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General Framework for Rotation Invariant Texture Classification Through Co-occurrence of Patterns

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The use of co-occurrences of patterns in image analysis has been recently suggested as one of the possible strategies to improve on the bag-of-features model. The intrinsically high number of features of the method, however, is a potential limit to its widespread application. Its extension into rotation invariant versions also requires careful consideration. In this paper we present a general, rotation invariant framework for co-occurrences of patterns and investigate possible solutions to the dimensionality problem. Using local binary patterns as bag-of-features model, we experimentally evaluate the potential advantages that co-occurrences can provide in comparison with bag-of-features. The results show that co-occurrences remarkably improve classification accuracy in some datasets, but in others the gain is negligible, or even negative. We found that this surprising outcome has an interesting explanation in terms of the degree of association between pairs of patterns in an image, and, in particular, that the higher the degree of association, the lower the gain provided by co-occurrences in comparison with bag-of-features.

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  1. 1.

    Amsterdam library of textures (ALOT). Available online at http://staff.science.uva.nl/~aloi/public_alot/ (2009). Last accessed on February 4, 2014

  2. 2.

    Bianconi, F., Fernández, A., González, E., Armesto, J.: Robust colour texture features based on ranklets and discrete Fourier transform. J. Electron. Imaging 18, 043012-1–043012-8 (2009). doi:10.1117/1.3273946

  3. 3.

    Bianconi, F., González, E., Fernández, A., Saetta, S.A.: Automatic classification of granite tiles through colour and texture features. Expert Syst. Appl. 39(12), 11212–11218 (2012). doi:10.1016/j.eswa.2012.03.052

  4. 4.

    Boureau, Y.L., Ponce, J., LeCun, Y.: A theoretical analysis of feature pooling in visual recognition. In: Proceedings of the 27th International Conference on Machine Learning (ICML-10), pp. 111–118. Haifa, Israel (2010)

  5. 5.

    Brodatz, P.: Textures: a photographic album for artists and designers. Dover Publications, New York (1966)

  6. 6.

    Burghouts, G.J., Geusebroek, J.M.: Material-specific adaptation of color invariant features. Pattern Recognit. Lett. 30(3), 306–313 (2009)

  7. 7.

    Crosier, M., Griffin, L.D.: Using basic image features for texture classification. Int. J. Comput. Vis. 88(3), 447–460 (2010)

  8. 8.

    Csurka, G., Dance, C., Fan, L., Willamowski, J., Bray, C.: Adapted vocabularies for generic visual categorization. In: Proceedings of Workshop on Statistical Learning in Computer Vision, 8th European Conference on Computer Vision. Prague, Czech Republic (2004)

  9. 9.

    Ershad, S.: Texture classification approach based on combination of edge & co-occurrence and local binary pattern. In: Proceedings of International Conference on Image Processing. Computer Vision, and Pattern Recognition (IPCV), vol. 2, pp. 626–629. Nevada, USA (2011)

  10. 10.

    Fernández, A., Ghita, O., González, E., Bianconi, F., Whelan, P.F.: Evaluation of robustness against rotation of LBP, CCR and ILBP features in granite texture classification. Mach. Vis. Appl. 22(6), 913–926 (2011). doi:10.1007/s00138-010-0253-4

  11. 11.

    Fernández, A., Álvarez, M.X., Bianconi, F.: Texture description through histograms of equivalent patterns. J. Math. Imaging Vis. 45(1), 76–102 (2013). doi:10.1007/s10851-012-0349-8

  12. 12.

    Goodman, L., Kruskal, W.: Measures of association for cross classifications. J. Am. Stat. Assoc. 49(268), 732–764 (1954)

  13. 13.

    Guo, Z., Zhang, L., Zhang, D.: A completed modeling of local binary pattern operator for texture classification. IEEE Trans. Image Process. 19(6), 1657–1663 (2010)

  14. 14.

    Guo, Y., Zhao, G., Pietikäinen, M.: Discriminant features for texture description. Pattern Recognit. 45(10), 3825–3843 (2012)

  15. 15.

    Hsu, C., Chang, C., Lin, C.: A practical guide to support vector classification. Available online at http://www.csie.ntu.edu.tw/cjlin/papers/guide/guide.pdf (2010). Last accessed on December 27, 2013

  16. 16.

