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Binary random fields, random closed sets, and morphological sampling.

K Sivakumar1, J Goutsias

  • 1Dept. of Electr. and Comput. Eng., Johns Hopkins Univ., Baltimore, MD.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|January 1, 1996
PubMed
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This study introduces mathematical morphology for analyzing continuous-space binary random fields. Morphological discretization is proposed as a solution to technical challenges in the continuous domain, enabling discrete analysis.

Area of Science:

  • Image analysis
  • Mathematical morphology
  • Probability theory

Background:

  • Continuous-space binary random fields are challenging to analyze directly using mathematical morphology.
  • Existing methods face measurability issues with morphological transformations in continuous spaces.

Purpose of the Study:

  • To theoretically formulate the processing of continuous-space binary random fields using mathematical morphology.
  • To develop novel statistical techniques for analyzing binary random images.
  • To address technical challenges in applying morphological operators to continuous fields.

Main Methods:

  • Theoretical formulation of continuous-space binary random fields processing.
  • Investigation of the relationship between random fields and random closed sets.

Related Experiment Videos

  • Development of morphological discretization techniques for fields and operators.

    • Main Results:

    • Established a framework for employing mathematical morphology in continuous-space binary random field analysis.
    • Identified the necessity of using random closed sets as intermediate representations.
    • Presented new results on the separability of random closed sets.
    • Proposed morphological discretization as a viable alternative for practical implementation.

    Conclusions:

    • Morphological discretization offers a practical approach to analyzing binary random fields by overcoming continuous-space limitations.
    • The study bridges theoretical concepts of random fields and random closed sets with practical image analysis techniques.
    • This work facilitates the development of advanced statistical methods for binary image analysis.