Abstract

Color-difference formulas modified by power functions provide results in better agreement with visually perceived color differences. Each of the modified color-difference formulas proposed here adds only one relevant parameter to the corresponding original color-difference formula. Results from 16 visual data sets and 11 color-difference formulas indicate that the modified formulas achieve an average decrease of 5.7 STRESS (Standardized Residual Sum of Squares) units with respect to the original formulas, signifying an improvement of 17.3%. In particular, for these 16 visual data sets, the average decrease for the current CIE/ISO recommended color-difference formula CIEDE2000 modified by an exponent 0.70 was 5.4 STRESS units (17.5%). The improvements of all modified color-difference formulas with respect to the original ones held for each of the 16 visual data sets and were statistically significant in most cases, particularly for all data sets with color differences close to the threshold. Results for 2 additional data sets with color pairs in the blue and black regions of the color space confirmed the usefulness of the proposed power functions. The main reason of the improvements found for the modified color-difference formulas with respect to the original color-difference formulas seems to be the compression provided by power functions.

© 2015 Optical Society of America

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References

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2015 (1)

D.-H. Kim, “The ULAB colour space,” Color Res. Appl. 40(1), 17-29 (2015).

2014 (4)

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(6), 589-598 (2014).

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(3), 3458–3467 (2014).
[Crossref] [PubMed]

F. Mirjalili, S. Moradian, and F. Ameri, “A new approach to investigate relationships between certain instrumentally measured appearance parameters and their visually perceived equivalents in the automotive industry,” J. Coat. Technol. Res. 11(3), 341–350 (2014).
[Crossref]

G. Khashayar, P. A. Bain, S. Salari, A. Dozic, C. J. Kleverlaan, and A. J. Feilzer, “Perceptibility and acceptability thresholds for colour differences in dentistry,” J. Dent. 42(6), 637–644 (2014).
[Crossref] [PubMed]

2013 (1)

L. Gómez-Robledo, N. López-Ruiz, M. Melgosa, A. J. Palma, and M. Sánchez-Marañón, “Using the mobile phone as Munsell soil-colour sensor: An experiment under controlled illumination conditions,” Comput. Electron. Agric. 99, 200–208 (2013).
[Crossref]

2012 (5)

H. Wang, G. Cui, M. R. Luo, and H. Xu, “Evaluation of colour-difference formulae for different colour-difference magnitudes,” Color Res. Appl. 37(5), 316–325 (2012).
[Crossref]

M. Huang, H. Liu, G. Cui, and M. R. Luo, “Testing uniform colour spaces and color-difference formulae using printed samples,” Color Res. Appl. 37(5), 326–335 (2012).
[Crossref]

J. F. Salmerón, L. Gómez-Robledo, M. A. Carvajal, R. Huertas, M. J. Moyano, B. Gordillo, A. J. Palma, F. J. Heredia, and M. Melgosa, “Measuring the colour of virgin olive oils in a new colour scale using a low-cost portable electronic device,” J. Food Eng. 111(2), 247–254 (2012).
[Crossref]

M. Hauptmann, H. Pleschberger, C. Mai, J. Follrich, and C. Hansmann, “The potential of color measurements with the CIEDE2000 equation in wood science,” Eur. J. Wood Wood Prod. 70(4), 415–420 (2012).
[Crossref]

M. Huang, H. Liu, G. Cui, M. R. Luo, and M. Melgosa, “Evaluation of threshold color differences using printed samples,” J. Opt. Soc. Am. A 29(6), 883–891 (2012).
[Crossref] [PubMed]

2011 (3)

2010 (3)

M. Huang, L. Wang, and H. Liu, “Study on small color difference evaluation using printed samples with different gloss,” Acta Opt. Sin. 30(6), 1851–1856 (2010) .
[Crossref]

M. Inoue, Y. Miyake, T. Odaka, T. Sato, Y. Watanabe, A. Sakama, S. Zenbutsu, and O. Yokosuka, “Objective evaluation of visibility in virtual chromoendoscopy for esophageal squamous carcinoma using a color difference formula,” J. Biomed. Opt. 15(5), 056019 (2010).
[Crossref] [PubMed]

W. G. Kuo, “The performance of the well-known color-difference formulae on predicting the visual color difference of the pairs of specimens in woolen serge under various light sources,” Text. Res. J. 80(2), 145–158 (2010).
[Crossref]

