Simon MASNOU

Professor at Claude Bernard University Lyon 1

Head of the "Applied Mathematics, Statistics" Master's degree
Head of the "M2 Maths in Action" Master's program

2018-2022: Director of the Camille Jordan Institute

Institut Camille Jordan
CNRS UMR 5208
Université Claude Bernard Lyon 1
43, Boulevard du 11 novembre 1918
69622 Villeurbanne Cedex
France

Braconnier building (campus de la Doua)
Room 256 (2nd floor)
Phone: + 33 (0)4 72 43 13 86
Email: masnou 'at' math.univ-lyon1.fr

Research interests

Applied mathematics
Image processing
Shape optimization
Learning / Deep learning
Geometric flows
Geometry of discrete datasets
Calculus of variations
Geometric measure theory

Current/recent research projects

Member of ANR project STOIQUES (Optimisation de forme et topologique : questions importantes et sujets émergents, 2024-2028)
Member of PEPR project PDE-AI (Partial Differential Equations for Artificial Intelligence: numerical analysis, optimal control and optimal transport, 2023-2027)
Member of RISE project NoMADS (Nonlocal Methods for Arbitrary Data Sources, 2018-2023)
Member of ANR project MiMESis-3D (Métamorphoses et propriétés de la neige à partir d'images 3D, 2020-2024)
Member of ANR project
BEEP (Ingéniérie d'électrodes à base de nanofils pour la photocatalyse, 2018-2022)
Member of ANR project MIRIAM (Restauration multi-images : des mathématiques appliquées à l'industrie de l'imagerie, 2014-2019)
Member of ANR project GEOMETRYA (Geometric measure theory and its applications, 2012-2017)
Member of PGMO project COCA (Connexions Optimales, Calcul et Approximations, 2016-2018).

PhD supervision

Abdelmouksit Sagueni, 2024, Approximate mean curvature flows of varifolds and limit Brakke flows, cosupervised with Blanche Buet (Univ. Paris-Saclay) and Gian Paolo Leonardi (Univ. Trento).
Garry Terii, 2022, Approximation of geometric flows: from phase field methods to neural networks, cosupervised with Elie Bretin (INSA Lyon).
Chih-Kang Huang, 2021, Questions of approximation and compactness for geometric variational problems, cosupervised with Olivier Druet (CNRS, Lyon).
Thuc Trinh Le, 2019, Video inpainting and semi-supervised object removal, cosupervised with Andrés Almansa (Paris 5) and Yann Gousseau (Telecom ParisTech).
Simone Parisotto, 2019, Anisotropic variational models and PDEs for inverse imaging problems, cosupervised with Carola-Bibiane Schönlieb (Univ. Cambridge).
François Dayrens, 2016, Constrained minimizations and flows of the perimeter or the Willmore energy, cosupervised with Matteo Novaga (Univ. Pisa).
Xiaofang Wang, 2015, Graph methods for image segmentation and dynamic objects tracking, cosupervised with Liming Chen (Ecole Centrale de Lyon).
Blanche Buet, 2014, Surface approximation by discrete varifolds: representation, rectifiability, curvature, cosupervised with Gian Paolo Leonardi (Univ. Modena).
Giacomo Nardi, 2011, On a characterization of the relaxation of a generalized Willmore functional.

Teaching

Algèbre linéaire et bilinéaire, analyse matricielle (cours, TD, TP), L3
Optimisation (cours, TD), M1 Mathématiques appliquées, statistiques
Optimisation et machine learning (cours), M2 Maths en Action
Approches géométriques pour les images et les formes (cours), M2 Maths en Action

Manuscripts

Accreditation to supervise research (Habilitation à diriger des recherches): Questions variationnelles autour d'un problème de restauration d'images (defended on Dec 1st, 2008, Univ. Paris 6).
PhD thesis: Filtrage et désocclusion d'images par méthodes d'ensembles de niveau (defended on Dec 15, 1998, Univ. Paris-Dauphine).

