Abstract

Color-constancy mechanisms have been studied and discussed in a number of investigations. However, there has been little attempt to reveal how color constancy deteriorates as the conditions for it become less than optimal. We carried out a series of asymmetric color-matching experiments, using two criteria: surface-color match and apparent-color match. With brief adaptation the degree of color constancy increased as chromatic cues were added in the surround. In the condition of black surround, the test stimuli appeared self-luminous, and chromaticities of the chosen matching stimuli were the same as the physical chromaticities of the test stimulus, indicating a total deficiency of color constancy. With 15 min of preadaptation to the illuminant, the surface-color matches showed almost perfect color constancy under illuminant change. In both adaptation conditions, the chromatic-shift of matches from what would be expected for perfect color constancy increased gradually between 1,700- and 30,000-K illuminant, as chromaticity of the illuminant departed from 6,500-K illuminant. Under 1,000-K illuminant the surface-color appearance became totally achromatic, and color constancy was completely lost. Our results show that, even with brief adaptation to the illuminant, the contribution of the surrounding stimulus is large enough to achieve a fair degree of color constancy, but complete adaptation to the illuminant helps to achieve almost perfect color constancy.

© 1996 Optical Society of America

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References

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  1. H. von Helmholtz, Treatise on Physiological Optics, 2nd ed. (Dover, New York, 1866, 1962).
  2. R. M. Boynton, K. F. Purl, “Categorical colour perception under low-pressure sodium lighting with small amounts of added incandescent illumination,” Lighting Res. Technol. 21, 23–27 (1989).
    [CrossRef]
  3. J. A. Worthey, “Limitations of color constancy,” J. Opt. Soc. Am. A 2, 1014–1026 (1985).
    [CrossRef]
  4. H. Helson, V. B. Jeffers, “Fundamental problems in color vision. II. Hue lightness and saturation of selective samples in chromatic illumination,”J. Exp. Psychol. 26, 1–27 (1940).
    [CrossRef]
  5. L. E. Arend, “How much does illuminant color affect unattributed colors?” J. Opt. Soc. Am. A 10, 2134–2147 (1993).
    [CrossRef]
  6. L. E. Arend, A. Reeves, “Simultaneous color constancy,” J. Opt. Soc. Am. A 3, 1743–1751 (1986).
    [CrossRef] [PubMed]
  7. E. Hering, Outline of a Theory of the Light Sense (Harvard U. Press, Cambridge, Mass., 1920; English translation by L. Hurvich, D. Jameson, 1964).
  8. M. D. Fairchild, P. Lennie, “Chromatic adaptation to natural and incandescent illuminants,” Vision Res. 32, 2077–2085 (1992).
    [CrossRef] [PubMed]
  9. I. Kuriki, D. I. A. MacLeod, “Chromatic adaptation aftereffects on luminance and chromatic channels,” in John Dalton’s Colour Vision Legacy, C. M. Dickinson, I. J. Murray, D. Carden, eds. (Taylor & Francis, London, to be published).
  10. M. D. Fairchild, L. Feniff, “Time course of chromatic adaptation for color-appearance judgments,” J. Opt. Soc. Am. A 12, 824–833 (1995).
    [CrossRef]
  11. S. Hecht, C. Haig, A. M. Chase, “The influence of light adaptation on subsequent dark adaptation of the eye,”J. Gen. Physiol. 20, 831–850 (1937).
    [CrossRef] [PubMed]
  12. B. J. Craven, D. H. Foster, “An operational approach to color constancy,” Vision Res. 32, 1359–1366 (1992).
    [CrossRef] [PubMed]
  13. H. Uchikawa, K. Uchikawa, R. M. Boynton, “Influence of achromatic surrounds on categorical perception of surface colors,” Vision Res. 29, 881–890 (1989).
    [CrossRef] [PubMed]
  14. A. Valberg, B. Lange-Malecki, “‘Color constancy’ in Mondrian patterns: a partial cancellation of physical chormaticity shifts by simultaneous contrast,” Vision Res. 30, 371–380 (1990).
    [CrossRef]
  15. J. Walraven, T. L. Benzshawel, B. E. Rogowitz, M. P. Lucassen, “Testing the contrast explanation of color constancy,” in From Pigments to Perception, A. Valberg, B. B. Lee, eds. (Plenum, New York, 1991), pp. 369–377.
    [CrossRef]
  16. D. L. MacAdam, “Uniform color scales,”J. Opt. Soc. Am. 64, 1691–1702 (1974).
    [CrossRef] [PubMed]
  17. W. B. Cowan, “An inexpensive scheme for calibration of a colour monitor in terms of CIE standard coordinates,” Comput. Graph. 17, 315–321 (1983).
    [CrossRef]
  18. L. E. Arend, A. Reeves, J. Schirillo, R. Goldstein, “Simultaneous color constancy: paper with diverse Munsell values,” J. Opt. Soc. Am. A 8, 661–672 (1991).
    [CrossRef] [PubMed]
  19. E. Brunswik, “Zur Entwicklung der Albedowahrnehmung,”Z. Psychol. 109 (1929).
  20. J. A. Worthey, M. H. Brill, “Heuristic analysis of von Kries color constancy,” J. Opt. Soc. Am. A 3, 1708–1712 (1986).
    [CrossRef] [PubMed]
  21. D. Brainard, B. Wandell, “Asymmetric color matching: how color appearance depends on the illuminant,” J. Opt. Soc. Am. A 9, 1433–1448 (1992).
    [CrossRef] [PubMed]
  22. V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal one photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
    [CrossRef] [PubMed]
  23. E. H. Land, J. J. McCann, “Lightness and retinex theory,”J. Opt. Soc. Am. 61, 1–11 (1971).
    [CrossRef] [PubMed]
  24. J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in retinex theory: a comparison between theoretical predictions and observer responses to the ‘color Mondrian’ experiments,” Vision Res. 16, 445–458 (1976).
    [CrossRef]

