Ricci Curvature Tensor-Based Volumetric Segmentation.

Area of Science:

• Medical Imaging
• Computer Vision
• Computational Geometry

Background:

• Current level set models for 3D image segmentation utilize limited regularization based on gradient or lower-dimensional curvature.
• A well-defined 3D curvature energy is crucial for effective regularization in 3D image segmentation.

Purpose of the Study:

• To introduce a novel regularization energy incorporating 3D scalar curvature for 3D image segmentation.
• To address the limitations of existing regularization techniques in 3D image segmentation.

Main Methods:

• Developed a regularization energy inspired by the Einstein-Hilbert functional, utilizing 3D scalar curvature.
• Employed a two-step gradient descent strategy for deriving the Euler-Lagrange equation, involving alternate updates of the level set function and its gradient.
• Established the existence and uniqueness of the viscosity solution for the proposed model.

Main Results:

• The proposed model successfully incorporates 3D scalar curvature for regularization in 3D image segmentation.
• The existence and uniqueness of the viscosity solution were mathematically established.
• Experimental results showed superior performance compared to state-of-the-art models in 3D image segmentation tasks.

Conclusions:

• The novel 3D scalar curvature regularization offers a significant advancement for 3D image segmentation.
• The proposed model provides a more robust and accurate approach for segmenting 3D image data.
• This work lays the foundation for future research in curvature-based regularization for medical image analysis.