Abstract

An investigation of the color metrics and the complexity of the CIEDE2000 formula shows that CIELAB space is inadequate to represent small–medium color differences. The OSA-UCS (Uniform Color Space) Committee has shown that no space with uniform scale for large color differences exists. Therefore the practical way for color-difference specification is a color-difference formula in a nonuniform space. First, the BFD (Bradford University) ellipses are considered in the OSA-UCS space, and their very high regularity suggests a new and very simple color-difference formula at constant luminance. Then the COM (combined) data set used for the development of the CIEDE2000 formula is considered in the OSA-UCS space, and the color-difference formula is extended to sample pairs with a different luminance factor. The value of the performance factor PF3 for the proposed OSA-UCS-based formula shows that the formula performs like the more complex CIEDE2000 formula for small–medium color differences.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Huertas, M. Melgosa, and C. Oleari, "A new colour-difference formula defined in the OSA-UCS space," in Proceedings of the Tenth Congress of the International Colour Association (AIC Colour, 2005), pp. 1071-1074.
  2. Improvement to Industrial Color-Difference Evaluation, CIE Publication 142 (CIE Central Bureau, 2001).
  3. D. L. MacAdam, Color Measurement (Springer-Verlag, 1985), pp. 165-177.
  4. D. L. MacAdam, "Uniform color scales," J. Opt. Soc. Am. 64, 1691-1702 (1974).
    [CrossRef] [PubMed]
  5. D. L. MacAdam, "Colorimetric data for samples of OSA uniform color scales," J. Opt. Soc. Am. 68, 121-130 (1978).
    [CrossRef]
  6. R. G. Kuehni, "Towards an improved uniform color space," Color Res. Appl. 24, 253-265 (1999).
    [CrossRef]
  7. C. Oleari, "Comparison between color-space scales, uniform color-scales atlases and color-difference formulae," Color Res. Appl. 26, 351-361 (2001).
    [CrossRef]
  8. M. R. Luo and B. Rigg, "Chromaticity-discrimination ellipses for surface colors," Color Res. Appl. 11, 25-42 (1986).
    [CrossRef]
  9. M. R. Luo, G. Cui, and B. Rigg, "The development of CIE 2000 colour-difference formula: CIEDE2000," Color Res. Appl. 26, 340-350 (2001).
    [CrossRef]
  10. D. H. Kim and J. H. Nobbs, "New weightings functions for the weighted CIELAB color difference formula," in Proceedings of the 8th Congress of the International Colour Association (AIC Colour 97) (Association Internationale de la Couleur, 1997), Vol. 1, pp. 446-449.
  11. R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, "Visual determination of suprathreshold color tolerances using probit analysis," Color Res. Appl. 16, 297-316 (1991).
    [CrossRef]
  12. K. Witt, "Geometric relations between scales of small colour differences," Color Res. Appl. 24, 78-92 (1999).
    [CrossRef]
  13. S. S. Guan and M. R. Luo, "Investigation of parametric effects using small colour-differences," Color Res. Appl. 24, 331-343 (1999).
    [CrossRef]
  14. A. Yebra, R. Huertas, M. M. Pérez, and M. Melgosa, "On the relationship between tilt of a*b* tolerance ellipses in blue region and tritanopic confusion lines," Color Res. Appl. 27, 180-184 (2002).
    [CrossRef]
  15. J. A. Nelder and R. Mead, "A simplex method for function minimization," Comput. J. 7, 308-313 (1965).
  16. G. Cui, M. R. Luo, and B. Rigg, "Crispening effect on lightness differences," in 9th Congress of the International Colour Association, R.Chung and A.Rodrigues, eds. Proc. SPIE 4421, 634-637 (2002).
  17. T. Seim and A. Valberg, "Towards a uniform color space: a better formula to describe the Munsell and OSA color scales," Color Res. Appl. 11, 11-24 (1986).
    [CrossRef]
  18. C. Oleari, "Color opponencies in the system of the uniform color scales of the Optical Society of America," J. Opt. Soc. Am. A 21, 677-682 (2004).
    [CrossRef]
  19. M. Kobayasi and K. Yosiki, "Effective conversion algorithm from OSA-UCS to CIEXYZ," in 9th Congress of the International Color Association, R.Chung and A.Rodrigues, eds., Proc. SPIE 4421, 848-851 (2002).
  20. E. Coates, K. Y. Fong, and B. Rigg, "Uniform lightness scales," J. Soc. Dyers Colour. 97, 179-183 (1981).
    [CrossRef]
  21. W. Schultze, "The usefulness of colour-difference formulas for fixing colour tolerances," in Colour Metrics, Proceedings of the Helmholtz Memorial Symposium, J.J.Vos. L.F. C.Friele, and P.L. Walraven, eds. (Association Internationale de la Couleur (AIC), 1971), pp. 254-265.

