Abstract

In this paper, a method to characterize texture images based on discrete Tchebichef moments is presented. A global signature vector is derived from the moment matrix by taking into account both the magnitudes of the moments and their order. The performance of our method in several texture classification problems was compared with that achieved through other standard approaches. These include Haralick’s gray-level co-occurrence matrices, Gabor filters, and local binary patterns. An extensive texture classification study was carried out by selecting images with different contents from the Brodatz, Outex, and VisTex databases. The results show that the proposed method is able to capture the essential information about texture, showing comparable or even higher performance than conventional procedures. Thus, it can be considered as an effective and competitive technique for texture characterization.

© 2013 Optical Society of America

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    [CrossRef]
  40. F. Bianconi and A. Fernández, “Evaluation of the effects of Gabor filter parameters on texture classification,” Pattern Recogn. 40, 3325–3335 (2007).
    [CrossRef]
  41. P. Gallinari, S. Thiria, F. Badran, and F. Fogelman-Soulie, “On the relations between discriminant analysis and multilayer perceptrons,” Neural Networks 4, 349–360 (1991).
    [CrossRef]
  42. R. Mukundan, “A new class of rotational invariants using discrete orthogonal moments,” in Proceedings of the 6th IASTED International Conference on Signal and Image Processing (IASTED, 2004), pp. 80–84.
  43. H. Zhu, H. Shu, T. Xia, L. Luo, and J. L. Coatrieux, “Translation and scale invariants of Tchebichef moments,” Pattern Recogn. 40, 2530–2542 (2007).
    [CrossRef]

2012 (1)

K. H. Thung, R. Paramesan, and C. L. Lim, “Content-based image quality metric using similarity measure of moment vectors,” Pattern Recogn. 45, 2193–2204 (2012).
[CrossRef]

2010 (1)

C. Y. Wee, R. Paramesran, R. Mukundan, and X. Jiang, “Image quality assessment by discrete orthogonal moments,” Pattern Recogn. 43, 4055–4068 (2010).
[CrossRef]

2009 (2)

C. Deng, X. Gao, X. Li, and D. Tao, “A local Tchebichef moments-based robust image watermarking,” Signal Process. 89, 1531–1539 (2009).
[CrossRef]

B. Li and M. Q. H. Meng, “Computer-aided detection of bleeding regions for capsule endoscopy images,” IEEE Trans. Biomed. Eng. 56, 1032–1039 (2009).
[CrossRef]

2008 (1)

V. S. Bharathi and L. Ganesan, “Orthogonal moments based texture analysis of CT liver images,” Pattern Recogn. Lett. 29, 1868–1872 (2008).
[CrossRef]

2007 (6)

K. Nakagaki and R. Mukundan, “A fast 4×4 forward discrete Tchebichef transform algorithm,” IEEE Signal Process. Lett. 14, 684–687 (2007).
[CrossRef]

B. Bayraktar, T. Bernas, J. P. Robinson, and B. Rajwa, “A numerical recipe for accurate image reconstruction from discrete orthogonal moments,” Pattern Recogn. 40, 659–669 (2007).
[CrossRef]

K. W. See, K. S. Loke, P. A. Lee, and K. F. Loe, “Image reconstruction using various discrete orthogonal polynomials in comparison with DCT,” Appl. Math. Comput. 193, 346–359 (2007).
[CrossRef]

F. Bianconi and A. Fernández, “Evaluation of the effects of Gabor filter parameters on texture classification,” Pattern Recogn. 40, 3325–3335 (2007).
[CrossRef]

H. Zhu, H. Shu, T. Xia, L. Luo, and J. L. Coatrieux, “Translation and scale invariants of Tchebichef moments,” Pattern Recogn. 40, 2530–2542 (2007).
[CrossRef]

M. Wang and A. Knoesen, “Rotation- and scale-invariant texture features based on spectral moment invariants,” J. Opt. Soc. Am. A 24, 2550–2557 (2007).
[CrossRef]

2004 (3)

