Abstract

Our study deals with color synthesis of a three-dimensional object in an image; i.e., given a single image, a target color can be accurately mapped onto the object such that the color appearance of the synthesized object closely resembles that of the actual one. As it is almost impossible to acquire the complete geometric description of the surfaces of an object in an image, this study attempted to recover the implicit description of geometry for the color synthesis. The description was obtained from either a series of spectral reflectances or the RGB signals at different surface positions on the basis of the dichromatic reflection model. The experimental results showed that this implicit image-based representation is related to the object geometry and is sufficient for accurate color synthesis of three-dimensional objects in an image. The method established is applicable to the color synthesis of both rigid and deformable objects and should contribute to color fidelity in virtual design, manufacturing, and retailing.

© 2004 Optical Society of America

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References

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  1. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Monograph 160 (National Institute of Standards and Technology, Rockville, Md., 1997).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. H. B. Westlund, G. W. Meyer, “A BRDF database employing the Beard–Maxwell reflection model,” in Graphics Interface 2002 (Canadian Human-Computer Communications Society, Mississauga, Ontario, Canada, 2002), pp. 189–200.
  9. L. B. Wolff, S. A. Shafer, G. E. Healey, Physics-Based Vision Principles and Practice: Shape Recovery (Jones & Bartlett, Boston, Mass., 1992).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. S. Tominaga, “Dichromatic reflection models for rendering object surfaces,” J. Imaging Sci. Technol. 40, 549–555 (1996).
  15. H. L. Shen, J. H. Xin, “Dichromatic based rendering of texture images with high color fidelity,” J. Imaging Sci. Technol. (to be published).
  16. E. Reinhard, M. Ashikhmin, B. Gooch, P. Shirley, “Color transfer between images,” IEEE Comput. Graphics Appl. 21, 34–41 (2001).
    [CrossRef]
  17. L. Peng, “Dichromatic based photographic modification,” in Proceedings of the Sixth Color Imaging Conference (Society for Imaging Science and Technology, Springfield, Va., 1998), pp. 96–99.
  18. L. Liu, G. Xu, “Color change method based on dichromatic reflection model,” Proceedings of International Con-ference on Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 1246–1249.
  19. B. K. P. Horn, R. W. Sjoberg, “Calculating the reflectance map,” Appl. Opt. 18, 1770–1779 (1979).
    [CrossRef] [PubMed]
  20. K. Barnard, B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 152–163 (2002).
    [CrossRef]
  21. F. J. Clarke, R. McDonald, R. Rigg, “Modification to the JPC79 color difference formula,” J. Soc. Dyers Colorists 100, 117–148 (1984).

2002 (1)

K. Barnard, B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 152–163 (2002).
[CrossRef]

2001 (1)

E. Reinhard, M. Ashikhmin, B. Gooch, P. Shirley, “Color transfer between images,” IEEE Comput. Graphics Appl. 21, 34–41 (2001).
[CrossRef]

2000 (1)

1999 (1)

K. J. Dana, B. Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real world surfaces,” ACM Trans. Graphics 18, 1–34 (1999).
[CrossRef]

1996 (1)

S. Tominaga, “Dichromatic reflection models for rendering object surfaces,” J. Imaging Sci. Technol. 40, 549–555 (1996).

1994 (1)

S. Tominaga, “Dichromatic reflection model for a variety of materials,” Color Res. Appl. 19, 277–285 (1994).
[CrossRef]

1992 (1)

G. J. Ward, “Measuring and modeling anisotropic reflection,” Comput. Graph. 26, 265–272 (1992).
[CrossRef]

1990 (1)

H. C. Lee, E. J. Breneman, C. P. Schulte, “Modeling light reflection for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402–409 (1990).
[CrossRef]

1989 (1)

1985 (1)

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

1984 (1)

F. J. Clarke, R. McDonald, R. Rigg, “Modification to the JPC79 color difference formula,” J. Soc. Dyers Colorists 100, 117–148 (1984).

1979 (1)

1977 (1)

J. Fi. Blinn, “Models of light refection for computer synthesized pictures,” Comput. Graph. 11, 192–198 (1977).
[CrossRef]

1975 (1)

B. T. Phong, “Illumination for computer generated images,” Commun. ACM 18, 311–317 (1975).
[CrossRef]

1967 (1)

Ashikhmin, M.