Publications / Preprints

E. Bretin, C.-K. Huang, S. Masnou, A penalized Allen-Cahn equation for the mean curvature flow of thin structures, submitted, 2024.
J. Lee, X. Cai, C.-B. Schönlieb, S. Masnou, Neural varifolds: an aggregate representation for quantifying the geometry of point clouds, submitted, 2024.
E. Bretin, L. Calatroni, S. Masnou, A mobility-SAV approach for a Cahn-Hilliard equation with degenerate mobilities, Discrete and Continuous Dynamical Systems Series S, 17(1):131-159, 2024
E. Bretin, R. Denis, S. Masnou, A. Sengers, G. Terii, A multiphase Cahn-Hilliard system with mobilities and the numerical simulation of dewetting, ESAIM: M2AN (Mathematical Modelling and Numerical Analysis), 57(3):1473-1509, 2023
E. Bonnetier, E. Bretin, S. Masnou, Approximation of multiphase mean curvature flows with arbitrary nonnegative mobilities, Mathematical Methods in the Applied Sciences, 46(9):11262-11282, 2023.
E. Bretin, R. Denis, S. Masnou, G. Terii, Learning phase field mean curvature flows with neural networks, Journal of Computational Physics, 111579, 470, 2022.
B. Buet, G.P. Leonardi, S. Masnou, Weak and approximate curvatures of a measure: a varifold perspective, Nonlinear Analysis, 222, 2022.
E. Guérin, A. Peytavie, S. Masnou, J. Digne, B. Sauvage, J. Gain, E. Galin, Gradient Terrain Authoring, Computer Graphics Forum, 41(2), Proceedings of Eurographics, 2022.
E. Bretin, S. Masnou, A. Sengers, G. Terii, Approximation of surface diffusion flow: a second order variational Cahn-Hilliard model with degenerate mobilities, Mathematical Models and Methods in Applied Sciences, 32(04):793-829, 2022.
F. Dayrens, S. Masnou, M. Novaga, M. Pozzetta, Connected perimeter of planar sets, Advances in Calculus of Variations, 5(2):213-234, 2022.
S. Parisotto, J. Lellmann, S. Masnou, C.-B. Schönlieb, Higher-Order Total Directional Variation: Imaging Applications, SIAM Journal on Imaging Sciences, 13(4):2063-2104, 2020.
S. Parisotto, S. Masnou, C.-B. Schönlieb, Higher-Order Total Directional Variation: Analysis, SIAM Journal on Imaging Sciences, 13(1):474-496, 2020.
B. Buet, J.-M. Mirebeau, Y. van Gennip, F. Desquilbet, J. Dreo, F. Barbaresco, G.P. Leonardi, S. Masnou, C.-B. Schönlieb, Partial differential equations and variational methods for geometric processing of images, SMAI Journal of Computational Mathematics, S5:109-128, 2019.
T.T. Le, A. Almansa, Y. Gousseau, S. Masnou, Object removal from complex videos using a few annotations, Computational Visual Media, 5(3):267-291, 2019, see the project page
B. Buet, G.P. Leonardi, S. Masnou, Discretization and approximation of surfaces using varifolds, Geometric Flows, 3(1):28-56, 2018.
T.T. Le, A. Almansa, Y. Gousseau, S. Masnou, Removing objects from videos with a few strokes, SIGGRAPH Asia 2018 Technical Briefs, article no 22, 1-4, 2018.
E. Bretin, A. Danescu, J. Penuelas, S. Masnou, Multiphase mean curvature flows with high mobility contrasts: a phase-field approach, with applications to nanowires, Journal of Computational Physics, 365:324-349, 2018.
F. Dayrens, S. Masnou, and M. Novaga, Existence, regularity and structure of confined elasticae, ESAIM:Control, Optimisation and Calculus of Variations, 24(1):25-43, 2018.
E. Bretin, F. Dayrens, S. Masnou, Volume reconstruction from slices, SIAM J. Imaging Sciences, 10(4):2326-2358, 2017.