R. Mukundan, “Some computational aspects of discrete orthonormal moments,” IEEE Trans. Image Process. 13, 1055–1059 (2004).
[CrossRef]

P. T. Yap and P. Raveendran, “Image focus measure based on Chebyshev moments,” IEEE Proc. Vis. Image Sig. Proc. 151, 128–136 (2004).
[CrossRef]

J. Daugman, “How iris recognition works,” IEEE Trans. Circuits Syst. Video Technol. 14, 21–30 (2004).
[CrossRef]

2003 (3)

X. Liu and D. Wang, “Texture classification using spectral histograms,” IEEE Trans. Image Process. 12, 661–670 (2003).
[CrossRef]

S. Arivazhagan and L. Ganesan, “Texture classification using wavelet transform,” Pattern Recogn. Lett. 24, 1513–1521 (2003).
[CrossRef]

P. T. Yap, R. Paramesran, and S. H. Ong, “Image analysis by Krawtchouk moments,” IEEE Trans. Image Process. 12, 1367–1377 (2003).
[CrossRef]

2002 (1)

T. Ojala, M. Pietikäinen, and T. Mäenpää, “Multiresolution gray-scale and rotation invariant texture classification with local binary patterns,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 971–987 (2002).
[CrossRef]

2001 (2)

R. Mukundan, S. H. Ong, and P. A. Lee, “Image analysis by Tchebichef moments,” IEEE Trans. Image Process. 10, 1357–1364 (2001).
[CrossRef]

D. G. Sim, H. K. Kim, and R. H. Park, “Fast texture description and retrieval of DCT-based compressed images,” Electron. Lett. 37, 18–19 (2001).
[CrossRef]

1999 (3)

G. M. Haley and B. S. Manjunath, “Rotation-invariant texture classification using a complete space-frequency model,” IEEE Trans. Image Process. 8, 255–269 (1999).
[CrossRef]

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

L. K. Soh and C. Tsatsoulis, “Texture analysis of SAR sea ice imagery using gray level co-occurrence matrices,” IEEE Trans. Geosci. Remote Sens. 37, 780–795 (1999).
[CrossRef]

1996 (1)

S. X. Liao and M. Pawlak, “On image analysis by moments,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 254–266 (1996).
[CrossRef]

1994 (1)

J. Bigun and J. M. Hans du Buf, “N-folded symmetries by complex moments in Gabor space and their application to unsupervised texture segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 80–87 (1994).
[CrossRef]

1991 (2)

A. K. Jain and F. Farrokhnia, “Unsupervised texture segmentation using Gabor filters,” Pattern Recogn. 24, 1167–1186 (1991).
[CrossRef]

P. Gallinari, S. Thiria, F. Badran, and F. Fogelman-Soulie, “On the relations between discriminant analysis and multilayer perceptrons,” Neural Networks 4, 349–360 (1991).
[CrossRef]

1989 (1)

J. H. Friedman, “Regularized discriminant analysis,” J. Am. Stat. Assoc. 84, 165–175 (1989).
[CrossRef]

1988 (1)

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]

1987 (1)

J. Beck, A. Sutter, and R. Ivry, “Spatial frequency channels and perceptual grouping in texture segregation,” Comput. Graph. Image Process. 37, 299–325 (1987).
[CrossRef]

1985 (1)

1980 (2)

M. R. Teague, “Image analysis via the general theory of moments,” J. Opt. Soc. Am. 70, 920–930 (1980).
[CrossRef]

J. G. Daugman, “Two-dimensional spectral analysis of cortical receptive fields profile,” Vis. Res. 20, 847–856 (1980).
[CrossRef]

1973 (1)

R. M. Haralick, K. Shanmugam, and I. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern. 3, 610–621 (1973).
[CrossRef]

1962 (1)

M. K. Hu, “Visual pattern recognition by moment invariants,” IEEE Trans. Inf. Theory 8, 179–187 (1962).

Arivazhagan, S.

S. Arivazhagan and L. Ganesan, “Texture classification using wavelet transform,” Pattern Recogn. Lett. 24, 1513–1521 (2003).
[CrossRef]

Badran, F.