E. Reinhard, M. Ashikhmin, B. Gooch, P. Shirley, “Color transfer between images,” IEEE Comput. Graphics Appl. 21, 34–41 (2001).
[CrossRef]

Barnard, K.

K. Barnard, B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 152–163 (2002).
[CrossRef]

Blinn, J. Fi.

J. Fi. Blinn, “Models of light refection for computer synthesized pictures,” Comput. Graph. 11, 192–198 (1977).
[CrossRef]

Breneman, E. J.

H. C. Lee, E. J. Breneman, C. P. Schulte, “Modeling light reflection for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402–409 (1990).
[CrossRef]

Clarke, F. J.

F. J. Clarke, R. McDonald, R. Rigg, “Modification to the JPC79 color difference formula,” J. Soc. Dyers Colorists 100, 117–148 (1984).

Dana, K. J.

K. J. Dana, B. Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real world surfaces,” ACM Trans. Graphics 18, 1–34 (1999).
[CrossRef]

Funt, B.

K. Barnard, B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 152–163 (2002).
[CrossRef]

Ginneken, B.

K. J. Dana, B. Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real world surfaces,” ACM Trans. Graphics 18, 1–34 (1999).
[CrossRef]

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Monograph 160 (National Institute of Standards and Technology, Rockville, Md., 1997).

Gooch, B.

E. Reinhard, M. Ashikhmin, B. Gooch, P. Shirley, “Color transfer between images,” IEEE Comput. Graphics Appl. 21, 34–41 (2001).
[CrossRef]

Healey, G.

Healey, G. E.

L. B. Wolff, S. A. Shafer, G. E. Healey, Physics-Based Vision Principles and Practice: Shape Recovery (Jones & Bartlett, Boston, Mass., 1992).

Horn, B. K. P.

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Monograph 160 (National Institute of Standards and Technology, Rockville, Md., 1997).

Koenderink, J. J.

K. J. Dana, B. Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real world surfaces,” ACM Trans. Graphics 18, 1–34 (1999).
[CrossRef]

Lafortune, E. P. F.

Lee, H. C.

H. C. Lee, E. J. Breneman, C. P. Schulte, “Modeling light reflection for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402–409 (1990).
[CrossRef]

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Monograph 160 (National Institute of Standards and Technology, Rockville, Md., 1997).

Liu, L.

L. Liu, G. Xu, “Color change method based on dichromatic reflection model,” Proceedings of International Con-ference on Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 1246–1249.

Marscher, S. R.

McDonald, R.

F. J. Clarke, R. McDonald, R. Rigg, “Modification to the JPC79 color difference formula,” J. Soc. Dyers Colorists 100, 117–148 (1984).

Meyer, G. W.

H. B. Westlund, G. W. Meyer, “A BRDF database employing the Beard–Maxwell reflection model,” in Graphics Interface 2002 (Canadian Human-Computer Communications Society, Mississauga, Ontario, Canada, 2002), pp. 189–200.

Nayar, S. K.

K. J. Dana, B. Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real world surfaces,” ACM Trans. Graphics 18, 1–34 (1999).
[CrossRef]

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Monograph 160 (National Institute of Standards and Technology, Rockville, Md., 1997).

Peng, L.

L. Peng, “Dichromatic based photographic modification,” in Proceedings of the Sixth Color Imaging Conference (Society for Imaging Science and Technology, Springfield, Va., 1998), pp. 96–99.

Phong, B. T.

B. T. Phong, “Illumination for computer generated images,” Commun. ACM 18, 311–317 (1975).
[CrossRef]

Reinhard, E.

E. Reinhard, M. Ashikhmin, B. Gooch, P. Shirley, “Color transfer between images,” IEEE Comput. Graphics Appl. 21, 34–41 (2001).
[CrossRef]

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Monograph 160 (National Institute of Standards and Technology, Rockville, Md., 1997).

Rigg, R.

F. J. Clarke, R. McDonald, R. Rigg, “Modification to the JPC79 color difference formula,” J. Soc. Dyers Colorists 100, 117–148 (1984).

