Abstract

We derive a sensitivity analysis for moment invariants of multidimensional distributions. These invariants have many uses in computational systems and have recently been used for illumination-invariant recognition in color images. In this context, the sensitivity analysis predicts the response of moment invariants to partial occlusion. Using the results of the sensitivity analysis, we develop a novel surface representation called the invariant profile, which captures color distribution and spatial information while remaining invariant to the spectral content of the scene illumination. Unlike for previous representations, the recognition of invariant profiles does not require illumination correction. We demonstrate the sensitivity analysis and the use of invariant profiles for recognition with a set of experiments on color images.

© 1998 Optical Society of America

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References

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  1. M. Swain, D. Ballard, “Color indexing,” Int. J. Comput. Vis. 7, 11–32 (1991).
    [CrossRef]
  2. B. Funt, G. Finlayson, “Color constant color indexing,” IEEE Trans. Pattern. Anal. Mach. Intell. 17, 522–529 (1995).
    [CrossRef]
  3. 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]
  4. D. Slater, G. Healey, “The illumination-invariant matching of deterministic local structure in color images,” IEEE Trans. Pattern. Anal. Mach. Intell. 19, 1146–1151 (1997).
    [CrossRef]
  5. G. Taubin, D. Cooper, “Object recognition based on moment (or algebraic) invariants,” in Geometric Invariance in Computer Vision, J. Mundy, A. Zisserman, eds. (MIT Press, Cambridge, Mass, 1992), pp. 375–397.
  6. D. Slater, G. Healey, “The illumination-invariant recognition of 3D objects using local color invariants,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 206–210 (1996).
    [CrossRef]
  7. G. Healey, D. Slater, “Computing illumination-invariant descriptors of spatially filtered color image regions,” IEEE Trans. Image Process. 6, 1002–1013 (1997).
    [CrossRef]
  8. G. Healey, A. Jain, “Retrieving multispectral satellite images using physics-based invariant representations,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 842–848 (1996).
    [CrossRef]
  9. R. W. Picard, T. P. Minka, “Vision texture for annotation,” Multimed. Syst. 3, 3–14 (1995).
  10. G. Finlayson, S. Chatterjee, B. Funt, “Color angular indexing.” Presented at the European Conference on Computer Vision, Cambridge, UK, May 1996.
  11. J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychonom. Sci. 1, 369–370 (1964).
  12. 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]
  13. J. P. S. Parkkinen, J. Hallikainen, T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318–322 (1989).
    [CrossRef]
  14. D. Marimont, B. Wandell, “Linear models of surface and illuminant spectra,” J. Opt. Soc. Am. A 9, 1905–1913 (1992).
    [CrossRef] [PubMed]
  15. B. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-9, 2–13 (1987).
    [CrossRef]
  16. K. Atkinson, An Introduction to Numerical Analysis (Wiley, New York, 1978).
  17. J. H. Wilkinson, The Algebraic Eigenvalue Problem (Clarendon, Oxford, 1965).
  18. G. Healey, R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern. Anal. Mach. Intell. 16, 267–276 (1994).
    [CrossRef]
  19. B. Bamieh, R. J. P. de Figueiredo, “A general moment-invariants/attributed-graph method for three-dimensional object recognition from a single image,” IEEE J. Robotics Automation 2, 31–41 (1986).
  20. R. Kondepudy, G. Healey, “Use of invariants for recognition of three-dimensional color textures,” J. Opt. Soc. Am. A 11, 3037–3049 (1994).
    [CrossRef]

1997 (2)

G. Healey, D. Slater, “Computing illumination-invariant descriptors of spatially filtered color image regions,” IEEE Trans. Image Process. 6, 1002–1013 (1997).
[CrossRef]

D. Slater, G. Healey, “The illumination-invariant matching of deterministic local structure in color images,” IEEE Trans. Pattern. Anal. Mach. Intell. 19, 1146–1151 (1997).
[CrossRef]

1996 (2)

D. Slater, G. Healey, “The illumination-invariant recognition of 3D objects using local color invariants,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 206–210 (1996).
[CrossRef]

G. Healey, A. Jain, “Retrieving multispectral satellite images using physics-based invariant representations,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 842–848 (1996).
[CrossRef]

1995 (2)

R. W. Picard, T. P. Minka, “Vision texture for annotation,” Multimed. Syst. 3, 3–14 (1995).

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

1994 (3)

1992 (1)

1991 (1)

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

1989 (1)

1987 (1)

B. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-9, 2–13 (1987).
[CrossRef]

1986 (2)

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]

B. Bamieh, R. J. P. de Figueiredo, “A general moment-invariants/attributed-graph method for three-dimensional object recognition from a single image,” IEEE J. Robotics Automation 2, 31–41 (1986).

1964 (1)

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

Atkinson, K.

K. Atkinson, An Introduction to Numerical Analysis (Wiley, New York, 1978).

Ballard, D.

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

Bamieh, B.

