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Related Experiment Videos

Using line segments as structuring elements for sampling-invariant measurements.

C L Luengo Hendriks1, L J van Vliet

  • 1Life Sciences Division, Lawrence Berkeley National Laboratory, MS 84R171, Berkeley, CA 94720, USA. clluengo@lbl.gov

IEEE Transactions on Pattern Analysis and Machine Intelligence
|November 16, 2005
PubMed
Summary

Accurate image measurements are possible beyond pixel limits. Morphological filters with line segments can approximate sampling invariance using a skew-filter-unskew method, balancing accuracy and computational cost.

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Area of Science:

  • Digital Image Processing
  • Computer Vision
  • Mathematical Morphology

Background:

  • Pixel pitch does not inherently limit measurement accuracy in digitized images.
  • Proper sampling preserves image information, allowing for theoretically identical continuous and discrete domain measurements.
  • Strict sampling invariance is unattainable for nonlinear mathematical morphology filters, but approximations are possible.

Purpose of the Study:

  • To investigate morphological filters utilizing line segments as structuring elements.
  • To compare existing and novel implementation methods for these filters.
  • To determine optimal strategies for measuring line segment lengths in digitized images.

Main Methods:

  • Comparison of six methods (three known, three new) for implementing morphological filters with line segments.

Related Experiment Videos

  • Utilizing a (subpixel) skew of image data, followed by filtering along grid axes with a discrete line segment, and then an inverse skew.
  • Modeling staircase approximations of line segments under random orientations via skewing.

    • Main Results:

    • A skew-filter-unskew method offers a balance between accuracy and computational cost.
    • Skewing image data, rather than the structuring element, significantly reduces quantization error.
    • The study determines the optimal number of orientations for measuring line segment lengths with unknown orientation.

    Conclusions:

    • Achieving sampling invariance in morphological filters is feasible through approximation techniques.
    • The proposed skew-filter-unskew method provides an effective approach for accurate and computationally efficient image analysis.
    • Optimal orientation selection enhances the precision of length measurements for line segments in digitized images.