Schulte, C. P.

H. C. Lee, E. J. Breneman, C. P. Schulte, “Modeling light reflection for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402–409 (1990).
[CrossRef]

Shafer, S. A.

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

L. B. Wolff, S. A. Shafer, G. E. Healey, Physics-Based Vision Principles and Practice: Shape Recovery (Jones & Bartlett, Boston, Mass., 1992).

Shen, H. L.

H. L. Shen, J. H. Xin, “Dichromatic based rendering of texture images with high color fidelity,” J. Imaging Sci. Technol. (to be published).

Shirley, P.

E. Reinhard, M. Ashikhmin, B. Gooch, P. Shirley, “Color transfer between images,” IEEE Comput. Graphics Appl. 21, 34–41 (2001).
[CrossRef]

Sjoberg, R. W.

Sparrow, E. M.

Tominaga, S.

S. Tominaga, “Dichromatic reflection models for rendering object surfaces,” J. Imaging Sci. Technol. 40, 549–555 (1996).

S. Tominaga, “Dichromatic reflection model for a variety of materials,” Color Res. Appl. 19, 277–285 (1994).
[CrossRef]

Torrance, K. E.

Ward, G. J.

G. J. Ward, “Measuring and modeling anisotropic reflection,” Comput. Graph. 26, 265–272 (1992).
[CrossRef]

Westin, S. H.

Westlund, H. B.

H. B. Westlund, G. W. Meyer, “A BRDF database employing the Beard–Maxwell reflection model,” in Graphics Interface 2002 (Canadian Human-Computer Communications Society, Mississauga, Ontario, Canada, 2002), pp. 189–200.

Wolff, L. B.

L. B. Wolff, S. A. Shafer, G. E. Healey, Physics-Based Vision Principles and Practice: Shape Recovery (Jones & Bartlett, Boston, Mass., 1992).

Xin, J. H.

H. L. Shen, J. H. Xin, “Dichromatic based rendering of texture images with high color fidelity,” J. Imaging Sci. Technol. (to be published).

Xu, G.

L. Liu, G. Xu, “Color change method based on dichromatic reflection model,” Proceedings of International Con-ference on Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 1246–1249.

ACM Trans. Graphics (1)

K. J. Dana, B. Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real world surfaces,” ACM Trans. Graphics 18, 1–34 (1999).
[CrossRef]

Appl. Opt. (2)

Color Res. Appl. (3)

K. Barnard, B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 152–163 (2002).
[CrossRef]

S. Tominaga, “Dichromatic reflection model for a variety of materials,” Color Res. Appl. 19, 277–285 (1994).
[CrossRef]

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

Commun. ACM (1)

B. T. Phong, “Illumination for computer generated images,” Commun. ACM 18, 311–317 (1975).
[CrossRef]

Comput. Graph. (2)

J. Fi. Blinn, “Models of light refection for computer synthesized pictures,” Comput. Graph. 11, 192–198 (1977).
[CrossRef]

G. J. Ward, “Measuring and modeling anisotropic reflection,” Comput. Graph. 26, 265–272 (1992).
[CrossRef]

IEEE Comput. Graphics Appl. (1)

E. Reinhard, M. Ashikhmin, B. Gooch, P. Shirley, “Color transfer between images,” IEEE Comput. Graphics Appl. 21, 34–41 (2001).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

H. C. Lee, E. J. Breneman, C. P. Schulte, “Modeling light reflection for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402–409 (1990).
[CrossRef]

J. Imaging Sci. Technol. (1)

S. Tominaga, “Dichromatic reflection models for rendering object surfaces,” J. Imaging Sci. Technol. 40, 549–555 (1996).

J. Opt. Soc. Am. (1)

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

J. Soc. Dyers Colorists (1)

F. J. Clarke, R. McDonald, R. Rigg, “Modification to the JPC79 color difference formula,” J. Soc. Dyers Colorists 100, 117–148 (1984).

Other (6)

L. Peng, “Dichromatic based photographic modification,” in Proceedings of the Sixth Color Imaging Conference (Society for Imaging Science and Technology, Springfield, Va., 1998), pp. 96–99.

