Abstract

Moment invariants previously developed for the analysis of two-dimensional patterns and objects regardless of orientation, scale, and position are extended to the Fourier transform domain to quantify signatures of textures in the power spectrum of images. The moment invariants of the power spectrum, which we call spectral moment invariants (SMIs), systematically extract rotation- and scale-invariant texture features by complex spectral moments instead of by performing ad hoc measurements of the shape of the two-dimensional power spectrum as do most of the existing Fourier transform domain methods. To our knowledge, the method of using SMIs to quantify texture features is the first to extract invariant texture information directly from the Fourier spectrum. The discriminative capability of SMIs in recognizing rotation- and scale-independent texture features is demonstrated by texture classification experiments. The results indicate that algorithms using SMIs can achieve performances comparable with, or better than, those algorithms using the spatial or wavelet transform domain texture features.

© 2007 Optical Society of America

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  3. R. M. Haralick, "Statistical and structural approaches to texture," in Proc. IEEE 67, 786-804 (1979).
  4. K. Jafari-Khouzani and H. Soltanian-Zadeh, "Radon transform orientation estimation for rotation invariant texture analysis," IEEE Trans. Pattern Anal. Mach. Intell. 27, 1004-1008 (2005).
  5. X. Tang and W. K. Stewart, "Optical and sonar image classification: wavelet packet transforms vs. Fourier transforms," Comput. Vis. Image Underst. 79, 25-46 (2000).
  6. A. C. Bovik, M. Clark, and W. S. Geisler, "Multichannel texture analysis using localized spatial filters," IEEE Trans. Pattern Anal. Mach. Intell. 12, 55-73 (1990).
    [CrossRef]
  7. D. Dunn, W. E. Higgins, and J. Wakeley, "Texture segmentation using 2-D Gabor elementary functions," IEEE Trans. Pattern Anal. Mach. Intell. 16, 130-149 (1994).
    [CrossRef]
  8. P. Couteron, N. Barbier, and D. Gautier, "Textural ordination based on Fourier spectral decomposition: a method to analyze and compare landscape patterns," Landscape Ecol. 21, 555-567 (2006).
  9. T. Randen and J. H. Husøy, "Filtering for texture classification: a comparative study," IEEE Trans. Pattern Anal. Mach. Intell. 21, 291-310 (1999).
    [CrossRef]
  10. R. Porter and N. Canagarajah, "Robust rotation-invariant texture classification: wavelet, Gabor filter and GMRF based schemes," IEE Proc. Vision Image Signal Process. 144, 108-188 (1997).
    [CrossRef]
  11. S. Fountain, T. Tan, and K. Baker, "A comparative study of rotation invariant classification and retrieval of texture images," in Proceedings of the British Machine Vision Conference 1998 (British Machine Vision Association, 1998), pp. 266-275.
  12. R. Bajcsy, "Computer description of textured surfaces," in Proceedings of the Third International Joint Conference on Artificial Intelligence (International Joint Conference on Artificial Intelligence, 1973), pp. 572-579.
  13. S. S. Liu and M. E. Jernigan, "Texture analysis and discrimination in additive noise," Comput. Vis. Graph. Image Process. 49, 52-67 (1990).
    [CrossRef]
  14. B. Julesz, "Visual pattern discrimination," IEEE Trans. Inf. Theory 8, 84-92 (1962).
  15. B. Julesz, "A theory of preattentive texture discrimination based on first-order statistics of textons," Biol. Cybern. 41, 131-138 (1981).
  16. B. Julesz, "Spatial nonlinearities in the instantaneous perception of textures with identical power spectra," Philos. Trans. R. Soc. London, Ser. B 29, 83-94 (1980).
  17. H. Lin, L. Wang, and S. Yang, "Extracting periodicity of a regular texture based on autocorrelation functions," Pattern Recogn. Lett. 18, 433-443 (1997).
  18. J. S. Weszka, C. R. Dyer, and A. Rosenfeld, "A comparative study of texture measures for terrain classification," IEEE Trans. Syst. Man Cybern. 6, 269-285 (1976).
  19. P. Campisi, G. Panci, and G. Scarano, "Robust rotation-invariant texture classification using a model based approach," IEEE Trans. Image Process. 13, 782-791 (2004).
  20. M. K. Hu, "Visual pattern recognition by moment invariants," IRE Trans. Inf. Theory 49, 179-187 (1962).
  21. Y. S. Abu-Mostafa and D. Psaltis, "Recognitive aspects of moment invariants," IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 698-806 (1984).
  22. J. Flusser, "On the independence of rotation moment invariants," Pattern Recogn. 30, 1405-1410 (2000).
  23. J. Flusser and B. Zitova, "Combined invariants to linear filtering and rotation," Int. J. Pattern Recognit. Artif. Intell. 13, 1123-1135 (1999).
  24. J. Flusser and T. Suk, "Pattern recognition by affine moment invariants," Pattern Recogn. 26, 167-174 (1993).
    [CrossRef]
  25. J. Flusser and T. Suk, "Rotation moment invariants for recognition of symmetric objects," IEEE Trans. Image Process. 15, 3784-3790 (2006).
  26. M. R. Teague, "Image analysis via the general theory of moments," J. Opt. Soc. Am. 70, 920-930 (1980).
  27. L. Wang and G. Healey, "Using Zernike moments for the illumination and geometry invariant classification of multispectral texture," IEEE Trans. Image Process. 7, 196-203 (1998).
    [CrossRef]
  28. G. Amayeh, A. Erol, G. Bebis, and M. Nicolescu, "An Accurate and efficient computation of high order Zernike moments," in International Symposium on Visual Computing (Springer, 2005), pp. 462-469.
  29. A. Khotanzad and Y. H. Hong, "Invariant image recognition by Zernike moments," IEEE Trans. Pattern Anal. Mach. Intell. 12, 489-497 (1990).
    [CrossRef]
  30. B. Ye and J. Peng, "Invariance analysis of improved Zernike moments," J. Opt. A, Pure Appl. Opt. 4, 606-614 (2002).
  31. C. H. Teh and R. T. Chin, "On image analysis by the methods of moments," IEEE Trans. Pattern Anal. Mach. Intell. 10, 496-513 (1988).
    [CrossRef]
  32. Mayang's online texture library, http://www.mayang.com/textures.
  33. Y. Ricard and R. J. Blakely, "A method to minimize edge effects in two-dimensional discrete Fourier transforms," Geophysics 53, 1113-1117 (1988).
    [CrossRef]
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  35. M. M. Leung and A. M. Peteson, "Scale and rotation invariant texture classification," in Proceedings of 26th Asilomar Conference on Signals, Systems and Computers (IEEE, 1992), pp. 461-465.

