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Related Experiment Video

Updated: Jan 26, 2026

A Whole Body Dosimetry Protocol for Peptide-Receptor Radionuclide Therapy PRRT: 2D Planar Image and Hybrid 2D+3D SPECT/CT Image Methods
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Optimal Paths for Variants of the 2D and 3D Reeds-Shepp Car with Applications in Image Analysis.

R Duits1, S P L Meesters1, J-M Mirebeau2

  • 11CASA, Eindhoven University of Technology, Eindhoven, The Netherlands.

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|April 23, 2019
PubMed
Summary

This study introduces a novel PDE-based method for optimal Reeds-Shepp car paths, incorporating curvature and length penalties. The approach enhances tubular structure extraction in medical imaging and improves bifurcation handling without reverse gear.

Keywords:
BifurcationsFast-marchingFinsler geometrySub-Riemannian geometryTracking

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Area of Science:

  • Computational Mathematics
  • Image Analysis
  • Robotics

Background:

  • The Reeds-Shepp car model is fundamental for analyzing nonholonomic motion planning.
  • Existing methods often struggle with complex structures and incomplete data in medical imaging.
  • Controllability and path optimization for such systems require advanced mathematical frameworks.

Purpose of the Study:

  • To develop a robust, PDE-based approach for optimal path finding in Reeds-Shepp car models.
  • To generalize the model to 2D and 3D, including state-dependent costs and removal of reverse gear.
  • To apply the method for extracting complex tubular structures from medical images.

Main Methods:

  • Minimizing a data-driven functional with curvature and length penalization.
  • Utilizing eikonal equations on a manifold with anisotropic Finsler metrics.
  • Employing a fast-marching (FM) method with specialized discretization stencils.
  • Applying gradient descent on computed distance maps for path extraction.

Main Results:

  • Global and local controllability results are proven for the generalized models.
  • The FM method accurately approximates singular quasi-distances using anisotropic Finsler metrics.
  • The model successfully extracts complex tubular structures from medical images, handling occlusions and low contrast.
  • The variant without reverse gear demonstrates improved bifurcation handling.

Conclusions:

  • The proposed PDE-based method offers a powerful tool for optimal path planning in Reeds-Shepp car models.
  • This approach significantly advances the analysis of nonholonomic systems and their applications in medical image analysis.
  • The method shows high potential for applications like retinal vessel tracking and brain connectivity analysis.