T.T. Le, A. Almansa, Y. Gousseau, S. Masnou, Motion-Consistent Video Inpainting, Proc. IEEE ICIP, Beijing, 2017, see the project page
B. Buet, G.P. Leonardi, and S. Masnou, A varifold approach to surface approximation, Archive for Rational Mechanics and Analysis, 226(2):639-694,2017.
E. Bretin and S. Masnou, A new phase field model for inhomogeneous minimal partitions, and applications to droplets dynamics, Interfaces and Free Boundaries, 19(2):141-182, 2017.
B. Buet, G.P. Leonardi, and S. Masnou, Discrete varifolds and surface approximation, Topological Optimization and Optimal Transport in the Applied Sciences, 17:159, Berlin, Boston: De Gruyter, 2017
E. Bretin and S. Masnou, On a new phase field model for the approximation of interfacial energies of multiphase systems, Topological Optimization and Optimal Transport in the Applied Sciences, 17:123, Berlin, Boston: De Gruyter, 2017
J. Dalphin, A. Henrot, S. Masnou, and T. Takahashi, On the minimization of total mean curvature, J. Geometric Analysis, 26(4):2729-2750, 2016.
X. Wang, B. Gao, S. Masnou, L. Chen, I. Theurkauff, C. Cottin-Bizonne, Y. Zhao, F. Shih, Active colloids segmentation and tracking, Pattern Recognition, 60:177-188, 2016.
B. Buet, G.P. Leonardi, S. Masnou Discrete varifolds: a unified framework for discrete approximations of surfaces and mean curvature, Proc. SSVM2015, LNCS volume 9087, 2015.
X. Wang, Y. Tang, S. Masnou, and L. Chen A Global/Local Affinity Graph for Image Segmentation, IEEE Trans. Image Processing, 24(4): 1399-1411, 2015.
E. Bretin, S. Masnou, and E. Oudet Phase-field approximations of the Willmore functional and flow, Numerische Mathematik, 131(1):115-171, 2015.
Y. Tang, X. Wang, E. Dellandrea, S. Masnou, and L. Chen, Fusing generic objectness and deformable part-based models for weakly supervised object detection, Proc. IEEE International Conference on Image Processing, Paris, pp. 4072-4076. 2014.
E. Bretin, S. Masnou, and E. Oudet Phase-field models for the approximation of the Willmore functional and flow, ESAIM: ProcS 45 118-127, 2014.
X. Wang, H. Li, S. Masnou, and L. Chen Sparse coding and mid-level superpixel-feature for l0-graph based unsupervised image segmentation, Computer Analysis of Images and Patterns, II:160-168, Lecture Notes in Comput. Sci., 8048, 2013.
X. Wang, H. Li, C.-E. Bichot, S. Masnou, and L. Chen A graph-cut approach to image segmentation using an affinity graph based on l0-sparse representation of features, IEEE International Conference on Image Processing, Melbourne (Australia), 2013.
X. Wang, C. Zhu, C.-E. Bichot, S. Masnou Graph-based image segmentation using weighted color patch, IEEE International Conference on Image Processing, Melbourne (Australia), 2013.
S. Masnou and G. Nardi, Gradient Young measures, varifolds, and a generalized Willmore functional, Advances in Calculus of Variations, 6(4):433-482, 2013.
S. Masnou and G. Nardi, A coarea-type formula for the relaxation of a generalized elastica functional, Journal of Convex Analysis, 20(3): 617-653, 2013.
T. Schoenemann, F. Kahl, S. Masnou, and D. Cremers, A linear framework for region-based image segmentation and inpainting involving curvature penalization, International Journal of Computer Vision, 99:1, pages 53-68, 2012.
F. Cao, Y. Gousseau, S. Masnou and P. Pérez, Geometrically guided exemplar-based inpainting, SIAM Journal on Imaging Sciences 4(4), pp. 1143-1179, 2011.