1995 (1)

1993 (1)

1992 (3)

D. Brainard, B. Wandell, “Asymmetric color matching: how color appearance depends on the illuminant,” J. Opt. Soc. Am. A 9, 1433–1448 (1992).
[CrossRef] [PubMed]

B. J. Craven, D. H. Foster, “An operational approach to color constancy,” Vision Res. 32, 1359–1366 (1992).
[CrossRef] [PubMed]

M. D. Fairchild, P. Lennie, “Chromatic adaptation to natural and incandescent illuminants,” Vision Res. 32, 2077–2085 (1992).
[CrossRef] [PubMed]

1991 (1)

1990 (1)

A. Valberg, B. Lange-Malecki, “‘Color constancy’ in Mondrian patterns: a partial cancellation of physical chormaticity shifts by simultaneous contrast,” Vision Res. 30, 371–380 (1990).
[CrossRef]

1989 (2)

H. Uchikawa, K. Uchikawa, R. M. Boynton, “Influence of achromatic surrounds on categorical perception of surface colors,” Vision Res. 29, 881–890 (1989).
[CrossRef] [PubMed]

R. M. Boynton, K. F. Purl, “Categorical colour perception under low-pressure sodium lighting with small amounts of added incandescent illumination,” Lighting Res. Technol. 21, 23–27 (1989).
[CrossRef]

1986 (2)

1985 (1)

1983 (1)

W. B. Cowan, “An inexpensive scheme for calibration of a colour monitor in terms of CIE standard coordinates,” Comput. Graph. 17, 315–321 (1983).
[CrossRef]

1976 (1)

J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in retinex theory: a comparison between theoretical predictions and observer responses to the ‘color Mondrian’ experiments,” Vision Res. 16, 445–458 (1976).
[CrossRef]

1975 (1)

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal one photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

1974 (1)

1971 (1)

1940 (1)

H. Helson, V. B. Jeffers, “Fundamental problems in color vision. II. Hue lightness and saturation of selective samples in chromatic illumination,”J. Exp. Psychol. 26, 1–27 (1940).
[CrossRef]

1937 (1)

S. Hecht, C. Haig, A. M. Chase, “The influence of light adaptation on subsequent dark adaptation of the eye,”J. Gen. Physiol. 20, 831–850 (1937).
[CrossRef] [PubMed]

1929 (1)

E. Brunswik, “Zur Entwicklung der Albedowahrnehmung,”Z. Psychol. 109 (1929).

Arend, L. E.