2005 (1)

R. Huertas, M. Melgosa, and C. Oleari, "A new colour-difference formula defined in the OSA-UCS space," in Proceedings of the Tenth Congress of the International Colour Association (AIC Colour, 2005), pp. 1071-1074.

2004 (1)

2002 (3)

M. Kobayasi and K. Yosiki, "Effective conversion algorithm from OSA-UCS to CIEXYZ," in 9th Congress of the International Color Association, R.Chung and A.Rodrigues, eds., Proc. SPIE 4421, 848-851 (2002).

A. Yebra, R. Huertas, M. M. Pérez, and M. Melgosa, "On the relationship between tilt of a*b* tolerance ellipses in blue region and tritanopic confusion lines," Color Res. Appl. 27, 180-184 (2002).
[CrossRef]

G. Cui, M. R. Luo, and B. Rigg, "Crispening effect on lightness differences," in 9th Congress of the International Colour Association, R.Chung and A.Rodrigues, eds. Proc. SPIE 4421, 634-637 (2002).

2001 (3)

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

Improvement to Industrial Color-Difference Evaluation, CIE Publication 142 (CIE Central Bureau, 2001).

C. Oleari, "Comparison between color-space scales, uniform color-scales atlases and color-difference formulae," Color Res. Appl. 26, 351-361 (2001).
[CrossRef]

1999 (3)

R. G. Kuehni, "Towards an improved uniform color space," Color Res. Appl. 24, 253-265 (1999).
[CrossRef]

K. Witt, "Geometric relations between scales of small colour differences," Color Res. Appl. 24, 78-92 (1999).
[CrossRef]

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

1997 (1)

D. H. Kim and J. H. Nobbs, "New weightings functions for the weighted CIELAB color difference formula," in Proceedings of the 8th Congress of the International Colour Association (AIC Colour 97) (Association Internationale de la Couleur, 1997), Vol. 1, pp. 446-449.

1991 (1)

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

1986 (2)

T. Seim and A. Valberg, "Towards a uniform color space: a better formula to describe the Munsell and OSA color scales," Color Res. Appl. 11, 11-24 (1986).
[CrossRef]

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

1985 (1)

D. L. MacAdam, Color Measurement (Springer-Verlag, 1985), pp. 165-177.

1981 (1)

E. Coates, K. Y. Fong, and B. Rigg, "Uniform lightness scales," J. Soc. Dyers Colour. 97, 179-183 (1981).
[CrossRef]

1978 (1)

1974 (1)

1971 (1)

W. Schultze, "The usefulness of colour-difference formulas for fixing colour tolerances," in Colour Metrics, Proceedings of the Helmholtz Memorial Symposium, J.J.Vos. L.F. C.Friele, and P.L. Walraven, eds. (Association Internationale de la Couleur (AIC), 1971), pp. 254-265.

1965 (1)

J. A. Nelder and R. Mead, "A simplex method for function minimization," Comput. J. 7, 308-313 (1965).

Alman, D. H.

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

Berns, R. S.

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

Coates, E.

E. Coates, K. Y. Fong, and B. Rigg, "Uniform lightness scales," J. Soc. Dyers Colour. 97, 179-183 (1981).
[CrossRef]

Cui, G.

G. Cui, M. R. Luo, and B. Rigg, "Crispening effect on lightness differences," in 9th Congress of the International Colour Association, R.Chung and A.Rodrigues, eds. Proc. SPIE 4421, 634-637 (2002).

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

Fong, K. Y.

E. Coates, K. Y. Fong, and B. Rigg, "Uniform lightness scales," J. Soc. Dyers Colour. 97, 179-183 (1981).
[CrossRef]

Guan, S. S.

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

Huertas, R.

R. Huertas, M. Melgosa, and C. Oleari, "A new colour-difference formula defined in the OSA-UCS space," in Proceedings of the Tenth Congress of the International Colour Association (AIC Colour, 2005), pp. 1071-1074.

A. Yebra, R. Huertas, M. M. Pérez, and M. Melgosa, "On the relationship between tilt of a*b* tolerance ellipses in blue region and tritanopic confusion lines," Color Res. Appl. 27, 180-184 (2002).
[CrossRef]

Kim, D. H.

