MRF based construction of statistical operator and its application
Based on the Markov random field (MRF) theory, a new nonlinear operator is defined according to the statistical information in the image, and the corresponding 2D nonlinear wavelet transform is also provided. It is proved that many detail coefficients being zero (or almost zero) in the smooth gray-level variation areas can be achieved under the conditional probability density function in MRF model, which shows that this operator is suitable for the task of image compression, especially for lossless coding applications. Experimental results using several test images indicate good performances of the proposed method with the smaller entropy for the compound and smooth medical images with respect to the other nonlinear transform methods based on median and morphological operator and some well-known linear lifting wavelet transform methods (5/3, 9/7, and S+P).
Keywordsnonlinear wavelet transform MRF statistical operator
- 3.Sweldens, W., The lifting scheme: A new philosophy in biorthogonal wavelet constructions. Proc. SPIE Wavelet Applications Signal Image Processing III, New York: SPIE, the International Society for Optical Engineering, 1995, Vol. 2569, 68–79.Google Scholar
- 7.Van den Boomgaard, R., Smeulders, A., The morphological structure of images: the differential equations of morphological scale-space, IEEE Trans. Image Processing, 1994, 16(11): 1101–1113.Google Scholar
- 11.Ceman, S., Geman, D., Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Trans. Pattern Analysis and Machine Intelligence, 1984, vol. PAMI-6, 721–741.Google Scholar
- 12.Derin, H., Elliott, H., Modeling and segmentation of noisy and textured images using gibbs random field, IEEE Trans. Pattern Analysis and Machine Intelligence, 1987, vol. PAMI-9, 39–55.Google Scholar
- 15.Kretzmer, E. R., Statistics of television signals, The Bell System Technical Journal, July 1952, 31(4): 7551–7763.Google Scholar