Abstract

We consider the problem of texture analysis with a fast algorithm. For that purpose we propose to use coefficients of the decomposition of co-occurrence matrices on an orthonormal and separable basis. We apply this method for texture discrimination, and we thus demonstrate with some examples its efficiency in terms of rapidity, discrimination performance, and robustness. We compare this method with classifiers that use a Fisher linear discrimination on features a priori defined in the co-occurrence matrices.

© 1997 Optical Society of America

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References

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  1. H. Wechler, “Texture analysis: a survey,” Signal Process. 2, 271–282 (1980).
    [CrossRef]
  2. R. M. Harralick, K. Shanmugam, I. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern.610–621 (1973).
    [CrossRef]
  3. R. M. Harralick, “Statistical and structural approach to texture,” Proc. IEEE 67, 786–804 (1979).
    [CrossRef]
  4. C. C. Gotlieb, H. E. Kreyszig, “Texture descriptors based on cooccurrence matrices,” Comput. Vision Graphics Image Process. 51, 70–86 (1990).
    [CrossRef]
  5. M. M. Galloway, “Texture analysis using gray level run lengths,” Comput. Graphics Image Process. 4, 172–179 (1975).
    [CrossRef]
  6. J. S. Weszka, C. R. Dyer, A. Rosenfeld, “A comparative study of texture for terrain classification,” IEEE Trans. Syst. Man Cybern. 6, 269–285 (1976).
    [CrossRef]
  7. K. L. Laws, “Visual pattern discrimination,” paper presented at the Image Understanding Workshop, Los Angeles, Calif., 7–8 November 1979.
  8. Z. Q. Liu, S. V. R. Madiraju, “Covariance-based approach to texture processing,” Appl. Opt. 35, 848–853 (1996).
    [CrossRef] [PubMed]
  9. F. D’Astous, M. E. Jernigan, “Texture discrimination based on detailed measures of the power spectral,” paper presented at the Seventh International Conference on Pattern Recognition, Montreal, Quebec, Canada, 30 July–2 August 1984.
  10. B. Julesz, “Visual pattern discrimination,” IRE Trans. Inf. Theory IT8, 84–92 (1962).
    [CrossRef]
  11. R. W. Conners, C. A. Harlow, “A theorical comparison of texture algorithm,” IEEE Trans. Pattern Anal. Mach. Intell. 3, 204–222 (1980).
    [CrossRef]
  12. R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

1996 (1)

1990 (1)

C. C. Gotlieb, H. E. Kreyszig, “Texture descriptors based on cooccurrence matrices,” Comput. Vision Graphics Image Process. 51, 70–86 (1990).
[CrossRef]

1980 (2)

H. Wechler, “Texture analysis: a survey,” Signal Process. 2, 271–282 (1980).
[CrossRef]

R. W. Conners, C. A. Harlow, “A theorical comparison of texture algorithm,” IEEE Trans. Pattern Anal. Mach. Intell. 3, 204–222 (1980).
[CrossRef]

1979 (1)

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

1976 (1)

J. S. Weszka, C. R. Dyer, A. Rosenfeld, “A comparative study of texture for terrain classification,” IEEE Trans. Syst. Man Cybern. 6, 269–285 (1976).
[CrossRef]

1975 (1)

M. M. Galloway, “Texture analysis using gray level run lengths,” Comput. Graphics Image Process. 4, 172–179 (1975).
[CrossRef]

1973 (1)

R. M. Harralick, K. Shanmugam, I. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern.610–621 (1973).
[CrossRef]

1962 (1)

B. Julesz, “Visual pattern discrimination,” IRE Trans. Inf. Theory IT8, 84–92 (1962).
[CrossRef]

Conners, R. W.

R. W. Conners, C. A. Harlow, “A theorical comparison of texture algorithm,” IEEE Trans. Pattern Anal. Mach. Intell. 3, 204–222 (1980).
[CrossRef]

D’Astous, F.

