A variational model for infin ite perimeter segmentations based on lipschitz level set functions: Denoising while keeping finely oscillatory boundaries

Abstract

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 e. 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.