2006 (2)

P. Couteron, N. Barbier, and D. Gautier, "Textural ordination based on Fourier spectral decomposition: a method to analyze and compare landscape patterns," Landscape Ecol. 21, 555-567 (2006).

J. Flusser and T. Suk, "Rotation moment invariants for recognition of symmetric objects," IEEE Trans. Image Process. 15, 3784-3790 (2006).

2005 (1)

K. Jafari-Khouzani and H. Soltanian-Zadeh, "Radon transform orientation estimation for rotation invariant texture analysis," IEEE Trans. Pattern Anal. Mach. Intell. 27, 1004-1008 (2005).

2004 (1)

P. Campisi, G. Panci, and G. Scarano, "Robust rotation-invariant texture classification using a model based approach," IEEE Trans. Image Process. 13, 782-791 (2004).

2002 (1)

B. Ye and J. Peng, "Invariance analysis of improved Zernike moments," J. Opt. A, Pure Appl. Opt. 4, 606-614 (2002).

2000 (2)

J. Flusser, "On the independence of rotation moment invariants," Pattern Recogn. 30, 1405-1410 (2000).

X. Tang and W. K. Stewart, "Optical and sonar image classification: wavelet packet transforms vs. Fourier transforms," Comput. Vis. Image Underst. 79, 25-46 (2000).

1999 (2)

T. Randen and J. H. Husøy, "Filtering for texture classification: a comparative study," IEEE Trans. Pattern Anal. Mach. Intell. 21, 291-310 (1999).
[CrossRef]

J. Flusser and B. Zitova, "Combined invariants to linear filtering and rotation," Int. J. Pattern Recognit. Artif. Intell. 13, 1123-1135 (1999).

