A Variational Model for Infinite Perimeter Segmentations Based on Lipschitz Level Set Functions: Denoising while Keeping Finely Oscillatory Boundaries
Marco Barchiesi, S. H. Kang, Tri Le, Massimiliano Morini, Marcello Ponsiglione · Multiscale Modeling and Simulation · 2010
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.