Benzshawel, T. L.

J. Walraven, T. L. Benzshawel, B. E. Rogowitz, M. P. Lucassen, “Testing the contrast explanation of color constancy,” in From Pigments to Perception, A. Valberg, B. B. Lee, eds. (Plenum, New York, 1991), pp. 369–377.
[CrossRef]

Boynton, R. M.

R. M. Boynton, K. F. Purl, “Categorical colour perception under low-pressure sodium lighting with small amounts of added incandescent illumination,” Lighting Res. Technol. 21, 23–27 (1989).
[CrossRef]

H. Uchikawa, K. Uchikawa, R. M. Boynton, “Influence of achromatic surrounds on categorical perception of surface colors,” Vision Res. 29, 881–890 (1989).
[CrossRef] [PubMed]

Brainard, D.

Brill, M. H.

Brunswik, E.

E. Brunswik, “Zur Entwicklung der Albedowahrnehmung,”Z. Psychol. 109 (1929).

Chase, A. M.

S. Hecht, C. Haig, A. M. Chase, “The influence of light adaptation on subsequent dark adaptation of the eye,”J. Gen. Physiol. 20, 831–850 (1937).
[CrossRef] [PubMed]

Cowan, W. B.

W. B. Cowan, “An inexpensive scheme for calibration of a colour monitor in terms of CIE standard coordinates,” Comput. Graph. 17, 315–321 (1983).
[CrossRef]

Craven, B. J.

B. J. Craven, D. H. Foster, “An operational approach to color constancy,” Vision Res. 32, 1359–1366 (1992).
[CrossRef] [PubMed]

Fairchild, M. D.

M. D. Fairchild, L. Feniff, “Time course of chromatic adaptation for color-appearance judgments,” J. Opt. Soc. Am. A 12, 824–833 (1995).
[CrossRef]

M. D. Fairchild, P. Lennie, “Chromatic adaptation to natural and incandescent illuminants,” Vision Res. 32, 2077–2085 (1992).
[CrossRef] [PubMed]

Feniff, L.

Foster, D. H.

B. J. Craven, D. H. Foster, “An operational approach to color constancy,” Vision Res. 32, 1359–1366 (1992).
[CrossRef] [PubMed]

Goldstein, R.

Haig, C.

S. Hecht, C. Haig, A. M. Chase, “The influence of light adaptation on subsequent dark adaptation of the eye,”J. Gen. Physiol. 20, 831–850 (1937).
[CrossRef] [PubMed]

Hecht, S.

S. Hecht, C. Haig, A. M. Chase, “The influence of light adaptation on subsequent dark adaptation of the eye,”J. Gen. Physiol. 20, 831–850 (1937).
[CrossRef] [PubMed]

Helson, H.

H. Helson, V. B. Jeffers, “Fundamental problems in color vision. II. Hue lightness and saturation of selective samples in chromatic illumination,”J. Exp. Psychol. 26, 1–27 (1940).
[CrossRef]

Hering, E.

E. Hering, Outline of a Theory of the Light Sense (Harvard U. Press, Cambridge, Mass., 1920; English translation by L. Hurvich, D. Jameson, 1964).

Jeffers, V. B.

H. Helson, V. B. Jeffers, “Fundamental problems in color vision. II. Hue lightness and saturation of selective samples in chromatic illumination,”J. Exp. Psychol. 26, 1–27 (1940).
[CrossRef]

Kuriki, I.

I. Kuriki, D. I. A. MacLeod, “Chromatic adaptation aftereffects on luminance and chromatic channels,” in John Dalton’s Colour Vision Legacy, C. M. Dickinson, I. J. Murray, D. Carden, eds. (Taylor & Francis, London, to be published).