1998 (1)

L. Wang and G. Healey, "Using Zernike moments for the illumination and geometry invariant classification of multispectral texture," IEEE Trans. Image Process. 7, 196-203 (1998).
[CrossRef]

1997 (2)

R. Porter and N. Canagarajah, "Robust rotation-invariant texture classification: wavelet, Gabor filter and GMRF based schemes," IEE Proc. Vision Image Signal Process. 144, 108-188 (1997).
[CrossRef]

H. Lin, L. Wang, and S. Yang, "Extracting periodicity of a regular texture based on autocorrelation functions," Pattern Recogn. Lett. 18, 433-443 (1997).

1994 (1)

D. Dunn, W. E. Higgins, and J. Wakeley, "Texture segmentation using 2-D Gabor elementary functions," IEEE Trans. Pattern Anal. Mach. Intell. 16, 130-149 (1994).
[CrossRef]

1993 (1)

J. Flusser and T. Suk, "Pattern recognition by affine moment invariants," Pattern Recogn. 26, 167-174 (1993).
[CrossRef]

1990 (3)

A. Khotanzad and Y. H. Hong, "Invariant image recognition by Zernike moments," IEEE Trans. Pattern Anal. Mach. Intell. 12, 489-497 (1990).
[CrossRef]

S. S. Liu and M. E. Jernigan, "Texture analysis and discrimination in additive noise," Comput. Vis. Graph. Image Process. 49, 52-67 (1990).
[CrossRef]

A. C. Bovik, M. Clark, and W. S. Geisler, "Multichannel texture analysis using localized spatial filters," IEEE Trans. Pattern Anal. Mach. Intell. 12, 55-73 (1990).
[CrossRef]

1988 (2)

C. H. Teh and R. T. Chin, "On image analysis by the methods of moments," IEEE Trans. Pattern Anal. Mach. Intell. 10, 496-513 (1988).
[CrossRef]

Y. Ricard and R. J. Blakely, "A method to minimize edge effects in two-dimensional discrete Fourier transforms," Geophysics 53, 1113-1117 (1988).
[CrossRef]

1984 (1)

Y. S. Abu-Mostafa and D. Psaltis, "Recognitive aspects of moment invariants," IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 698-806 (1984).

1981 (1)

B. Julesz, "A theory of preattentive texture discrimination based on first-order statistics of textons," Biol. Cybern. 41, 131-138 (1981).

1980 (3)

B. Julesz, "Spatial nonlinearities in the instantaneous perception of textures with identical power spectra," Philos. Trans. R. Soc. London, Ser. B 29, 83-94 (1980).

R. W. Conners and C. A. Harlow, "A theoretical comparison of texture algorithms," IEEE Trans. Pattern Anal. Mach. Intell. PAM-2, 741-755 (1980).

M. R. Teague, "Image analysis via the general theory of moments," J. Opt. Soc. Am. 70, 920-930 (1980).

1979 (1)

R. M. Haralick, "Statistical and structural approaches to texture," in Proc. IEEE 67, 786-804 (1979).

1976 (1)

J. S. Weszka, C. R. Dyer, and A. Rosenfeld, "A comparative study of texture measures for terrain classification," IEEE Trans. Syst. Man Cybern. 6, 269-285 (1976).

1962 (2)

M. K. Hu, "Visual pattern recognition by moment invariants," IRE Trans. Inf. Theory 49, 179-187 (1962).

B. Julesz, "Visual pattern discrimination," IEEE Trans. Inf. Theory 8, 84-92 (1962).

Abu-Mostafa, Y. S.

Y. S. Abu-Mostafa and D. Psaltis, "Recognitive aspects of moment invariants," IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 698-806 (1984).

Amayeh, G.

G. Amayeh, A. Erol, G. Bebis, and M. Nicolescu, "An Accurate and efficient computation of high order Zernike moments," in International Symposium on Visual Computing (Springer, 2005), pp. 462-469.

Bajcsy, R.

R. Bajcsy, "Computer description of textured surfaces," in Proceedings of the Third International Joint Conference on Artificial Intelligence (International Joint Conference on Artificial Intelligence, 1973), pp. 572-579.

Baker, K.

S. Fountain, T. Tan, and K. Baker, "A comparative study of rotation invariant classification and retrieval of texture images," in Proceedings of the British Machine Vision Conference 1998 (British Machine Vision Association, 1998), pp. 266-275.

Barbier, N.

