Ricci curvature based volumetric segmentation

The level set method has played a critical role among many image segmentation approaches. Several edge detectors, such as the gradient, have been applied to its regularisation term. However, traditional edge detectors lack high-order information and are sensitive to image noise. To tackle this problem, we introduce a method to calculate the Ricci curvature, a vital curvature in three-dimensional Riemannian geometry. In addition, we propose incorporating the curvature into the regularisation term. Experiments suggest that our method outperforms the state-of-the-art level set methods and achieves a comparable result with the Swin UNETR and Segment Anything.