2009 (3)

J. G. Kim, B. Yu, and Y. K. Lee, “Correlations between color differences based on three color-difference formulas using dental shade guide tabs,” J. Prosthodont. 18(2), 135–140 (2009).
[Crossref] [PubMed]

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(1), 121–134 (2009).
[Crossref] [PubMed]

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(13), 1447–1456 (2009).
[Crossref]

2008 (1)

2007 (1)

2006 (1)

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31(4), 320–330 (2006).
[Crossref]

2003 (1)

R. G. Kuehni, “Colour difference formulas: accurate enough for objective colour quality control of textiles?” Color Technol. 119(3), 164–169 (2003).
[Crossref]

2002 (2)

R. G. Kuehni, “CIEDE2000, milestone or final answer?” Color Res. Appl. 27(2), 126–127 (2002).
[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(4), 282–290 (2002).
[Crossref]

2000 (1)

G. G. Attridge and M. R. Pointer, “Some aspects of the visual scaling of large colour differences-II,” Color Res. Appl. 25(2), 116–122 (2000).
[Crossref]

1999 (3)

S. Guan and M. R. Luo, “Investigation of parametric effects using small colour-differences,” Color Res. Appl. 24(5), 331–343 (1999).
[Crossref]

K. Witt, “Geometric relations between scales of small colour differences,” Color Res. Appl. 24(2), 78–92 (1999).
[Crossref]

S.-S. Guan and M. R. Luo, “A colour-difference formula for assessing large colour differences,” Color Res. Appl. 24(5), 344–355 (1999).
[Crossref]

1997 (1)

M. R. Pointer and G. G. Attridge, “Some aspects of the visual scaling of large color differences,” Color Res. Appl. 22(5), 298–307 (1997).
[Crossref]

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(5), 297–316 (1991).
[Crossref]

1986 (1)

M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colors,” Color Res. Appl. 11(1), 25–42 (1986).
[Crossref]

1984 (1)

F. J. J. Clarke, R. McDonald, and B. Rigg, “Modification to the JPC79 colour-difference formula,” J. Soc. Dyers Colour. 100(4), 128–132 (1984).
[Crossref]

1974 (2)

1957 (1)

S. S. Stevens, “On the psychophysical law,” Psychol. Rev. 64(3), 153–181 (1957).
[Crossref] [PubMed]

1943 (1)

1940 (1)

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(5), 297–316 (1991).
[Crossref]

Ameri, F.

F. Mirjalili, S. Moradian, and F. Ameri, “A new approach to investigate relationships between certain instrumentally measured appearance parameters and their visually perceived equivalents in the automotive industry,” J. Coat. Technol. Res. 11(3), 341–350 (2014).
[Crossref]

Attridge, G. G.

G. G. Attridge and M. R. Pointer, “Some aspects of the visual scaling of large colour differences-II,” Color Res. Appl. 25(2), 116–122 (2000).
[Crossref]

M. R. Pointer and G. G. Attridge, “Some aspects of the visual scaling of large color differences,” Color Res. Appl. 22(5), 298–307 (1997).
[Crossref]

Bain, P. A.

G. Khashayar, P. A. Bain, S. Salari, A. Dozic, C. J. Kleverlaan, and A. J. Feilzer, “Perceptibility and acceptability thresholds for colour differences in dentistry,” J. Dent. 42(6), 637–644 (2014).
[Crossref] [PubMed]

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(5), 297–316 (1991).
[Crossref]

Berns, R. S.

M. Melgosa, R. Huertas, and R. S. Berns, “Performance of recent advanced color-difference formulae using the Standardized Residual Sum of Squares index,” J. Opt. Soc. Am. A 25(7), 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(5), 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(6), 589-598 (2014).

Carvajal, M. A.

J. F. Salmerón, L. Gómez-Robledo, M. A. Carvajal, R. Huertas, M. J. Moyano, B. Gordillo, A. J. Palma, F. J. Heredia, and M. Melgosa, “Measuring the colour of virgin olive oils in a new colour scale using a low-cost portable electronic device,” J. Food Eng. 111(2), 247–254 (2012).
[Crossref]

Clarke, F. J. J.

