Ngo, A. Thorseth, T. Gerloff, P. Dekker, and et al., “Development of white LED illuminants for colorimetry and recommendation of white LED reference spectrum for photometry,” Metrologia 55, 526 (2018).
[Crossref]

Rabal, A. M.

Rattunde, R.

R. Rattunde and P. Blattner, “CIE International Standard: CIE S 023/E:2013,” in “Characterization of the Performance of Illuminance Meters and Luminance Meters,” (CIE, 2013).

Reynders, P.

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments-past, present and future,” Prog. organic coatings 54, 150–163 (2005).
[Crossref]

Richards, W.

W. Richards, “Quantifying sensory channels: generalizing colorimetry to orientation and texture, touch, and tones,” Sens. Process. 3, 207–229 (1979).

Robson, J.

F. W. Campbell and J. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[Crossref] [PubMed]

Rovamo, J.

K. Tiippana, R. Näsänen, and J. Rovamo, “Contrast matching of two-dimensional compound gratings,” Vis. Res. 34, 1157–1163 (1994).
[Crossref] [PubMed]

Schanda, J.

J. Schanda, Colorimetry: Understanding the CIE System (John Wiley & Sons, 2007).
[Crossref]

Schwartz, R. J.

E. B. Faulkner and R. J. Schwartz, High Performance Pigments (John Wiley & Sons, 2009).
[Crossref]

Streitberger, H.-J.

H.-J. Streitberger and K.-F. Dossel, Automotive Paints and Coatings (Wiley-Vch, 2008).
[Crossref]

Sùper, R.

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Sùper, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Col. Res. Appl. 32, 256–266 (2007).
[Crossref]

Tadmor, Y.

D. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229–232 (1992).
[Crossref] [PubMed]

Thorseth, A.

A. Kokka, T. Poikonen, P. Blattner, S. Jost, A. Ferrero, T. Pulli, M. Ngo, A. Thorseth, T. Gerloff, P. Dekker, and et al., “Development of white LED illuminants for colorimetry and recommendation of white LED reference spectrum for photometry,” Metrologia 55, 526 (2018).
[Crossref]

Tiippana, K.

K. Tiippana, R. Näsänen, and J. Rovamo, “Contrast matching of two-dimensional compound gratings,” Vis. Res. 34, 1157–1163 (1994).
[Crossref] [PubMed]

Tolhurst, D.

D. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229–232 (1992).
[Crossref] [PubMed]

Tsou, B. H.

V. A. Billock, D. W. Cunningham, P. R. Havig, and B. H. Tsou, “Perception of spatiotemporal random fractals: an extension of colorimetric methods to the study of dynamic texture,” JOSA A 18, 2404–2413 (2001).
[Crossref] [PubMed]

Tukey, J. W.

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications, 1958).

van den Kieboom, G. J.

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Sùper, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Col. Res. Appl. 32, 256–266 (2007).
[Crossref]

van den Kieboom, G.-J.

S. Kitaguchi, M. R. Luo, E. J. Kirchner, and G.-J. van den Kieboom, “Computational model for perceptual coarseness prediction,” in “Conference on Colour in Graphics, Imaging, and Vision,” (Society for Imaging Science and Technology, 2006), pp. 278–282.

Wißling, P.

P. Wißling, Metallic Effect Pigments: Fundamentals and Applications (Vincentz Network GmbH & Co KG, 2006).

Col. Res. Appl. (1)

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Sùper, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Col. Res. Appl. 32, 256–266 (2007).
[Crossref]

J. Physiol. (1)

F. W. Campbell and J. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[Crossref] [PubMed]

J. Soc. for Inf. Disp. (1)

M. E. Becker, “Sparkle measurement revisited: A closer look at the details,” J. Soc. for Inf. Disp. 23, 472–485 (2015).
[Crossref]

JOSA (2)

D. L. MacAdam, “Visual sensitivities to color differences in daylight,” JOSA 32, 247–274 (1942).
[Crossref]

C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” JOSA 44, 838–850 (1954).
[Crossref]