    Kandaswamy, U., Schuckers, S.A., Adjeroh, D.: Comparison of texture analysis schemes under nonideal conditions. IEEE Trans. Image Process. 20(8), 2260–2275 (2011)

  17. 17.

    Khan, R., Barat, C., Muselet, D., Ducottet, C.: Spatial orientations of visual word pairs to improve bag-of-visual-words model. In: Proceedings of British Machine Vision Conference (BMVC 2012). Guildford, UK (2012)

  18. 18.

    Kobayashi, T., Otsu, N.: Bag of hierarchical co-occurrence features for image classification. In: Proceedings of the 20th International Conference on Pattern Recognition (ICPR), pp. 3882–3885. Istanbul, Turkey (2010).

  19. 19.

    Kylberg Sintorn Rotation dataset. Available online at http://www.cb.uu.se/gustaf/KylbergSintornRotation/ (2013). Last accessed on October 24, 2013

  20. 20.

    Lazebnik, S., Schmid, C., J., P.: Beyond bags of features: Spatial pyramid matching for recognizing natural scene categories. In: Proceedings of Computer Vision and Pattern Recognition, vol. 2, pp. 2169–2178. New York, USA (2006)

  21. 21.

    Lee, Y.S., Hao, S.S., Lin, S.W., Li, S.Y.: Image retrieval by region of interest motif co-occurrence matrix. In: IEEE International Symposium on Intelligent Signal Processing and Communication System (ISPACS), pp. 270–274. New Taipei, Taiwan (2012)

  22. 22.

    Li, Q., Shi, Z.: A high order contextual descriptor for image retrieval using generalized texton co-occurrence matrix. Information 16(1A), 155–174 (2013)

  23. 23.

    Liao, S., Law, M.W.K., Chung, A.C.S.: Dominant local binary patterns for texture classification. IEEE Trans. Image Process. 18(5), 1107–1118 (2009)

  24. 24.

    LIBSVM - A Library for Support Vector Machines. Available online at http://www.csie.ntu.edu.tw/cjlin/libsvm/ (2014). Last accessed on January 9, 2014

  25. 25.

    Liu, G.H., Yang, J.Y.: Image retrieval based on the texton co-occurrence matrix. Pattern Recognit. 41(2), 3521–3527 (2008)

  26. 26.

    Mirkin, B.: Eleven ways to look at the chi-squared coefficient for contingency tables. Am. Stat. 55(2), 111–120 (2001)

  27. 27.

    Mondial Marmi: a granite image database for colour and texture analysis. v1.1.. Available online at http://dismac.dii.unipg.it/mm. (2011). Last accessed on October 24, 2013

  28. 28.

    Nanni, L., Brahnam, S., Lumini, A.: Selecting the best performing rotation invariant patterns in local binary/ternary patterns. In: Proceedings of the 2010 International Conference on Image Processing. Computer Vision, and Pattern Recognition (IPCV’10), pp. 369–375. Las Vegas, USA (2010)

  29. 29.

    Nanni, L., Brahnam, S., Lumini, A.: Random interest regions for object recognition based on texture descriptors and bag of features. Expert Syst. Appl. 39(1), 973–977 (2012)

  30. 30.

    Nosaka, R., Okhawa, Y., Fukui, K.: Feature extraction based on co-occurrence of adjacent local binary patterns. Advances in Image and Video Technology. In: Proceedings of the 5th Pacific Rim Symposium on Image and Video Technology, 2011, Lecture Notes in Computer Science, vol. 7088, pp. 82–91. Springer, Gwangju, South Korea (2012)

  31. 31.

    Nosaka, R., Suryanto, C., Fukui, K.: Rotation invariant co-occurrence among adjacent LBPs. Computer Vision - ACCV 2012 International Workshops. Lecture Notes in Computer Science, vol. 7728, pp. 15–25. Springer, Daejon, South Korea (2013)

  32. 32.

    Ojala, T., Pietikäinen, M., Mäenpää, T.: Multiresolution gray-scale and rotation invariant texture classification with local binary patterns. IEEE Trans. Pattern Anal. Mach. Intell. 24(7), 971–987 (2002)

  33. 33.

    Olver, P.: Classical invariant theory, London Mathematical Society Student Texts, vol. 44. Cambridge University Press, Cambridge (1999)

  34. 34.

