Abstract

We propose a fuzzy method to analyze datasets of perceptual color differences with two main objectives: to detect inconsistencies between couples of color pairs and to assign a degree of consistency to each color pair in a dataset. This method can be thought as the outcome of a previous one developed for a similar purpose [J. Mod. Opt. 56, 1447 (2009) [CrossRef]  ], whose performance is compared with the proposed one. In this work, we present the results achieved using the dataset employed to develop the current CIE/ISO color-difference formula, CIEDE2000, but the method could be applied to any dataset. Specifically, in the mentioned dataset, we find that some couples of color pairs have contradictory information, which can interfere in the successful development of future color-difference formulas as well as in checking the performance of current ones.

© 2016 Optical Society of America

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References

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  1. M. Melgosa, A. Trémeau, and G. Cui, “Colour difference evaluation,” in Advanced Color Imaging Processing and Analysis, C. Fernandez-Maloigne, ed. (Springer, 2013), pp. 59–79.
  2. R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991).
    [Crossref]
  3. M. Melgosa, R. Huertas, and R. S. Berns, “Performance of recent advanced color-difference formulas using the standardized residual sum of squares index,” J. Opt. Soc. Am. A 25, 1828–1834 (2008).
    [Crossref]
  4. M. Melgosa, E. Hita, J. Romero, and L. Jiménez del Barco, “Some classical color differences calculated with new formulas,” J. Opt. Soc. Am. A 9, 1247–1254 (1992).
    [Crossref]
  5. M. Melgosa, J. J. Quesada, and E. Hita, “Uniformity of some recent color metrics tested with an accurate color-difference tolerance dataset,” Appl. Opt. 33, 8069–8077 (1994).
    [Crossref]
  6. M. R. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340–350 (2001).
    [Crossref]
  7. I. Farup, “Hyperbolic geometry for colour metrics,” Opt. Express 22, 12369–12378 (2014).
    [Crossref]
  8. M. Melgosa, J. Martínez-García, L. Gómez-Robledo, E. Perales, F. M. Martínez-Verdú, and T. Dauser, “Measuring color differences in automotive samples with lightness flop: a test of the AUDI2000 color-difference formula,” Opt. Express 22, 3458–3467 (2014).
    [Crossref]
  9. M. Huang, G. Cui, M. Melgosa, M. Sánchez-Marañón, C. Li, M. R. Luo, and H. Liu, “Power functions improving the performance of color-difference formulas,” Opt. Express 23, 597–610 (2015).
    [Crossref]
  10. International Commission on Illumination (CIE), Parametric Effects in Colour Difference Evaluation (CIE Central Bureau, 1993).
  11. A. R. Robertson, “CIE guidelines for coordinated research on color-difference evaluation,” Color Res. Appl. 3, 149–151 (1978).
  12. K. Witt, “CIE guidelines for coordinated future work on industrial colour-difference evaluation,” Color Res. Appl. 20, 399–403 (1995).
    [Crossref]
  13. M. Melgosa, “Request for existing experimental datasets on color differences,” Color Res. Appl. 32, 159 (2007).
    [Crossref]
  14. CIE 217:2016, Recommended Method for Evaluating the Performance of Colour-Difference Formulae (CIE Central Bureau, 2016).
  15. E. D. Montag and D. C. Wilber, “A comparison of constant stimuli and gray-scale methods of color difference scaling,” Col. Res. Appl. 28, 36–44 (2003).
    [Crossref]
  16. E. Kirchner, N. Dekker, M. Lucassen, L. Njo, I. van der Lans, P. Urban, and R. Huertas, “How psychophysical methods influence optimizations of color difference formulas,” J. Opt. Soc. Am. A 32, 357–366 (2015).
    [Crossref]
  17. M. Melgosa, P. A. García, L. Gómez-Robledo, R. Shamey, D. Hinks, G. Cui, and M. R. Luo, “Notes on the application of the standardized residual sum of squares index for the assessment of intra- and inter-observer variability,” J. Opt. Soc. Am. A 28, 949–953 (2011).
    [Crossref]
  18. R. Shamey, J. Lin, W. Sawatwarakul, and R. Cao, “Evaluation of performance of various color-difference formulae using an experimental black dataset,” Color Res. Appl. 39, 589–598 (2014).
    [Crossref]
  19. International Commission on Illumination (CIE) and International Organization for Standardization (ISO), “Colorimetry—Part 6: CIEDE2000 Colour-Difference Formula,” (CIE Central Bureau, 2014).
  20. M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colors,” Color Res. Appl. 11, 25–42 (1986).
    [Crossref]
  21. D. H. Kim and J. Nobbs, “New weighting functions for the weighted CIELAB color difference formula,” in Proceedings of AIC Colour 97 (Color Science Association of Japan, 1997), Vol. 1, pp. 446–449.
  22. K. Witt, “Geometrical relations between scales of small colour differences,” Color Res. Appl. 24, 78–92 (1999).
    [Crossref]
  23. S. Morillas, L. Gómez-Robledo, R. Huertas, and M. Melgosa, “Fuzzy analysis for detection of inconsistent data in experimental datasets employed at the development of the CIEDE2000 colour-difference formula,” J. Mod. Opt. 56, 1447–1456 (2009).
    [Crossref]
  24. P. A. García, R. Huertas, M. Melgosa, and G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007).
    [Crossref]
  25. R. S. Berns and B. Hou, “RIT-DuPont supra-threshold color-tolerances individual color-difference pair dataset,” Color Res. Appl. 35, 274–283 (2010).
    [Crossref]
  26. M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006).
    [Crossref]
  27. G. Cui, M. R. Luo, B. Rigg, G. Roesler, and K. Witt, “Uniform colour spaces based on the DIN99 colour-difference formula,” Color Res. Appl. 27, 282–290 (2002).
    [Crossref]
  28. C. Oleari, M. Melgosa, and R. Huertas, “Euclidean color-difference formula for small-medium color differences in log-compressed OSA-UCS space,” J. Opt. Soc. Am. A 26, 121–134 (2009).
    [Crossref]
  29. D. H. Kim, “The ULAB colour space,” Color Res. Appl. 40, 17–29 (2015).
    [Crossref]
  30. M. W. Derhak and R. S. Berns, “Introducing WLab—Going from Wpt (Waypoint) to a uniform material color equivalence space,” Color Res. Appl. 40, 550–563 (2015).
    [Crossref]
  31. E. E. Kerre, Fuzzy Sets and Approximate Reasoning (Xian Jiaotong University, 1998).
  32. A. George and P. Veeramani, “On some results in fuzzy metrics spaces,” Fuzzy Sets Syst. 64, 395–399 (1994).
    [Crossref]
  33. S. Morillas, V. Gregori, G. Peris-Fajarnes, and A. Sapena, “New adaptive vector filter using fuzzy metrics,” J. Electron. Imaging 16, 33007 (2007).
    [Crossref]
  34. S. Morillas, “Fuzzy metrics and fuzzy logic for colour image filtering,” Ph.D. thesis (Universidad Politécnica de Valencia, 2007).