L. Liu, G. Xu, “Color change method based on dichromatic reflection model,” Proceedings of International Con-ference on Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 1246–1249.

H. L. Shen, J. H. Xin, “Dichromatic based rendering of texture images with high color fidelity,” J. Imaging Sci. Technol. (to be published).

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Monograph 160 (National Institute of Standards and Technology, Rockville, Md., 1997).

H. B. Westlund, G. W. Meyer, “A BRDF database employing the Beard–Maxwell reflection model,” in Graphics Interface 2002 (Canadian Human-Computer Communications Society, Mississauga, Ontario, Canada, 2002), pp. 189–200.

L. B. Wolff, S. A. Shafer, G. E. Healey, Physics-Based Vision Principles and Practice: Shape Recovery (Jones & Bartlett, Boston, Mass., 1992).

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Figures (11)

Fig. 1
Fig. 1

Geometry of incident and reflected light defined in the BRDF.

Fig. 2
Fig. 2

Reflection from an inhomogeneous surface with two components: surface reflection and body reflection (After Fig. 1 in Ref. 10).

Fig. 3
Fig. 3

Relationship between coefficient pair ( a ,   b ) and surface reflectance at different geometric positions. First, the geometric coefficient pair ( a ,   b ) can be recovered from the reflectance data at different positions (denoted y) with respect to a reference position x (left-hand part), and then ( a ,   b ) can be used to synthesize new colors for a 3-D object (right-hand part).

Fig. 4
Fig. 4

Distribution of ( a i ,   b i ) for a material with mainly body reflection.

Fig. 5
Fig. 5

Measured reflectance of four plastic cups at five different geometric positions. (a) blue cup, (b) green cup, (c) red cup, (d) yellow cup.

Fig. 6
Fig. 6

Distribution of the geometric coefficient ( a i ,   b i ) pairs for the plastic cups.

Fig. 7
Fig. 7

Calculation of the geometric coefficient ( A ,   B ) from an image. (a) An image of a plastic cup, (b) coefficient A, (c) coefficient B, (d) residual error, (e) estimated coefficient variation calculated from four plastic cups of same size but of different colors. Note that images (b)–(e) were arbitrarily scaled for display.

Fig. 8
Fig. 8

Synthesized images (top) and their corresponding target images (bottom) under the same illumination, where the geometric coefficient ( A ,   B ) for synthesis is the same as that in Fig. 7. (Figures 8,911 may be found at the website http://www.acad.polyu.edu.hk/∼tcxinjh/research/publications.htm.)

Fig. 9
Fig. 9

Color synthesis for fabrics under the same illumination condition. (a) Original blue fabric image, (b) synthesized purple fabric image, (c) target purple fabric image.

Fig. 10
Fig. 10

Color synthesis for draping fabric under different illuminations. (a) Original red fabric image under the first illumination, (b) synthesized blue fabric image under the second illumination, (c) target blue fabric image under the second illumination.

Fig. 11
Fig. 11

Color synthesis of (a) red, (b) green, and (c) blue plastic cups by the color transfer method. The target images were the same as those in Fig. 8.

Tables (3)

Tables Icon

Table 1 Color Difference Δ E CMC ( 1 : 1 ) * between Synthesized and Measured Reflectance with Use of Different ( a i ,   b i ) Pairs for the Four Plastic Cups a

Tables Icon

Table 2 Color Difference Δ E CMC ( 1 : 1 ) * between Synthesized and Measured Reflectance with Use of Different ( a i ,   b i ) Pairs for the Three Fabrics

Tables Icon

Table 3 Estimated Reflectance Difference E for Two Types of Materials

Equations (35)