    PRTools: A Matlab toolbox for pattern recognition. Available online at http://prtools.org/ (2014). Last accessed on January 9, 2014

  35. 35.

    Qi, X., Xiao, R., Guo, J., Zhang, L.: Pairwise rotation invariant co-occurrence local binary pattern. In: Proceedings of the European Computer Vision Conference. Lecture Notes in Computer Science, vol. 7577, pp. 158–171. Springer, Florence, Italy (2012)

  36. 36.

    General framework for rotation invariant texture classification through co-occurrence of patterns. Code, data and results of this paper. Available online at http://webs.uvigo.es/antfdez/downloads.html (2013). Last updated on Jan 14, 2013

  37. 37.

    Ros, J., Laurent, C., Jolion, J.: A bag of strings representation for image categorizations. J. Math. Imaging Vis. 35(1), 51–67 (2009)

  38. 38.

    Shadkam, N., Helfroush, M.A.: Texture classification by using co-occurrences of local binary patterns. In: Proceedings of the 20th Iranian Conference on Electrical Engineering, pp. 1442–1446. Tehran, Iran (2012)

  39. 39.

    Song, Q.: Illumination invariant texture classification with pattern co-occurrence matrix. In: Shen, G., Huang, X. (eds.) Advanced research on computer science and information engineering, communications in computer and information science, pp. 67–72. Springer, Verlag (2011)

  40. 40.

    Sujatha, B., Vijayakumar, V., Harini, P.: A new logical compact LBP co-occurrence matrix for texture analysis. Int. J. Sci. Eng. Res. 3(2), 1–5 (2012)

  41. 41.

    Sun, X., Wang, J., Chen, R., She, M., Kong, L.: Multi-scale local pattern co-occurrence matrix for textural image classification. In: Proceedings of the IEEE World Congress on Computational Intelligence, pp. 1–7. Brisbane, Australia (2012)

  42. 42.

    Tan, C.M., Wang, Y.F., Lee, C.D.: The use of bigrams to enhance text categorization. Inf. Process. Manag. 38(4), 529–546 (2002)

  43. 43.

    Theil, H.: Statistical decomposition analysis: with applications in the social and administrative sciences, studies in mathematical and managerial economics. North-Holland, Amsterdam (1972)

  44. 44.

    Varma, M., Zisserman, A.: A statistical approach to material classification using image patch exemplars. IEEE Trans. Pattern Anal. Mach. Intell. 31(11), 2032–2047 (2009)

  45. 45.

    Wang, Z., Liu, H., Xu, T.: Crowd density estimation based on local binary pattern co-occurrence matrix. In: Proceedings of the IEEE International Conference on Multimedia and Expo Workshops, pp. 372–377. Melbourne, Australia (2012)

  46. 46.

    Wu, Z., Huang, Y., Wang, L., Tan, T.: Spatial graph for image classification. Lect. Notes Comput. Sci. 7724, 716–729 (2013)

  47. 47.

    Zhang, J., Marszałek, M., Lazebnik, S., Schmid, C.: Local features and kernels for classification of texture and object categories: a comprehensive study. Int. J. Comput. Vis. 73(2), 213–238 (2007)

  48. 48.

    Zou, J., Liu, C.C., Zhang, Y., Lu, G.F.: Object recognition using Gabor co-occurrence similarity. Pattern Recognit. 46(1), 434–448 (2013)

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This work was partly supported by the Spanish Government within projects no. CTM 2010-16573 and TRA 2011-29454-C03-01, and by the European Union within projects no. Life 09 ENV/FI/000568 and Life 12 ENV/IT/000411. The authors wish to thank the anonymous reviewers for their fruitful and fitting remarks.

Author information

Correspondence to Elena González.

Additional information

Elena González performed part of this work as a Visiting Professor in the Department of Industrial Engineering, Università degli Studi di Perugia, Italy.

Contingency Tables and Measures of Association

Contingency Tables and Measures of Association

Given a population and two sets of unordered, categorical attributes (polytomies) \(\mathcal {A} = \{A_0,A_1,\ldots ,A_{\alpha -1}\}\) and \(\mathcal {B} = \{B_0,B_1,\ldots ,B_{\beta -1}\}\) a contingency table is an \(\alpha \times \beta \) matrix of which each \((\rho _a,\rho _b)\) entry (\(a \in \{0,\ldots ,\alpha -1\}\); \(b \in \{0,\ldots ,\beta -1\}\)), reports the fraction of the population that is classified as both \(A_a\) and \(B_b\) [12]. The degree of association between the attributes can be estimated through a number of parameters, some of which are breifly recalled here below.