F. J. J. Clarke, R. McDonald, and B. Rigg, “Modification to the JPC79 colour-difference formula,” J. Soc. Dyers Colour. 100(4), 128–132 (1984).
[Crossref]

Cui, G.

M. Huang, H. Liu, G. Cui, M. R. Luo, and M. Melgosa, “Evaluation of threshold color differences using printed samples,” J. Opt. Soc. Am. A 29(6), 883–891 (2012).
[Crossref] [PubMed]

M. Huang, H. Liu, G. Cui, and M. R. Luo, “Testing uniform colour spaces and color-difference formulae using printed samples,” Color Res. Appl. 37(5), 326–335 (2012).
[Crossref]

H. Wang, G. Cui, M. R. Luo, and H. Xu, “Evaluation of colour-difference formulae for different colour-difference magnitudes,” Color Res. Appl. 37(5), 316–325 (2012).
[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 in color-difference experiments,” J. Opt. Soc. Am. A 28(5), 949–953 (2011).
[Crossref] [PubMed]

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(7), 1823–1829 (2007).
[Crossref] [PubMed]

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31(4), 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(4), 282–290 (2002).
[Crossref]

Dauser, T.

Dekker, N.

Dozic, A.

G. Khashayar, P. A. Bain, S. Salari, A. Dozic, C. J. Kleverlaan, and A. J. Feilzer, “Perceptibility and acceptability thresholds for colour differences in dentistry,” J. Dent. 42(6), 637–644 (2014).
[Crossref] [PubMed]

Feilzer, A. J.

G. Khashayar, P. A. Bain, S. Salari, A. Dozic, C. J. Kleverlaan, and A. J. Feilzer, “Perceptibility and acceptability thresholds for colour differences in dentistry,” J. Dent. 42(6), 637–644 (2014).
[Crossref] [PubMed]

Follrich, J.

M. Hauptmann, H. Pleschberger, C. Mai, J. Follrich, and C. Hansmann, “The potential of color measurements with the CIEDE2000 equation in wood science,” Eur. J. Wood Wood Prod. 70(4), 415–420 (2012).
[Crossref]

García, P. A.

Gómez-Robledo, L.

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(3), 3458–3467 (2014).
[Crossref] [PubMed]

L. Gómez-Robledo, N. López-Ruiz, M. Melgosa, A. J. Palma, and M. Sánchez-Marañón, “Using the mobile phone as Munsell soil-colour sensor: An experiment under controlled illumination conditions,” Comput. Electron. Agric. 99, 200–208 (2013).
[Crossref]

J. F. Salmerón, L. Gómez-Robledo, M. A. Carvajal, R. Huertas, M. J. Moyano, B. Gordillo, A. J. Palma, F. J. Heredia, and M. Melgosa, “Measuring the colour of virgin olive oils in a new colour scale using a low-cost portable electronic device,” J. Food Eng. 111(2), 247–254 (2012).
[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 in color-difference experiments,” J. Opt. Soc. Am. A 28(5), 949–953 (2011).
[Crossref] [PubMed]

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(13), 1447–1456 (2009).
[Crossref]

Gordillo, B.

J. F. Salmerón, L. Gómez-Robledo, M. A. Carvajal, R. Huertas, M. J. Moyano, B. Gordillo, A. J. Palma, F. J. Heredia, and M. Melgosa, “Measuring the colour of virgin olive oils in a new colour scale using a low-cost portable electronic device,” J. Food Eng. 111(2), 247–254 (2012).
[Crossref]

Guan, S.

S. Guan and M. R. Luo, “Investigation of parametric effects using small colour-differences,” Color Res. Appl. 24(5), 331–343 (1999).
[Crossref]

Guan, S.-S.

S.-S. Guan and M. R. Luo, “A colour-difference formula for assessing large colour differences,” Color Res. Appl. 24(5), 344–355 (1999).
[Crossref]

Hansmann, C.

M. Hauptmann, H. Pleschberger, C. Mai, J. Follrich, and C. Hansmann, “The potential of color measurements with the CIEDE2000 equation in wood science,” Eur. J. Wood Wood Prod. 70(4), 415–420 (2012).
[Crossref]

Hauptmann, M.