Land, E. H.

Lange-Malecki, B.

A. Valberg, B. Lange-Malecki, “‘Color constancy’ in Mondrian patterns: a partial cancellation of physical chormaticity shifts by simultaneous contrast,” Vision Res. 30, 371–380 (1990).
[CrossRef]

Lennie, P.

M. D. Fairchild, P. Lennie, “Chromatic adaptation to natural and incandescent illuminants,” Vision Res. 32, 2077–2085 (1992).
[CrossRef] [PubMed]

Lucassen, M. P.

J. Walraven, T. L. Benzshawel, B. E. Rogowitz, M. P. Lucassen, “Testing the contrast explanation of color constancy,” in From Pigments to Perception, A. Valberg, B. B. Lee, eds. (Plenum, New York, 1991), pp. 369–377.
[CrossRef]

MacAdam, D. L.

MacLeod, D. I. A.

I. Kuriki, D. I. A. MacLeod, “Chromatic adaptation aftereffects on luminance and chromatic channels,” in John Dalton’s Colour Vision Legacy, C. M. Dickinson, I. J. Murray, D. Carden, eds. (Taylor & Francis, London, to be published).

McCann, J. J.

J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in retinex theory: a comparison between theoretical predictions and observer responses to the ‘color Mondrian’ experiments,” Vision Res. 16, 445–458 (1976).
[CrossRef]

E. H. Land, J. J. McCann, “Lightness and retinex theory,”J. Opt. Soc. Am. 61, 1–11 (1971).
[CrossRef] [PubMed]

McKee, S. P.

J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in retinex theory: a comparison between theoretical predictions and observer responses to the ‘color Mondrian’ experiments,” Vision Res. 16, 445–458 (1976).
[CrossRef]

Pokorny, J.

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal one photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

Purl, K. F.

R. M. Boynton, K. F. Purl, “Categorical colour perception under low-pressure sodium lighting with small amounts of added incandescent illumination,” Lighting Res. Technol. 21, 23–27 (1989).
[CrossRef]

Reeves, A.

Rogowitz, B. E.

J. Walraven, T. L. Benzshawel, B. E. Rogowitz, M. P. Lucassen, “Testing the contrast explanation of color constancy,” in From Pigments to Perception, A. Valberg, B. B. Lee, eds. (Plenum, New York, 1991), pp. 369–377.
[CrossRef]

Schirillo, J.

Smith, V. C.

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal one photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

Taylor, T. H.

J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in retinex theory: a comparison between theoretical predictions and observer responses to the ‘color Mondrian’ experiments,” Vision Res. 16, 445–458 (1976).
[CrossRef]

Uchikawa, H.

H. Uchikawa, K. Uchikawa, R. M. Boynton, “Influence of achromatic surrounds on categorical perception of surface colors,” Vision Res. 29, 881–890 (1989).
[CrossRef] [PubMed]

Uchikawa, K.

H. Uchikawa, K. Uchikawa, R. M. Boynton, “Influence of achromatic surrounds on categorical perception of surface colors,” Vision Res. 29, 881–890 (1989).
[CrossRef] [PubMed]

Valberg, A.

A. Valberg, B. Lange-Malecki, “‘Color constancy’ in Mondrian patterns: a partial cancellation of physical chormaticity shifts by simultaneous contrast,” Vision Res. 30, 371–380 (1990).
[CrossRef]

von Helmholtz, H.

H. von Helmholtz, Treatise on Physiological Optics, 2nd ed. (Dover, New York, 1866, 1962).

Walraven, J.

J. Walraven, T. L. Benzshawel, B. E. Rogowitz, M. P. Lucassen, “Testing the contrast explanation of color constancy,” in From Pigments to Perception, A. Valberg, B. B. Lee, eds. (Plenum, New York, 1991), pp. 369–377.
[CrossRef]

Wandell, B.

Worthey, J. A.