2015 (4)

2014 (3)

2011 (1)

2010 (1)

R. S. Berns and B. Hou, “RIT-DuPont supra-threshold color-tolerances individual color-difference pair dataset,” Color Res. Appl. 35, 274–283 (2010).
[Crossref]

2009 (2)

S. Morillas, L. Gómez-Robledo, R. Huertas, and M. Melgosa, “Fuzzy analysis for detection of inconsistent data in experimental datasets employed at the development of the CIEDE2000 colour-difference formula,” J. Mod. Opt. 56, 1447–1456 (2009).
[Crossref]

C. Oleari, M. Melgosa, and R. Huertas, “Euclidean color-difference formula for small-medium color differences in log-compressed OSA-UCS space,” J. Opt. Soc. Am. A 26, 121–134 (2009).
[Crossref]

2008 (1)

2007 (3)

P. A. García, R. Huertas, M. Melgosa, and G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007).
[Crossref]

S. Morillas, V. Gregori, G. Peris-Fajarnes, and A. Sapena, “New adaptive vector filter using fuzzy metrics,” J. Electron. Imaging 16, 33007 (2007).
[Crossref]

M. Melgosa, “Request for existing experimental datasets on color differences,” Color Res. Appl. 32, 159 (2007).
[Crossref]

2006 (1)

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006).
[Crossref]

2003 (1)

E. D. Montag and D. C. Wilber, “A comparison of constant stimuli and gray-scale methods of color difference scaling,” Col. Res. Appl. 28, 36–44 (2003).
[Crossref]

2002 (1)

G. Cui, M. R. Luo, B. Rigg, G. Roesler, and K. Witt, “Uniform colour spaces based on the DIN99 colour-difference formula,” Color Res. Appl. 27, 282–290 (2002).
[Crossref]

2001 (1)