P. Couteron, N. Barbier, and D. Gautier, "Textural ordination based on Fourier spectral decomposition: a method to analyze and compare landscape patterns," Landscape Ecol. 21, 555-567 (2006).

Bebis, G.

G. Amayeh, A. Erol, G. Bebis, and M. Nicolescu, "An Accurate and efficient computation of high order Zernike moments," in International Symposium on Visual Computing (Springer, 2005), pp. 462-469.

Blakely, R. J.

Y. Ricard and R. J. Blakely, "A method to minimize edge effects in two-dimensional discrete Fourier transforms," Geophysics 53, 1113-1117 (1988).
[CrossRef]

Bovik, A. C.

A. C. Bovik, M. Clark, and W. S. Geisler, "Multichannel texture analysis using localized spatial filters," IEEE Trans. Pattern Anal. Mach. Intell. 12, 55-73 (1990).
[CrossRef]

Campisi, P.

P. Campisi, G. Panci, and G. Scarano, "Robust rotation-invariant texture classification using a model based approach," IEEE Trans. Image Process. 13, 782-791 (2004).

Canagarajah, N.

R. Porter and N. Canagarajah, "Robust rotation-invariant texture classification: wavelet, Gabor filter and GMRF based schemes," IEE Proc. Vision Image Signal Process. 144, 108-188 (1997).
[CrossRef]

Chin, R. T.

C. H. Teh and R. T. Chin, "On image analysis by the methods of moments," IEEE Trans. Pattern Anal. Mach. Intell. 10, 496-513 (1988).
[CrossRef]

Clark, M.

A. C. Bovik, M. Clark, and W. S. Geisler, "Multichannel texture analysis using localized spatial filters," IEEE Trans. Pattern Anal. Mach. Intell. 12, 55-73 (1990).
[CrossRef]

Conners, R. W.

R. W. Conners and C. A. Harlow, "A theoretical comparison of texture algorithms," IEEE Trans. Pattern Anal. Mach. Intell. PAM-2, 741-755 (1980).

Couteron, P.

P. Couteron, N. Barbier, and D. Gautier, "Textural ordination based on Fourier spectral decomposition: a method to analyze and compare landscape patterns," Landscape Ecol. 21, 555-567 (2006).

Dunn, D.

D. Dunn, W. E. Higgins, and J. Wakeley, "Texture segmentation using 2-D Gabor elementary functions," IEEE Trans. Pattern Anal. Mach. Intell. 16, 130-149 (1994).
[CrossRef]

Dyer, C. R.

J. S. Weszka, C. R. Dyer, and A. Rosenfeld, "A comparative study of texture measures for terrain classification," IEEE Trans. Syst. Man Cybern. 6, 269-285 (1976).

Erol, A.

G. Amayeh, A. Erol, G. Bebis, and M. Nicolescu, "An Accurate and efficient computation of high order Zernike moments," in International Symposium on Visual Computing (Springer, 2005), pp. 462-469.

Flusser, J.

J. Flusser and T. Suk, "Rotation moment invariants for recognition of symmetric objects," IEEE Trans. Image Process. 15, 3784-3790 (2006).

J. Flusser, "On the independence of rotation moment invariants," Pattern Recogn. 30, 1405-1410 (2000).

J. Flusser and B. Zitova, "Combined invariants to linear filtering and rotation," Int. J. Pattern Recognit. Artif. Intell. 13, 1123-1135 (1999).

J. Flusser and T. Suk, "Pattern recognition by affine moment invariants," Pattern Recogn. 26, 167-174 (1993).
[CrossRef]

Fountain, S.

S. Fountain, T. Tan, and K. Baker, "A comparative study of rotation invariant classification and retrieval of texture images," in Proceedings of the British Machine Vision Conference 1998 (British Machine Vision Association, 1998), pp. 266-275.

Gautier, D.

P. Couteron, N. Barbier, and D. Gautier, "Textural ordination based on Fourier spectral decomposition: a method to analyze and compare landscape patterns," Landscape Ecol. 21, 555-567 (2006).

Geisler, W. S.

A. C. Bovik, M. Clark, and W. S. Geisler, "Multichannel texture analysis using localized spatial filters," IEEE Trans. Pattern Anal. Mach. Intell. 12, 55-73 (1990).
[CrossRef]

Haralick, R. M.

