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Fitting unbranching skeletal structures to objects.

Zhiyuan Liu1, Junpyo Hong2, Jared Vicory3

  • 1Department of Computer Science, University of North Carolina at Chapel Hill, USA.

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Summary
This summary is machine-generated.

We developed a novel method to create discrete skeletal structures (d-s-reps) for 3D shapes, ensuring consistent representation across populations for statistical shape analysis. This technique accurately captures geometric properties for applications like brain structure analysis.

Keywords:
Shape representationSkeletal modelStatistical shape analysis

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Area of Science:

  • Computational geometry
  • Statistical shape analysis
  • Medical image analysis

Background:

  • Skeletal representations are valuable for statistical shape analysis when correspondence is established.
  • Many anatomical structures possess genus-zero boundaries suitable for smooth, unbranching skeletal representation.
  • Existing methods may lack consistent correspondence across diverse anatomical shapes.

Purpose of the Study:

  • To compute a discrete skeletal structure (d-s-rep) for individual 3D shapes that ensures correspondence across a population.
  • To develop a method for fitting d-s-reps to object boundaries based on geometric properties.
  • To demonstrate the applicability of the method for analyzing human brain structures.

Main Methods:

  • A two-stage framework is employed: initial rough fitting followed by refinement of the skeletal structure.
  • The first stage uses stratified diffeomorphisms for topologically consistent, smooth, and unbranching skeletal structures.
  • The second stage minimizes geometric disagreement between the skeletally implied and target boundaries, avoiding self-overlaps.

Main Results:

  • The method successfully computes discrete skeletal structures (d-s-reps) for individual 3D shapes.
  • The fitted d-s-reps accurately approximate target surfaces based on position, tangent fields, and curvature.
  • Demonstrated successful application to various human brain structures, showing good correspondence.

Conclusions:

  • The proposed d-s-rep computation method provides a robust way to achieve skeletal representations with good correspondence.
  • The framework is accessible and extensible, particularly for clinical users and researchers via SlicerSALT (3D Slicer).
  • This approach facilitates advanced statistical shape analysis of anatomical objects.