M. R. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340–350 (2001).
[Crossref]

1999 (1)

K. Witt, “Geometrical relations between scales of small colour differences,” Color Res. Appl. 24, 78–92 (1999).
[Crossref]

1995 (1)

K. Witt, “CIE guidelines for coordinated future work on industrial colour-difference evaluation,” Color Res. Appl. 20, 399–403 (1995).
[Crossref]

1994 (2)

1992 (1)

1991 (1)

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991).
[Crossref]

1986 (1)

M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colors,” Color Res. Appl. 11, 25–42 (1986).
[Crossref]

1978 (1)

A. R. Robertson, “CIE guidelines for coordinated research on color-difference evaluation,” Color Res. Appl. 3, 149–151 (1978).

Alman, D. H.

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991).
[Crossref]

Balonon-Rosen, M. R.

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991).
[Crossref]

Berns, R. S.

M. W. Derhak and R. S. Berns, “Introducing WLab—Going from Wpt (Waypoint) to a uniform material color equivalence space,” Color Res. Appl. 40, 550–563 (2015).
[Crossref]

R. S. Berns and B. Hou, “RIT-DuPont supra-threshold color-tolerances individual color-difference pair dataset,” Color Res. Appl. 35, 274–283 (2010).
[Crossref]

M. Melgosa, R. Huertas, and R. S. Berns, “Performance of recent advanced color-difference formulas using the standardized residual sum of squares index,” J. Opt. Soc. Am. A 25, 1828–1834 (2008).
[Crossref]

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991).
[Crossref]

Cao, R.

R. Shamey, J. Lin, W. Sawatwarakul, and R. Cao, “Evaluation of performance of various color-difference formulae using an experimental black dataset,” Color Res. Appl. 39, 589–598 (2014).
[Crossref]

Cui, G.

M. Huang, G. Cui, M. Melgosa, M. Sánchez-Marañón, C. Li, M. R. Luo, and H. Liu, “Power functions improving the performance of color-difference formulas,” Opt. Express 23, 597–610 (2015).
[Crossref]

M. Melgosa, P. A. García, L. Gómez-Robledo, R. Shamey, D. Hinks, G. Cui, and M. R. Luo, “Notes on the application of the standardized residual sum of squares index for the assessment of intra- and inter-observer variability,” J. Opt. Soc. Am. A 28, 949–953 (2011).
[Crossref]

P. A. García, R. Huertas, M. Melgosa, and G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007).
[Crossref]

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006).
[Crossref]

G. Cui, M. R. Luo, B. Rigg, G. Roesler, and K. Witt, “Uniform colour spaces based on the DIN99 colour-difference formula,” Color Res. Appl. 27, 282–290 (2002).
[Crossref]

M. R. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340–350 (2001).
[Crossref]

M. Melgosa, A. Trémeau, and G. Cui, “Colour difference evaluation,” in Advanced Color Imaging Processing and Analysis, C. Fernandez-Maloigne, ed. (Springer, 2013), pp. 59–79.

Dauser, T.

Dekker, N.

Derhak, M. W.

M. W. Derhak and R. S. Berns, “Introducing WLab—Going from Wpt (Waypoint) to a uniform material color equivalence space,” Color Res. Appl. 40, 550–563 (2015).
[Crossref]

Farup, I.

García, P. A.

George, A.

A. George and P. Veeramani, “On some results in fuzzy metrics spaces,” Fuzzy Sets Syst. 64, 395–399 (1994).
[Crossref]

Gómez-Robledo, L.

Gregori, V.

S. Morillas, V. Gregori, G. Peris-Fajarnes, and A. Sapena, “New adaptive vector filter using fuzzy metrics,” J. Electron. Imaging 16, 33007 (2007).
[Crossref]

Hinks, D.

Hita, E.

Hou, B.

R. S. Berns and B. Hou, “RIT-DuPont supra-threshold color-tolerances individual color-difference pair dataset,” Color Res. Appl. 35, 274–283 (2010).
[Crossref]

Huang, M.

Huertas, R.

Jiménez del Barco, L.

Kerre, E. E.

E. E. Kerre, Fuzzy Sets and Approximate Reasoning (Xian Jiaotong University, 1998).

Kim, D. H.

D. H. Kim, “The ULAB colour space,” Color Res. Appl. 40, 17–29 (2015).
[Crossref]

D. H. Kim and J. Nobbs, “New weighting functions for the weighted CIELAB color difference formula,” in Proceedings of AIC Colour 97 (Color Science Association of Japan, 1997), Vol. 1, pp. 446–449.