R. M. Haralick, "Statistical and structural approaches to texture," in Proc. IEEE 67, 786-804 (1979).

Harlow, C. A.

R. W. Conners and C. A. Harlow, "A theoretical comparison of texture algorithms," IEEE Trans. Pattern Anal. Mach. Intell. PAM-2, 741-755 (1980).

Healey, G.

L. Wang and G. Healey, "Using Zernike moments for the illumination and geometry invariant classification of multispectral texture," IEEE Trans. Image Process. 7, 196-203 (1998).
[CrossRef]

Higgins, W. E.

D. Dunn, W. E. Higgins, and J. Wakeley, "Texture segmentation using 2-D Gabor elementary functions," IEEE Trans. Pattern Anal. Mach. Intell. 16, 130-149 (1994).
[CrossRef]

Hong, Y. H.

A. Khotanzad and Y. H. Hong, "Invariant image recognition by Zernike moments," IEEE Trans. Pattern Anal. Mach. Intell. 12, 489-497 (1990).
[CrossRef]

Hu, M. K.

M. K. Hu, "Visual pattern recognition by moment invariants," IRE Trans. Inf. Theory 49, 179-187 (1962).

Husøy, J. H.

T. Randen and J. H. Husøy, "Filtering for texture classification: a comparative study," IEEE Trans. Pattern Anal. Mach. Intell. 21, 291-310 (1999).
[CrossRef]

Jafari-Khouzani, K.

K. Jafari-Khouzani and H. Soltanian-Zadeh, "Radon transform orientation estimation for rotation invariant texture analysis," IEEE Trans. Pattern Anal. Mach. Intell. 27, 1004-1008 (2005).

Jernigan, M. E.

S. S. Liu and M. E. Jernigan, "Texture analysis and discrimination in additive noise," Comput. Vis. Graph. Image Process. 49, 52-67 (1990).
[CrossRef]

Julesz, B.

B. Julesz, "A theory of preattentive texture discrimination based on first-order statistics of textons," Biol. Cybern. 41, 131-138 (1981).

B. Julesz, "Spatial nonlinearities in the instantaneous perception of textures with identical power spectra," Philos. Trans. R. Soc. London, Ser. B 29, 83-94 (1980).

B. Julesz, "Visual pattern discrimination," IEEE Trans. Inf. Theory 8, 84-92 (1962).

Khotanzad, A.

A. Khotanzad and Y. H. Hong, "Invariant image recognition by Zernike moments," IEEE Trans. Pattern Anal. Mach. Intell. 12, 489-497 (1990).
[CrossRef]

Leung, M. M.

M. M. Leung and A. M. Peteson, "Scale and rotation invariant texture classification," in Proceedings of 26th Asilomar Conference on Signals, Systems and Computers (IEEE, 1992), pp. 461-465.

Lin, H.

H. Lin, L. Wang, and S. Yang, "Extracting periodicity of a regular texture based on autocorrelation functions," Pattern Recogn. Lett. 18, 433-443 (1997).

Liu, S. S.

S. S. Liu and M. E. Jernigan, "Texture analysis and discrimination in additive noise," Comput. Vis. Graph. Image Process. 49, 52-67 (1990).
[CrossRef]

Nicolescu, M.

G. Amayeh, A. Erol, G. Bebis, and M. Nicolescu, "An Accurate and efficient computation of high order Zernike moments," in International Symposium on Visual Computing (Springer, 2005), pp. 462-469.

Panci, G.

P. Campisi, G. Panci, and G. Scarano, "Robust rotation-invariant texture classification using a model based approach," IEEE Trans. Image Process. 13, 782-791 (2004).

Peng, J.

B. Ye and J. Peng, "Invariance analysis of improved Zernike moments," J. Opt. A, Pure Appl. Opt. 4, 606-614 (2002).

Peteson, A. M.

M. M. Leung and A. M. Peteson, "Scale and rotation invariant texture classification," in Proceedings of 26th Asilomar Conference on Signals, Systems and Computers (IEEE, 1992), pp. 461-465.

Porter, R.

R. Porter and N. Canagarajah, "Robust rotation-invariant texture classification: wavelet, Gabor filter and GMRF based schemes," IEE Proc. Vision Image Signal Process. 144, 108-188 (1997).
[CrossRef]

Psaltis, D.

