Computation of Image Spatial Entropy Using Quadrilateral Markov Random Field

• Published in: IEEE transactions on image processing Vol. 18; no. 12; pp. 2629 - 2639
• Main Authors: Razlighi, Q.R., Kehtarnavaz, N., Nosratinia, A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-12-2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Computation; Density measurement; Distributed computing; Entropy; Exact sciences and technology; Histograms; Homogeneity; Image analysis; Image histogram; Image processing; image spatial entropy; Information theory; Information, signal and communications theory; Lattices; Markov mesh random field (MMRF); Markov processes; Markov random field (MRF); Markov random fields; Mathematical analysis; Mathematical models; Mutual information; Pixel; Power system modeling; quadrilateral Markov random field (QMRF); Quadrilaterals; Signal and communications theory; Signal processing; Signal representation. Spectral analysis; Signal, noise; Telecommunications and information theory; Performance evaluation; Dimensionality; Histogram; quadrilateral Markov random field (QMRF); Markov mesh random field (MMRF); Probabilistic approach; Image histogram; Markov random field (MRF); Entropy; Markov model; Joint; Shannon theory; Random field; Image analysis; Homogeneity; image spatial entropy; Causality; Mutual information
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2009.2029988

Shannon entropy is a powerful tool in image analysis, but its reliable computation from image data faces an inherent dimensionality problem that calls for a low-dimensional and closed form model for the pixel value distributions. The most promising such models are Markovian, however, the conventional Markov random field is hampered by noncausality and its causal versions are also not free of difficulties. For example, the Markov mesh random field has its own limitations due to the strong diagonal dependency in its local neighboring system. A new model, named quadrilateral Markov random field (QMRF) is introduced in this paper in order to overcome these limitations. A property of QMRF with neighboring size of 2 is then used to decompose an image prior into a product of 2-D joint pdfs in which they are estimated using a joint histogram under the homogeneity assumption. In addition, the paper includes an extension of the introduced method to the computation of image spatial mutual information. Comparisons on synthesized images as well as two applications with real images are presented to motivate the developments in this paper and demonstrate the advantages in the performance of the introduced method over the existing ones.