Author: "INSA de Rouen" / Language: english - Searchworks@Jio Institute Digital Library Search Results

Your search keyword '"INSA de Rouen"' showing total 621 results

Start Over Author "INSA de Rouen" Language english

621 results on '"INSA de Rouen"'

1. Laser-material interaction during atom probe tomography of oxides with embedded metal nanoparticles

Author: Vella, A. [Univ. et INSA de Rouen - UMR CNRS 6634 - Normandie Univ., Saint Etienne du Rouvray (France)]
Published: 2016
Full Text: View/download PDF

2. A multiscale medium approximation method for the propagation P-waves in highly heterogeneous geophysical media

Author: Chaumont-Frelet , Théophile, Barucq , Hélène, Calandra , H., Gout , C., Basque Center for Applied Mathematics ( BCAM ), Basque Center for Applied Mathematics, Advanced 3D Numerical Modeling in Geophysics ( Magique 3D ), Laboratoire de Mathématiques et de leurs Applications [Pau] ( LMAP ), Université de Pau et des Pays de l'Adour ( UPPA ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Pau et des Pays de l'Adour ( UPPA ) -Centre National de la Recherche Scientifique ( CNRS ) -Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ), Laboratoire de Mathématiques de l'INSA de Rouen Normandie ( LMI ), Institut national des sciences appliquées Rouen Normandie ( INSA Rouen Normandie ), Normandie Université ( NU ) -Normandie Université ( NU ), Université de Pau et des Pays de l'Adour ( UPPA ) -Centre National de la Recherche Scientifique ( CNRS ), Total E&P, Basque Center for Applied Mathematics (BCAM), Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), and Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: [ MATH ] Mathematics [math], [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA], [MATH]Mathematics [math], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: Approximating the solution of Helmholtz problems is a tricky task, especially at high frequency. Indeed, because of the numerical dispersion, it is mandatory to increase the number of discretization points per wavelength for higher frequencies. Using high degree polynomial shape functions on a coarse mesh is an interesting approach because it contributes to reduce such numerical dispersion as compared to linear functions set on a fine mesh. While this solution is very efficient for wave propagation in homogeneous media, it is not obvious how the variations of the medium inside a cell have to be taken into account. Recently the Multiscale Medium Approximation method (MMAm) has been proposed to overcome this difficulty. High-order shape functions are used with a coarse mesh to reduce dispersion and hence, the pollution effect. Then, the key idea is to introduce a multiscale approximation of the medium to take into account fine scale heterogeneities on the coarse mesh. This approach has proven to be efficient on academic test cases and a convergence theory has been developed. In this work, we further validate the MMAm by demonstrating its efficiency on geophysical benchmarks. Highly heterogeneous media, Seismic wave propagation, Time-harmonic modelling, High-order methods, Mulsticale methods, Finite element methods
Published: 2018

3. Constructing flat inputs for two-output systems

Author: Nicolau, Florentina, Respondek, Witold, Barbot, Jean-Pierre, Nicolau, Florentina, Laboratoire QUARTZ (QUARTZ ), Université Paris 8 Vincennes-Saint-Denis (UP8)-SUPMECA - Institut supérieur de mécanique de Paris-Ecole Nationale Supérieure de l'Electronique et de ses Applications (ENSEA)-Ecole Internationale des Sciences du Traitement de l'Information (EISTI), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA), Equipe Commande des Systèmes (ECS), Ecole Nationale Supérieure de l'Electronique et de ses Applications, Université Paris 8 Vincennes-Saint-Denis (UP8)-Ecole Nationale Supérieure de l'Electronique et de ses Applications (ENSEA)-SUPMECA - Institut supérieur de mécanique de Paris (SUPMECA)-Ecole Internationale des Sciences du Traitement de l'Information (EISTI), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Université Paris 8 Vincennes-Saint-Denis (UP8)-SUPMECA - Institut supérieur de mécanique de Paris (SUPMECA)-Ecole Nationale Supérieure de l'Electronique et de ses Applications (ENSEA)-Ecole Internationale des Sciences du Traitement de l'Information (EISTI), Laboratoire Quartz ( Quartz ), Ecole Internationale des Sciences du Traitement de l'Information ( EISTI ) -Ecole Nationale Supérieure de l'Electronique et de ses Applications ( ENSEA ) -SUPMECA - Institut supérieur de mécanique de Paris, Laboratoire de Mathématiques de l'INSA de Rouen Normandie ( LMI ), Institut national des sciences appliquées Rouen Normandie ( INSA Rouen Normandie ), Normandie Université ( NU ) -Normandie Université ( NU ), and Equipe Commande des Systèmes ( ECS )
Subjects: [ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC], [ MATH.MATH-DG ] Mathematics [math]/Differential Geometry [math.DG], [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], [ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]
Abstract: International audience; In this paper, we study the problem of constructing flat inputs for two-output dynamical systems. The notion of flat inputs has been introduced by Waldherr and Zeitz [2008, 2010] and can be seen as dual to that of flat outputs. In the single-output case, a flat input can be constructed if and only if the original system together with its output is observable. In the multi-output case, the observability is not necessary for the existence of flat inputs. We start by discussing the case when the dynamical system together with the given output is observable and we present a generalization of the results of Waldherr and Zeitz [2010] by relating them with the notion of minimal differential weight. Then, we give our main theorems. We consider the unobservable case for which we study the local and global problems. We completely describe the local case, discuss the issue of the minimal modification of the original system, and propose a solution for the global problem. Finally, we explain how our results can be applied to secure communication.
Published: 2018