P. Gallinari, S. Thiria, F. Badran, and F. Fogelman-Soulie, “On the relations between discriminant analysis and multilayer perceptrons,” Neural Networks 4, 349–360 (1991).
[CrossRef]

Bayraktar, B.

B. Bayraktar, T. Bernas, J. P. Robinson, and B. Rajwa, “A numerical recipe for accurate image reconstruction from discrete orthogonal moments,” Pattern Recogn. 40, 659–669 (2007).
[CrossRef]

Beck, J.

J. Beck, A. Sutter, and R. Ivry, “Spatial frequency channels and perceptual grouping in texture segregation,” Comput. Graph. Image Process. 37, 299–325 (1987).
[CrossRef]

Bernas, T.

B. Bayraktar, T. Bernas, J. P. Robinson, and B. Rajwa, “A numerical recipe for accurate image reconstruction from discrete orthogonal moments,” Pattern Recogn. 40, 659–669 (2007).
[CrossRef]

Bharathi, V. S.

V. S. Bharathi and L. Ganesan, “Orthogonal moments based texture analysis of CT liver images,” Pattern Recogn. Lett. 29, 1868–1872 (2008).
[CrossRef]

Bianconi, F.

F. Bianconi and A. Fernández, “Evaluation of the effects of Gabor filter parameters on texture classification,” Pattern Recogn. 40, 3325–3335 (2007).
[CrossRef]

Bigun, J.

J. Bigun and J. M. Hans du Buf, “N-folded symmetries by complex moments in Gabor space and their application to unsupervised texture segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 80–87 (1994).
[CrossRef]

Bishop, C. M.

C. M. Bishop, Neural Networks for Pattern Recognition (Oxford University, 1995).

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]

Coatrieux, J. L.

H. Zhu, H. Shu, T. Xia, L. Luo, and J. L. Coatrieux, “Translation and scale invariants of Tchebichef moments,” Pattern Recogn. 40, 2530–2542 (2007).
[CrossRef]

K. Wu, C. Garnier, J. L. Coatrieux, and H. Shu, “A preliminary study of moment-based texture analysis for medical images,” in Proceedings of the 32nd Annual International Conference of the IEEE-EMBS (IEEE, 2010), pp. 5581–5584.

Daugman, J.

J. Daugman, “How iris recognition works,” IEEE Trans. Circuits Syst. Video Technol. 14, 21–30 (2004).
[CrossRef]

Daugman, J. G.

Deng, C.

C. Deng, X. Gao, X. Li, and D. Tao, “A local Tchebichef moments-based robust image watermarking,” Signal Process. 89, 1531–1539 (2009).
[CrossRef]

Dinstein, I.

R. M. Haralick, K. Shanmugam, and I. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern. 3, 610–621 (1973).
[CrossRef]

Farrokhnia, F.

A. K. Jain and F. Farrokhnia, “Unsupervised texture segmentation using Gabor filters,” Pattern Recogn. 24, 1167–1186 (1991).
[CrossRef]

Fernández, A.

F. Bianconi and A. Fernández, “Evaluation of the effects of Gabor filter parameters on texture classification,” Pattern Recogn. 40, 3325–3335 (2007).
[CrossRef]

Flusser, J.

J. Flusser, T. Suk, and B. Zitová, Moments and Moment Invariants in Pattern Recognition (Wiley, 2009).

Fogelman-Soulie, F.

P. Gallinari, S. Thiria, F. Badran, and F. Fogelman-Soulie, “On the relations between discriminant analysis and multilayer perceptrons,” Neural Networks 4, 349–360 (1991).
[CrossRef]

Friedman, J. H.

J. H. Friedman, “Regularized discriminant analysis,” J. Am. Stat. Assoc. 84, 165–175 (1989).
[CrossRef]

Gallinari, P.

P. Gallinari, S. Thiria, F. Badran, and F. Fogelman-Soulie, “On the relations between discriminant analysis and multilayer perceptrons,” Neural Networks 4, 349–360 (1991).
[CrossRef]

Ganesan, L.