M. Hauptmann, H. Pleschberger, C. Mai, J. Follrich, and C. Hansmann, “The potential of color measurements with the CIEDE2000 equation in wood science,” Eur. J. Wood Wood Prod. 70(4), 415–420 (2012).
[Crossref]

Heredia, F. J.

J. F. Salmerón, L. Gómez-Robledo, M. A. Carvajal, R. Huertas, M. J. Moyano, B. Gordillo, A. J. Palma, F. J. Heredia, and M. Melgosa, “Measuring the colour of virgin olive oils in a new colour scale using a low-cost portable electronic device,” J. Food Eng. 111(2), 247–254 (2012).
[Crossref]

Hinks, D.

S. G. Lee, R. Shamey, D. Hinks, and W. Jasper, “Development of a comprehensive visual dataset based on a CIE blue color center: Assessment of color difference formulae using various statistical methods,” Color Res. Appl. 36(1), 27–41 (2011).
[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 in color-difference experiments,” J. Opt. Soc. Am. A 28(5), 949–953 (2011).
[Crossref] [PubMed]

Huang, M.

M. Huang, H. Liu, G. Cui, M. R. Luo, and M. Melgosa, “Evaluation of threshold color differences using printed samples,” J. Opt. Soc. Am. A 29(6), 883–891 (2012).
[Crossref] [PubMed]

M. Huang, H. Liu, G. Cui, and M. R. Luo, “Testing uniform colour spaces and color-difference formulae using printed samples,” Color Res. Appl. 37(5), 326–335 (2012).
[Crossref]

M. Huang, L. Wang, and H. Liu, “Study on small color difference evaluation using printed samples with different gloss,” Acta Opt. Sin. 30(6), 1851–1856 (2010) .
[Crossref]

Huertas, R.

J. F. Salmerón, L. Gómez-Robledo, M. A. Carvajal, R. Huertas, M. J. Moyano, B. Gordillo, A. J. Palma, F. J. Heredia, and M. Melgosa, “Measuring the colour of virgin olive oils in a new colour scale using a low-cost portable electronic device,” J. Food Eng. 111(2), 247–254 (2012).
[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(1), 121–134 (2009).
[Crossref] [PubMed]

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(13), 1447–1456 (2009).
[Crossref]

M. Melgosa, R. Huertas, and R. S. Berns, “Performance of recent advanced color-difference formulae using the Standardized Residual Sum of Squares index,” J. Opt. Soc. Am. A 25(7), 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(7), 1823–1829 (2007).
[Crossref] [PubMed]

Inoue, M.

M. Inoue, Y. Miyake, T. Odaka, T. Sato, Y. Watanabe, A. Sakama, S. Zenbutsu, and O. Yokosuka, “Objective evaluation of visibility in virtual chromoendoscopy for esophageal squamous carcinoma using a color difference formula,” J. Biomed. Opt. 15(5), 056019 (2010).
[Crossref] [PubMed]

Jasper, W.

S. G. Lee, R. Shamey, D. Hinks, and W. Jasper, “Development of a comprehensive visual dataset based on a CIE blue color center: Assessment of color difference formulae using various statistical methods,” Color Res. Appl. 36(1), 27–41 (2011).
[Crossref]

Judd, D. B.

Khashayar, G.

G. Khashayar, P. A. Bain, S. Salari, A. Dozic, C. J. Kleverlaan, and A. J. Feilzer, “Perceptibility and acceptability thresholds for colour differences in dentistry,” J. Dent. 42(6), 637–644 (2014).
[Crossref] [PubMed]

Kim, D.-H.

D.-H. Kim, “The ULAB colour space,” Color Res. Appl. 40(1), 17-29 (2015).

Kim, J. G.

J. G. Kim, B. Yu, and Y. K. Lee, “Correlations between color differences based on three color-difference formulas using dental shade guide tabs,” J. Prosthodont. 18(2), 135–140 (2009).
[Crossref] [PubMed]

Kirchner, E.

Kleverlaan, C. J.

G. Khashayar, P. A. Bain, S. Salari, A. Dozic, C. J. Kleverlaan, and A. J. Feilzer, “Perceptibility and acceptability thresholds for colour differences in dentistry,” J. Dent. 42(6), 637–644 (2014).
[Crossref] [PubMed]

Kuehni, R. G.