F. D’Astous, M. E. Jernigan, “Texture discrimination based on detailed measures of the power spectral,” paper presented at the Seventh International Conference on Pattern Recognition, Montreal, Quebec, Canada, 30 July–2 August 1984.

Dinstein, I.

R. M. Harralick, K. Shanmugam, I. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern.610–621 (1973).
[CrossRef]

Duda, R. O.

R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

Dyer, C. R.

J. S. Weszka, C. R. Dyer, A. Rosenfeld, “A comparative study of texture for terrain classification,” IEEE Trans. Syst. Man Cybern. 6, 269–285 (1976).
[CrossRef]

Galloway, M. M.

M. M. Galloway, “Texture analysis using gray level run lengths,” Comput. Graphics Image Process. 4, 172–179 (1975).
[CrossRef]

Gotlieb, C. C.

C. C. Gotlieb, H. E. Kreyszig, “Texture descriptors based on cooccurrence matrices,” Comput. Vision Graphics Image Process. 51, 70–86 (1990).
[CrossRef]

Harlow, C. A.

R. W. Conners, C. A. Harlow, “A theorical comparison of texture algorithm,” IEEE Trans. Pattern Anal. Mach. Intell. 3, 204–222 (1980).
[CrossRef]

Harralick, R. M.

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

R. M. Harralick, K. Shanmugam, I. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern.610–621 (1973).
[CrossRef]

Hart, P. E.

R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

Jernigan, M. E.

F. D’Astous, M. E. Jernigan, “Texture discrimination based on detailed measures of the power spectral,” paper presented at the Seventh International Conference on Pattern Recognition, Montreal, Quebec, Canada, 30 July–2 August 1984.

Julesz, B.

B. Julesz, “Visual pattern discrimination,” IRE Trans. Inf. Theory IT8, 84–92 (1962).
[CrossRef]

Kreyszig, H. E.

C. C. Gotlieb, H. E. Kreyszig, “Texture descriptors based on cooccurrence matrices,” Comput. Vision Graphics Image Process. 51, 70–86 (1990).
[CrossRef]

Laws, K. L.

K. L. Laws, “Visual pattern discrimination,” paper presented at the Image Understanding Workshop, Los Angeles, Calif., 7–8 November 1979.

Liu, Z. Q.

Madiraju, S. V. R.

Rosenfeld, A.

J. S. Weszka, C. R. Dyer, A. Rosenfeld, “A comparative study of texture for terrain classification,” IEEE Trans. Syst. Man Cybern. 6, 269–285 (1976).
[CrossRef]

Shanmugam, K.

R. M. Harralick, K. Shanmugam, I. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern.610–621 (1973).
[CrossRef]

Wechler, H.

H. Wechler, “Texture analysis: a survey,” Signal Process. 2, 271–282 (1980).
[CrossRef]

Weszka, J. S.

J. S. Weszka, C. R. Dyer, A. Rosenfeld, “A comparative study of texture for terrain classification,” IEEE Trans. Syst. Man Cybern. 6, 269–285 (1976).
[CrossRef]

Appl. Opt. (1)

Comput. Graphics Image Process. (1)

M. M. Galloway, “Texture analysis using gray level run lengths,” Comput. Graphics Image Process. 4, 172–179 (1975).
[CrossRef]

Comput. Vision Graphics Image Process. (1)

C. C. Gotlieb, H. E. Kreyszig, “Texture descriptors based on cooccurrence matrices,” Comput. Vision Graphics Image Process. 51, 70–86 (1990).
[CrossRef]

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

R. W. Conners, C. A. Harlow, “A theorical comparison of texture algorithm,” IEEE Trans. Pattern Anal. Mach. Intell. 3, 204–222 (1980).
[CrossRef]

IEEE Trans. Syst. Man Cybern. (2)

