Fuzzy analysis for detection of inconsistent data in experimental datasets employed at the development of the CIEDE2000 colour-difference formula

Relating instrumental measurements to visually perceived colour-differences, under specific illuminating and viewing conditions, is one of the challenges of advanced colorimetry. Experimental data are used to devise new colour-difference formulas as well as to assess the performance of other colour-difference formulas. In this paper, we analyse the consistency of experimental data employed at the development of the last CIE recommended colour-difference formula, CIEDE2000. Because of the subjective and imprecise nature of these data, we adopt a fuzzy approach, so that finally, for each experimental datum, we establish the fuzzy degree to which it can be considered consistent with the remaining data. The results of our analyses show that only a few data are associated with a rather low degree of consistency. These data in many cases correspond to colour pairs with a very small colour-difference for which visual assessments seem to be overestimated.

[1]  Manuel Melgosa.  Request for existing experimental datasets on color differences , 2007 .

[2]  Valentín Gregory,et al.  Some properites of fuzzy metric spaces , 2000 .

[3]  Rafael Huertas,et al.  Performance of recent advanced color-difference formulas using the standardized residual sum of squares index. , 2008, Journal of the Optical Society of America. A, Optics, image science, and vision.

[4]  D. L. Macadam.  Visual Sensitivities to Color Differences in Daylight , 1942 .

[5]  Mitchell R. Balonon-Rosen,et al.  Visual determination of suprathreshold color‐difference tolerances using probit analysis , 1991 .

[6]  M. Luo,et al.  Chromaticity‐discrimination ellipses for surface colours , 1986 .

[7]  M. Vanrell,et al.  Parametric fuzzy sets for automatic color naming. , 2008, Journal of the Optical Society of America. A, Optics, image science, and vision.

[8]  M. Melgosa,et al.  Some classical color differences calculated with new formulas , 1992 .

[9]  M. Melgosa,et al.  Uniformity of some recent color metrics tested with an accurate color-difference tolerance dataset. , 1994, Applied optics.

[10]  Guihua Cui,et al.  Measurement of the relationship between perceived and computed color differences. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[11]  Samuel Morillas,et al.  New adaptive vector filter using fuzzy metrics , 2007, J. Electronic Imaging.

[12]  Guihua Cui,et al.  Uniform colour spaces based on the DIN99 colour‐difference formula , 2002 .

[13]  Samuel Morillas Gómez.  Fuzzy metrics and fuzzy logic for colour image filtering , 2011 .

[14]  K. Witt.  GEOMETRIC RELATIONS BETWEEN SCALES OF SMALL COLOUR DIFFERENCES , 1999 .

[15]  Rafael Huertas,et al.  Euclidean color-difference formula for small-medium color differences in log-compressed OSA-UCS space. , 2009, Journal of the Optical Society of America. A, Optics, image science, and vision.

[16]  Lotfi A. Zadeh,et al.  Fuzzy sets and systems , 1990 .

[17]  Valentín Gregori,et al.  Characterizing completable fuzzy metric spaces , 2004, Fuzzy Sets Syst..

[18]  Roy S. Berns,et al.  Suprathreshold color‐difference ellipsoids for surface colors , 1997 .

[19]  A. George,et al.  On some results in fuzzy metric spaces , 1994 .

[20]  M. Luo,et al.  Uniform colour spaces based on CIECAM02 colour appearance model , 2006 .

[21]  M. Luo,et al.  The development of the CIE 2000 Colour Difference Formula , 2001 .