Abstract
Generalized Gaussian density (GGD) is a well established model for high frequency wavelet subbands and has been applied in texture image retrieval with very good results. In this paper, we propose to adopt the GGD model in a supervised learning context for texture classification. Given a training set of GGDs, we define a characteristic GGD (CGGD) that minimizes its Kullback-Leibler distance (KLD) to the training set. We present mathematical analysis that proves the existence of our characteristic GGD and provide a sufficient condition for the uniqueness of CGGD, thus establishing a theoretical basis for its use. Our experimental results show that the proposed CGGD signature together with the use of KLD has a very promising recognition performance compared with existing approaches.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Do, M.N., Vetterli, M.: Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance. IEEE Trans. Image Process. 11(2), 146–158 (2002)
Sharifi, K., Leon-Garcia, A.: Estimation of shape parameter for generalized Gaussian distribution in subband decomposition of video. IEEE Trans. Circuits Syst. Video Technol. 5(1), 52–56 (1995)
Unser, M.: Texture classification and segmentation using wavelet frames. IEEE Trans. Image Process. 4(2), 1549–1560 (1995)
Amet, A.L., Ertuzun, A., Erqil, A.: Texture defect detection using subband domain co-occurrence matrices. In: Proceedings of IEEE Southeast Symp. for Image Analysis and Interpretation, 6–7 April 1998, pp. 976–979 (1998)
Fan, G.L., Xia, X.G.: On context-based Bayesian image segmentation: joint multi-context and multiscale approach and wavelet-domain hidden Markov models. In: Proceedings of the 35th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, 4–7 November 2001
Fan, G.L., Xia, X.G.: Maximum likelihood texture analysis and classification using wavelet-domain hidden Markov models. In: Proceedings of the 34th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, 29 October–1 November 2000
Aiazzi, B., Alparone, L., Baronti, S.: Estimation based on entropy matching for generalized Gaussian PDF modeling. IEEE Signal Process. Lett. 6(6), 138–140 (1999)
Mallat, S.: A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 11(7), 674–693 (1989)
Aujol, J.F., Aubert, G., Blanc-Feraud, L.: Wavelet-based level set evolution for classification of textured images. IEEE Trans. Image Process. 12(12), 1634–1641 (2003)
Moulin, P., Liu, J.: Analysis of multiresolution image denoising schemes using generalized Gaussian and complexity prior. IEEE Trans. Inf. Theory 45(3), 909–919 (1999)
Van de Wouwer, G., Scheunders, P., Van Dyck, D.: Statistical texture characterization from discrete wavelet representation. IEEE Trans. Image Process. 8(4), 592–598 (1999)
Weszka, J.S., Dyer, C.R., Rosenfeld, A.: A comparative study of texture measures for terrain classification. IEEE Trans. Syst. Man. Cybern. 6, 269–285 (1976)
Conners, R.W., Harlow, C.A.: A theoretical comparison of texture algorithms. IEEE Trans. Pattern Anal. Mach. Intell. 2, 204–221 (1980)
Randen, T., Husoy, J.H.: Filtering for texture classification: a comparative study. IEEE Trans. Pattern Anal. Mach. Intell. 21(4), 291–310 (1999)
Liu, X., Wang, D.: Texture classification using spectral histograms. IEEE Trans. Image Process. 12(6), 661–670 (2003)
Laine, A., Fan, J.: Texture classification by wavelet packet signatures. IEEE Trans. Pattern Anal. Mach. Intell. 15(11), 1186–1191 (1993)
JPEG2000 Part 2 Final Committee Draft, ISO/IEC JTC1/SC29/WC1 N2000, December 2000
Choy, S.K., Tong, C.S.: Supervised learning using characteristic generalized Gaussian density and its application to Chinese materia medica identification. In: Qian, T., Vai, M.I., Yuesheng, X. (eds.) Wavelet Analysis and Applications. Applied and Numerical Harmonic Analysis Series, pp. 443–452. Springer, Basel (2006)
Varanasi, M.K., Aazhang, B.: Parametric generalized Gaussian density estimation. J. Acoust. Soc. Am. 86, 1404–1415 (1989)
Pi, M., Tong, C.S., Choy, S.K., Zhang, H.: A fast and effective model for wavelet subband histograms and its application in texture image retrieval. IEEE Trans. Image Process. 15(10), 3078–3088 (2006)
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1970)
Spiegel, M.R.: Mathematical Handbook of Formulas and Tables. McGraw-Hill, Singapore (1990)
Srivastava, A., Liu, X., Grenander, U.: Universal analytical forms for modeling image probabilities. IEEE Trans. Pattern Anal. Mach. Intell. 24(9), 1200–1214 (2002)
Meignen, S., Meignen, H.: On the modeling of small sample distributions with generalized Gaussian density in a maximum likelihood framework. IEEE Trans. Image Process. 15(6), 1647–1652 (2006)
Tuceryan, M., Jain, A.K.: Texture analysis. In: Chen, C.H., Lau, L.F., Wang, P.S.P. (eds.) Handbook Pattern Recognition and Computer Vision, pp. 235–276. World Scientific, Singapore (1993), Chap. 2
Chang, T., Kuo, C.C.J.: Texture analysis and classification with tree-structured wavelet transform. IEEE Trans. Image Process. 2(4), 429–441 (1993)
Author information
Authors and Affiliations
Corresponding author
Additional information
This research is supported by HKBU’s Centre for Mathematical Imaging and Vision, HKBU Faculty Research Grant, and a CERG Grant
Rights and permissions
About this article
Cite this article
Choy, SK., Tong, CS. Supervised Texture Classification Using Characteristic Generalized Gaussian Density. J Math Imaging Vis 29, 35–47 (2007). https://doi.org/10.1007/s10851-007-0023-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10851-007-0023-8