A variational surface deformation and subdivision-based modeling framework for noisy and small n-furcated tube-like...

Area of Science:

• Medical Imaging and Computational Anatomy
• Biomedical Engineering
• Computer Graphics and Geometric Modeling

Background:

• Accurate meshing of complex vascular structures (arteries, veins) is crucial but challenging due to noise, small size, and bifurcations.
• Existing methods struggle with topological correctness and positional accuracy for irregular, pathological vessels.

Purpose of the Study:

• To develop a robust framework for constructing accurate and smooth 3D meshes of n-furcated, tube-like structures.
• To enhance the efficiency and accuracy of mesh generation for biomedical applications.

Main Methods:

• A two-step framework: initial mesh construction focusing on topological correctness, followed by mesh refinement using variational surface deformation.
• Iterative solving of Euler-Lagrange equations to minimize shell and distance energies, refining mesh positions towards vessel boundaries.
• Incorporation of a mesh dilation method to prevent deviations and a coarse-to-fine approach combining deformation and subdivision.

Main Results:

• The proposed method successfully generates accurate and smooth meshes for noisy and small n-furcated tube-like structures.
• Demonstrated improvement in positional accuracy and topological correctness compared to traditional methods.

Conclusions:

• The coarse-to-fine modeling framework effectively addresses the challenges of meshing complex vascular geometries.
• The generated meshes are suitable for downstream applications such as hemodynamics, quantitative measurements, and vessel analysis.