D. H. Kim and J. H. Nobbs, "New weightings functions for the weighted CIELAB color difference formula," in Proceedings of the 8th Congress of the International Colour Association (AIC Colour 97) (Association Internationale de la Couleur, 1997), Vol. 1, pp. 446-449.

Kobayasi, M.

M. Kobayasi and K. Yosiki, "Effective conversion algorithm from OSA-UCS to CIEXYZ," in 9th Congress of the International Color Association, R.Chung and A.Rodrigues, eds., Proc. SPIE 4421, 848-851 (2002).

Kuehni, R. G.

R. G. Kuehni, "Towards an improved uniform color space," Color Res. Appl. 24, 253-265 (1999).
[CrossRef]

Luo, M. R.

G. Cui, M. R. Luo, and B. Rigg, "Crispening effect on lightness differences," in 9th Congress of the International Colour Association, R.Chung and A.Rodrigues, eds. Proc. SPIE 4421, 634-637 (2002).

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

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

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

MacAdam, D. L.

Mead, R.

J. A. Nelder and R. Mead, "A simplex method for function minimization," Comput. J. 7, 308-313 (1965).

Melgosa, M.

R. Huertas, M. Melgosa, and C. Oleari, "A new colour-difference formula defined in the OSA-UCS space," in Proceedings of the Tenth Congress of the International Colour Association (AIC Colour, 2005), pp. 1071-1074.

A. Yebra, R. Huertas, M. M. Pérez, and M. Melgosa, "On the relationship between tilt of a*b* tolerance ellipses in blue region and tritanopic confusion lines," Color Res. Appl. 27, 180-184 (2002).
[CrossRef]

Nelder, J. A.

J. A. Nelder and R. Mead, "A simplex method for function minimization," Comput. J. 7, 308-313 (1965).

Nobbs, J. H.

D. H. Kim and J. H. Nobbs, "New weightings functions for the weighted CIELAB color difference formula," in Proceedings of the 8th Congress of the International Colour Association (AIC Colour 97) (Association Internationale de la Couleur, 1997), Vol. 1, pp. 446-449.

Oleari, C.

R. Huertas, M. Melgosa, and C. Oleari, "A new colour-difference formula defined in the OSA-UCS space," in Proceedings of the Tenth Congress of the International Colour Association (AIC Colour, 2005), pp. 1071-1074.

C. Oleari, "Color opponencies in the system of the uniform color scales of the Optical Society of America," J. Opt. Soc. Am. A 21, 677-682 (2004).
[CrossRef]

C. Oleari, "Comparison between color-space scales, uniform color-scales atlases and color-difference formulae," Color Res. Appl. 26, 351-361 (2001).
[CrossRef]

Pérez, M. M.

A. Yebra, R. Huertas, M. M. Pérez, and M. Melgosa, "On the relationship between tilt of a*b* tolerance ellipses in blue region and tritanopic confusion lines," Color Res. Appl. 27, 180-184 (2002).
[CrossRef]

Reniff, L.

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

Rigg, B.

G. Cui, M. R. Luo, and B. Rigg, "Crispening effect on lightness differences," in 9th Congress of the International Colour Association, R.Chung and A.Rodrigues, eds. Proc. SPIE 4421, 634-637 (2002).

M. R. Luo, G. Cui, and B. Rigg, "The development of 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]

E. Coates, K. Y. Fong, and B. Rigg, "Uniform lightness scales," J. Soc. Dyers Colour. 97, 179-183 (1981).
[CrossRef]

Schultze, W.

W. Schultze, "The usefulness of colour-difference formulas for fixing colour tolerances," in Colour Metrics, Proceedings of the Helmholtz Memorial Symposium, J.J.Vos. L.F. C.Friele, and P.L. Walraven, eds. (Association Internationale de la Couleur (AIC), 1971), pp. 254-265.

Seim, T.

T. Seim and A. Valberg, "Towards a uniform color space: a better formula to describe the Munsell and OSA color scales," Color Res. Appl. 11, 11-24 (1986).
[CrossRef]

Snyder, G. D.

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

Valberg, A.

T. Seim and A. Valberg, "Towards a uniform color space: a better formula to describe the Munsell and OSA color scales," Color Res. Appl. 11, 11-24 (1986).
[CrossRef]

Witt, K.

K. Witt, "Geometric relations between scales of small colour differences," Color Res. Appl. 24, 78-92 (1999).
[CrossRef]

Yebra, A.

