A hybrid statistical approach for texture images classification based on scale invariant features and mixture gamma distribution

Said Benlakhdar1, Mohammed Rziza1, Rachid Oulad Haj Thami2

1LRIT URAC 29, Faculty of Sciences, Mohammed V University in Rabat, Morocco

2RIITM, ENSIAS, Mohammed V University in Rabat, Morocco




Image classification refers to an important process in computer vision. The purpose of this paper is to propose a novel approach named GGD-GMM and based on statistical modeling in wavelet domain to describe textured images and rely on number of principles which give its internal coherence and originality. Firstly, we propose a robust algorithm based on the combination of the wavelet transform and Scale Invariant Feature Transform. Secondly, we implement the aforementioned algorithm and fit the result using the finite mixture gamma distribution (GMM). The results, obtained for two benchmark datasets, show that the proposed algorithm has a good relevance as it provides higher classification accuracy compared to some other well known models see (Kohavi, 1995). Moreover, it shows other advantages relied to Noise-resistant and rotation invariant.

Cite as:

Benlakhdar, S., Rziza, M., & Thami, R.O.H. (2020). A hybrid statistical approach for texture images classification based on scale invariant features and mixture gamma distribution. Computer Methods in Materials Science, 20(3), 95–106. https://doi.org/10.7494/cmms.2020.3.0724

Article (PDF):

Key words:

Statistical image modeling, SIFT, Mixture gamma distribution, Uniform discrete curvelet transform, Classification


Au, Y.H.J., Eissa, S., & Jones, B.E. (2004). Receiver operating characteristic analysis for the selection of threshold values for detection of capping in powder compression. Ultrasonics, 42(1–9), 149–153.

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

Burba, F., Ferraty, F., & Vieu, P. (2009). k-Nearest Neighbour method in functional nonparametric regression. Journal of Nonparametric Statistics, 21(4), 453–469.

Candès, E., Demanet, L., Donoho, D., & Ying, L. (2006). Fast discrete curvelet transforms. Multiscale Modeling & Simulation, 5(3), 861–899.

Chen, C.C., DaPonte, J.S., & Fox, M.D. (1989). Fractal feature analysis and classification in medical imaging. IEEE Transactions on Medical Imaging, 8(2), 133–142.

Delacour, H., Servonnet, A., Perrot, A., Vigezzi, J.F., Ramirez, J.M. (2005). La courbe ROC (receiver operating characteristic): principes et principales applications en biologie Clinique. Annales de Biologie Clinique, 63(2), 145–154.

DeLong, E.R., DeLong, D.M., & Clarke-Pearson, D.L. (1988). Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach. Biometrics, 837–845.

Deng, Z., Zhu, X., Cheng, D., Zong, M., & Zhang, S. (2016). Efficient kNN classification algorithm for big data. Neurocomputing, 195, 143–148.

Do, M.N., & Vetterli, M. (2002a). Rotation invariant texture characterization and retrieval using steerable wavelet-domain hidden Markov models. IEEE transactions on multimedia, 4(4), 517–527.

Do, M.N., & Vetterli, M. (2002b). Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance. IEEE Transactions on Image Processing, 11(2), 146–158.

Erkel, A.R., van, Pattynama, P. (1998). Receiver operating characteristic (ROC) analysis: basic principles and applications in radiology, European Journal of Radiology, 27(2), 88–94.

Greiner, M., Pfeiffer, D., & Smith, R.D. (2000). Principles and practical application of the receiver-operating characteristic analysis for diagnostic tests. Preventive Veterinary Medicine, 45(1–2), 23–41.

Hamel, L.H. (2011). Knowledge discovery with support machines (Vol. 3). John Wiley & Sons.

Huang, C., Davis, L.S., & Townshend, J.R.G. (2002). An assessment of support vector machines for land cover classification. International Journal of remote sensing, 23(4), 725–749.

Jammalamadaka, S.R., SenGupta, A. (2001). Topics in Circular Statistics (Vol. 5). World Scientific Press.