R. G. Kuehni, “Colour difference formulas: accurate enough for objective colour quality control of textiles?” Color Technol. 119(3), 164–169 (2003).
[Crossref]

R. G. Kuehni, “CIEDE2000, milestone or final answer?” Color Res. Appl. 27(2), 126–127 (2002).
[Crossref]

Kuo, W. G.

W. G. Kuo, “The performance of the well-known color-difference formulae on predicting the visual color difference of the pairs of specimens in woolen serge under various light sources,” Text. Res. J. 80(2), 145–158 (2010).
[Crossref]

Lee, S. G.

S. G. Lee, R. Shamey, D. Hinks, and W. Jasper, “Development of a comprehensive visual dataset based on a CIE blue color center: Assessment of color difference formulae using various statistical methods,” Color Res. Appl. 36(1), 27–41 (2011).
[Crossref]

Lee, Y. K.

J. G. Kim, B. Yu, and Y. K. Lee, “Correlations between color differences based on three color-difference formulas using dental shade guide tabs,” J. Prosthodont. 18(2), 135–140 (2009).
[Crossref] [PubMed]

Li, C.

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31(4), 320–330 (2006).
[Crossref]

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(6), 589-598 (2014).

Liu, H.

M. Huang, H. Liu, G. Cui, M. R. Luo, and M. Melgosa, “Evaluation of threshold color differences using printed samples,” J. Opt. Soc. Am. A 29(6), 883–891 (2012).
[Crossref] [PubMed]

M. Huang, H. Liu, G. Cui, and M. R. Luo, “Testing uniform colour spaces and color-difference formulae using printed samples,” Color Res. Appl. 37(5), 326–335 (2012).
[Crossref]

M. Huang, L. Wang, and H. Liu, “Study on small color difference evaluation using printed samples with different gloss,” Acta Opt. Sin. 30(6), 1851–1856 (2010) .
[Crossref]

López-Ruiz, N.

L. Gómez-Robledo, N. López-Ruiz, M. Melgosa, A. J. Palma, and M. Sánchez-Marañón, “Using the mobile phone as Munsell soil-colour sensor: An experiment under controlled illumination conditions,” Comput. Electron. Agric. 99, 200–208 (2013).
[Crossref]

Luo, M. R.

H. Wang, G. Cui, M. R. Luo, and H. Xu, “Evaluation of colour-difference formulae for different colour-difference magnitudes,” Color Res. Appl. 37(5), 316–325 (2012).
[Crossref]

M. Huang, H. Liu, G. Cui, and M. R. Luo, “Testing uniform colour spaces and color-difference formulae using printed samples,” Color Res. Appl. 37(5), 326–335 (2012).
[Crossref]

M. Huang, H. Liu, G. Cui, M. R. Luo, and M. Melgosa, “Evaluation of threshold color differences using printed samples,” J. Opt. Soc. Am. A 29(6), 883–891 (2012).
[Crossref] [PubMed]

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 in color-difference experiments,” J. Opt. Soc. Am. A 28(5), 949–953 (2011).
[Crossref] [PubMed]

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31(4), 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(4), 282–290 (2002).
[Crossref]

S. Guan and M. R. Luo, “Investigation of parametric effects using small colour-differences,” Color Res. Appl. 24(5), 331–343 (1999).
[Crossref]

S.-S. Guan and M. R. Luo, “A colour-difference formula for assessing large colour differences,” Color Res. Appl. 24(5), 344–355 (1999).
[Crossref]

M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colors,” Color Res. Appl. 11(1), 25–42 (1986).
[Crossref]

MacAdam, D. L.

Mai, C.

M. Hauptmann, H. Pleschberger, C. Mai, J. Follrich, and C. Hansmann, “The potential of color measurements with the CIEDE2000 equation in wood science,” Eur. J. Wood Wood Prod. 70(4), 415–420 (2012).
[Crossref]

Martínez-García, J.

Martínez-Verdú, F. M.

McDonald, R.

F. J. J. Clarke, R. McDonald, and B. Rigg, “Modification to the JPC79 colour-difference formula,” J. Soc. Dyers Colour. 100(4), 128–132 (1984).
[Crossref]

Melgosa, M.