V. S. Bharathi and L. Ganesan, “Orthogonal moments based texture analysis of CT liver images,” Pattern Recogn. Lett. 29, 1868–1872 (2008).
[CrossRef]

S. Arivazhagan and L. Ganesan, “Texture classification using wavelet transform,” Pattern Recogn. Lett. 24, 1513–1521 (2003).
[CrossRef]

Gao, X.

C. Deng, X. Gao, X. Li, and D. Tao, “A local Tchebichef moments-based robust image watermarking,” Signal Process. 89, 1531–1539 (2009).
[CrossRef]

Garnier, C.

K. Wu, C. Garnier, J. L. Coatrieux, and H. Shu, “A preliminary study of moment-based texture analysis for medical images,” in Proceedings of the 32nd Annual International Conference of the IEEE-EMBS (IEEE, 2010), pp. 5581–5584.

Haley, G. M.

G. M. Haley and B. S. Manjunath, “Rotation-invariant texture classification using a complete space-frequency model,” IEEE Trans. Image Process. 8, 255–269 (1999).
[CrossRef]

Hans du Buf, J. M.

J. Bigun and J. M. Hans du Buf, “N-folded symmetries by complex moments in Gabor space and their application to unsupervised texture segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 80–87 (1994).
[CrossRef]

Haralick, R. M.

R. M. Haralick, K. Shanmugam, and I. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern. 3, 610–621 (1973).
[CrossRef]

Hu, M. K.

M. K. Hu, “Visual pattern recognition by moment invariants,” IEEE Trans. Inf. Theory 8, 179–187 (1962).

Huovinen, S.

T. Ojala, T. Mäenpää, M. Pietikäinen, J. Viertola, J. Kyllönen, and S. Huovinen, “Outex—new framework for empirical evaluation of texture analysis algorithms,” in Proceedings of the 16th International Conference on Pattern Recognition (IEEE, 2002), pp. 701–706.

Husoy, J. H.

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

Ivry, R.

J. Beck, A. Sutter, and R. Ivry, “Spatial frequency channels and perceptual grouping in texture segregation,” Comput. Graph. Image Process. 37, 299–325 (1987).
[CrossRef]

Jain, A. K.

A. K. Jain and F. Farrokhnia, “Unsupervised texture segmentation using Gabor filters,” Pattern Recogn. 24, 1167–1186 (1991).
[CrossRef]

M. Tuceryan and A. K. Jain, “Texture analysis,” in The Handbook of Pattern Recognition and Computer Vision, C. H. Chen, L. F. Pau, and P. S. P. Wang, eds. (World Scientific, 1993), 235–276.

Jiang, X.

C. Y. Wee, R. Paramesran, R. Mukundan, and X. Jiang, “Image quality assessment by discrete orthogonal moments,” Pattern Recogn. 43, 4055–4068 (2010).
[CrossRef]

Kim, H. K.

D. G. Sim, H. K. Kim, and R. H. Park, “Fast texture description and retrieval of DCT-based compressed images,” Electron. Lett. 37, 18–19 (2001).
[CrossRef]

Knoesen, A.

Kyllönen, J.

T. Ojala, T. Mäenpää, M. Pietikäinen, J. Viertola, J. Kyllönen, and S. Huovinen, “Outex—new framework for empirical evaluation of texture analysis algorithms,” in Proceedings of the 16th International Conference on Pattern Recognition (IEEE, 2002), pp. 701–706.

Lee, P. A.

K. W. See, K. S. Loke, P. A. Lee, and K. F. Loe, “Image reconstruction using various discrete orthogonal polynomials in comparison with DCT,” Appl. Math. Comput. 193, 346–359 (2007).
[CrossRef]

R. Mukundan, S. H. Ong, and P. A. Lee, “Image analysis by Tchebichef moments,” IEEE Trans. Image Process. 10, 1357–1364 (2001).
[CrossRef]

Li, B.