Comput. Graph. (1)

W. B. Cowan, “An inexpensive scheme for calibration of a colour monitor in terms of CIE standard coordinates,” Comput. Graph. 17, 315–321 (1983).
[CrossRef]

J. Exp. Psychol. (1)

H. Helson, V. B. Jeffers, “Fundamental problems in color vision. II. Hue lightness and saturation of selective samples in chromatic illumination,”J. Exp. Psychol. 26, 1–27 (1940).
[CrossRef]

J. Gen. Physiol. (1)

S. Hecht, C. Haig, A. M. Chase, “The influence of light adaptation on subsequent dark adaptation of the eye,”J. Gen. Physiol. 20, 831–850 (1937).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (7)

Lighting Res. Technol. (1)

R. M. Boynton, K. F. Purl, “Categorical colour perception under low-pressure sodium lighting with small amounts of added incandescent illumination,” Lighting Res. Technol. 21, 23–27 (1989).
[CrossRef]

Vision Res. (6)

B. J. Craven, D. H. Foster, “An operational approach to color constancy,” Vision Res. 32, 1359–1366 (1992).
[CrossRef] [PubMed]

H. Uchikawa, K. Uchikawa, R. M. Boynton, “Influence of achromatic surrounds on categorical perception of surface colors,” Vision Res. 29, 881–890 (1989).
[CrossRef] [PubMed]

A. Valberg, B. Lange-Malecki, “‘Color constancy’ in Mondrian patterns: a partial cancellation of physical chormaticity shifts by simultaneous contrast,” Vision Res. 30, 371–380 (1990).
[CrossRef]

M. D. Fairchild, P. Lennie, “Chromatic adaptation to natural and incandescent illuminants,” Vision Res. 32, 2077–2085 (1992).
[CrossRef] [PubMed]

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal one photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in retinex theory: a comparison between theoretical predictions and observer responses to the ‘color Mondrian’ experiments,” Vision Res. 16, 445–458 (1976).
[CrossRef]

Z. Psychol. (1)

E. Brunswik, “Zur Entwicklung der Albedowahrnehmung,”Z. Psychol. 109 (1929).

Other (4)

I. Kuriki, D. I. A. MacLeod, “Chromatic adaptation aftereffects on luminance and chromatic channels,” in John Dalton’s Colour Vision Legacy, C. M. Dickinson, I. J. Murray, D. Carden, eds. (Taylor & Francis, London, to be published).

J. Walraven, T. L. Benzshawel, B. E. Rogowitz, M. P. Lucassen, “Testing the contrast explanation of color constancy,” in From Pigments to Perception, A. Valberg, B. B. Lee, eds. (Plenum, New York, 1991), pp. 369–377.
[CrossRef]

H. von Helmholtz, Treatise on Physiological Optics, 2nd ed. (Dover, New York, 1866, 1962).

E. Hering, Outline of a Theory of the Light Sense (Harvard U. Press, Cambridge, Mass., 1920; English translation by L. Hurvich, D. Jameson, 1964).

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of the apparatus. The observer watched the stimuli with only his right eye through two timer-controlled shutters, by switching his view to the opened shutter. In experiment 2, the observer viewed the stimuli hapiscopically by means of a wall placed between the left and right eyes.

Fig. 2
Fig. 2

Three kinds of surround condition used in the experiments. The Mondrian surround was made with a uniform gray background and eight small Munsell color chips. The Munsell notations of these color chips were (1) 5R 4/12, (2) 5YR 5/10, (3) 5Y 8/10, (4) 5G 5/8, (5) 5RP 5/10, (6) 5PB 5/10, (7) 10B 5/10, and (8) 5P 5/10; the numbers in parentheses correspond to the numbers on each color chip in panel (c). These color chips were carefully selected so that their color appearances would be different from the test color chips.

