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Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data
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A triangulation-invariant method for anisotropic geodesic map computation on surface meshes.

Sang Wook Yoo1, Joon-Kyung Seong, Min-Hyuk Sung

  • 1Computer Graphics Laboratory, Korea Advanced Institute of Science and Technology-KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Korea. ysw81@jupiter.kaist.ac.kr

IEEE Transactions on Visualization and Computer Graphics
|February 1, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for calculating anisotropic geodesic distances on 3D surface meshes. The approach uses a curvature-based speed function and an ordered upwind method (OUM) solver for enhanced surface analysis.

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Area of Science:

  • Computer Graphics
  • Computational Geometry
  • Differential Geometry

Background:

  • Computing geodesic distances on surfaces is crucial for many applications.
  • Existing methods often struggle with anisotropic metrics and complex surface geometries.
  • Anisotropic metrics are essential for accurately reflecting local surface properties.

Purpose of the Study:

  • To develop a robust framework for computing anisotropic geodesic distance maps on surface meshes.
  • To adapt an existing ordered upwind method (OUM) solver for surface meshes.
  • To propose novel curvature-based speed functions for anisotropic geodesic computations.

Main Methods:

  • Formulating the problem as a Hamilton-Jacobi-Bellman (HJB) partial differential equation.
  • Adapting an OUM-based solver for unstructured planar meshes to surface meshes.
  • Developing a triangulation-invariant method for the OUM solver on surfaces.
  • Proposing two speed functions derived from classical curvature tensors.

Main Results:

  • The proposed method successfully computes anisotropic geodesic maps on surface meshes.
  • The resulting maps accurately reflect the underlying surface geometry.
  • Experiments demonstrate the method's effectiveness in applications like isocontour generation and medial axis extraction.
  • The approach allows for application-dependent speed function definitions.

Conclusions:

  • The developed framework provides an effective solution for anisotropic geodesic map computation on surfaces.
  • The curvature-based speed functions yield meaningful geodesic maps that capture surface features.
  • This work enhances capabilities in surface analysis and processing through flexible speed function design.