B. Li and M. Q. H. Meng, “Computer-aided detection of bleeding regions for capsule endoscopy images,” IEEE Trans. Biomed. Eng. 56, 1032–1039 (2009).
[CrossRef]

Li, X.

C. Deng, X. Gao, X. Li, and D. Tao, “A local Tchebichef moments-based robust image watermarking,” Signal Process. 89, 1531–1539 (2009).
[CrossRef]

Liao, S. X.

S. X. Liao and M. Pawlak, “On image analysis by moments,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 254–266 (1996).
[CrossRef]

Lim, C. L.

K. H. Thung, R. Paramesan, and C. L. Lim, “Content-based image quality metric using similarity measure of moment vectors,” Pattern Recogn. 45, 2193–2204 (2012).
[CrossRef]

Liu, X.

X. Liu and D. Wang, “Texture classification using spectral histograms,” IEEE Trans. Image Process. 12, 661–670 (2003).
[CrossRef]

Loe, K. F.

K. W. See, K. S. Loke, P. A. Lee, and K. F. Loe, “Image reconstruction using various discrete orthogonal polynomials in comparison with DCT,” Appl. Math. Comput. 193, 346–359 (2007).
[CrossRef]

Loke, K. S.

K. W. See, K. S. Loke, P. A. Lee, and K. F. Loe, “Image reconstruction using various discrete orthogonal polynomials in comparison with DCT,” Appl. Math. Comput. 193, 346–359 (2007).
[CrossRef]

Luo, L.

H. Zhu, H. Shu, T. Xia, L. Luo, and J. L. Coatrieux, “Translation and scale invariants of Tchebichef moments,” Pattern Recogn. 40, 2530–2542 (2007).
[CrossRef]

Mäenpää, T.

T. Ojala, M. Pietikäinen, and T. Mäenpää, “Multiresolution gray-scale and rotation invariant texture classification with local binary patterns,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 971–987 (2002).
[CrossRef]

T. Ojala, T. Mäenpää, M. Pietikäinen, J. Viertola, J. Kyllönen, and S. Huovinen, “Outex—new framework for empirical evaluation of texture analysis algorithms,” in Proceedings of the 16th International Conference on Pattern Recognition (IEEE, 2002), pp. 701–706.

Manjunath, B. S.

G. M. Haley and B. S. Manjunath, “Rotation-invariant texture classification using a complete space-frequency model,” IEEE Trans. Image Process. 8, 255–269 (1999).
[CrossRef]

Meng, M. Q. H.

B. Li and M. Q. H. Meng, “Computer-aided detection of bleeding regions for capsule endoscopy images,” IEEE Trans. Biomed. Eng. 56, 1032–1039 (2009).
[CrossRef]

Mukundan, R.

C. Y. Wee, R. Paramesran, R. Mukundan, and X. Jiang, “Image quality assessment by discrete orthogonal moments,” Pattern Recogn. 43, 4055–4068 (2010).
[CrossRef]

K. Nakagaki and R. Mukundan, “A fast 4×4 forward discrete Tchebichef transform algorithm,” IEEE Signal Process. Lett. 14, 684–687 (2007).
[CrossRef]

R. Mukundan, “Some computational aspects of discrete orthonormal moments,” IEEE Trans. Image Process. 13, 1055–1059 (2004).
[CrossRef]

R. Mukundan, S. H. Ong, and P. A. Lee, “Image analysis by Tchebichef moments,” IEEE Trans. Image Process. 10, 1357–1364 (2001).
[CrossRef]

R. Mukundan, “A new class of rotational invariants using discrete orthogonal moments,” in Proceedings of the 6th IASTED International Conference on Signal and Image Processing (IASTED, 2004), pp. 80–84.

Nakagaki, K.

K. Nakagaki and R. Mukundan, “A fast 4×4 forward discrete Tchebichef transform algorithm,” IEEE Signal Process. Lett. 14, 684–687 (2007).
[CrossRef]

Ojala, T.

