Statistical Wavelet Subband Characterization Based on Generalized Gamma Density and Its Application in Texture Retrieval

The modeling of image data by a general parametric family of statistical distributions plays an important role in many applications. In this paper, we propose to adopt the three-parameter generalized gamma density (G¿D) for modeling wavelet detail subband histograms and for texture image retrieval. The advantage of G¿D over the existing generalized Gaussian density (GGD) is that it provides more flexibility to control the shape of model which is critical for practical histogram-based applications. To measure the discrepancy between G¿Ds, we use the symmetrized Kullback-Leibler distance (SKLD) and derive a closed form for the SKLD between G¿Ds. Such a distance can be computed directly and effectively via the model parameters, making our proposed scheme particularly suitable for image retrieval systems with large image database. Experimental results on the well-known databases reveal the superior performance of our proposed method compared with the current existing approaches.

[1]  Robert D. Nowak,et al.  Wavelet-based statistical signal processing using hidden Markov models , 1998, IEEE Trans. Signal Process..

[2]  William T. Freeman,et al.  Presented at: 2nd Annual IEEE International Conference on Image , 1995 .

[3]  Minh N. Do,et al.  Rotation invariant texture characterization and retrieval using steerable wavelet-domain hidden Markov models , 2002, IEEE Trans. Multim..

[4]  Richard G. Baraniuk,et al.  Multiscale image segmentation using wavelet-domain hidden Markov models , 2001, IEEE Trans. Image Process..

[5]  Chong-Sze Tong,et al.  Supervised Texture Classification Using Characteristic Generalized Gaussian Density , 2007, Journal of Mathematical Imaging and Vision.

[6]  Eero P. Simoncelli,et al.  Image compression via joint statistical characterization in the wavelet domain , 1999, IEEE Trans. Image Process..

[7]  Edward H. Adelson,et al.  Shiftable multiscale transforms , 1992, IEEE Trans. Inf. Theory.

[8]  Erkki Oja,et al.  Reduced Multidimensional Co-Occurrence Histograms in Texture Classification , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  Paul Scheunders,et al.  Statistical texture characterization from discrete wavelet representations , 1999, IEEE Trans. Image Process..

[10]  Hong Zhang,et al.  A Fast and Effective Model for Wavelet Subband Histograms and Its Application in Texture Image Retrieval , 2006, IEEE Transactions on Image Processing.

[11]  D. R. Wingo Computing Maximum-Likelihood Parameter Estimates of the Generalized Gamma Distribution by Numerical Root Isolation , 1987, IEEE Transactions on Reliability.

[12]  Justin K. Romberg,et al.  Bayesian tree-structured image modeling using wavelet-domain hidden Markov models , 2001, IEEE Trans. Image Process..

[13]  Joon-Hyuk Chang,et al.  Statistical modeling of speech signals based on generalized gamma distribution , 2005, IEEE Signal Process. Lett..

[14]  Kai-Sheng Song,et al.  Globally Convergent Algorithms for Estimating Generalized Gamma Distributions in Fast Signal and Image Processing , 2008, IEEE Transactions on Image Processing.

[15]  Chong-Sze Tong,et al.  Statistical Properties of Bit-Plane Probability Model and Its Application in Supervised Texture Classification , 2008, IEEE Transactions on Image Processing.

[16]  Michael Unser,et al.  Sum and Difference Histograms for Texture Classification , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Hideo Hirose,et al.  Maximum likelihood parameter estimation by model augmentation with applications to the extended four-parameter generalized gamma distribution , 2000 .

[18]  Eero P. Simoncelli,et al.  Texture characterization via joint statistics of wavelet coefficient magnitudes , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[19]  Eero P. Simoncelli,et al.  A Parametric Texture Model Based on Joint Statistics of Complex Wavelet Coefficients , 2000, International Journal of Computer Vision.

[20]  Alain Dussauchoy,et al.  Parameter estimation of the generalized gamma distribution , 2008, Math. Comput. Simul..

[21]  Sanjit K. Mitra,et al.  Image probability distribution based on generalized gamma function , 2005, IEEE Signal Processing Letters.

[22]  A. Dussauchoy,et al.  Four-Parameter Generalized Gamma Distribution used for Stock Return Modelling , 2006, The Proceedings of the Multiconference on "Computational Engineering in Systems Applications".

[23]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Eric R. Ziegel,et al.  Statistical Size Distributions in Economics and Actuarial Sciences , 2004, Technometrics.

[25]  E. Stacy A Generalization of the Gamma Distribution , 1962 .

[26]  Pierre Moulin,et al.  Analysis of Multiresolution Image Denoising Schemes Using Generalized Gaussian and Complexity Priors , 1999, IEEE Trans. Inf. Theory.

[27]  Minh N. Do,et al.  Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance , 2002, IEEE Trans. Image Process..

[28]  Richard Baraniuk,et al.  Multiscale texture segmentation using wavelet-domain hidden Markov models , 1998, Conference Record of Thirty-Second Asilomar Conference on Signals, Systems and Computers (Cat. No.98CH36284).