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An efficient region expansion algorithm for regular triangulated meshes.

Brian Ondov1,2, Hanan Samet2

  • 1National Library of Medicine, National Institutes of Health, Bethesda, MD, USA.

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Summary
This summary is machine-generated.

This study adapts region expansion algorithms for triangulated meshes, improving efficiency for approximating growth in digital images. The new method achieves sublinear time complexity, making it faster for complex surface approximations.

Keywords:
Geographic information systemsQuadtreesTriangulated meshes

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Area of Science:

  • Computer Vision
  • Computational Geometry
  • Image Processing

Background:

  • Region expansion is a fundamental image processing operation.
  • Exact region expansion is computationally expensive.
  • Existing efficient methods rely on square quadtrees and the L∞-norm, limiting applicability.

Purpose of the Study:

  • To adapt the L∞-norm metric and region expansion algorithm for regular triangulated meshes.
  • To enable efficient approximation of region expansion on non-square grids.

Main Methods:

  • Adapted the L∞-norm metric for triangulated meshes.
  • Modified existing quadtree-based algorithms for triangular nodes.
  • Developed an efficient approximation algorithm for region expansion.

Main Results:

  • Achieved sublinear time complexity with respect to the expansion radius.
  • Demonstrated efficient region expansion approximation on triangulated meshes.
  • Enabled region expansion for applications like spherical surface approximation.

Conclusions:

  • The adapted algorithm efficiently approximates region expansion on triangulated meshes.
  • This method overcomes limitations of square quadtree approaches.
  • Offers a faster solution for region expansion in image processing and surface approximation.