T. Ojala, M. Pietikäinen, and T. Mäenpää, “Multiresolution gray-scale and rotation invariant texture classification with local binary patterns,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 971–987 (2002).
[CrossRef]

T. Ojala, T. Mäenpää, M. Pietikäinen, J. Viertola, J. Kyllönen, and S. Huovinen, “Outex—new framework for empirical evaluation of texture analysis algorithms,” in Proceedings of the 16th International Conference on Pattern Recognition (IEEE, 2002), pp. 701–706.

Ong, S. H.

P. T. Yap, R. Paramesran, and S. H. Ong, “Image analysis by Krawtchouk moments,” IEEE Trans. Image Process. 12, 1367–1377 (2003).
[CrossRef]

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K. H. Thung, R. Paramesan, and C. L. Lim, “Content-based image quality metric using similarity measure of moment vectors,” Pattern Recogn. 45, 2193–2204 (2012).
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Paramesran, R.

C. Y. Wee, R. Paramesran, R. Mukundan, and X. Jiang, “Image quality assessment by discrete orthogonal moments,” Pattern Recogn. 43, 4055–4068 (2010).
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P. T. Yap, R. Paramesran, and S. H. Ong, “Image analysis by Krawtchouk moments,” IEEE Trans. Image Process. 12, 1367–1377 (2003).
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D. G. Sim, H. K. Kim, and R. H. Park, “Fast texture description and retrieval of DCT-based compressed images,” Electron. Lett. 37, 18–19 (2001).
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S. X. Liao and M. Pawlak, “On image analysis by moments,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 254–266 (1996).
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T. Ojala, M. Pietikäinen, and T. Mäenpää, “Multiresolution gray-scale and rotation invariant texture classification with local binary patterns,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 971–987 (2002).
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P. T. Yap and P. Raveendran, “Image focus measure based on Chebyshev moments,” IEEE Proc. Vis. Image Sig. Proc. 151, 128–136 (2004).
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B. Bayraktar, T. Bernas, J. P. Robinson, and B. Rajwa, “A numerical recipe for accurate image reconstruction from discrete orthogonal moments,” Pattern Recogn. 40, 659–669 (2007).
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D. G. Sim, H. K. Kim, and R. H. Park, “Fast texture description and retrieval of DCT-based compressed images,” Electron. Lett. 37, 18–19 (2001).
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C. Deng, X. Gao, X. Li, and D. Tao, “A local Tchebichef moments-based robust image watermarking,” Signal Process. 89, 1531–1539 (2009).
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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).
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P. Gallinari, S. Thiria, F. Badran, and F. Fogelman-Soulie, “On the relations between discriminant analysis and multilayer perceptrons,” Neural Networks 4, 349–360 (1991).
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K. H. Thung, R. Paramesan, and C. L. Lim, “Content-based image quality metric using similarity measure of moment vectors,” Pattern Recogn. 45, 2193–2204 (2012).
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Viertola, J.

T. Ojala, T. Mäenpää, M. Pietikäinen, J. Viertola, J. Kyllönen, and S. Huovinen, “Outex—new framework for empirical evaluation of texture analysis algorithms,” in Proceedings of the 16th International Conference on Pattern Recognition (IEEE, 2002), pp. 701–706.

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A. G. Weber, “The ISC-SIPI image database,” Tech. Rep. (University of Southern California, 1997).

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C. Y. Wee, R. Paramesran, R. Mukundan, and X. Jiang, “Image quality assessment by discrete orthogonal moments,” Pattern Recogn. 43, 4055–4068 (2010).
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K. Wu, C. Garnier, J. L. Coatrieux, and H. Shu, “A preliminary study of moment-based texture analysis for medical images,” in Proceedings of the 32nd Annual International Conference of the IEEE-EMBS (IEEE, 2010), pp. 5581–5584.

