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). Copyright by Science in China Press 2004.