4. Online estimation of the asymptotic variance for averaged stochastic gradient algorithms

Author: Godichon , Antoine, Godichon-Baggioni , Antoine, Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Laboratoire de Mathématiques de l'INSA de Rouen Normandie ( LMI ), Institut national des sciences appliquées Rouen Normandie ( INSA Rouen Normandie ), Institut National des Sciences Appliquées ( INSA ) -Normandie Université ( NU ) -Institut National des Sciences Appliquées ( INSA ) -Normandie Université ( NU ), Institut de Mathématiques de Toulouse UMR5219 ( IMT ), Université Toulouse 1 Capitole ( UT1 ) -Université Toulouse - Jean Jaurès ( UT2J ) -Université Toulouse III - Paul Sabatier ( UPS ), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-PRES Université de Toulouse-Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), and Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS )
Subjects: Statistics and Probability, Asymptotic distribution, Mathematics - Statistics Theory, Statistics Theory (math.ST), Logistic regression, 01 natural sciences, Root mean square, 010104 statistics & probability, symbols.namesake, 0502 economics and business, FOS: Mathematics, 0101 mathematics, 050205 econometrics, Mathematics, Central limit theorem, Applied Mathematics, 05 social sciences, Hilbert space, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], [ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH], Delta method, Rate of convergence, symbols, Statistics, Probability and Uncertainty, Algorithm, Quantile
Abstract: International audience; Stochastic gradient algorithms are more and more studied since they can deal efficiently and online with large samples in high dimensional spaces. In this paper, we first establish a Central Limit Theorem for these estimates as well as for their averaged version in general Hilbert spaces. Moreover, since having the asymptotic normality of estimates is often unusable without an estimation of the asymptotic variance, we introduce a new recursive algorithm for estimating this last one, and we establish its almost sure rate of convergence as well as its rate of convergence in quadratic mean. Finally, two examples consisting in estimating the parameters of the logistic regression and estimating geometric quantiles are given.
Published: 2017

5. An averaged projected Robbins-Monro algorithm for estimating the parameters of a truncated spherical distribution

Author: Antoine Godichon-Baggioni, Bruno Portier, Institut de Mathématiques de Bourgogne [Dijon] ( IMB ), Université de Bourgogne ( UB ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques de l'INSA de Rouen Normandie ( LMI ), Institut national des sciences appliquées Rouen Normandie ( INSA Rouen Normandie ), Normandie Université ( NU ) -Normandie Université ( NU ), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), and Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)
Subjects: Statistics and Probability, [ MATH ] Mathematics [math], averaging, 010102 general mathematics, Point cloud, Asymptotic distribution, Mathematics - Statistics Theory, Radius, Statistics Theory (math.ST), 01 natural sciences, Projected Robbins-Monro algorithm, Root mean square, 010104 statistics & probability, Distribution (mathematics), sphere fitting, Convergence of random variables, Sample size determination, asymptotic properties, Convergence (routing), FOS: Mathematics, [MATH]Mathematics [math], 0101 mathematics, Statistics, Probability and Uncertainty, Algorithm, Mathematics
Abstract: International audience; The objective of this work is to propose a new algorithm to fit a sphere on a noisy 3D point cloud distributed around a complete or a truncated sphere. More precisely, we introduce a projected Robbins-Monro algorithm and its averaged version for estimating the center and the radius of the sphere. We give asymptotic results such as the almost sure convergence of these algorithms as well as the asymptotic normality of the averaged algorithm. Furthermore, some non-asymptotic results will be given, such as the rates of convergence in quadratic mean. Some numerical experiments show the efficiency of the proposed algorithm on simulated data for small to moderate sample sizes and for modeling an object in 3D.
Published: 2017