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H. Zhu, H. Shu, T. Xia, L. Luo, and J. L. Coatrieux, “Translation and scale invariants of Tchebichef moments,” Pattern Recogn. 40, 2530–2542 (2007).
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P. T. Yap and P. Raveendran, “Image focus measure based on Chebyshev moments,” IEEE Proc. Vis. Image Sig. Proc. 151, 128–136 (2004).
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P. T. Yap, R. Paramesran, and S. H. Ong, “Image analysis by Krawtchouk moments,” IEEE Trans. Image Process. 12, 1367–1377 (2003).
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H. Zhu, H. Shu, T. Xia, L. Luo, and J. L. Coatrieux, “Translation and scale invariants of Tchebichef moments,” Pattern Recogn. 40, 2530–2542 (2007).
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J. Flusser, T. Suk, and B. Zitová, Moments and Moment Invariants in Pattern Recognition (Wiley, 2009).

Appl. Math. Comput. (1)

K. W. See, K. S. Loke, P. A. Lee, and K. F. Loe, “Image reconstruction using various discrete orthogonal polynomials in comparison with DCT,” Appl. Math. Comput. 193, 346–359 (2007).
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Comput. Graph. Image Process. (1)

J. Beck, A. Sutter, and R. Ivry, “Spatial frequency channels and perceptual grouping in texture segregation,” Comput. Graph. Image Process. 37, 299–325 (1987).
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Electron. Lett. (1)

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L. K. Soh and C. Tsatsoulis, “Texture analysis of SAR sea ice imagery using gray level co-occurrence matrices,” IEEE Trans. Geosci. Remote Sens. 37, 780–795 (1999).
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IEEE Trans. Image Process. (5)

X. Liu and D. Wang, “Texture classification using spectral histograms,” IEEE Trans. Image Process. 12, 661–670 (2003).
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G. M. Haley and B. S. Manjunath, “Rotation-invariant texture classification using a complete space-frequency model,” IEEE Trans. Image Process. 8, 255–269 (1999).
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R. Mukundan, “Some computational aspects of discrete orthonormal moments,” IEEE Trans. Image Process. 13, 1055–1059 (2004).
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[CrossRef]

T. Randen and J. H. Husoy, “Filtering for texture classification: a comparative study,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 291–310 (1999).
[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]

S. X. Liao and M. Pawlak, “On image analysis by moments,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 254–266 (1996).
[CrossRef]

IEEE Trans. Syst. Man Cybern. (1)

R. M. Haralick, K. Shanmugam, and I. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern. 3, 610–621 (1973).
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[CrossRef]

C. Y. Wee, R. Paramesran, R. Mukundan, and X. Jiang, “Image quality assessment by discrete orthogonal moments,” Pattern Recogn. 43, 4055–4068 (2010).
[CrossRef]

K. H. Thung, R. Paramesan, and C. L. Lim, “Content-based image quality metric using similarity measure of moment vectors,” Pattern Recogn. 45, 2193–2204 (2012).
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V. S. Bharathi and L. Ganesan, “Orthogonal moments based texture analysis of CT liver images,” Pattern Recogn. Lett. 29, 1868–1872 (2008).
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C. Deng, X. Gao, X. Li, and D. Tao, “A local Tchebichef moments-based robust image watermarking,” Signal Process. 89, 1531–1539 (2009).
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Other (8)

R. Mukundan, “A new class of rotational invariants using discrete orthogonal moments,” in Proceedings of the 6th IASTED International Conference on Signal and Image Processing (IASTED, 2004), pp. 80–84.

J. Flusser, T. Suk, and B. Zitová, Moments and Moment Invariants in Pattern Recognition (Wiley, 2009).

C. M. Bishop, Neural Networks for Pattern Recognition (Oxford University, 1995).

A. G. Weber, “The ISC-SIPI image database,” Tech. Rep. (University of Southern California, 1997).

T. Ojala, T. Mäenpää, M. Pietikäinen, J. Viertola, J. Kyllönen, and S. Huovinen, “Outex—new framework for empirical evaluation of texture analysis algorithms,” in Proceedings of the 16th International Conference on Pattern Recognition (IEEE, 2002), pp. 701–706.

MIT Media Laboratory, “VisTex Vision Texture Database,” http://vismod.media.mit.edu/vismod/imagery/VisionTexture/ .