Kirchner, E.

Li, C.

Lin, J.

R. Shamey, J. Lin, W. Sawatwarakul, and R. Cao, “Evaluation of performance of various color-difference formulae using an experimental black dataset,” Color Res. Appl. 39, 589–598 (2014).
[Crossref]

Liu, H.

Lucassen, M.

Luo, M. R.

M. Huang, G. Cui, M. Melgosa, M. Sánchez-Marañón, C. Li, M. R. Luo, and H. Liu, “Power functions improving the performance of color-difference formulas,” Opt. Express 23, 597–610 (2015).
[Crossref]

M. Melgosa, P. A. García, L. Gómez-Robledo, R. Shamey, D. Hinks, G. Cui, and M. R. Luo, “Notes on the application of the standardized residual sum of squares index for the assessment of intra- and inter-observer variability,” J. Opt. Soc. Am. A 28, 949–953 (2011).
[Crossref]

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006).
[Crossref]

G. Cui, M. R. Luo, B. Rigg, G. Roesler, and K. Witt, “Uniform colour spaces based on the DIN99 colour-difference formula,” Color Res. Appl. 27, 282–290 (2002).
[Crossref]

M. R. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340–350 (2001).
[Crossref]

M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colors,” Color Res. Appl. 11, 25–42 (1986).
[Crossref]

Martínez-García, J.

Martínez-Verdú, F. M.

Melgosa, M.

M. Huang, G. Cui, M. Melgosa, M. Sánchez-Marañón, C. Li, M. R. Luo, and H. Liu, “Power functions improving the performance of color-difference formulas,” Opt. Express 23, 597–610 (2015).
[Crossref]

M. Melgosa, J. Martínez-García, L. Gómez-Robledo, E. Perales, F. M. Martínez-Verdú, and T. Dauser, “Measuring color differences in automotive samples with lightness flop: a test of the AUDI2000 color-difference formula,” Opt. Express 22, 3458–3467 (2014).
[Crossref]

M. Melgosa, P. A. García, L. Gómez-Robledo, R. Shamey, D. Hinks, G. Cui, and M. R. Luo, “Notes on the application of the standardized residual sum of squares index for the assessment of intra- and inter-observer variability,” J. Opt. Soc. Am. A 28, 949–953 (2011).
[Crossref]

C. Oleari, M. Melgosa, and R. Huertas, “Euclidean color-difference formula for small-medium color differences in log-compressed OSA-UCS space,” J. Opt. Soc. Am. A 26, 121–134 (2009).
[Crossref]

S. Morillas, L. Gómez-Robledo, R. Huertas, and M. Melgosa, “Fuzzy analysis for detection of inconsistent data in experimental datasets employed at the development of the CIEDE2000 colour-difference formula,” J. Mod. Opt. 56, 1447–1456 (2009).
[Crossref]

M. Melgosa, R. Huertas, and R. S. Berns, “Performance of recent advanced color-difference formulas using the standardized residual sum of squares index,” J. Opt. Soc. Am. A 25, 1828–1834 (2008).
[Crossref]

P. A. García, R. Huertas, M. Melgosa, and G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007).
[Crossref]

M. Melgosa, “Request for existing experimental datasets on color differences,” Color Res. Appl. 32, 159 (2007).
[Crossref]

M. Melgosa, J. J. Quesada, and E. Hita, “Uniformity of some recent color metrics tested with an accurate color-difference tolerance dataset,” Appl. Opt. 33, 8069–8077 (1994).
[Crossref]

M. Melgosa, E. Hita, J. Romero, and L. Jiménez del Barco, “Some classical color differences calculated with new formulas,” J. Opt. Soc. Am. A 9, 1247–1254 (1992).
[Crossref]

M. Melgosa, A. Trémeau, and G. Cui, “Colour difference evaluation,” in Advanced Color Imaging Processing and Analysis, C. Fernandez-Maloigne, ed. (Springer, 2013), pp. 59–79.

Montag, E. D.

E. D. Montag and D. C. Wilber, “A comparison of constant stimuli and gray-scale methods of color difference scaling,” Col. Res. Appl. 28, 36–44 (2003).
[Crossref]

Morillas, S.

