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Morphological pyramids with alternating sequential filters.

A Morales1, R Acharya, S J Ko

  • 1Coll. of Eng., Pennsylvania State Univ., DuBois, PA.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|January 1, 1995
PubMed
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This study reveals a relationship between alternating sequential filters (ASF) and the morphological sampling theorem (MST), enabling efficient implementation of morphological operations. It establishes bounds and conditions for equivalence in image processing tasks.

Area of Science:

  • Digital Image Processing
  • Mathematical Morphology
  • Computer Vision

Background:

  • Morphological operations are fundamental in image analysis.
  • Existing methods for morphological operations can be computationally intensive.
  • The morphological sampling theorem (MST) offers potential computational efficiencies.

Purpose of the Study:

  • To establish a relationship between alternating sequential filters (ASF) and the morphological sampling theorem (MST).
  • To leverage MST for computationally efficient implementation of morphological operations.
  • To analyze the properties of morphological operations in sampled and unsampled domains.

Main Methods:

  • Developed alternative proofs for opening and closing using basis functions.
  • Investigated the relationship between open-closing in sampled and unsampled domains.

Related Experiment Videos

  • Utilized the Hausdorff metric to analyze image reconstruction accuracy.

    • Main Results:

    • Demonstrated that morphological pyramids can be constructed in a single step.
    • Established upper and lower bounds for the relationship between sampled and unsampled morphological operations.
    • Showed conditions for equivalence of open-closing between domains.
    • Proposed extensions for complex algorithms like unions of openings and intersections of closings.

    Conclusions:

    • The study provides a theoretical framework connecting ASF and MST for efficient morphological image processing.
    • Image reconstruction accuracy is bounded by twice the radius of the structuring element.
    • The findings facilitate optimized implementation of advanced morphological algorithms.