M. Tuceryan and A. K. Jain, “Texture analysis,” in The Handbook of Pattern Recognition and Computer Vision, C. H. Chen, L. F. Pau, and P. S. P. Wang, eds. (World Scientific, 1993), 235–276.

K. Wu, C. Garnier, J. L. Coatrieux, and H. Shu, “A preliminary study of moment-based texture analysis for medical images,” in Proceedings of the 32nd Annual International Conference of the IEEE-EMBS (IEEE, 2010), pp. 5581–5584.

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Figures (5)

Fig. 1.
Fig. 1.

Complete set of Tchebichef kernels ( N = 8 ) in both (a) spatial and (b) frequency domains.

Fig. 2.
Fig. 2.

Spatial analysis of Tchebichef kernels of order s = 4 : (a)  r 0 , 4 ( x , y ) , (b)  r 1 , 3 ( x , y ) , and (c)  r 2 , 2 ( x , y ) .

Fig. 3.
Fig. 3.

Bandpass filters resulting from the combination of s -order Tchebichef kernels (highlighted bands correspond to frequency components with higher energy content).

Fig. 4.
Fig. 4.

Evolution of the SI of coefficients M ( s ) as a function of the moment order for Brodatz, Outex, and VisTex datasets.

Fig. 5.
Fig. 5.

Analysis of the SI between M ( s ) curves from the same texture captured at different orientation angles. Results computed from textures in the Brodatz dataset.

Tables (2)

Tables Icon

Table 1. Classification of Nonrotated Texturesa

Tables Icon

Table 2. Classification of Rotated Texturesa

Equations (15)

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

T p q = 1 ρ ˜ ( p , N ) ρ ˜ ( q , N ) x = 0 N 1 y = 0 N 1 t ˜ p ( x ) t ˜ q ( y ) f ( x , y ) ,
t ˜ n ( x , N ) = t n ( x , N ) / β ( n , N ) .
β ( n , N ) = [ N ( N 2 1 ) ( N 2 2 2 ) ( N 2 n 2 ) 2 n + 1 ] 1 / 2 ,
f ( x , y ) = p = 0 N 1 q = 0 N 1 T p q t ˜ p ( x ) t ˜ q ( y ) .
r p q ( x , y ) = 1 ρ ˜ ( p , N ) ρ ˜ ( q , N ) t ˜ p ( x ) t ˜ q ( y ) .
M ( s ) = p + q = s | T p q | .
g p q ( x , y ) = f ( x , y ) * r p q ( x , y ) = i = 0 N 1 j = 0 N 1 f ( i , j ) r p q ( x i , y j ) .
g p q ( x , y ) = ( 1 ) p + q f ( x , y ) r p q ( x , y ) = ( 1 ) p + q i = 0 N 1 j = 0 N 1 f ( i , j ) r p q ( i + x , j + y ) .
T p q = ( 1 ) p + q g p q ( 0 , 0 ) .
g p q ( x , y ) = DFT 1 { G p q ( u , v ) } = K u = 0 N 1 v = 0 N 1 F ( u , v ) R p q ( u , v ) exp [ j 2 π ( u x + v y N ) ] ,
T p q = ( 1 ) p + q K u = 0 N 1 v = 0 N 1 G p q ( u , v ) = ( 1 ) p + q K u = 0 N 1 v = 0 N 1 F ( u , v ) R p q ( u , v ) .
T p q = ( 1 ) p + q K u = 0 N 1 v = 0 N 1 | G p q ( u , v ) | cos [ ϕ G p q ( u , v ) ] ,
Σ k ( λ , μ ) = ( 1 μ ) Σ k ( λ ) + μ l trace [ Σ k ( λ ) ] I ,
Σ k ( λ ) = ( 1 λ ) S k + λ S ( 1 λ ) N k + λ N T .
S I = σ B 2 σ W 2 = k = 1 N C N k ( z ¯ k z ¯ ) 2 k = 1 N C i C k ( z i z ¯ k ) 2 ,

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