T. Schoenemann, S. Masnou and D. Cremers, The elastic ratio: introducing curvature into ratio-based globally optimal image segmentation, IEEE Transactions on Image Processing, 20(9), pp 2565-2581, 2011.
T. Schoenemann, S. Masnou, and D. Cremers, On a linear programming approach to the discrete Willmore boundary value problem and generalizations, J.-D. Boissonnat et al. (Eds.): Curves and Surfaces 2011, LNCS 6920, pp. 629--646. Springer, Heidelberg (2011).
M. Bertalmío, V. Caselles, S. Masnou, and G. Sapiro, Inpainting, Encyclopedia of Computer Vision, Springer, 2011.
A. Buades, J. Delon, Y. Gousseau, and S. Masnou, Adaptive blotches detection for film restoration, IEEE Int. Conference on Image Processing, Hong-Kong, sept. 2010.
J.-F. Aujol, S. Ladjal and S. Masnou, Exemplar-based inpainting from a variational point of view, SIAM Journal on Mathematical Analysis, 42(3):1246-1285, 2010.
G.P Leonardi and S. Masnou. Locality of the mean curvature of rectifiable varifolds, Advances in Calculus of variations, 2(1):17-42, 2009.
S. Masnou and J.-M. Morel. On a variational theory of image amodal completion. Rendiconti del Seminario Matematico della Università di Padova, 116:211-252, 2006.
G.P. Leonardi and S. Masnou. On the isoperimetric problem in the Heisenberg group Hn. Annali di Matematica Pura ed Applicata, 184(4):533-553, 2005.
L. Ambrosio and S. Masnou. A direct variational approach to a problem arising in image reconstruction, Interfaces and Free Boundaries, 5:63-81, 2003.
L. Ambrosio and S. Masnou. On a variational problem arising in image reconstruction. In Proc. Free Boundary Problems (Trento, 2002). Internat. Series of Num. Math., 147, Birkhaser, Basel, 2004.
S. Masnou. Disocclusion : a variational approach using level lines, IEEE Trans. On Image Processing, 11(2):68-76, 2002.
V. Caselles, S. Masnou, et J.-M. Morel. La vision, une machine géométrique ? La Recherche, Octobre 2001.
L. Ambrosio, V. Caselles, S. Masnou and J.-M. Morel. Connected components of sets of finite perimeter and applications to image processing, Journal of the European Mathematical Society, 3:39-92, 2001.
V. Caselles, S. Masnou, J.-M. Morel and C. Sbert. Image interpolation, Notes du Séminaire Equations aux Dérivées Partielles, vol. XII. Ecole Polytechnique, 1998.
S. Masnou et J.-M. Morel. La formalisation mathématique du traitement des images, C.R. Journée annuelle de la Société Mathématique de France (Trois Applications des Mathématiques), 1-14, 1998.
S. Masnou and J.-M. Morel. Image restoration involving connectedness, Proc. DIP'97 (Wien), vol. 3346, 84-95. SPIE, 1998.
S. Masnou and J.-M. Morel. Level lines based disocclusion, Proc. IEEE ICIP (Chicago 1998), vol.3, 259-263, 1998.
S. Masnou et J.-M. Morel. Restauration d'images et filtres de Yaroslavsky, Proc. Gretsi'97 (Grenoble), 1233-1236, 1997.

Past local events

Journées SMAI Mode 2024, Lyon, March 27-29, 2024.
Thematic period on Calculus of variations, optimal transportation, and geometric measure theory: from theory to applications, Lyon, June 27-- July 15, 2016.
Journées de l'ANR Geometrya / Onzièmes rencontres d'analyse, Oct. 11-12, 2012, Lyon.
Conférence Mathématiques et grandes dimensions -- de la théorie aux développements industriels (Mathematics and High dimensions: from theory to industrial applications), Dec 10, 2012, Lyon
Seconde Semaine d'Etude Mathématiques et Entreprises (SEME, Study Group for Industry), Nov. 28--Dec 2, 2011, Lyon