Diffusive smoothing of 3D segmented medical data

Area of Science:

• Computer Graphics
• Geometric Processing
• Numerical Analysis

Background:

• Heat diffusion smoothing is crucial for processing 3D shapes represented as triangle meshes.
• Existing methods often require parameter tuning and can be computationally expensive.
• Robust and efficient smoothing techniques are needed for applications in computer graphics and medical imaging.

Purpose of the Study:

• To propose an accurate, computationally efficient, and spectrum-free formulation for heat diffusion smoothing on 3D triangle meshes.
• To develop a method that is robust to surface discretization and free of user-defined parameters.
• To provide a criterion for selecting the optimal time parameter for balancing accuracy and smoothness.

Main Methods:

• Utilizing a [Formula: see text]-degree Padé-Chebyshev rational approximation for the heat diffusion equation.
• Formulating the problem as solving sparse, symmetric linear systems.
• Implementing a criterion for time parameter selection to optimize accuracy and smoothness.

Main Results:

• The proposed spectrum-free formulation significantly reduces computational cost.
• Achieves higher approximation accuracy compared to previous methods.
• Demonstrates robustness to surface discretization and eliminates user-defined parameters.
• Experiments on anatomical data validate the effectiveness and efficiency.

Conclusions:

• The spectrum-free heat diffusion smoothing offers a superior alternative for processing 3D triangle meshes.
• The method provides a significant reduction in computational cost and enhanced accuracy.
• It is a parameter-free and robust solution applicable to complex geometric data.