Variational Level Set Segmentation in Riemannian Sobolev Spaces

Gradient flows in the Sobolev space H1 have been shown to enjoy favorable regularity properties. We propose a generalization of prior approaches for Sobolev active contour segmentation by changing the notion of distance in the Sobolev space, which is achieved through treatment of the function and its derivative in Riemannian manifolds. The resulting generalized Riemannian Sobolev space provides the flexibility of choosing an appropriate metric, which can be used to design efficient gradient flows. We select this metric based on the rationale of preconditioning resulting in a significant improvement of convergence and overall runtime in case of variational level set segmentation.