We consider a second order variational model dedicated to crack detection on bituminous surfacing. It is based on a variant of the weak formulation of the Blake-Zisserman functional that involves the discontinuity set of the gradient of the unknown, set that encodes the geometrical thin structures we aim to recover. Following Ambrosio, Faina and March, an approximation of this cost function by elliptic functionals is provided. Theoretical results including existence of minimizers, existence of a unique viscosity solution to the derived evolution problem, and a Gamma-convergence result relating the elliptic functionals to the initial weak formulation are given. Extending then the ideas developed in the case of first order nonlocal regularization to higher order derivatives, we provide and analyze a nonlocal version of the model and an MPI implementation.

This is poster number 44 in Poster Session

Authors:

Carole Le Guyader (INSA Rouen)

Nathan Rouxelin (INSA Rouen)

Timothée Schmoderer (INSA Rouen)

Emeric Quesnel (INSA Rouen)

Patrick Bousquet-Melou (CRIANN)

Noémie Debroux (University of Cambridge)

Keywords:

fractional sobolev space, image enhancement, image segmentation, nonlinear optimization, nonlocal second order operators, partial differential equation models, space of generalized special functions of bounded variation, viscosity solutions