Calculus of Variations and Geometric Measure Theory

M. Barchiesi - S. H. Kang - T. M. Le - M. Morini - M. Ponsiglione

A variational model for infinite perimeter segmentations based on Lipschitz level set functions: denoising while keeping finely oscillatory boundaries

created by ponsiglio on 09 Oct 2009
modified by barchiesi on 05 Oct 2010


Published Paper

Inserted: 9 oct 2009
Last Updated: 5 oct 2010

Journal: Multiscale Model. Simul.
Volume: 8
Pages: 1715-1741
Year: 2010


We propose a new model for segmenting piecewise constant images with irregular object boundaries: a variant of the Chan-Vese model, where the length penalization of the boundaries is replaced by the area of their neighborhood of thickness $\epsilon$. 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 considering suitable Lipschitz level set functions instead of $BV$ ones.

Keywords: level set, Denoising, Variational segmentation