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

Boundaries

Marco Barchiesi BCAM 48160 Derio, Spain barchiesi@bcamath.org

Sung Ha Kang Georgia Institute of Technology School of Mathematics Atlanga, GA 30332-0160 kang@math.gatech.edu

Triet M. Le Yale Univeristy Department of Mathematics New Haven, CT 06511 triet.le@yale.edu

Massimiliano Morini SISSA 30414 Trieste, Italy morini@sissa.it

Marcello Ponsiglione Università di Roma “La Sapienza” Dipartimento di matematica 00185 Roma, Italy ponsigli@mat.uniroma1.it

Abstract: We propose a new model for segmenting piecewise constant images with irregular object boundaries: a variant of the Chan-Vese model [10], where the length penalization of the boundaries is replaced by the area of their neighborhood of thickness .. 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 [23] considering suitable Lipschitz level set functions instead of BV ones.