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The aim of this paper is to present a new method for skin tumor segmentation in the 3D ultrasound images. We consider a variational formulation, the energy of which combines a diffuse interface phase field model (regularization term) and a log-likelihood computed using nonparametric estimates (data attachment term). We propose a multi-grid implementation with the exact solutions which has the advantage to avoid space discretization and numerical instabilities. The resulting algorithm is simple and easy to implement in multi-dimensions. Concerning applications, we focus on skin tumor segmentation. The clinical dataset used for the experiments is composed of 12 images with the ground truth given by a dermatologist. Comparisons with the reference methods show that the proposed method is more robust to the choice of the volume initialization. Moreover, thanks to the flexibility introduced by the diffuse interface, the sensitivity increases by 12% if the initialization is inside the lesion, and the Dice index increases by 59%, if the initialization covers the entire lesion. These results show that this new method is well designed to tackle the problem of underestimation of tumor volumes.
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