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. •We develop a novel level set model incorporating Ricci curvature in the edge term.•We present a method to calculate Ricci curvature for 3D images.•Our proposed Ricci curvature term can adapt to other models to serve as an edge descriptor for 3D image.