Y. S. Abu-Mostafa and D. Psaltis, "Recognitive aspects of moment invariants," IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 698-806 (1984).

Randen, T.

T. Randen and J. H. Husøy, "Filtering for texture classification: a comparative study," IEEE Trans. Pattern Anal. Mach. Intell. 21, 291-310 (1999).
[CrossRef]

Ricard, Y.

Y. Ricard and R. J. Blakely, "A method to minimize edge effects in two-dimensional discrete Fourier transforms," Geophysics 53, 1113-1117 (1988).
[CrossRef]

Rosenfeld, A.

J. S. Weszka, C. R. Dyer, and A. Rosenfeld, "A comparative study of texture measures for terrain classification," IEEE Trans. Syst. Man Cybern. 6, 269-285 (1976).

Scarano, G.

P. Campisi, G. Panci, and G. Scarano, "Robust rotation-invariant texture classification using a model based approach," IEEE Trans. Image Process. 13, 782-791 (2004).

Soltanian-Zadeh, H.

K. Jafari-Khouzani and H. Soltanian-Zadeh, "Radon transform orientation estimation for rotation invariant texture analysis," IEEE Trans. Pattern Anal. Mach. Intell. 27, 1004-1008 (2005).

Stewart, W. K.

X. Tang and W. K. Stewart, "Optical and sonar image classification: wavelet packet transforms vs. Fourier transforms," Comput. Vis. Image Underst. 79, 25-46 (2000).

Suk, T.

J. Flusser and T. Suk, "Rotation moment invariants for recognition of symmetric objects," IEEE Trans. Image Process. 15, 3784-3790 (2006).

J. Flusser and T. Suk, "Pattern recognition by affine moment invariants," Pattern Recogn. 26, 167-174 (1993).
[CrossRef]

Tan, T.

J. Zhang and T. Tan, "New texture signatures and their use in rotation invariant texture classification," in Proceedings of Texture, the 2nd International Workshop on Texture Analysis and Synthesis (School of Mathematical and Computer Sciences, Heriot-Watt University, 2002) pp. 157-162.

S. Fountain, T. Tan, and K. Baker, "A comparative study of rotation invariant classification and retrieval of texture images," in Proceedings of the British Machine Vision Conference 1998 (British Machine Vision Association, 1998), pp. 266-275.

Tang, X.

X. Tang and W. K. Stewart, "Optical and sonar image classification: wavelet packet transforms vs. Fourier transforms," Comput. Vis. Image Underst. 79, 25-46 (2000).

Teague, M. R.

Teh, C. H.

C. H. Teh and R. T. Chin, "On image analysis by the methods of moments," IEEE Trans. Pattern Anal. Mach. Intell. 10, 496-513 (1988).
[CrossRef]

Wakeley, J.

D. Dunn, W. E. Higgins, and J. Wakeley, "Texture segmentation using 2-D Gabor elementary functions," IEEE Trans. Pattern Anal. Mach. Intell. 16, 130-149 (1994).
[CrossRef]

Wang, L.

L. Wang and G. Healey, "Using Zernike moments for the illumination and geometry invariant classification of multispectral texture," IEEE Trans. Image Process. 7, 196-203 (1998).
[CrossRef]

H. Lin, L. Wang, and S. Yang, "Extracting periodicity of a regular texture based on autocorrelation functions," Pattern Recogn. Lett. 18, 433-443 (1997).

Weszka, J. S.

J. S. Weszka, C. R. Dyer, and A. Rosenfeld, "A comparative study of texture measures for terrain classification," IEEE Trans. Syst. Man Cybern. 6, 269-285 (1976).

Yang, S.

H. Lin, L. Wang, and S. Yang, "Extracting periodicity of a regular texture based on autocorrelation functions," Pattern Recogn. Lett. 18, 433-443 (1997).

Ye, B.

B. Ye and J. Peng, "Invariance analysis of improved Zernike moments," J. Opt. A, Pure Appl. Opt. 4, 606-614 (2002).

Zhang, J.

J. Zhang and T. Tan, "New texture signatures and their use in rotation invariant texture classification," in Proceedings of Texture, the 2nd International Workshop on Texture Analysis and Synthesis (School of Mathematical and Computer Sciences, Heriot-Watt University, 2002) pp. 157-162.

