Abstract

We represent texture in a color image by using spatial correlation functions defined within and between sensor bands. This representation has been shown to be useful for surface recognition, but the structure of spatial correlation functions depends on the spectral properties of the scene illumination. Using a linear model for surface spectral reflectance with the same number of parameters as the number of classes of photoreceptors, we show that illumination changes correspond to linear transformations of a surface correlation matrix. From this relationship we derive a distance function for comparing sets of spatial correlation functions that can be used for illumination-invariant recognition. This distance function can be computed efficiently from estimated correlation functions. We demonstrate, using a large body of experiments, that this distance function can be used for accurate surface recognition in the presence of large changes in illumination spectral distribution.

© 1995 Optical Society of America

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References

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  1. G. Healey, S. Shafer, L. Wolff, eds., Physics-Based Vision: Principles and Practice. COLOR (Jones & Bartlett, Boston, Mass., 1992).
  2. M. Nagao, T. Matsuyama, Y. Ikeda, “Region extraction and shape analysis in aerial photographs,” Comput. Graphics Image Process. 10, 195–223 (1979).
    [CrossRef]
  3. M. Swain, D. Ballard, “Color indexing,” Int. J. Comput. Vision 7, 11–32 (1991).
    [CrossRef]
  4. G. Healey, D. Slater, “Global color constancy: recognition of objects by use of illumination-invariant properties of color distributions,” J. Opt. Soc. Am. A 11, 3003–3010 (1994).
    [CrossRef]
  5. R. Chellappa, A. K. Jain, eds., Markov Random Fields: Theory and Applications (Academic, San Diego, Calif., 1993).
  6. F. S. Cohen, Z. Fan, M. S. Patel, “Classification of rotated and scaled textured images using Gaussian Markov random field models,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 192–202 (1991).
    [CrossRef]
  7. R. Haralick, “Statistical and structural approaches to texture,” Proc. IEEE 67, 786–804 (1979).
    [CrossRef]
  8. R. L. Kashyap, A. Khotanzad, “A model based method for rotation invariant texture classification,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-8, 472–481 (1986).
    [CrossRef]
  9. A. Gagalowicz, S. D. Ma, C. Tournier-Lasserve, “Efficient models for color textures,” in Proceedings of the 8th International Conference on Pattern Recognition (IEEE Computer Society Press, Washington, D.C., 1986), pp. 412–414.
  10. D. Panjwani, G. Healey, “Results using random field models for the segmentation of color images of natural scenes,” in Proceedings of the Fifth International Conference on Computer Vision (IEEE, Cambridge, Mass., 1995), pp. 714–719.
  11. D. Panjwani, G. Healey, “Selecting neighbors in random field models for color images,” in Proceedings of the First IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1994).
    [CrossRef]
  12. R. Kondepudy, G. Healey, “Use of invariants for recognition of three-dimensional color textures,” J. Opt. Soc. Am. A 11, 3037–3049 (1994).
    [CrossRef]
  13. J. Scharcanski, J. K. Hovis, H. C. Shen, “Color texture representation using multiscale feature boundaries,” in Visual Communications and Image Processing, P. Maragos, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1818, 156–165 (1992).
  14. M. Brill, “A device performing illuminant-invariant assessment of chromatic relations,” J. Theor. Biol. 71, 473–478 (1978).
    [CrossRef] [PubMed]
  15. G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
    [CrossRef]
  16. P. Sallstrom, “Colour and physics; some remarks concerning the physical aspects of human colour vision,” Tech. Rep. 73-09 (Institute of Physics, University of Stockholm, 1973).
  17. L. Maloney, B. Wandell, “Color constancy: a method for recovering surface spectral reflectance,” J. Opt. Soc. Am. A 3, 29–33 (1986).
    [CrossRef] [PubMed]
  18. J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychonom. Sci. 1, 369–370 (1964).
  19. L. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. A 3, 1673–1683 (1986).
    [CrossRef] [PubMed]
  20. J. P. S. Parkkinen, J. Hallikainen, T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318–322 (1989).
    [CrossRef]
  21. D. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vision 5, 5–36 (1990).
    [CrossRef]
  22. J. Ho, B. V. Funt, M. S. Drew, “Separating a color signal into illumination and surface reflectance components: theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966–977 (1990).
    [CrossRef]
  23. M. D’Zmura, “Color constancy: surface color from changing illumination,” J. Opt. Soc. Am. A 9, 490–493 (1992).
    [CrossRef]
  24. B. Funt, G. Finlayson, “Color constant color indexing,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 522–529 (1995).
    [CrossRef]
  25. G. H. Golub, C. F. van Loan, Matrix Computations (Johns Hopkins University Press, Baltimore, Md., 1983).