S. Morillas, L. Gómez-Robledo, R. Huertas, and M. Melgosa, “Fuzzy analysis for detection of inconsistent data in experimental datasets employed at the development of the CIEDE2000 colour-difference formula,” J. Mod. Opt. 56, 1447–1456 (2009).
[Crossref]

S. Morillas, V. Gregori, G. Peris-Fajarnes, and A. Sapena, “New adaptive vector filter using fuzzy metrics,” J. Electron. Imaging 16, 33007 (2007).
[Crossref]

S. Morillas, “Fuzzy metrics and fuzzy logic for colour image filtering,” Ph.D. thesis (Universidad Politécnica de Valencia, 2007).

Njo, L.

Nobbs, J.

D. H. Kim and J. Nobbs, “New weighting functions for the weighted CIELAB color difference formula,” in Proceedings of AIC Colour 97 (Color Science Association of Japan, 1997), Vol. 1, pp. 446–449.

Oleari, C.

Perales, E.

Peris-Fajarnes, G.

S. Morillas, V. Gregori, G. Peris-Fajarnes, and A. Sapena, “New adaptive vector filter using fuzzy metrics,” J. Electron. Imaging 16, 33007 (2007).
[Crossref]

Quesada, J. J.

Reniff, L.

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991).
[Crossref]

Rigg, B.

G. Cui, M. R. Luo, B. Rigg, G. Roesler, and K. Witt, “Uniform colour spaces based on the DIN99 colour-difference formula,” Color Res. Appl. 27, 282–290 (2002).
[Crossref]

M. R. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340–350 (2001).
[Crossref]

M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colors,” Color Res. Appl. 11, 25–42 (1986).
[Crossref]

Robertson, A. R.

A. R. Robertson, “CIE guidelines for coordinated research on color-difference evaluation,” Color Res. Appl. 3, 149–151 (1978).

Roesler, G.

G. Cui, M. R. Luo, B. Rigg, G. Roesler, and K. Witt, “Uniform colour spaces based on the DIN99 colour-difference formula,” Color Res. Appl. 27, 282–290 (2002).
[Crossref]

Romero, J.

Sánchez-Marañón, M.

Sapena, A.

S. Morillas, V. Gregori, G. Peris-Fajarnes, and A. Sapena, “New adaptive vector filter using fuzzy metrics,” J. Electron. Imaging 16, 33007 (2007).
[Crossref]

Sawatwarakul, W.

R. Shamey, J. Lin, W. Sawatwarakul, and R. Cao, “Evaluation of performance of various color-difference formulae using an experimental black dataset,” Color Res. Appl. 39, 589–598 (2014).
[Crossref]

Shamey, R.

Snyder, G. D.

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991).
[Crossref]

Trémeau, A.

M. Melgosa, A. Trémeau, and G. Cui, “Colour difference evaluation,” in Advanced Color Imaging Processing and Analysis, C. Fernandez-Maloigne, ed. (Springer, 2013), pp. 59–79.

Urban, P.

van der Lans, I.

Veeramani, P.

A. George and P. Veeramani, “On some results in fuzzy metrics spaces,” Fuzzy Sets Syst. 64, 395–399 (1994).
[Crossref]

Wilber, D. C.

E. D. Montag and D. C. Wilber, “A comparison of constant stimuli and gray-scale methods of color difference scaling,” Col. Res. Appl. 28, 36–44 (2003).
[Crossref]

Witt, K.

G. Cui, M. R. Luo, B. Rigg, G. Roesler, and K. Witt, “Uniform colour spaces based on the DIN99 colour-difference formula,” Color Res. Appl. 27, 282–290 (2002).
[Crossref]

K. Witt, “Geometrical relations between scales of small colour differences,” Color Res. Appl. 24, 78–92 (1999).
[Crossref]

K. Witt, “CIE guidelines for coordinated future work on industrial colour-difference evaluation,” Color Res. Appl. 20, 399–403 (1995).
[Crossref]

Appl. Opt. (1)

Col. Res. Appl. (1)

E. D. Montag and D. C. Wilber, “A comparison of constant stimuli and gray-scale methods of color difference scaling,” Col. Res. Appl. 28, 36–44 (2003).
[Crossref]

Color Res. Appl. (13)

R. Shamey, J. Lin, W. Sawatwarakul, and R. Cao, “Evaluation of performance of various color-difference formulae using an experimental black dataset,” Color Res. Appl. 39, 589–598 (2014).
[Crossref]

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color-difference tolerances using probit analysis,” Color Res. Appl. 16, 297–316 (1991).
[Crossref]

M. R. Luo, G. Cui, and B. Rigg, “The development of the CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340–350 (2001).
[Crossref]

A. R. Robertson, “CIE guidelines for coordinated research on color-difference evaluation,” Color Res. Appl. 3, 149–151 (1978).

