22 citations · 46 across the 16 of their papers we have counts for
23 papers
Learning the Willmore flow with a lightweight neural operator
Elie Bretin, Roland Denis, Tokuhiro Eto +1
We extend to the Willmore flow the phase-field neural operator approach proposed by Bretin, Denis, Masnou, and Terii (2022) for mean curvature motion in two and three dimensions. T…
Approximate mean curvature flows of a general varifold, and their limit spacetime Brakke flow
Blanche Buet, Gian Paolo Leonardi, Simon Masnou +1
We propose a construction of mean curvature flows by approximation for very general initial data, in the spirit of the works of Brakke and of Kim & Tonegawa based on the theory of…
Turing patterns on polymerized membranes: a coarse-grained lattice modelling with internal degree of freedom for polymer direction
F. Kato, H. Koibuchi, E. Bretin +6
We numerically study Turing patterns (TPs) on two-dimensional surfaces with a square boundary in using a surface model for polymerized membranes. The variables used to…
A Cahn--Hilliard--Willmore phase field model for non-oriented interfaces
Elie Bretin, Antonin Chambolle, Simon Masnou
We investigate a new phase field model for representing non-oriented interfaces, approximating their area and simulating their area-minimizing flow. Our contribution is related to…
A penalized Allen-Cahn equation for the mean curvature flow of thin structures
Elie Bretin, Chih-Kang Huang, Simon Masnou
This paper addresses the approximation of the mean curvature flow of thin structures for which classical phase field methods are not suitable. By thin structures, we mean surfaces…
A mobility-SAV approach for a Cahn-Hilliard equation with degenerate mobilities
Elie Bretin, Luca Calatroni, Simon Masnou
A novel numerical strategy is introduced for computing approximations of solutions to a Cahn-Hilliard model with degenerate mobilities. This model has recently been introduced as a…
Learning phase field mean curvature flows with neural networks
Elie Bretin, Roland Denis, Simon Masnou +1
We introduce in this paper new and very effective numerical methods based on neural networks for the approximation of the mean curvature flow of either oriented or non-orientable s…
Approximation of multiphase mean curvature flows with arbitrary nonnegative mobilities
Eric Bonnetier, Elie Bretin, Simon Masnou
This paper is devoted to the robust approximation with a variational phase field approach of multiphase mean curvature flows with possibly highly contrasted mobilities. The case of…
A multiphase Cahn-Hilliard system with mobilities and the numerical simulation of dewetting
Elie Bretin, Roland Denis, Simon Masnou +2
We propose in this paper a new multiphase Cahn-Hilliard model with doubly degenerate mobilities. We prove by a formal asymptotic analysis that it approximates with second order acc…
Approximation of surface diffusion flow: a second order variational Cahn--Hilliard model with degenerate mobilities
Elie Bretin, Simon Masnou, Arnaud Sengers +1
This paper tackles the approximation of surface diffusion flow using a Cahn--Hilliard-type model. We introduce and analyze a new second order variational phase field model which as…
Connected perimeter of planar sets
François Dayrens, Simon Masnou, Matteo Novaga +1
We introduce a notion of connected perimeter for planar sets defined as the lower semi-continuous envelope of perimeters of approximating sets which are measure-theoretically conne…
Weak and approximate curvatures of a measure: a varifold perspective
Blanche Buet, Gian Paolo Leonardi, Simon Masnou
By revisiting the notion of generalized second fundamental form originally introduced by Hutchinson for a special class of integral varifolds, we define a weak curvature tensor tha…
Higher-Order Total Directional Variation: Analysis
Simone Parisotto, Simon Masnou, Carola-Bibiane Schönlieb
We analyse a new notion of total anisotropic higher-order variation which, differently from the Total Generalized Variation by Bredies et al., quantifies for possibly non-symmetric…
Higher-Order Total Directional Variation: Imaging Applications
Simone Parisotto, Jan Lellmann, Simon Masnou +1
We introduce a class of higher-order anisotropic total variation regularisers, which are defined for possibly inhomogeneous, smooth elliptic anisotropies, that extends the Total Ge…
Multiphase mean curvature flows with high mobility contrasts: a phase-field approach, with applications to nanowires
Elie Bretin, Alexandre Danescu, José Penuelas +1
The structure of many multiphase systems is governed by an energy that penalizes the area of interfaces between phases weighted by surface tension coefficients. However, interface…
A varifold approach to surface approximation
Blanche Buet, Gian Paolo Leonardi, Simon Masnou
We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations…
Existence, regularity and structure of confined elasticae
François Dayrens, Simon Masnou, Matteo Novaga
We consider the problem of minimizing the bending or elastic energy among Jordan curves confined in a given open set . We prove existence, regularity and some structural propert…
On the minimization of total mean curvature
Jeremy Dalphin, Antoine Henrot, Simon Masnou +1
In this paper we are interested in possible extensions of an inequality due to Minkowski: valid for any regular open set $Ω\subs…
Phase-field approximations of the Willmore functional and flow
Elie Bretin, Simon Masnou, Edouard Oudet
We discuss in this paper phase-field approximations of the Willmore functional and the associated L2-flow. After recollecting known results on the approximation of the Willmore ene…
A coarea-type formula for the relaxation of a generalized elastica functional
Simon Masnou, Giacomo Nardi
We consider in R^2 the generalized elastica functional defined, for smooth functions, as the p-elastica energies of the level lines integrated over all levels. Extending the functi…
Gradient Young measures, varifolds, and a generalized Willmore functional
Simon Masnou, Giacomo Nardi
Being Omega an open and bounded Lipschitz domain of R^n, we consider the generalized Willmore functional on Omega defined, for smooth functions, as the p-Willmore energy of each is…
A linear framework for region-based image segmentation and inpainting involving curvature penalization
Thomas Schoenemann, Fredrik Kahl, Simon Masnou +1
We present the first method to handle curvature regularity in region-based image segmentation and inpainting that is independent of initialization. To this end we start from a new…
On a linear programming approach to the discrete Willmore boundary value problem and generalizations
Thomas Schoenemann, Simon Masnou, Daniel Cremers
We consider the problem of finding (possibly non connected) discrete surfaces spanning a finite set of discrete boundary curves in the three-dimensional space and minimizing (globa…