6. Construction and analysis of a HDG+ method for the diffusive-flux formulation of the convected Helmholtz equation

Author: Barucq, Hélène, Rouxelin, Nathan, Tordeux, Sébastien, Modélisation et simulation de la propagation des ondes fondées sur des mesures expérimentales pour caractériser des milieux géophysiques et héliophysiques et concevoir des objets complexes (MAKUTU), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Polytechnique de Bordeaux (Bordeaux INP), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), and Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)
Subjects: harmonic regime, Hybridizable Discontinuous Galerkin Method (HDG), aeroacoustics, error analysis, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], convected Helmholtz equation
Abstract: We construct HDG methods based on the diffusive flux formulation of the convected acoustic wave equation.We mostly describe the HDG+ method which involves different polynomial degrees for approximating the unknowns, hence leading to a more efficient method with a super-convergencelike behaviour. A detailed analysis of the methods including local and global well-posedness, as well as convergence estimates is carried out. The HDG+ method is also compared with a more conventional HDG method to demonstrate its effectiveness.
Published: 2023

7. Finite element approximation of Helmholtz problems with application to seismic wave propagation

Author: Chaumont Frelet, Théophile, Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria), Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), INSA de Rouen, Christian Gout, and Hélène Barucq
Subjects: Pollution effect, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], Finite element, Helmholtz equation, Seismic wave propagation, Méthodes d'ordre élevé
Abstract: The main objective of this work is the design of an efficient numerical strategy to solve the Helmholtz equation in highly heterogeneous media. We propose a methodology based on coarse meshes and high order polynomials together with a special quadrature scheme to take into account fine scale heterogeneities. The idea behind this choice is that high order polynomials are known to be robust with respect to the pollution effect and therefore, efficient to solve wave problems in homogeneous media. In this work, we are able to extend so-called "asymptotic error-estimate" derived for problems homogeneous media to the case of heterogeneous media. These results are of particular interest because they show that high order polynomials bring more robustness with respect to the pollution effect even if the solution is not regular, because of the fine scale heterogeneities. We propose special quadrature schemes to take int account fine scale heterogeneities. These schemes can also be seen as an approximation of the medium parameters. If we denote by h the finite-element mesh step and by e the approximation level of the medium parameters, we are able to show a convergence theorem which is explicit in terms of h, e and f, where f is the frequency. The main theoretical results are further validated through numerical experiments. 2D and 3D geophysica benchmarks have been considered. First, these experiments confirm that high-order finite-elements are more efficient to approximate the solution if they are coupled with our multiscale strategy. This is in agreement with our results about the pollution effect. Furthermore, we have carried out benchmarks in terms of computational time and memory requirements for 3D problems. We conclude that our multiscale methodology is able to greatly reduce the computational burden compared to the standard finite-element method; Dans cette thèse, on s'intéresse à la propagation d'ondes en milieu fortement hétérogène modélisée par l'équation d'Helmholtz. Les méthodes numériques permettant de résoudre ce problème souffrent de dispersion numérique, en particulier à haute fréquence. Ce phénomène, appelé "effet de pollution", est largement analysé dans la littérature quand le milieu de propagation est homogène et l'utilisation de "méthodes d'ordre élevé" est souvent proposée pour minimiser ce problème. Dans ce travail, on s'intéresse à un milieu de propagation hétérogène, cas pour lequel on dispose de moins de connaissances. On propose d'adapter des méthodes éléments finis d'ordre élevé pour résoudre l'équation d'Helmholtz en milieu hétérogène, afin de réduire l'effet de pollution. Les méthodes d'ordre élevé étant généralement basées sur des maillages "larges", une stratégie multi-échelle originale est développée afin de prendre en compte des hétérogénéités de petite échelle. La convergence de la méthode est démontrée. En particulier, on montre que la méthode est robuste vis-a-vis de l'effet de pollution. D'autre part, on applique la méthode a plusieurs cas-tests numériques. On s'intéresse d'abord à des problèmes académiques, qui permettent de valider la théorie de convergence développée. On considère ensuite des cas-tests "industriels" appliqués à la Géophysique. Ces derniers nous permettent de conclure que la méthode multi-échelle proposée est plus performante que les éléments finis "classiques" et que des problèmes 3D réalistes peuvent être considérés.
Published: 2015