Zitova, B.

J. Flusser and B. Zitova, "Combined invariants to linear filtering and rotation," Int. J. Pattern Recognit. Artif. Intell. 13, 1123-1135 (1999).

Biol. Cybern. (1)

B. Julesz, "A theory of preattentive texture discrimination based on first-order statistics of textons," Biol. Cybern. 41, 131-138 (1981).

Comput. Vis. Graph. Image Process. (1)

S. S. Liu and M. E. Jernigan, "Texture analysis and discrimination in additive noise," Comput. Vis. Graph. Image Process. 49, 52-67 (1990).
[CrossRef]

Comput. Vis. Image Underst. (1)

X. Tang and W. K. Stewart, "Optical and sonar image classification: wavelet packet transforms vs. Fourier transforms," Comput. Vis. Image Underst. 79, 25-46 (2000).

Geophysics (1)

Y. Ricard and R. J. Blakely, "A method to minimize edge effects in two-dimensional discrete Fourier transforms," Geophysics 53, 1113-1117 (1988).
[CrossRef]

IEE Proc. Vision Image Signal Process. (1)

R. Porter and N. Canagarajah, "Robust rotation-invariant texture classification: wavelet, Gabor filter and GMRF based schemes," IEE Proc. Vision Image Signal Process. 144, 108-188 (1997).
[CrossRef]

IEEE Trans. Image Process. (3)

L. Wang and G. Healey, "Using Zernike moments for the illumination and geometry invariant classification of multispectral texture," IEEE Trans. Image Process. 7, 196-203 (1998).
[CrossRef]

P. Campisi, G. Panci, and G. Scarano, "Robust rotation-invariant texture classification using a model based approach," IEEE Trans. Image Process. 13, 782-791 (2004).

J. Flusser and T. Suk, "Rotation moment invariants for recognition of symmetric objects," IEEE Trans. Image Process. 15, 3784-3790 (2006).

IEEE Trans. Inf. Theory (1)

B. Julesz, "Visual pattern discrimination," IEEE Trans. Inf. Theory 8, 84-92 (1962).

IEEE Trans. Pattern Anal. Mach. Intell. (8)

T. Randen and J. H. Husøy, "Filtering for texture classification: a comparative study," IEEE Trans. Pattern Anal. Mach. Intell. 21, 291-310 (1999).
[CrossRef]

A. C. Bovik, M. Clark, and W. S. Geisler, "Multichannel texture analysis using localized spatial filters," IEEE Trans. Pattern Anal. Mach. Intell. 12, 55-73 (1990).
[CrossRef]

D. Dunn, W. E. Higgins, and J. Wakeley, "Texture segmentation using 2-D Gabor elementary functions," IEEE Trans. Pattern Anal. Mach. Intell. 16, 130-149 (1994).
[CrossRef]

R. W. Conners and C. A. Harlow, "A theoretical comparison of texture algorithms," IEEE Trans. Pattern Anal. Mach. Intell. PAM-2, 741-755 (1980).

K. Jafari-Khouzani and H. Soltanian-Zadeh, "Radon transform orientation estimation for rotation invariant texture analysis," IEEE Trans. Pattern Anal. Mach. Intell. 27, 1004-1008 (2005).

Y. S. Abu-Mostafa and D. Psaltis, "Recognitive aspects of moment invariants," IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 698-806 (1984).

A. Khotanzad and Y. H. Hong, "Invariant image recognition by Zernike moments," IEEE Trans. Pattern Anal. Mach. Intell. 12, 489-497 (1990).
[CrossRef]

C. H. Teh and R. T. Chin, "On image analysis by the methods of moments," IEEE Trans. Pattern Anal. Mach. Intell. 10, 496-513 (1988).
[CrossRef]

IEEE Trans. Syst. Man Cybern. (1)

J. S. Weszka, C. R. Dyer, and A. Rosenfeld, "A comparative study of texture measures for terrain classification," IEEE Trans. Syst. Man Cybern. 6, 269-285 (1976).

Int. J. Pattern Recognit. Artif. Intell. (1)

J. Flusser and B. Zitova, "Combined invariants to linear filtering and rotation," Int. J. Pattern Recognit. Artif. Intell. 13, 1123-1135 (1999).

