Variational model with kernel metric-based data term for noisy image segmentation

The segmentation of images with severe noise has always been a very challenging task because noise has great influence on the accuracy of segmentation. This paper proposes a robust variational level set model for image segmentation, involving the kernel metric based on the Gaussian radial basis function (GRBF) kernel as the data fidelity metric. The kernel metric can adaptively emphasize the contribution of pixels close to the mean intensity value inside (or outside) the evolving curve and so reduce the influence of noise. We prove that the proposed energy functional is strictly convex and has a unique global minimizer in BV(Ω). A three-step time-splitting scheme, in which the evolution equation is decomposed into two linear differential equations and a nonlinear differential equation, is developed to numerically solve the proposed model efficiently. Experimental results show that the proposed method is very robust to some types of noise (namely, salt & pepper noise, Gaussian noise and mixed noise) and has better performance than six state-of-the-art related models.