1995 (1)

B. Funt, G. Finlayson, “Color constant color indexing,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 522–529 (1995).
[CrossRef]

1994 (2)

1992 (1)

1991 (2)

F. S. Cohen, Z. Fan, M. S. Patel, “Classification of rotated and scaled textured images using Gaussian Markov random field models,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 192–202 (1991).
[CrossRef]

M. Swain, D. Ballard, “Color indexing,” Int. J. Comput. Vision 7, 11–32 (1991).
[CrossRef]

1990 (2)

D. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vision 5, 5–36 (1990).
[CrossRef]

J. Ho, B. V. Funt, M. S. Drew, “Separating a color signal into illumination and surface reflectance components: theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966–977 (1990).
[CrossRef]

1989 (1)

1986 (3)

1980 (1)

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
[CrossRef]

1979 (2)

M. Nagao, T. Matsuyama, Y. Ikeda, “Region extraction and shape analysis in aerial photographs,” Comput. Graphics Image Process. 10, 195–223 (1979).
[CrossRef]

R. Haralick, “Statistical and structural approaches to texture,” Proc. IEEE 67, 786–804 (1979).
[CrossRef]

1978 (1)

M. Brill, “A device performing illuminant-invariant assessment of chromatic relations,” J. Theor. Biol. 71, 473–478 (1978).
[CrossRef] [PubMed]

1964 (1)

J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychonom. Sci. 1, 369–370 (1964).

Ballard, D.

M. Swain, D. Ballard, “Color indexing,” Int. J. Comput. Vision 7, 11–32 (1991).
[CrossRef]

Brill, M.

M. Brill, “A device performing illuminant-invariant assessment of chromatic relations,” J. Theor. Biol. 71, 473–478 (1978).
[CrossRef] [PubMed]

Buchsbaum, G.

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
[CrossRef]

Cohen, F. S.

F. S. Cohen, Z. Fan, M. S. Patel, “Classification of rotated and scaled textured images using Gaussian Markov random field models,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 192–202 (1991).
[CrossRef]

Cohen, J.

J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychonom. Sci. 1, 369–370 (1964).

D’Zmura, M.

Drew, M. S.

J. Ho, B. V. Funt, M. S. Drew, “Separating a color signal into illumination and surface reflectance components: theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966–977 (1990).
[CrossRef]

Fan, Z.

F. S. Cohen, Z. Fan, M. S. Patel, “Classification of rotated and scaled textured images using Gaussian Markov random field models,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 192–202 (1991).
[CrossRef]

Finlayson, G.

B. Funt, G. Finlayson, “Color constant color indexing,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 522–529 (1995).
[CrossRef]

Forsyth, D.

D. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vision 5, 5–36 (1990).
[CrossRef]

Funt, B.

B. Funt, G. Finlayson, “Color constant color indexing,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 522–529 (1995).
[CrossRef]

Funt, B. V.

J. Ho, B. V. Funt, M. S. Drew, “Separating a color signal into illumination and surface reflectance components: theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966–977 (1990).
[CrossRef]

Gagalowicz, A.