B. Bamieh, R. J. P. de Figueiredo, “A general moment-invariants/attributed-graph method for three-dimensional object recognition from a single image,” IEEE J. Robotics Automation 2, 31–41 (1986).

Chatterjee, S.

G. Finlayson, S. Chatterjee, B. Funt, “Color angular indexing.” Presented at the European Conference on Computer Vision, Cambridge, UK, May 1996.

Cohen, J.

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

Cooper, D.

G. Taubin, D. Cooper, “Object recognition based on moment (or algebraic) invariants,” in Geometric Invariance in Computer Vision, J. Mundy, A. Zisserman, eds. (MIT Press, Cambridge, Mass, 1992), pp. 375–397.

de Figueiredo, R. J. P.

B. Bamieh, R. J. P. de Figueiredo, “A general moment-invariants/attributed-graph method for three-dimensional object recognition from a single image,” IEEE J. Robotics Automation 2, 31–41 (1986).

Finlayson, G.

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

G. Finlayson, S. Chatterjee, B. Funt, “Color angular indexing.” Presented at the European Conference on Computer Vision, Cambridge, UK, May 1996.

Funt, B.

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

G. Finlayson, S. Chatterjee, B. Funt, “Color angular indexing.” Presented at the European Conference on Computer Vision, Cambridge, UK, May 1996.

Hallikainen, J.

Healey, G.

G. Healey, D. Slater, “Computing illumination-invariant descriptors of spatially filtered color image regions,” IEEE Trans. Image Process. 6, 1002–1013 (1997).
[CrossRef]

D. Slater, G. Healey, “The illumination-invariant matching of deterministic local structure in color images,” IEEE Trans. Pattern. Anal. Mach. Intell. 19, 1146–1151 (1997).
[CrossRef]

G. Healey, A. Jain, “Retrieving multispectral satellite images using physics-based invariant representations,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 842–848 (1996).
[CrossRef]

D. Slater, G. Healey, “The illumination-invariant recognition of 3D objects using local color invariants,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 206–210 (1996).
[CrossRef]

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]

G. Healey, R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern. Anal. Mach. Intell. 16, 267–276 (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]

Jaaskelainen, T.

Jain, A.

G. Healey, A. Jain, “Retrieving multispectral satellite images using physics-based invariant representations,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 842–848 (1996).
[CrossRef]

Kondepudy, R.

G. Healey, R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern. Anal. Mach. Intell. 16, 267–276 (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]

Maloney, L.

Marimont, D.

Minka, T. P.

R. W. Picard, T. P. Minka, “Vision texture for annotation,” Multimed. Syst. 3, 3–14 (1995).

Parkkinen, J. P. S.

Picard, R. W.

R. W. Picard, T. P. Minka, “Vision texture for annotation,” Multimed. Syst. 3, 3–14 (1995).

Slater, D.

G. Healey, D. Slater, “Computing illumination-invariant descriptors of spatially filtered color image regions,” IEEE Trans. Image Process. 6, 1002–1013 (1997).
[CrossRef]

D. Slater, G. Healey, “The illumination-invariant matching of deterministic local structure in color images,” IEEE Trans. Pattern. Anal. Mach. Intell. 19, 1146–1151 (1997).
[CrossRef]

D. Slater, G. Healey, “The illumination-invariant recognition of 3D objects using local color invariants,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 206–210 (1996).
[CrossRef]

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]

Swain, M.

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

Taubin, G.

G. Taubin, D. Cooper, “Object recognition based on moment (or algebraic) invariants,” in Geometric Invariance in Computer Vision, J. Mundy, A. Zisserman, eds. (MIT Press, Cambridge, Mass, 1992), pp. 375–397.

Wandell, B.

D. Marimont, B. Wandell, “Linear models of surface and illuminant spectra,” J. Opt. Soc. Am. A 9, 1905–1913 (1992).
[CrossRef] [PubMed]

B. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-9, 2–13 (1987).
[CrossRef]

Wilkinson, J. H.

J. H. Wilkinson, The Algebraic Eigenvalue Problem (Clarendon, Oxford, 1965).

IEEE J. Robotics Automation (1)

B. Bamieh, R. J. P. de Figueiredo, “A general moment-invariants/attributed-graph method for three-dimensional object recognition from a single image,” IEEE J. Robotics Automation 2, 31–41 (1986).