JOSA A (3)

P. J. Bex and W. Makous, “Spatial frequency, phase, and the contrast of natural images,” JOSA A 19, 1096–1106 (2002).
[Crossref] [PubMed]

V. A. Billock, D. W. Cunningham, P. R. Havig, and B. H. Tsou, “Perception of spatiotemporal random fractals: an extension of colorimetric methods to the study of dynamic texture,” JOSA A 18, 2404–2413 (2001).
[Crossref] [PubMed]

D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” JOSA A 4, 2379–2394 (1987).
[Crossref]

Metrologia (1)

A. Kokka, T. Poikonen, P. Blattner, S. Jost, A. Ferrero, T. Pulli, M. Ngo, A. Thorseth, T. Gerloff, P. Dekker, and et al., “Development of white LED illuminants for colorimetry and recommendation of white LED reference spectrum for photometry,” Metrologia 55, 526 (2018).
[Crossref]

Ophthalmic Physiol. Opt. (1)

D. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229–232 (1992).
[Crossref] [PubMed]

Opt. Express (1)

Perception (1)

B. Moulden, F. Kingdom, and L. F. Gatley, “The standard deviation of luminance as a metric for contrast in random-dot images,” Perception 19, 79–101 (1990).
[Crossref] [PubMed]

Phys. D: Nonlinear Phenom. (1)

V. A. Billock, “Neural acclimation to 1/f spatial frequency spectra in natural images transduced by the human visual system,” Phys. D: Nonlinear Phenom. 137, 379–391 (2000).
[Crossref]

Prog. organic coatings (1)

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments-past, present and future,” Prog. organic coatings 54, 150–163 (2005).
[Crossref]

Sens. Process. (1)

W. Richards, “Quantifying sensory channels: generalizing colorimetry to orientation and texture, touch, and tones,” Sens. Process. 3, 207–229 (1979).

Vis. Res. (1)

K. Tiippana, R. Näsänen, and J. Rovamo, “Contrast matching of two-dimensional compound gratings,” Vis. Res. 34, 1157–1163 (1994).
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Figures (7)

Fig. 1
Fig. 1 Set of 25 graininess samples (8 cm × 13 cm) used in this study.
Fig. 2
Fig. 2 Experimental set-up for the reflectance measurement.
Fig. 3
Fig. 3 Spectral power distribution of the phosphor-based LED used as light source in Fig. 2.
Fig. 4
Fig. 4 Graininess images (R) of a reduced set of samples (those with odd pigment concentration and size Ids.). Only a squared and centered region of interest of 6.9 mm × 6.9 mm (151 pixels × 151 pixels) is shown. The grey bars represent the luminance factor values of the pixels.
Fig. 5
Fig. 5 Decimal logarithms of the PSDs for the samples with odd Ids., together with the PSD of a white sample without graininess (“No Graininess”).
Fig. 6
Fig. 6 Relation of the reflectance-based quantities with pigment concentration and size: (left graph) average luminance factor (β); (right graph) graininess variance (VG).
Fig. 7
Fig. 7 Representation of graininess using (a) BYK-mac’s graininess index and (b) UA’s visual data as visual data.

Equations (5)

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A ( f s , f t ) = K f s α s f t α t ,
R i j = I i j D i j W i j D i j × R W
F = W i j / W i j , V I i j / I i j , V = = 360 nm 830 nm S ( λ ) s ( λ ) R is ( λ ) R W ( λ ) d λ 360 nm 830 nm S ( λ ) V ( λ ) R is ( λ ) R I ( λ ) d λ 360 nm 830 nm S ( λ ) V ( λ ) R is ( λ ) R W ( λ ) d λ 360 nm 830 nm S ( λ ) s ( λ ) R is ( λ ) R I ( λ ) d λ
V G ( f 1 , f 2 ) = 2 f 1 f 2 PSD ( f ) d f ,
G = V G ( f 1 , f 2 ) × ( 1 + a β b ) ,

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