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Fast recursive algorithms for morphological operators based on the basis matrix representation.

S J Ko1, A Morales, K H Lee

  • 1Dept. of Electron. Eng., Korea Univ., Seoul.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|January 1, 1996
PubMed
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This study introduces a faster, real-time method for grayscale function processing (FP) using recursive algorithms. The new approach significantly reduces computations and memory for image processing tasks like opening and closing.

Area of Science:

  • Image Processing
  • Computer Vision
  • Mathematical Morphology

Background:

  • Grayscale function processing (FP) is a general morphological system.
  • Previous work utilized matrix representations (BM, BBM) of FP systems with grayscale structuring elements (GSE).

Purpose of the Study:

  • To develop a computationally efficient, real-time implementation method for grayscale function processing.
  • To improve upon existing matrix representation methods for FP systems.

Main Methods:

  • Proposed recursive algorithms based on observations of the basis matrix (BM) and block basis matrix (BBM).
  • Algorithms avoid redundant calculations in local maximum/minimum operations for enhanced efficiency.
  • Utilized grayscale structuring elements (GSE) of size N.

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Main Results:

  • Achieved real-time processing for opening and closing operations with 2N-2 additions and comparisons.
  • Enabled real-time processing for OC and CO operations with 4N-4 additions and comparisons.
  • Demonstrated reduced memory requirements, needing only 3N-3 elements for recursive opening and closing.

Conclusions:

  • The proposed recursive algorithms offer significant computational and memory efficiency for grayscale function processing.
  • This method enables real-time performance for complex morphological operations in image analysis.
  • The approach provides a practical solution for efficient implementation of general morphological systems.