A. Gagalowicz, S. D. Ma, C. Tournier-Lasserve, “Efficient models for color textures,” in Proceedings of the 8th International Conference on Pattern Recognition (IEEE Computer Society Press, Washington, D.C., 1986), pp. 412–414.

Golub, G. H.

G. H. Golub, C. F. van Loan, Matrix Computations (Johns Hopkins University Press, Baltimore, Md., 1983).

Hallikainen, J.

Haralick, R.

R. Haralick, “Statistical and structural approaches to texture,” Proc. IEEE 67, 786–804 (1979).
[CrossRef]

Healey, G.

G. Healey, D. Slater, “Global color constancy: recognition of objects by use of illumination-invariant properties of color distributions,” J. Opt. Soc. Am. A 11, 3003–3010 (1994).
[CrossRef]

R. Kondepudy, G. Healey, “Use of invariants for recognition of three-dimensional color textures,” J. Opt. Soc. Am. A 11, 3037–3049 (1994).
[CrossRef]

D. Panjwani, G. Healey, “Results using random field models for the segmentation of color images of natural scenes,” in Proceedings of the Fifth International Conference on Computer Vision (IEEE, Cambridge, Mass., 1995), pp. 714–719.

D. Panjwani, G. Healey, “Selecting neighbors in random field models for color images,” in Proceedings of the First IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1994).
[CrossRef]

Ho, J.

J. Ho, B. V. Funt, M. S. Drew, “Separating a color signal into illumination and surface reflectance components: theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966–977 (1990).
[CrossRef]

Hovis, J. K.

J. Scharcanski, J. K. Hovis, H. C. Shen, “Color texture representation using multiscale feature boundaries,” in Visual Communications and Image Processing, P. Maragos, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1818, 156–165 (1992).

Ikeda, Y.

M. Nagao, T. Matsuyama, Y. Ikeda, “Region extraction and shape analysis in aerial photographs,” Comput. Graphics Image Process. 10, 195–223 (1979).
[CrossRef]

Jaaskelainen, T.

Kashyap, R. L.

R. L. Kashyap, A. Khotanzad, “A model based method for rotation invariant texture classification,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-8, 472–481 (1986).
[CrossRef]

Khotanzad, A.

R. L. Kashyap, A. Khotanzad, “A model based method for rotation invariant texture classification,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-8, 472–481 (1986).
[CrossRef]

Kondepudy, R.

Ma, S. D.

A. Gagalowicz, S. D. Ma, C. Tournier-Lasserve, “Efficient models for color textures,” in Proceedings of the 8th International Conference on Pattern Recognition (IEEE Computer Society Press, Washington, D.C., 1986), pp. 412–414.

Maloney, L.

Matsuyama, T.

M. Nagao, T. Matsuyama, Y. Ikeda, “Region extraction and shape analysis in aerial photographs,” Comput. Graphics Image Process. 10, 195–223 (1979).
[CrossRef]

Nagao, M.

M. Nagao, T. Matsuyama, Y. Ikeda, “Region extraction and shape analysis in aerial photographs,” Comput. Graphics Image Process. 10, 195–223 (1979).
[CrossRef]

Panjwani, D.

D. Panjwani, G. Healey, “Selecting neighbors in random field models for color images,” in Proceedings of the First IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1994).
[CrossRef]

D. Panjwani, G. Healey, “Results using random field models for the segmentation of color images of natural scenes,” in Proceedings of the Fifth International Conference on Computer Vision (IEEE, Cambridge, Mass., 1995), pp. 714–719.

Parkkinen, J. P. S.

Patel, M. S.

F. S. Cohen, Z. Fan, M. S. Patel, “Classification of rotated and scaled textured images using Gaussian Markov random field models,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 192–202 (1991).
[CrossRef]

Sallstrom, P.

P. Sallstrom, “Colour and physics; some remarks concerning the physical aspects of human colour vision,” Tech. Rep. 73-09 (Institute of Physics, University of Stockholm, 1973).