K. Witt, “CIE guidelines for coordinated future work on industrial colour-difference evaluation,” Color Res. Appl. 20, 399–403 (1995).
[Crossref]

M. Melgosa, “Request for existing experimental datasets on color differences,” Color Res. Appl. 32, 159 (2007).
[Crossref]

M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colors,” Color Res. Appl. 11, 25–42 (1986).
[Crossref]

K. Witt, “Geometrical relations between scales of small colour differences,” Color Res. Appl. 24, 78–92 (1999).
[Crossref]

R. S. Berns and B. Hou, “RIT-DuPont supra-threshold color-tolerances individual color-difference pair dataset,” Color Res. Appl. 35, 274–283 (2010).
[Crossref]

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. Example of the two options to compute Δ M i j , 1 and Δ M i j , 2 from Eq. (1), in two specific cases where the distances between the centers C i and C j of the two color pairs (with samples indicated by triangles and circles, respectively) were null.
Fig. 2.
Fig. 2. Plot of μ function in Eq. (3), for the different values of parameters α i and γ i considered in the text. Below the value α i the membership of the neighborhoods is equal to 0; then the membership increases smoothly until value γ i ; and finally, above value γ i , the membership is equal to 1.
Fig. 3.
Fig. 3. Number of couples of color pairs with inconsistencies higher than the inconsistency thresholds indicated in the x -axis, using the I i j (inconsistencies when Δ Δ E 00 is very small and Δ Δ V is not small) and I i j * (inconsistencies when Δ Δ E 00 is not small and Δ Δ V is very small) indices.
Fig. 4.
Fig. 4. Number of color pairs ( y -axis) for different numbers of fuzzy neighbors ( x -axis, where the bar width is equal to 3). It should be remembered that α 4 = 1 and γ 4 = 10 fixed the adopted neighborhood criterion.
Fig. 5.
Fig. 5. Histogram with number of color pairs with a degree of consistency lower than C ( S i ) values shown in the x -axis. The continuous line in the plot (associated to the right y -axis units) corresponds to STRESS values calculated for the CIEDE2000 color-difference formula after removing color pairs with degrees of consistency equal to or lower than specific C ( S i ) values shown on the x -axis.
Fig. 6.
Fig. 6. Degrees of consistency for color pairs in the COM-corrected dataset from the method in [23] against those taken from step 2 of our current method.

Tables (1)

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Table 1. Example of Two Inconsistent Color Pairs in the BFD-P Subset a

Equations (13)

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( Δ M i j , 1 , Δ M i j , 2 ) = ( A i A j , B i B j ) if A i A j + B i B j A i B j + B i A j , otherwise ( Δ M i j , 1 , Δ M i j , 2 ) = ( A i B j , B i A j ) ,
Δ M i j , 1 small = 1 μ ( Δ M i j , 1 , α 1 , γ 1 ) ,
μ ( x , α , γ ) = { 0 if    x α 1 2 ( x γ γ α ) 2 if    α < x α + γ 2 2 ( x α γ α ) 2 if    α + γ 2 < x γ 1 if    x > γ .
Δ Δ E i j very small = 1 μ ( Δ Δ E i j , α 2 , γ 2 ) ,
Δ Δ V i j not small = μ ( Δ Δ V i j , α 3 , γ 3 ) ,
I i j = Δ M i j , 1 small · Δ M i j , 2 small · Δ Δ E i j very small · Δ Δ V i j not small ,
I i j * = Δ M i j , 1 small · Δ M i j , 2 small · Δ Δ V i j very small · Δ Δ E i j not small ,
Δ M i j , 1 not large = 1 μ ( Δ M i j , 1 , α 4 , γ 4 ) ,
Δ Δ V i j not large = 1 μ ( Δ Δ V i j , α 5 , γ 5 ) .
S S i ( S j ) = Δ M i j , 1 not large · Δ M i j , 2 not large · Δ Δ V i j not large .
C ( S i ) = FM S ( D i , D ˜ i , σ ˜ i ) = σ ˜ i σ ˜ i + | D i D ˜ i | ,
D ˜ i = S j S , S j S i S S i ( S j ) D j S j S , S j S i S S i ( S j )
σ ˜ i = S j S , S j S i S S i ( S j ) ( D j D ˜ i ) 2 S j S , S j S i S S i ( S j ) ,

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