Fig. 3
Fig. 3

Results of color-appearance matches in the DARK condition for observer IK. The left-hand panels show the matched colors in each illuminant condition on the CIE 1931 xy chromaticity diagram. The matched results are shown by open squares. Circles stand for physical chromaticities of stimuli: open symbols indicate chromaticities of the test color chips under D65 illuminant, which represents perfect color constancy, and filled symbols indicate physical chromaticities of the test stimuli. Numbers at the top-right of each panel indicate illuminant chromaticity in Tc, and the chromaticity is shown by the open cross. The filled cross stands for the chromaticity of the D65 illuminant. The large triangle in the panel for the 1,700-K illuminant condition shows the chromatic gamut of the CRT display used in the experiment. The right-hand panels show luminance profiles of the results. The meanings of the symbols are the same as for the chromaticity diagrams. The numbers on the horizontal axis correspond to test color chips in the OSA UCS notation as follows: 1, (L, j, g)=(−2, −2, 0); 2, (−2, −2, 2); 3, (−2, 0, −2); 4, (−2, 0, 0); 5, (−2, 0, 2); 6, (−2, 2, −2); 7, (−2, 2, 0); and 8, (−2, 2, 2).

Fig. 4
Fig. 4

Results of color matching in the GRAY condition for observer IK. Open squares stand for the chromaticities of matched results at the apparent-color matches, and filled squares stand for the chromaticities of matched results at the surface-color matches. The meanings of symbols are the same as in Fig. 3.

Fig. 5
Fig. 5

Results of color matching under the MOND condition for observer IK. The meanings of symbols are the same as those in Fig. 4.

Fig. 6
Fig. 6

Plots of E(j), the mean normalized distance of matched color from perfect color constancy, defined by Eq. (3), for four observers. The horizontal axes stand for the difference of illuminant from D65 in terms uυ distance. The vertical axes show E(j) in each stimulus condition. The symbols indicate different surround conditions and criteria. Diamonds indicate physical chromaticity shifts of test stimuli at each illuminant. Squares stand for the results in the DARK condition. Circles stand for the results in the GRAY condition. Triangles stand for the results in the MOND condition. Open and filled symbols stand for the apparent-color and the surface-color match, respectively. The horizontal position of the matched results were intentionally shifted to the left (apparent-color matches) or the right (surface-color matches) from the colorimetric point, so that most of the symbols are visible. Error bars show ±1 SD.

Fig. 7
Fig. 7

Results of color matching under the ADAPT condition (Mondrian surround after 15 min of preadaptation to the illuminant) for observer IK. The meanings of symbols are the same as those in Fig. 3.

Fig. 8
Fig. 8

Plots of E(j), the mean normalized distance of matched color from perfect color constancy, defined by Eq. (3) in the ADAPT condition. Meanings of the axes are the same as those in Fig. 6. Diamonds indicate physical chromaticity shifts of test stimuli at each illuminant. Squares stand for the results in the DARK condition. Circles stand for the results in the MOND condition with no-adaptation. Triangles stand for the results in the MOND condition with full adaptation. Open and filled symbols stand for apparent-color and surface color-matches, respectively. Error bars show ±1 SD.

Fig. 9
Fig. 9

Replot of the results for surface-color matches in the GRAY condition for observer IK. Panels (a), (b), and (c) show data converted into L-, M-, and S-cone responses, respectively, scaled in arbitrary units. The horizontal axes stand for the cone responses for test color chips under D65 illuminant. The vertical axes stand for the cone responses for matched results. Symbols represent data under different illuminants. Each dashed-line segment in (c) represents the fit for each illuminant condition.

Fig. 10
Fig. 10

Gradients of linear fitting for the results of each illuminant condition, surround condition, and criterion. The horizontal axes show each combination of surround condition and criterion. The vertical axes show the magnitude of the gradient for linear fitting. The less the spread across the illuminants, the higher the degree of color constancy in terms of each cone response.

Equations (3)

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dist i ( match j D 65 ) = [ ( u i j u i D 65 ) 2 + ( ν i j ν i D 65 ) 2 ] 1 / 2 dist i ( test j D 65 ) = [ ( u i j u i D 65 ) 2 + ( ν i j ν i D 65 ) 2 ] 1 / 2 ,
E r ( j ) = E { dist i ( match j D 65 ) / dist i ( test j D 65 ) } .
E ( j ) = E { dist i ( test j D 65 ) } * E r ( j ) .

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