Scharcanski, J.

J. Scharcanski, J. K. Hovis, H. C. Shen, “Color texture representation using multiscale feature boundaries,” in Visual Communications and Image Processing, P. Maragos, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1818, 156–165 (1992).

Shen, H. C.

J. Scharcanski, J. K. Hovis, H. C. Shen, “Color texture representation using multiscale feature boundaries,” in Visual Communications and Image Processing, P. Maragos, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1818, 156–165 (1992).

Slater, D.

Swain, M.

M. Swain, D. Ballard, “Color indexing,” Int. J. Comput. Vision 7, 11–32 (1991).
[CrossRef]

Tournier-Lasserve, C.

A. Gagalowicz, S. D. Ma, C. Tournier-Lasserve, “Efficient models for color textures,” in Proceedings of the 8th International Conference on Pattern Recognition (IEEE Computer Society Press, Washington, D.C., 1986), pp. 412–414.

van Loan, C. F.

G. H. Golub, C. F. van Loan, Matrix Computations (Johns Hopkins University Press, Baltimore, Md., 1983).

Wandell, B.

Comput. Graphics Image Process. (1)

M. Nagao, T. Matsuyama, Y. Ikeda, “Region extraction and shape analysis in aerial photographs,” Comput. Graphics Image Process. 10, 195–223 (1979).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (4)

R. L. Kashyap, A. Khotanzad, “A model based method for rotation invariant texture classification,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-8, 472–481 (1986).
[CrossRef]

F. S. Cohen, Z. Fan, M. S. Patel, “Classification of rotated and scaled textured images using Gaussian Markov random field models,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 192–202 (1991).
[CrossRef]

J. Ho, B. V. Funt, M. S. Drew, “Separating a color signal into illumination and surface reflectance components: theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966–977 (1990).
[CrossRef]

B. Funt, G. Finlayson, “Color constant color indexing,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 522–529 (1995).
[CrossRef]

Int. J. Comput. Vision (2)

D. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vision 5, 5–36 (1990).
[CrossRef]

M. Swain, D. Ballard, “Color indexing,” Int. J. Comput. Vision 7, 11–32 (1991).
[CrossRef]

J. Franklin Inst. (1)

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
[CrossRef]

J. Opt. Soc. Am. A (6)

J. Theor. Biol. (1)

M. Brill, “A device performing illuminant-invariant assessment of chromatic relations,” J. Theor. Biol. 71, 473–478 (1978).
[CrossRef] [PubMed]

Proc. IEEE (1)

R. Haralick, “Statistical and structural approaches to texture,” Proc. IEEE 67, 786–804 (1979).
[CrossRef]

Psychonom. Sci. (1)

J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychonom. Sci. 1, 369–370 (1964).

Other (8)

G. H. Golub, C. F. van Loan, Matrix Computations (Johns Hopkins University Press, Baltimore, Md., 1983).

J. Scharcanski, J. K. Hovis, H. C. Shen, “Color texture representation using multiscale feature boundaries,” in Visual Communications and Image Processing, P. Maragos, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1818, 156–165 (1992).

G. Healey, S. Shafer, L. Wolff, eds., Physics-Based Vision: Principles and Practice. COLOR (Jones & Bartlett, Boston, Mass., 1992).

P. Sallstrom, “Colour and physics; some remarks concerning the physical aspects of human colour vision,” Tech. Rep. 73-09 (Institute of Physics, University of Stockholm, 1973).

R. Chellappa, A. K. Jain, eds., Markov Random Fields: Theory and Applications (Academic, San Diego, Calif., 1993).

A. Gagalowicz, S. D. Ma, C. Tournier-Lasserve, “Efficient models for color textures,” in Proceedings of the 8th International Conference on Pattern Recognition (IEEE Computer Society Press, Washington, D.C., 1986), pp. 412–414.

