A Variational Model for Infinite Perimeter Segmentations Based on Lipschitz Level Set Functions: Denoising while Keeping Finely Oscillatory Boundaries

We propose a new model for segmenting piecewise constant images with irregular object boundaries: a variant of the Chan–Vese model [T. F. Chan and L. A. Vese, IEEE Trans. Image Process., 10 (2000), pp. 266–277], where the length penalization of the boundaries is replaced by the area of their neighborhood of thickness $\varepsilon$. Our aim is to keep fine details and irregularities of the boundaries while denoising additive Gaussian noise. For the numerical computation we revisit the classical $BV$ level set formulation [S. Osher and J. A. Sethian, J. Comput. Phys., 79 (1988), pp. 12–49] considering suitable Lipschitz level set functions instead of $BV$ ones.

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