Pearson’s Chi-squared Coefficient and Cramér’s \(V\)

A traditional measure of association is Pearson’s chi-squared coefficient, which estimates the bias of cross-classification from statistical independence [26]. For a population of \(\nu \) members it is defined as follows:

$$\begin{aligned} \chi ^2 = \nu \sum _{a=0}^{\alpha -1} \sum _{b=0}^{\beta -1} \frac{\left( \rho _{ab} - \rho _{a \cdot } \rho _{\cdot b}\right) ^2}{\rho _{a \cdot } \rho _{\cdot b}} \end{aligned}$$

where \(\rho _{a \cdot }\) and \(\rho _{\cdot b}\) are the proportions of the population classified as \(A_a\) and \(B_b\), respectively.

A normalized version of Pearson’s \(\chi ^2\) is Cramér’s \(V\), which takes value between 0 and 1 (where 0 means ‘independence’ and 1 ‘complete association’) and is defined as follows:

$$\begin{aligned} V = \sqrt{\frac{\chi ^2}{\nu \left[ \text {max}\left( \alpha -1,\beta -1\right) \right] }} \end{aligned}$$

Goodman’s \(\lambda \)

Suppose a situation in which we had to guess the \(B\)-class (or the \(A\)-class) of an individual chosen at random from the population and were given: (1) no further information about the individual, or (2) its A class (or its B class). Goodman’s \(\lambda \) estimates the relative decrease in the error probability that we experience when switching from case (1) to case (2):

$$\begin{aligned} \lambda = \frac{\frac{1}{2} \left( \sum _{a=0}^{\alpha -1} \rho _{am} + \sum _{b=0}^{\beta -1} \rho _{bm} - \rho _{\cdot m} -\rho _{m \cdot } \right) }{1 - \frac{1}{2} \left( \rho _{\cdot m} + \rho _{m \cdot } \right) } \end{aligned}$$


$$\begin{aligned} \rho _{\cdot m}&= \mathop {\mathrm{max}}\limits _{b} \rho _{\cdot b}, \quad \rho _{am} = \mathop {\mathrm{max}}\limits _{b} \rho _{ab} \end{aligned}$$
$$\begin{aligned} \rho _{m \cdot }&= \mathop {\mathrm{max}}\limits _{a} \rho _{a \cdot }, \quad \rho _{mb} = \mathop {\mathrm{max}}\limits _{a} \rho _{ab} \end{aligned}$$

Theil’s \(U\)

The last measure of association considered here is based on the concept of cross-information and was discussed by Theil [43]. It considers on the amount of information conveyed about \(A\) by \(B\) and vice-versa. This is properly scaled to give a value between 0 and 1. In formulas:

$$\begin{aligned} U^2 = \frac{2I}{H(A) + H(B)} \end{aligned}$$


$$\begin{aligned} I&= \sum _{a=0}^{\alpha -1} \sum _{b=0}^{\beta -1} \left( \rho _{ab} \right) \text {log} \left( \frac{\rho _{ab}}{ \rho _{a \cdot } \rho _{\cdot b}} \right) \end{aligned}$$
$$\begin{aligned} H(A)&= -\sum _{a=0}^{\alpha -1} \left( \rho _{a \cdot } \right) \text {log} \left( \rho _{a \cdot } \right) \end{aligned}$$
$$\begin{aligned} H(B)&= -\sum _{b=0}^{\beta -1} \left( \rho _{\cdot b} \right) \text {log} \left( \rho _{\cdot b} \right) \end{aligned}$$

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González, E., Fernández, A. & Bianconi, F. General Framework for Rotation Invariant Texture Classification Through Co-occurrence of Patterns. J Math Imaging Vis 50, 300–313 (2014). https://doi.org/10.1007/s10851-014-0500-9

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  • Support Vector Machine
  • Local Binary Pattern
  • Feature Selection Scheme
  • Uniform Local Binary Pattern
  • Oriented Pair