Ricci curvature tensor based volumetric segmentation

Existing level set models employ regularization based only on gradient information, 1D curvature or 2D curvature. For 3D image segmentation, however, an appropriate curvature-based regularization should involve a well-defined 3D curvature energy. This is the first paper to introduce a regularization energy that incorporates 3D scalar curvature for 3D image segmentation, inspired by the Einstein-Hilbert functional. To derive its Euler-Lagrange equation, we employ a two-step gradient descent strategy, alternately updating the level set function and its gradient. The paper also establishes the existence and uniqueness of the viscosity solution for the proposed model. Experimental results demonstrate that our proposed model outperforms other state-of-the-art models in 3D image segmentation.