IRE Trans. Inf. Theory (1)

M. K. Hu, "Visual pattern recognition by moment invariants," IRE Trans. Inf. Theory 49, 179-187 (1962).

J. Opt. A, Pure Appl. Opt. (1)

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Figures (4)

Fig. 1
Fig. 1

Neural network classifier with one hidden layer.

Fig. 2
Fig. 2

Texture samples from Mayang’s online texture library [32]. From left to right—row 1: T1, Bright Oil; T2, Impasto Stripes; T3, Zigzag; T4, Beehive. Row 2: T5, Solarized; T6, Artificial Wood; T7, Piano Keys; T8, Waves. Row 3: T9, Tie; T10, Silk; T11, Silk2; T12, Hard Textured Plastic. Row 4, T13, Plastic Stripes; T14, Dotted Ceramic; T15, Gray Ceramic; T16, Raked Surface. Row 5: T17, Carpet; T18, Animal Skin Plastic; T19, Fine Textile; T20, Patterned Fabric.

Fig. 3
Fig. 3

Average classification rate for rotated texture samples using the dominant spectrum method (DSM), 98.26%; SMI features (SMI), 96.67%; the wavelet domain features (WA), 94.65%; the power spectrum method (PSM), 84.47%; and the co-occurrence matrix features (CO), 81.57%.

Fig. 4
Fig. 4

Average classification rate for rotated and scaled texture samples using the SMI features (SMI), 93.85%; the Gabor wavelet features (GWA), 95.74%.

Tables (1)

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Table 1 Computation of Real-Valued SMIs from the Complex ϕ ( p , q )

Equations (17)

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PSD f ( f 1 , f 2 ) = F { corr ( f , f ) ( Δ x , Δ y ) } = F ( f 1 , f 2 ) 2 ,
m p q = + + f 1 p f 2 q PSD f ( f 1 , f 2 ) d f 1 d f 2 .
ϕ ( m ) = i k i m p 1 ( i ) q 1 ( i ) m p c ( i ) q c ( i ) .
[ x y ] = ( a 0 0 a ) ( cos α sin α sin α cos α ) [ x y ] + r 0 ,
m p q = f 1 p f 2 q PSD f ( f 1 , f 2 ) d f 1 d f 2 = a 4 f 1 p f 2 q PSD f ( a 1 f 1 cos α + a 1 f 2 sin α , a 1 f 1 sin α + a 1 f 2 cos α ) d f 1 d f 2 .
ϕ ( m ) = i k i m p 1 ( i ) q 1 ( i ) m p c ( i ) q c ( i ) = i k i m p 1 ( i ) q 1 ( i ) m p c ( i ) q c ( i ) = ϕ ( m ) .
c p q = ( f 1 + j f 2 ) p ( f 1 j f 2 ) q PSD f ( f 1 , f 2 ) d f 2 d f 2 ,
c p q = n = 0 p k = 0 q ( p n ) ( q k ) ( 1 ) q k j p + q n k m n + k , p + q n k .
c p q = 0 0 2 π ρ p + q + 1 exp { j ( p q ) ϕ } PSD f ( ρ , ϕ ) d ρ d ϕ = a 2 + ( p + q ) exp { j ( p q ) α } c p q .
c ̃ p q = c p q c 00 [ 2 ( p + q ) ] 2 = exp { j ( p q ) α } c p q c 00 [ 2 ( p + q ) ] 2 = c ̃ p q .
Φ ( C ) = { ϕ ( p , q ) = c ̃ p q c ̃ q 0 p 0 ( p q ) 2 : p q , c ̃ p q C } .
C = { c ̃ p q : p + q = 2 , 4 , 6 , 8 , 10 } ,
Φ ( C ) = { ϕ ( p , q ) = c ̃ p q c ̃ 2 , 4 ( p q ) 2 : p q p + q = 2 , 4 , 6 , 8 , 10 } .
f ̃ ( x , y ) = [ f ( x , y ) ( E [ f ( x , y ) ] ) σ ( f ( x , y ) ) ] ,
w ( r ) = { 0.54 + 0.46 cos ( 2 π r M ) for r M 2 0 for r > M 2 } ,
r = [ ( x M 2 ) 2 + ( y M 2 ) 2 ] 1 2
f ̃ w ( x , y ) = f ̃ ( x , y ) w ( r ) .

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