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Computationally tractable stochastic image modeling based on symmetric Markov mesh random fields.

Siamak Yousefi1, Nasser Kehtarnavaz, Yan Cao

  • 1Department of Electrical Engineering, University of Texas at Dallas, Richardson, TX 75080, USA. sxy072100@utdallas.edu

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 16, 2013
PubMed
Summary

A new symmetric Markov mesh random field offers improved image modeling. This computationally feasible model enhances image restoration by considering pixel dependencies, outperforming traditional methods.

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Area of Science:

  • Computer Vision
  • Image Processing
  • Statistical Modeling

Background:

  • Markov random fields (MRFs) are widely used for image modeling.
  • Conventional MRFs often have limitations in capturing complex pixel dependencies and computational efficiency.
  • A need exists for advanced image models that are both accurate and computationally tractable.

Purpose of the Study:

  • To introduce and analyze a novel class of causal Markov random fields: symmetric Markov mesh random fields (SMMRFs).
  • To derive a new image model based on SMMRFs that is symmetric, corner-independent, and isotropic.
  • To demonstrate the practical applicability and effectiveness of the proposed image model in image restoration tasks.

Main Methods:

  • Developed the theory and properties of symmetric Markov mesh random fields.
  • Derived a novel image model incorporating dependencies on all neighboring pixels.
  • Utilized histogram and joint histogram approximations for computationally feasible parameter estimation.
  • Applied the model to an image restoration problem.

Main Results:

  • Established the equivalence between upper and lower corner symmetric Markov mesh random fields.
  • The derived image model is computationally tractable and practically feasible.
  • The SMMRF-based model demonstrated superior performance in image restoration compared to conventional MRF models.

Conclusions:

  • Symmetric Markov mesh random fields provide a robust foundation for advanced image modeling.
  • The proposed image model offers an effective and computationally efficient tool for image processing applications.
  • This research advances the field of image modeling with a novel and improved approach.