R. M. Harralick, K. Shanmugam, I. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern.610–621 (1973).
[CrossRef]

J. S. Weszka, C. R. Dyer, A. Rosenfeld, “A comparative study of texture for terrain classification,” IEEE Trans. Syst. Man Cybern. 6, 269–285 (1976).
[CrossRef]

IRE Trans. Inf. Theory (1)

B. Julesz, “Visual pattern discrimination,” IRE Trans. Inf. Theory IT8, 84–92 (1962).
[CrossRef]

Proc. IEEE (1)

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

Signal Process. (1)

H. Wechler, “Texture analysis: a survey,” Signal Process. 2, 271–282 (1980).
[CrossRef]

Other (3)

K. L. Laws, “Visual pattern discrimination,” paper presented at the Image Understanding Workshop, Los Angeles, Calif., 7–8 November 1979.

F. D’Astous, M. E. Jernigan, “Texture discrimination based on detailed measures of the power spectral,” paper presented at the Seventh International Conference on Pattern Recognition, Montreal, Quebec, Canada, 30 July–2 August 1984.

R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

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Figures (5)

Fig. 1
Fig. 1

Synthetic-textures image set. S 1: Gaussian noise values with the same mean. S 2: Anisotropic noise. S 3: Markovian textures. The index L denotes the design of the learning image, and the index R denotes the generalization image.

Fig. 2
Fig. 2

Natural-textures image set. N 1: Carpet and marble textures. N 2: Wood-panel and bark textures. N 3: Two Brodatz textures. The index L denotes the design of the learning image, and the index R denotes the generalization image.

Fig. 3
Fig. 3

Learning-error rate for image N 2 with respect to the threshold level.

Fig. 4
Fig. 4

Feature extraction by use of four elementary tasks.

Fig. 5
Fig. 5

Elementary decomposition of the EVBD algorithm on image S 3L: (a) The initial image. (b) The image transformed by the lookup table. (c) The product of image b with its t translated. (d) The average of the 15 × 15 image in (c). (e) The threshold of image d at Sopt.

Tables (3)

Tables Icon

Table 1 Decomposition Classifier Results

Tables Icon

Table 2 Fisher Linear Discriminant Results for the Six Features Defined in Section 4

Tables Icon

Table 3 Feature Extraction: Processing Time

Equations (21)

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

Pt=pi, j|t, i, jG2,
pi, j|t=1NTx,ySδIx, y-i δ Ix+tx, y+ty-j,
Mt=12Pt+PtT,
Mt=mi, j|t,
mi, j|t=12pi, j|t+pj, i|t.
b=FPt,
Mt=nGmG Cm,ntfnfmT.
mi, j|t=nGmG cm,ntfnifmj,
cm,nt=ijmi, j|tfnifmj.
mi, j|t=12Ntx,ySδIx, y-i×δIx+tx, y+ty-j+x,ySδIx, y-jδIx+tx, y+ty-i.
cm,nt=12NtiGjGx,ySδIx, y-i×δIx+tx, y+ty-j+x,ySδIx, y-j×δIx+tx, y+ty-ifnifmj,
cm,nt=12Ntx,ySfnIx, yfmIx+tx, y+ty+12Ntx,ySfmIx,yfnIx+tx, y+ty.
vnx, y=fnIx, y.
ρm,nt=1Ntx,ySvnx, yvmx+tx, y+ty.
cm,nt=12ρm,nt+ρn,mt.
cm,nt=i=0Ng-1j=0Ng-1fnimi, j|tfmj=fnTMtfm.
c1,1t=ρ1,1t=1Ntx,ySv1x, yv1x+tx, y+ty.
c1,1tx0, y0=1NDx,yDx0,y0 v1x, yv1x+tx, y+ty.
c1,1tx0, y0=1NDx,yDx0,y0Utx, y,
τ=100N1+N2NT,
Efn, fm=fnTMt1-Mt2fm.

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