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Variational level set methods are formulated as energy minimisation problems, which are often solved by gradient-based optimisation methods, such as gradient descent. Unfortunately, the gradient obtained by applying the calculus of variations is not suitable, because it is only an element of the function space L 2 making it prone to lead into wrong local minima. Consequently, some regularisation strategy - be it the restriction to signed distance functions or the choice of smooth function spaces - is necessary. In this paper we propose diffusion-based regularisation strategies and compare them to the recently proposed ones of Charpiat et al. and Sundaramoorthi et al. From this comparison we derive two general regularisation paradigms at the level of update equations and show that the diffusion-based paradigm enjoys both theoretical and practical advantages, such as an improved convergence rate, while being of the same computational complexity as the other paradigm.

Diffusion-based Regularisation Strategies for Variational Level Set Segmentation