8. Entire Reflective Object Surface Structure Understanding

Author: Olivier Laligant, Anastasia Zakharova, Qinglin Lu, Eric Fauvet, Laboratoire Electronique, Informatique et Image ( Le2i ), Université de Bourgogne ( UB ) -AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques de l'INSA de Rouen Normandie ( LMI ), Institut national des sciences appliquées Rouen Normandie ( INSA Rouen Normandie ), Normandie Université ( NU ) -Normandie Université ( NU ), Laboratoire Electronique, Informatique et Image [UMR6306] (Le2i), Université de Bourgogne (UB)-École Nationale Supérieure d'Arts et Métiers (ENSAM), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), and Fauvet, Eric
Subjects: [ INFO.INFO-TS ] Computer Science [cs]/Signal and Image Processing, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Computer science, business.industry, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, Surface structure, Computer vision, Artificial intelligence, Object (computer science), business, ComputingMilieux_MISCELLANEOUS
Abstract: International audience
Published: 2015

9. Local surface curvature analysis based on reflection estimation

Author: Olivier Laligant, Qinglin Lu, Anastasia Zakharova, Eric Fauvet, Laboratoire Electronique, Informatique et Image ( Le2i ), Université de Bourgogne ( UB ) -AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques de l'INSA de Rouen Normandie ( LMI ), Institut national des sciences appliquées Rouen Normandie ( INSA Rouen Normandie ), Normandie Université ( NU ) -Normandie Université ( NU ), Laboratoire Electronique, Informatique et Image [UMR6306] (Le2i), Université de Bourgogne (UB)-École Nationale Supérieure d'Arts et Métiers (ENSAM), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), and Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)
Subjects: Surface (mathematics), [ INFO.INFO-TS ] Computer Science [cs]/Signal and Image Processing, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Mirror image, Plane of incidence, Reflection (physics), Geometry, Diffuse reflection, Specular reflection, Image plane, Curvature, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract: In this paper, we propose a novel reflection based method to estimate the local orientation of a specular surface. For a calibrated scene with a fixed light band, the band is reflected by the surface to the image plane of a camera. Then the local geometry between the surface and reflected band is estimated. Firstly, in order to find the relationship relying the object position, the object surface orientation and the band reflection, we study the fundamental theory of the geometry between a specular mirror surface and a band source. Then we extend our approach to the spherical surface with arbitrary curvature. Experiments are conducted with mirror surface and spherical surface. Results show that our method is able to obtain the local surface orientation merely by measuring the displacement and the form of the reflection.
Published: 2015

10. Local surface orientation analysis based on reflection estimation

Author: Eric Fauvet, Olivier Laligant, Anatasia Zakharova, Qinglin Lu, Laboratoire Electronique, Informatique et Image ( Le2i ), Université de Bourgogne ( UB ) -AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques de l'INSA de Rouen Normandie ( LMI ), Institut national des sciences appliquées Rouen Normandie ( INSA Rouen Normandie ), Normandie Université ( NU ) -Normandie Université ( NU ), Laboratoire Electronique, Informatique et Image [UMR6306] (Le2i), Université de Bourgogne (UB)-École Nationale Supérieure d'Arts et Métiers (ENSAM), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), and Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)
Subjects: Physics, Surface (mathematics), [ INFO.INFO-TS ] Computer Science [cs]/Signal and Image Processing, business.industry, Image plane, Curvature, Displacement (vector), Optics, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Position (vector), Orientation (geometry), Reflection (physics), Specular reflection, business, ComputingMilieux_MISCELLANEOUS
Abstract: In this paper, we propose a novel reflection based method to estimate the local orientation of a specular surface. For a calibrated scene with a fixed light band, the band is reflected by the surface to the image plane of a camera. Then the local geometry between the surface and reflected band is estimated. Firstly, in order to find the relationship relying the object position, the object surface orientation and the band reflection, we study the fundamental theory of the geometry between a specular mirror surface and a band source. Then we extend our approach to the spherical surface with arbitrary curvature. Experiments are conducted with mirror surface and spherical surface. Results show that our method is able to obtain the local surface orientation merely by measuring the displacement and the form of the reflection.
Published: 2015