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(3), 3458–3467 (2014).
[Crossref] [PubMed]

L. Gómez-Robledo, N. López-Ruiz, M. Melgosa, A. J. Palma, and M. Sánchez-Marañón, “Using the mobile phone as Munsell soil-colour sensor: An experiment under controlled illumination conditions,” Comput. Electron. Agric. 99, 200–208 (2013).
[Crossref]

J. F. Salmerón, L. Gómez-Robledo, M. A. Carvajal, R. Huertas, M. J. Moyano, B. Gordillo, A. J. Palma, F. J. Heredia, and M. Melgosa, “Measuring the colour of virgin olive oils in a new colour scale using a low-cost portable electronic device,” J. Food Eng. 111(2), 247–254 (2012).
[Crossref]

M. Huang, H. Liu, G. Cui, M. R. Luo, and M. Melgosa, “Evaluation of threshold color differences using printed samples,” J. Opt. Soc. Am. A 29(6), 883–891 (2012).
[Crossref] [PubMed]

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 in color-difference experiments,” J. Opt. Soc. Am. A 28(5), 949–953 (2011).
[Crossref] [PubMed]

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(13), 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(1), 121–134 (2009).
[Crossref] [PubMed]

M. Melgosa, R. Huertas, and R. S. Berns, “Performance of recent advanced color-difference formulae using the Standardized Residual Sum of Squares index,” J. Opt. Soc. Am. A 25(7), 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(7), 1823–1829 (2007).
[Crossref] [PubMed]

Mirjalili, F.

F. Mirjalili, S. Moradian, and F. Ameri, “A new approach to investigate relationships between certain instrumentally measured appearance parameters and their visually perceived equivalents in the automotive industry,” J. Coat. Technol. Res. 11(3), 341–350 (2014).
[Crossref]

Miyake, Y.

M. Inoue, Y. Miyake, T. Odaka, T. Sato, Y. Watanabe, A. Sakama, S. Zenbutsu, and O. Yokosuka, “Objective evaluation of visibility in virtual chromoendoscopy for esophageal squamous carcinoma using a color difference formula,” J. Biomed. Opt. 15(5), 056019 (2010).
[Crossref] [PubMed]

Moradian, S.

F. Mirjalili, S. Moradian, and F. Ameri, “A new approach to investigate relationships between certain instrumentally measured appearance parameters and their visually perceived equivalents in the automotive industry,” J. Coat. Technol. Res. 11(3), 341–350 (2014).
[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(13), 1447–1456 (2009).
[Crossref]

Moyano, M. J.

J. F. Salmerón, L. Gómez-Robledo, M. A. Carvajal, R. Huertas, M. J. Moyano, B. Gordillo, A. J. Palma, F. J. Heredia, and M. Melgosa, “Measuring the colour of virgin olive oils in a new colour scale using a low-cost portable electronic device,” J. Food Eng. 111(2), 247–254 (2012).
[Crossref]

Newhall, S. M.

Nickerson, D.

Odaka, T.

M. Inoue, Y. Miyake, T. Odaka, T. Sato, Y. Watanabe, A. Sakama, S. Zenbutsu, and O. Yokosuka, “Objective evaluation of visibility in virtual chromoendoscopy for esophageal squamous carcinoma using a color difference formula,” J. Biomed. Opt. 15(5), 056019 (2010).
[Crossref] [PubMed]

Oleari, C.

Palma, A. J.

L. Gómez-Robledo, N. López-Ruiz, M. Melgosa, A. J. Palma, and M. Sánchez-Marañón, “Using the mobile phone as Munsell soil-colour sensor: An experiment under controlled illumination conditions,” Comput. Electron. Agric. 99, 200–208 (2013).
[Crossref]

J. F. Salmerón, L. Gómez-Robledo, M. A. Carvajal, R. Huertas, M. J. Moyano, B. Gordillo, A. J. Palma, F. J. Heredia, and M. Melgosa, “Measuring the colour of virgin olive oils in a new colour scale using a low-cost portable electronic device,” J. Food Eng. 111(2), 247–254 (2012).
[Crossref]

Perales, E.

Pleschberger, H.

M. Hauptmann, H. Pleschberger, C. Mai, J. Follrich, and C. Hansmann, “The potential of color measurements with the CIEDE2000 equation in wood science,” Eur. J. Wood Wood Prod. 70(4), 415–420 (2012).
[Crossref]

Pointer, M. R.