A. Yebra, R. Huertas, M. M. Pérez, and M. Melgosa, "On the relationship between tilt of a*b* tolerance ellipses in blue region and tritanopic confusion lines," Color Res. Appl. 27, 180-184 (2002).
[CrossRef]

Yosiki, K.

M. Kobayasi and K. Yosiki, "Effective conversion algorithm from OSA-UCS to CIEXYZ," in 9th Congress of the International Color Association, R.Chung and A.Rodrigues, eds., Proc. SPIE 4421, 848-851 (2002).

Color Res. Appl. (9)

R. G. Kuehni, "Towards an improved uniform color space," Color Res. Appl. 24, 253-265 (1999).
[CrossRef]

C. Oleari, "Comparison between color-space scales, uniform color-scales atlases and color-difference formulae," Color Res. Appl. 26, 351-361 (2001).
[CrossRef]

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

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

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

K. Witt, "Geometric relations between scales of small colour differences," Color Res. Appl. 24, 78-92 (1999).
[CrossRef]

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

A. Yebra, R. Huertas, M. M. Pérez, and M. Melgosa, "On the relationship between tilt of a*b* tolerance ellipses in blue region and tritanopic confusion lines," Color Res. Appl. 27, 180-184 (2002).
[CrossRef]

T. Seim and A. Valberg, "Towards a uniform color space: a better formula to describe the Munsell and OSA color scales," Color Res. Appl. 11, 11-24 (1986).
[CrossRef]

Comput. J. (1)

J. A. Nelder and R. Mead, "A simplex method for function minimization," Comput. J. 7, 308-313 (1965).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Soc. Dyers Colour. (1)

E. Coates, K. Y. Fong, and B. Rigg, "Uniform lightness scales," J. Soc. Dyers Colour. 97, 179-183 (1981).
[CrossRef]

Other (7)

W. Schultze, "The usefulness of colour-difference formulas for fixing colour tolerances," in Colour Metrics, Proceedings of the Helmholtz Memorial Symposium, J.J.Vos. L.F. C.Friele, and P.L. Walraven, eds. (Association Internationale de la Couleur (AIC), 1971), pp. 254-265.

M. Kobayasi and K. Yosiki, "Effective conversion algorithm from OSA-UCS to CIEXYZ," in 9th Congress of the International Color Association, R.Chung and A.Rodrigues, eds., Proc. SPIE 4421, 848-851 (2002).

G. Cui, M. R. Luo, and B. Rigg, "Crispening effect on lightness differences," in 9th Congress of the International Colour Association, R.Chung and A.Rodrigues, eds. Proc. SPIE 4421, 634-637 (2002).

R. Huertas, M. Melgosa, and C. Oleari, "A new colour-difference formula defined in the OSA-UCS space," in Proceedings of the Tenth Congress of the International Colour Association (AIC Colour, 2005), pp. 1071-1074.

Improvement to Industrial Color-Difference Evaluation, CIE Publication 142 (CIE Central Bureau, 2001).

D. L. MacAdam, Color Measurement (Springer-Verlag, 1985), pp. 165-177.

D. H. Kim and J. H. Nobbs, "New weightings functions for the weighted CIELAB color difference formula," in Proceedings of the 8th Congress of the International Colour Association (AIC Colour 97) (Association Internationale de la Couleur, 1997), Vol. 1, pp. 446-449.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

( J , G ) plane of the OSA-UCS space with the BFD ellipses[8]: BFD-P (thick ellipses) and BFD-A (thin ellipses).

Fig. 2
Fig. 2

Long (solid squares) and short (open squares) semiaxes of the whole BFD[8] set of ellipses as functions of the chroma C OSA , s of the center of the ellipse.

Fig. 3
Fig. 3

( J , G ) plane of the OSA-UCS space with the BFD ellipses (thick ellipses) and the ellipses representing the color-difference formula Δ E GP (thin ellipses), assuming the S C and S H functions given in Table 1, left side, for BFD.

Fig. 4
Fig. 4

Plot of Δ L OSA Δ V as a function of the average lightness L ¯ OSA for the color pairs with predominant lightness differences (i.e., Δ L OSA Δ E 0 > 0.9 ).

Fig. 5
Fig. 5

Plot of Δ C OSA Δ V as a function of the average lightness C ¯ OSA for the color pairs with predominant chroma differences (i.e., Δ C OSA Δ E 0 > 0.9 ).

Fig. 6
Fig. 6

Plot of Δ H OSA Δ V as a function of the average lightness C ¯ OSA for the color pairs with predominant hue differences (i.e., Δ H OSA Δ E 0 > 0.9 ).