Karaa, L.Z., Laksaci, A., Rachdi, M., & Vieu, P. (2017). Data-driven kNN estimation in nonparametric functional data analysis. Journal of Multivariate Analysis, 153, 176–188.

Khoshnood, B., Lelong, N., Houyel, L., Bonnet, D., Ballon, M., Jouannic, J.M., & Goffinet, F. (2017). Impact of prenatal diagnosis on survival of newborns with four congenital heart defects: a prospective, population-based cohort study in France (the EPICARD Study). BMJ Open, 7(11).

Kohavi, R. (1995). A study of cross-validation and bootstrap for accuracy estimation and model selection. In Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence, (Vol. 2, pp. 1137–1145).

Kudraszow, N.L., & Vieu, P. (2013). Uniform consistency of kNN regressors for functional variables. Statistics & Probability Letters, 83(8), 1863–1870.

Landais, P., Besson, C., Jais, J.P. (1994). Evaluation of the diagnostic contribution of a test. Main information indices, Journal de Radiologie, 75(2), 141–50.

Lian, H. (2011). Convergence of functional k-nearest neighbor regression estimate with functional responses. Electronic Journal of Statistics, 5, 31–40.

Lowe, D.G. (2004). Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision, 60(2), 91–110.

Lusted, L.B. (1960). Logical analysis in roentgen diagnosis: memorial fund lecture. Radiology, 74(2), 178–193.

Lusted, L.B. (1971). Signal detectability and medical decision-making. Science, 171(3977), 1217–1219.

Mallat, S. (1999). A wavelet tour of signal processing. Elsevier.

Manickam, A., Devarasan, E., Manogaran, G., Priyan, M.K., Varatharajan, R., Hsu, C.H., & Krishnamoorthi, R. (2019). Score level based latent fingerprint enhancement and matching using SIFT feature. Multimedia Tools and Applications, 78(3), 3065–3085.

Mardia, K.V., & Jupp, P.E. (2009). Directional statistics (Vol. 494). John Wiley & Sons.

Meeker, W.Q., Escobar, L.A., & Lu, C.J. (1998). Accelerated degradation tests: modeling and analysis. Technometrics, 40(2),89–99.

Moulin, P., & Liu, J. (1999). Analysis of multiresolution image denoising schemes using generalized Gaussian and complexity priors. IEEE transactions on Information Theory, 45(3), 909–919.

Nguyen, T.T., & Oraintara, S. (2008). The shiftable complex directional pyramid-Part II: Implementation and applications. IEEE Transactions on Signal Processing, 56(10), 4661–4672.

Oppenheim, A.V., & Lim, J.S. (1981). The importance of phase in signals. Proceedings of the IEEE, 69(5), 529–541.

Peel, D., & McLachlan, G.J. (2000). Robust mixture modelling using the t distribution. Statistics and computing, 10(4), 339–348.

Selesnick, I.W., Baraniuk, R.G., & Kingsbury, N.C. (2005). The dual-tree complex wavelet transform. IEEE signal processing magazine, 22(6), 123–151.

Sutton, R.N., & Hall, E.L. (1972). Texture measures for automatic classification of pulmonary disease. IEEE Transactions on Computers, 100(7), 667–676.

Tipples, J. (2002). Eye gaze is not unique: Automatic orienting in response to uninformative arrows. Psychonomic bulletin & review, 9(2), 314–318.

Vapnik, V.N. (1998). Statistical learning theory (1st ed.), Wiley.

Vo, A., & Oraintara, S. (2010). A study of relative phase in complex wavelet domain: Property, statistics and applications in texture image retrieval and segmentation. Signal Processing: Image Communication, 25(1), 28–46.

Vo, A., Oraintara, S., & Nguyen, N. (2011). Vonn distribution of relative phase for statistical image modeling in complex wavelet domain. Signal Processing, 91(1), 114–125.

Zhang, L., Zhou, W., & Jiao, L. (2004). Wavelet support vector machine. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 34(1), 34–39.