G. G. Attridge and M. R. Pointer, “Some aspects of the visual scaling of large colour differences-II,” Color Res. Appl. 25(2), 116–122 (2000).
[Crossref]

M. R. Pointer and G. G. Attridge, “Some aspects of the visual scaling of large color differences,” Color Res. Appl. 22(5), 298–307 (1997).
[Crossref]

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(5), 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(4), 282–290 (2002).
[Crossref]

M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colors,” Color Res. Appl. 11(1), 25–42 (1986).
[Crossref]

F. J. J. Clarke, R. McDonald, and B. Rigg, “Modification to the JPC79 colour-difference formula,” J. Soc. Dyers Colour. 100(4), 128–132 (1984).
[Crossref]

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(4), 282–290 (2002).
[Crossref]

Sakama, A.

M. Inoue, Y. Miyake, T. Odaka, T. Sato, Y. Watanabe, A. Sakama, S. Zenbutsu, and O. Yokosuka, “Objective evaluation of visibility in virtual chromoendoscopy for esophageal squamous carcinoma using a color difference formula,” J. Biomed. Opt. 15(5), 056019 (2010).
[Crossref] [PubMed]

Salari, S.

G. Khashayar, P. A. Bain, S. Salari, A. Dozic, C. J. Kleverlaan, and A. J. Feilzer, “Perceptibility and acceptability thresholds for colour differences in dentistry,” J. Dent. 42(6), 637–644 (2014).
[Crossref] [PubMed]

Salmerón, J. F.

J. F. Salmerón, L. Gómez-Robledo, M. A. Carvajal, R. Huertas, M. J. Moyano, B. Gordillo, A. J. Palma, F. J. Heredia, and M. Melgosa, “Measuring the colour of virgin olive oils in a new colour scale using a low-cost portable electronic device,” J. Food Eng. 111(2), 247–254 (2012).
[Crossref]

Sánchez-Marañón, M.

L. Gómez-Robledo, N. López-Ruiz, M. Melgosa, A. J. Palma, and M. Sánchez-Marañón, “Using the mobile phone as Munsell soil-colour sensor: An experiment under controlled illumination conditions,” Comput. Electron. Agric. 99, 200–208 (2013).
[Crossref]

Sato, T.

M. Inoue, Y. Miyake, T. Odaka, T. Sato, Y. Watanabe, A. Sakama, S. Zenbutsu, and O. Yokosuka, “Objective evaluation of visibility in virtual chromoendoscopy for esophageal squamous carcinoma using a color difference formula,” J. Biomed. Opt. 15(5), 056019 (2010).
[Crossref] [PubMed]

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(6), 589-598 (2014).

Shamey, 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(6), 589-598 (2014).

S. G. Lee, R. Shamey, D. Hinks, and W. Jasper, “Development of a comprehensive visual dataset based on a CIE blue color center: Assessment of color difference formulae using various statistical methods,” Color Res. Appl. 36(1), 27–41 (2011).
[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 in color-difference experiments,” J. Opt. Soc. Am. A 28(5), 949–953 (2011).
[Crossref] [PubMed]

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(5), 297–316 (1991).
[Crossref]

Stevens, S. S.

S. S. Stevens, “On the psychophysical law,” Psychol. Rev. 64(3), 153–181 (1957).
[Crossref] [PubMed]

Wang, H.

H. Wang, G. Cui, M. R. Luo, and H. Xu, “Evaluation of colour-difference formulae for different colour-difference magnitudes,” Color Res. Appl. 37(5), 316–325 (2012).
[Crossref]

Wang, L.

M. Huang, L. Wang, and H. Liu, “Study on small color difference evaluation using printed samples with different gloss,” Acta Opt. Sin. 30(6), 1851–1856 (2010) .
[Crossref]

Watanabe, Y.

M. Inoue, Y. Miyake, T. Odaka, T. Sato, Y. Watanabe, A. Sakama, S. Zenbutsu, and O. Yokosuka, “Objective evaluation of visibility in virtual chromoendoscopy for esophageal squamous carcinoma using a color difference formula,” J. Biomed. Opt. 15(5), 056019 (2010).
[Crossref] [PubMed]

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(4), 282–290 (2002).
[Crossref]

K. Witt, “Geometric relations between scales of small colour differences,” Color Res. Appl. 24(2), 78–92 (1999).
[Crossref]

Xu, H.

