Computation of image spatial entropy using quadrilateral Markov random field.

Area of Science:

• Image analysis
• Information theory
• Computer vision

Background:

• Shannon entropy is crucial for image analysis but faces computational challenges due to data dimensionality.
• Conventional Markov random fields (MRFs) have limitations like noncausality and strong dependencies.
• Existing causal MRFs, such as the Markov mesh, also have drawbacks in local neighborhood systems.

Purpose of the Study:

• To introduce a novel Quadrilateral Markov Random Field (QMRF) model to address the dimensionality problem in computing Shannon entropy from image data.
• To overcome the limitations of conventional and causal MRFs in image analysis.
• To extend the QMRF model for computing image spatial mutual information.

Main Methods:

• A new Quadrilateral Markov Random Field (QMRF) model is proposed.
• A QMRF property with a neighboring size of 2 is utilized to decompose image priors into 2-D joint probability density functions (PDFs).
• Joint histograms under a homogeneity assumption are used to estimate these PDFs, and the method is extended to image spatial mutual information.

Main Results:

• The QMRF model effectively decomposes image priors into estimable 2-D joint PDFs.
• The extended method accurately computes image spatial mutual information.
• Comparisons on synthesized and real images demonstrate superior performance over existing methods.

Conclusions:

• The Quadrilateral Markov Random Field (QMRF) offers a robust solution for the dimensionality problem in Shannon entropy computation for image analysis.
• QMRF provides improved performance in image processing tasks, including spatial mutual information calculation.
• The proposed model represents a significant advancement over traditional Markov random field approaches.