11. Manufactured object sub-segmentation based on reflection motion estimation

Author: Eric Fauvet, Qinglin Lu, Anastasia Zakharova, Olivier Laligant, Laboratoire Electronique, Informatique et Image ( Le2i ), Université de Bourgogne ( UB ) -AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques de l'INSA de Rouen Normandie ( LMI ), Institut national des sciences appliquées Rouen Normandie ( INSA Rouen Normandie ), Normandie Université ( NU ) -Normandie Université ( NU ), Iternational Association for Pattern Recognition, Laboratoire Electronique, Informatique et Image [UMR6306] (Le2i), Université de Bourgogne (UB)-École Nationale Supérieure d'Arts et Métiers (ENSAM), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), and Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)
Subjects: [ INFO.INFO-TS ] Computer Science [cs]/Signal and Image Processing, Segmentation-based object categorization, business.industry, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Scale-space segmentation, Pattern recognition, 02 engineering and technology, Image segmentation, 01 natural sciences, Scale space, 010309 optics, Image texture, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Region growing, Motion estimation, 0103 physical sciences, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Computer vision, Artificial intelligence, Reflection (computer graphics), business, Mathematics
Abstract: International audience; In computer vision, reflection is a long-standing problem, it covers image textures, makes original color difficult to recognize, complicates the understanding of the scene. Most of the time, it is considered as “noise”. Many methods are proposed in order to reduce or delete the reflection effects in the image, but generally, the performances are not quite satisfactory. While instead of working on “de-noising”, we propose a method to take advantage of moving reflections that can be used for different computer vision applications. For instance, the segmentation of reflective manufactured objects is presented in this paper. We focus on tracking reflection components and segmenting continuous surfaces of the object by taking motion information into account. In this paper, a comparison with several conventional segmentation methods is proposed to illustrate how our approach significantly improves the segmentation results.
Published: 2015

12. Modélisation mathématique de problèmes relatifs au recalage d'images

Author: Ozeré, Solène, STAR, ABES, Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), INSA de Rouen, Christian Gout, and Carole Le Guyader
Subjects: Mathematical modelling, Fonctions à varation bornée, [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Segmentattion, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Recalage, Image registration
Abstract: This work focuses on the modelling of problems related to image registration. Image registration consists in finding an optimal deformation such that a deformed image is aligned with a reference image. It is an important task encountered in a large range of applications such as medical imaging, comparison of data or shape tracking. The first chapter concerns the problem of topology preservation. This condition of topology preservation is important when the sought deformation reflects physical properties of the objects to be distorted. The following chapters propose several methods of image registration based on the nonlinear elasticity theory. Indeed, the objects to be matched are modelled as hyperelastic materials. Different fidelity terms have been investigated as well as two joint segmentation/registration models., Ce travail porte sur la modélisation de problèmes liés au recalage d'images. Le recalage consiste à trouver une déformation optimale de sorte qu'une image déformée s'aligne sur une image de référence. Il s'agit d'une technique que l'on rencontre dans de nombreux domaines, comme l'imagerie médicale, la comparaison de données ou le suivi de formes. Le premier chapitre se concentre sur le problème de préservation de la topologie. Cette condition de préservation de la topologie est importante lorsque la déformation recherchée traduit des propriétés physiques des objets soumis à la déformation. Les chapitres suivants proposent la construction de différentes méthodes de recalage d'images fondées sur la théorie de l'élasticité non linéaire. En effet, les objets à apparier sont supposés être des matériaux hyper-élastiques. Différents termes d'attaches aux données ont été explorés ainsi que deux modèles conjoints de segmentation et recalage.
Published: 2015