H. Wang, G. Cui, M. R. Luo, and H. Xu, “Evaluation of colour-difference formulae for different colour-difference magnitudes,” Color Res. Appl. 37(5), 316–325 (2012).
[Crossref]

Yokosuka, O.

M. Inoue, Y. Miyake, T. Odaka, T. Sato, Y. Watanabe, A. Sakama, S. Zenbutsu, and O. Yokosuka, “Objective evaluation of visibility in virtual chromoendoscopy for esophageal squamous carcinoma using a color difference formula,” J. Biomed. Opt. 15(5), 056019 (2010).
[Crossref] [PubMed]

Yu, B.

J. G. Kim, B. Yu, and Y. K. Lee, “Correlations between color differences based on three color-difference formulas using dental shade guide tabs,” J. Prosthodont. 18(2), 135–140 (2009).
[Crossref] [PubMed]

Zenbutsu, S.

M. Inoue, Y. Miyake, T. Odaka, T. Sato, Y. Watanabe, A. Sakama, S. Zenbutsu, and O. Yokosuka, “Objective evaluation of visibility in virtual chromoendoscopy for esophageal squamous carcinoma using a color difference formula,” J. Biomed. Opt. 15(5), 056019 (2010).
[Crossref] [PubMed]

Acta Opt. Sin. (1)

M. Huang, L. Wang, and H. Liu, “Study on small color difference evaluation using printed samples with different gloss,” Acta Opt. Sin. 30(6), 1851–1856 (2010) .
[Crossref]

Color Res. Appl. (15)

H. Wang, G. Cui, M. R. Luo, and H. Xu, “Evaluation of colour-difference formulae for different colour-difference magnitudes,” Color Res. Appl. 37(5), 316–325 (2012).
[Crossref]

M. Huang, H. Liu, G. Cui, and M. R. Luo, “Testing uniform colour spaces and color-difference formulae using printed samples,” Color Res. Appl. 37(5), 326–335 (2012).
[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(5), 297–316 (1991).
[Crossref]

R. G. Kuehni, “CIEDE2000, milestone or final answer?” Color Res. Appl. 27(2), 126–127 (2002).
[Crossref]

M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colors,” Color Res. Appl. 11(1), 25–42 (1986).
[Crossref]

K. Witt, “Geometric relations between scales of small colour differences,” Color Res. Appl. 24(2), 78–92 (1999).
[Crossref]

M. R. Pointer and G. G. Attridge, “Some aspects of the visual scaling of large color differences,” Color Res. Appl. 22(5), 298–307 (1997).
[Crossref]

S.-S. Guan and M. R. Luo, “A colour-difference formula for assessing large colour differences,” Color Res. Appl. 24(5), 344–355 (1999).
[Crossref]

G. G. Attridge and M. R. Pointer, “Some aspects of the visual scaling of large colour differences-II,” Color Res. Appl. 25(2), 116–122 (2000).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1 Percentage of color pairs in each one of the 16 visual data sets considering different ranges of ΔE*ab,10.
Fig. 2
Fig. 2 Percentage change produced by four modified color-difference formulas (Table 3) with respect to the ΔE values (x axis) provided by the corresponding original color-difference formulas.
Fig. 3
Fig. 3 Plot of visual (ΔV) against computed (ΔE) CIELAB color differences for the BIGC-T1-G data set [27], considering the original (shafts of the arrows) and modified (arrowheads) color-difference formulas. The straight line in the plot is the linear regression line through the origin of ΔV vs. ΔE.

Tables (6)

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Table 1 Some characteristics of the 16 visual color-difference data sets

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Table 2 STRESS values for the 16 visual data sets using the original 11 color-difference formulasa

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Table 3 Values of power-function coefficients putting all visual data sets on a common scale and minimizing STRESS values in 11 different color-difference formulas, from all 16 visual data sets together

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Table 4 STRESS values for the 16 visual data sets using the modified (see Table 3) color-difference formulasa

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Table 5 Square of ratios of STRESS values for the modified and original color-difference formulasa

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Table 6 STRESS and PF/3 values for different original and modified color-difference formulas in two data sets with color pairs in specific regions of the color space: blue [42] and black [43]*

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