Fig. 7
Fig. 7

Plots of the S L weighting functions obtained from different data sets by minimizing the PF 3 index.

Fig. 8
Fig. 8

Plots of the S C weighting functions obtained from different data sets by minimizing the PF 3 index.

Fig. 9
Fig. 9

Plots of the S H weighting functions obtained from different data sets by minimizing the PF 3 index.

Tables (4)

Tables Icon

Table 1 S C and S H Weights and Corresponding Linear Correlation Indices r Obtained by Linear Fits of the Long and Short Semiaxes of the Ellipses and Obtained by Minimizing the PF 3 Index as Functions of the Chroma C OSA , s of the Color Standard s (the Center of the Ellipse) a

Tables Icon

Table 2 Number of Color Pairs Corresponding to the Filtered Data Sets Used for the Computation of the Weighting Functions S L , S C , and S H (Table 3, Left Side) a

Tables Icon

Table 3 Weighting Functions S L , S C , and S H Obtained by Two Different Techniques and Computed for Different Subsets as Functions of the Average Lightness L ¯ OSA and Average Chroma C ¯ OSA a

Tables Icon

Table 4 Values of the PF 3 a Computed for Different Color-Difference Formulas and Related to the Three Sets of Ellipses BFD, BFD-P, and BFD-A (Evaluated on 100 Points per Ellipse) and Different Data Sets (BFD-P, b Leeds, c RIT–DuPont, d and Witt e ) Constituting the COM Data Set f

Equations (21)

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

( Δ E GP ) 2 = 10 2 [ ( Δ L OSA k L S L ) 2 + ( Δ C OSA k C S C ) 2 + ( Δ H OSA k H S H ) 2 ] ,
S L = 2.499 + 0.007 ( 10 L ¯ OSA ) ,
S C = 1.235 + 0.058 ( 10 C ¯ OSA ) ,
S H = 1.392 + 0.017 ( 10 C ¯ OSA ) ,
L OSA = { 5.9 [ ( Y 0 1 3 2 3 ) + 0.042 ( Y 0 30 ) 1 3 ] 14.4 } 1 2 ,
Y 0 = Y 10 ( 4.4934 x 10 2 + 4.3034 y 10 2 4.2760 x 10 y 10 1.3744 x 10 2.5643 y 10 + 1.8103 ) .
( A B C ) = [ 0.6597 0.4492 0.1089 0.3053 1.2126 0.0927 0.0374 0.4795 0.5579 ] ( X 10 Y 10 Z 10 ) ,
( J G ) = [ S J 0 0 S G ] [ sin α cos α sin β cos β ] ( ln ( A B A n B n ) ln ( B C B n C n ) ) = [ 2 ( 0.5735 L OSA + 7.0892 ) 0 0 2 ( 0.7640 L OSA + 9.2521 ) ] [ 0.1792 0.9837 0.9482 0.3175 ] ( ln ( A B 0.9366 ) ln ( B C 0.9807 ) ) .
C OSA = J 2 + G 2 , h OSA = arctan ( J G ) deg .
( Δ E 0 ) 2 = ( L OSA , s L OSA , b ) 2 + ( J s J b ) 2 + ( G s G b ) 2
( Δ E 0 ) 2 = ( Δ L OSA ) 2 + ( Δ C OSA ) 2 + ( Δ H OSA ) 2 ,
Δ L OSA = L OSA , s L OSA , b ,
Δ C OSA = C OSA , s C OSA , b ,
C OSA , s = J s 2 + G s 2 , C OSA , b = J b 2 + G b 2 ,
( Δ H OSA ) 2 = ( Δ E 0 ) 2 ( Δ L OSA ) 2 ( Δ C OSA ) 2 .
PF 3 = 100 [ ( γ 1 ) + V A B + C V 100 ] 3 ,
log 10 ( γ ) = 1 N i = 1 N [ log 10 ( Δ E i Δ V i ) log 10 ( Δ E i Δ V i ) ¯ ] 2 .
V A B = 1 N i = 1 N ( Δ E i F Δ V i ) 2 Δ E i F Δ V i ,
F = i = 1 N Δ E i Δ V i i = 1 N Δ V i Δ E i
C V = 100 1 N i = 1 N ( Δ E i f Δ V i ) 2 ( Δ E ¯ ) 2 ,
f = i = 1 N Δ E i Δ V i i = 1 N Δ V i 2 .

Metrics