IEEE Trans. Image Process. (1)

G. Healey, D. Slater, “Computing illumination-invariant descriptors of spatially filtered color image regions,” IEEE Trans. Image Process. 6, 1002–1013 (1997).
[CrossRef]

IEEE Trans. Pattern. Anal. Mach. Intell. (6)

G. Healey, A. Jain, “Retrieving multispectral satellite images using physics-based invariant representations,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 842–848 (1996).
[CrossRef]

D. Slater, G. Healey, “The illumination-invariant matching of deterministic local structure in color images,” IEEE Trans. Pattern. Anal. Mach. Intell. 19, 1146–1151 (1997).
[CrossRef]

D. Slater, G. Healey, “The illumination-invariant recognition of 3D objects using local color invariants,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 206–210 (1996).
[CrossRef]

B. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-9, 2–13 (1987).
[CrossRef]

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

G. Healey, R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern. Anal. Mach. Intell. 16, 267–276 (1994).
[CrossRef]

Int. J. Comput. Vis. (1)

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

J. Opt. Soc. Am. A (5)

Multimed. Syst. (1)

R. W. Picard, T. P. Minka, “Vision texture for annotation,” Multimed. Syst. 3, 3–14 (1995).

Psychonom. Sci. (1)

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

Other (4)

G. Taubin, D. Cooper, “Object recognition based on moment (or algebraic) invariants,” in Geometric Invariance in Computer Vision, J. Mundy, A. Zisserman, eds. (MIT Press, Cambridge, Mass, 1992), pp. 375–397.

G. Finlayson, S. Chatterjee, B. Funt, “Color angular indexing.” Presented at the European Conference on Computer Vision, Cambridge, UK, May 1996.

K. Atkinson, An Introduction to Numerical Analysis (Wiley, New York, 1978).

J. H. Wilkinson, The Algebraic Eigenvalue Problem (Clarendon, Oxford, 1965).

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Figures (23)

Fig. 1
Fig. 1

Perturbation example 1.

Fig. 2
Fig. 2

Perturbation example 2.

Fig. 3
Fig. 3

Perturbation example 3.

Fig. 4
Fig. 4

Toy block.

Fig. 5
Fig. 5

Computed invariants for R(t) on the toy block surface, 0<t60.

Fig. 6
Fig. 6

Database of image regions used to compute invariant profiles.

Fig. 7
Fig. 7

Matches, green illumination.

Fig. 8
Fig. 8

Invariant profiles for matching region 1.

Fig. 9
Fig. 9

Invariant profiles for matching region 2.

Fig. 10
Fig. 10

Matches, green illumination.

Fig. 11
Fig. 11

Invariant profiles for matching region 1.

Fig. 12
Fig. 12

Invariant profiles for matching region 2.

Fig. 13
Fig. 13

Matches, red illumination.

Fig. 14
Fig. 14

Invariant profiles for matching region 1.

Fig. 15
Fig. 15

Invariant profiles for matching region 2.

Fig. 16
Fig. 16

Match, red illumination.

Fig. 17
Fig. 17

Invariant profiles for matching region.

Fig. 18
Fig. 18

Matches, yellow illumination.

Fig. 19
Fig. 19

Invariant profiles for matching region 1.

Fig. 20
Fig. 20

Invariant profiles for matching region 2.

Fig. 21
Fig. 21

Match, yellow illumination.

Fig. 22
Fig. 22

Invariant profiles for matching region.

Fig. 23
Fig. 23

Approximation error.

Equations (14)

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

ρi(x, y)=λl(λ)s(x, y, λ)fi(λ)dλ,1in,
s(x, y, λ)=j=1mσj(x, y)Sj(λ),
ρ(x, y)=Aσ(x, y),
ρ˜(x, y)=Mρ(x, y),
H˜(ρ)=H(Mρ),
Hˆ(ρ)=H(ρ)+i=1Nαihi(ρ),
hi(ρ)=1ρ=ρi0otherwise,
Hˆ(ρ)Hˆ(Lρ)=H(ρ)+i=1Nαihi(ρ),
BˆB+E,
|λˆi-λi|E,1i6,
I(t)=I(at),
Ij(t)=I(ajt),1jK,
=min1jKi=16[Ti(t)-Iij(t)]2dt,
1H(ρ)dρH(ρ)ρˆ142ρˆ13ρˆ22ρˆ13ρˆ32ρˆ12ρˆ222ρˆ12ρˆ2ρˆ32ρˆ12ρˆ322ρˆ13ρˆ22ρˆ12ρˆ22ρˆ12ρˆ2ρˆ3ρˆ1ρˆ232ρˆ1ρˆ22ρˆ3ρˆ1ρˆ2ρˆ322ρˆ13ρˆ32ρˆ12ρˆ2ρˆ3ρˆ12ρˆ32ρˆ1ρˆ22ρˆ32ρˆ1ρˆ2ρˆ32ρˆ1ρˆ332ρˆ12ρˆ222ρˆ1ρˆ232ρˆ1ρˆ22ρˆ32ρˆ242ρˆ23ρˆ32ρˆ22ρˆ322ρˆ12ρˆ2ρˆ32ρˆ1ρˆ22ρˆ3ρˆ1ρˆ2ρˆ32ρˆ23ρˆ32ρˆ22ρˆ32ρˆ2ρˆ332ρˆ12ρˆ322ρˆ1ρˆ2ρˆ322ρˆ1ρˆ332ρˆ22ρˆ322ρˆ2ρˆ332ρˆ342dρ.

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