2-Dimensional Wavelet Packet Spectrum for Texture Analysis

The paper derives a 2-Dimensional spectrum estimator from some recent results on the statistical properties of wavelet packet coefficients of random processes. It provides an analysis of the bias of this estimator with respect to the wavelet order. The paper also discusses the performance of this wavelet based estimator, in comparison with the conventional 2-D Fourier-based spectrum estimator on texture analysis and content based image retrieval. It highlights the effectiveness of the wavelet based spectrum estimation.

[1]  Patrick Flandrin,et al.  Wavelet analysis and synthesis of fractional Brownian motion , 1992, IEEE Trans. Inf. Theory.

[2]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[3]  M. Victor Wickerhauser,et al.  Adapted wavelet analysis from theory to software , 1994 .

[4]  Stamatis Cambanis,et al.  On the continuous wavelet transform of second-order random processes , 1995, IEEE Trans. Inf. Theory.

[5]  Fang Liu,et al.  Periodicity, Directionality, and Randomness: Wold Features for Image Modeling and Retrieval , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  C. Burrus,et al.  Introduction to Wavelets and Wavelet Transforms: A Primer , 1997 .

[7]  Christian Houdré,et al.  Some Distributional Properties of the Continuous Wavelet Transform of Random Processes , 1998, IEEE Trans. Inf. Theory.

[8]  I Pitas,et al.  Image watermarking using block site selection and DCT domain constraints. , 1998, Optics express.

[9]  S. Mallat A wavelet tour of signal processing , 1998 .

[10]  E. Masry,et al.  On the Spectral Density of the Wavelet Transform of Fractional Brownian Motion , 1999 .

[11]  Yuan-Pei Lin,et al.  Wavelet tree quantization for copyright protection watermarking , 2004, IEEE Transactions on Image Processing.

[12]  Piotr Porwik,et al.  The Haar – Wavelet Transform in Digital Image Processing : Its Status and Achievements , 2004 .

[13]  Donald B. Percival,et al.  Asymptotic decorrelation of between-Scale Wavelet coefficients , 2005, IEEE Transactions on Information Theory.

[14]  Mohamed Najim,et al.  Three-Dimensional Textured Image Blocks Model Based on Wold Decomposition , 2007, IEEE Transactions on Signal Processing.

[15]  Dimitris A. Pados,et al.  Optimal Signature Design for Spread-Spectrum Steganography , 2007, IEEE Transactions on Image Processing.

[16]  I. Eckley,et al.  Locally stationary wavelet fields with application to the modelling and analysis of image texture , 2010 .

[17]  Abdourrahmane M. Atto,et al.  Wavelet Packets of Fractional Brownian Motion: Asymptotic Analysis and Spectrum Estimation , 2010, IEEE Transactions on Information Theory.

[18]  Lihong Cui,et al.  Adaptive Multiwavelet-Based Watermarking Through JPW Masking , 2011, IEEE Transactions on Image Processing.

[19]  Brani Vidakovic,et al.  2D wavelet-based spectra with applications , 2011, Comput. Stat. Data Anal..

[20]  Andreas Uhl,et al.  Lightweight Detection of Additive Watermarking in the DWT-Domain , 2011, IEEE Transactions on Image Processing.

[21]  Debashis Mondal,et al.  Wavelet Variance Analysis for Random Fields on a Regular Lattice , 2012, IEEE Transactions on Image Processing.

[22]  Abdourrahmane M. Atto,et al.  Wavelet Packets of Nonstationary Random Processes: Contributing Factors for Stationarity and Decorrelation , 2012, IEEE Transactions on Information Theory.

[23]  Damon M. Chandler,et al.  ${\bf S}_{3}$: A Spectral and Spatial Measure of Local Perceived Sharpness in Natural Images , 2012, IEEE Transactions on Image Processing.