D. Panjwani, G. Healey, “Results using random field models for the segmentation of color images of natural scenes,” in Proceedings of the Fifth International Conference on Computer Vision (IEEE, Cambridge, Mass., 1995), pp. 714–719.

D. Panjwani, G. Healey, “Selecting neighbors in random field models for color images,” in Proceedings of the First IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1994).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Patterned cloth (texture3).

Fig. 2
Fig. 2

Carpet (texture5).

Fig. 3
Fig. 3

Carpet (texture16).

Fig. 4
Fig. 4

Sand (texture17).

Fig. 5
Fig. 5

Tree (texture19).

Fig. 6
Fig. 6

Clouds (texture20).

Fig. 7
Fig. 7

Computed D values for texture1 under yellow illumination.

Tables (2)

Tables Icon

Table 1 Classification Results with Use of D

Tables Icon

Table 2 Results of Classification Experiments

Equations (19)

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

I i ( α , β ) = λ l ( λ ) s ( α , β , λ ) f i ( λ ) d λ ,             1 i N ,
s ( α , β , λ ) = 1 j N σ j ( α , β ) S j ( λ ) ,
I i ( α , β ) = a i T σ ( α , β )             1 i N ,
a i j = λ l ( λ ) S j ( λ ) f i ( λ ) d λ .
R i j ( n , m ) = E { [ I i ( α , β ) - I ¯ i ] [ I j ( α + n , β + m ) - I ¯ j ] } ,             1 i , j N ,
R i j ( n , m ) = E { a i T [ σ ( α , β ) - σ ¯ ] × [ σ ( α + n , β + m ) - σ ¯ ] T a j } ,
= a i T Φ ( n , m ) a j ,
Φ ( n , m ) = E { [ σ ( α , β ) - σ ¯ ] [ σ ( α + n , β + m ) - σ ¯ ] T } .
R ( n , m ) = [ R 11 ( n , m ) R 12 ( n , m ) R 13 ( n , m ) R 21 ( n , m ) R 22 ( n , m ) R 23 ( n , m ) R 31 ( n , m ) R 32 ( n , m ) R 33 ( n , m ) ] = A Φ ( n , m ) A T ,
R ( n , m ) = A Φ ( n , m ) A T ,
R ˜ ( n , m ) = A ˜ Φ ( n , m ) A ˜ T ,
R ( n , m ) = A Φ ( n , m ) A T = A A ˜ - 1 R ˜ ( n , m ) ( A ˜ T ) - 1 A T = A A ˜ - 1 R ˜ ( n , m ) ( A A ˜ - 1 ) T = M R ˜ ( n , m ) M T ,
C = [ R 11 ( 0 , 0 ) R 12 ( 0 , 0 ) R 13 ( 0 , 0 ) R 22 ( 0 , 0 ) R 23 ( 0 , 0 ) R 33 ( 0 , 0 ) R 11 ( 0 , 1 ) R 12 ( 0 , 1 ) R 13 ( 0 , 1 ) R 22 ( 0 , 1 ) R 23 ( 0 , 1 ) R 33 ( 0 , 1 ) R 11 ( 0 , 2 ) R 12 ( 0 , 2 ) R 13 ( 0 , 2 ) R 22 ( 0 , 2 ) R 23 ( 0 , 2 ) R 33 ( 0 , 2 ) R 11 ( i , j ) R 12 ( i , j ) R 13 ( i , j ) R 22 ( i , j ) R 23 ( i , j ) R 33 ( i , j ) ] .
C = C ˜ L ,
C = U Σ V T ,
C = σ 1 u 1 v 1 T + σ 2 u 2 v 2 T + + σ 6 u 6 v 6 T .
1 i 6 c i - ( k i 1 u 1 + k i 2 u 2 + + k i 6 u 6 ) 2
D = 1 i 6 c i - [ ( u 1 T c i ) u 1 + ( u 2 T c i ) u 2 + + ( u 6 T c i ) u 6 ] 2 ,
D = 1 i 6 c i - c i 2 .

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