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f r ( θ i ,   ϕ i ;   θ r ,   ϕ r ;   λ ) = d L r ( θ i ,   ϕ i ;   θ r ,   ϕ r ;   λ ;   E i ) d E i ( θ i ,   ϕ i ;   λ ) ,
L r ( θ r ,   ϕ r ;   λ ) = - π π 0 π / 2 f r ( θ i ,   ϕ i ;   θ r ,   ϕ r ;   λ ) L i × ( θ i ,   ϕ i ;   λ ) cos   θ i sin   θ i d θ i d ϕ i .
L i ( θ i ,   ϕ i ;   λ ) = L ( λ ) δ ( θ i - θ ) ,
δ ( θ i - θ ) = 1 , θ i = θ 0 , θ i θ .
L r ( θ r ,   ϕ r ;   λ ) = 1 2   L ( λ ) cos   2 θ - π π f r ( θ ,   ϕ i ;   θ r ,   ϕ r ;   λ ) d ϕ i .
f ¯ r ( θ r ,   ϕ r ;   λ ) = 1 2 cos   2 θ - π π f r ( θ ,   ϕ i ;   θ r ,   ϕ r ;   λ ) d ϕ i .
L r ( θ r ,   ϕ r ;   λ ) = L ( λ ) f ¯ r ( θ r ,   ϕ r ;   λ ) .
E p ( λ ) = c ( α ) L ( λ ) f ¯ r ( θ r ,   ϕ r ;   λ ) ,
V k = E p ( λ ) S k ( λ ) d λ = c ( α ) L ( λ ) S k ( λ ) f ¯ r ( θ r ,   ϕ r ;   λ ) d λ .
R ( x ;   λ ) f ¯ r ( θ r ,   ϕ r ;   λ ) .
V k x = c ( α x ) L ( λ ) S k ( λ ) R ( x ;   λ ) d λ ,
R ( x ;   λ ) g b ( x ) R b ( λ ) + g s ( x ) R s ( λ ) ,
R ( x ;   λ ) g b ( x ) R b ( λ ) + g s ( x ) R s .
R ( y ;   λ ) g b ( y ) R b ( λ ) + g s ( y ) R s .
R ( y ;   λ ) = aR ( x ;   λ ) + b + ( λ ) ,
a = g b ( y ) g b ( x ) ,
b = R s g s ( y ) - g b ( y ) g b ( x )   g s ( x ) .
w ( λ ) [ R ( y ;   λ ) - R * ( y ;   λ ) ] 2 d λ ,
R i ( y ;   λ ) = a i R i ( x ;   λ ) + b i + i ( λ ) ,
R a ( y ;   λ ) = a i R a ( x ;   λ ) + b i + i a ( λ ) for i = 1 N ,
( a i ,   b i ) ( a j ,   b j ) for i j .
E = R 1 N i = 1 N | ( a ¯ R + b ¯ ) - ( a i R + b i ) | p ( R ) d R ,
E = 1 N R i = 1 N | ( a ¯ - a i ) R + ( b ¯ - b i ) | p ( R ) d R .
| α 1 + α 2 | | α 1 | + | α 2 | ,
E 1 N i = 1 N | a ¯ - a i | R p ( R ) R d R + 1 N i = 1 N | b ¯ - b i | R p ( R ) d R .
E 1 2 N i = 1 N ( | a ¯ - a i | + 2 | b ¯ - b i | ) .
V k y = c ( α y ) L ( λ ) S k ( λ ) R ( y ;   λ ) d λ ,
V k y = c ( α y ) L ( λ ) S k ( λ ) ( aR ( x ;   λ ) + b ) d λ = c ( α y ) a L ( λ ) S k ( λ ) R ( x ;   λ ) d λ + b L ( λ ) S k ( λ ) d λ = AV k x + BW k ,
A = c ( α y ) c ( α x )   a ,
B = c ( α y ) b ,
W k = L ( λ ) S k ( λ ) d λ .
V = [ ( V 1 y - V ^ 1 y ) 2 + ( V 2 y - V ^ 2 y ) 2 + ( V 3 y - V ^ 3 y ) 2 ] 1 / 2 .
E V 1 N i = 1 N ( 128 | A ¯ - A i | + | B ¯ - B i | ) ,
V ˜ k x = c ( α x ) L ˜ ( λ ) S k ( λ ) R ˜ ( x ;   λ ) d λ .
V ˜ k y = A V ˜ k x + B   L ˜ ( λ ) S k ( λ ) d λ L ( λ ) S k ( λ ) d λ = A V ˜ k x + B   W ˜ k W k ,

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