13. Géométrie et platitude des systèmes de contrôle de poids différentiel minimal

Author: Nicolau, Florentina, Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), INSA de Rouen, Witold Respondek, and STAR, ABES
Subjects: Poids différentiel, Platitude, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], Linéarisation, Differential flatness, [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], Flat outputs, Sortie plate
Abstract: Firstly, we study flatness of multi-input control-affine systems. We give a complete geometric characterization of systems that become static feedback linearizable after a one-fold prolongation of a suitably chosen control. They form a particular class of flat systems, that is of differential weight equal to n+m+l, where n is the dimension of the state-space and m is the number of controls. We illustrate our results by several examples. Secondly, we give a complete geometric characterization of systems locally static feedback equivalent to a triangular form compatible with the m-chained form. We analyze and solve their flatness. We discuss singularities and provide a system of first order PDE's to be solved in order to find all x-flat outputs. We illustrate our results by an application to a mechanical system: the coin rolling without slipping on a moving table., Premièrement, nous avons caractérisé les systèmes multi-entrées, affines par rapport aux contrôles, linéarisables dynamiquement via une pré-intégration d'un contrôle bien choisi. Ils forment une classe particulière de systèmes plats : ils ont un poids différentiel de n+m+1, où m est le nombre de contrôles et n est la dimension de l'état. Nous avons présenté des formes normales compatibles avec les sorties plates minimales et décrit toutes les sorties plates minimales. Nous avons appliqué nos résultats à plusieurs exemples. Deuxièmement, nous avons décrit les systèmes multi-entrées statiquement équivalents à une forme triangulaire compatible avec la forme multi-chaînée. Ensuite, la platitude de ces systèmes a été analysée et résolue. Nous avons discuté les singularités dans l'espace de contrôle et déterminé toutes les sorties plates. Nous avons appliqué ces résultats au système mécanique d'une pièce roulant sans glissement sur une table en mouvement.
Published: 2014

14. Trivialisable control-affine systems revisited

Author: Schmoderer, Timothée, Respondek, Witold, Dynamical Interconnected Systems in COmplex Environments (DISCO), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), and Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)
Subjects: Control-affine systems, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Dynamical Systems (math.DS), Normal forms, 93A10, 93B52, 93B10, 93B27, 37N35, 37C79, Control curvature, Trivial control systems, Infinitesimal symmetries, Optimization and Control (math.OC), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], FOS: Mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Dynamical Systems, Mathematics - Optimization and Control, Feedback equivalence
Abstract: The purpose of this paper is to explore the concept of trivial control systems, namely systems whose dynamics depends on the controls only. Trivial systems have been introduced and studied by Serres in the the context of control-nonlinear systems on the plane with a scalar control. In our work, we begin by proposing an extension of the notion of triviality to control-ane systems with arbitrary number of states and controls. Next, our rst result concerns two novel characterisations of trivial control-ane systems, one of them is based on the study of innitesimal symmetries and is thus geometric. Second, we derive a normal form of trivial control-ane systems whose Lie algebra of innitesimal symmetries possesses a transitive almost abelian Lie subalgebra. Third, we study and propose a characterisation of trivial control-ane systems on 3-dimensional manifolds with scalar control. In particular, we give a novel proof of the previous characterisation obtained by Serres. Our characterisation is based on the properties of two functional feedback invariants: the curvature (introduced by Agrachev) and the centro-ane curvature (used by Wilkens). Finally, we give several normal forms of control-ane systems, for which the curvature and the centro-ane curvature have special properties.; L'objectif de cet article est d'explorer le concept de système de contrôles trivial,c'est-à-dire un système dont la dynamique dépend uniquement des commandes. Les systèmes triviaux ont été introduits et étudiés par Serres dans le contexte des systèmes bidimensionnels et non-linéaires par rapport à un contrôle scalaire. Dans notre travail, nous commençons par proposer une extension de la notion de trivialité aux systèmes affines par rapport aux contrôles et avec un nombre arbitraire d'états et de contrôles. Ensuite, notre premier résultat concerne deux nouvelles caractérisations des systèmes affines triviaux, l'une d'entre elles est basée sur l'étude des symétries infinitésimales et est donc géométrique. Deuxièmement, nous donnons une forme normale pour les systèmes affines triviaux dont l'algèbre de Lie des symétries infinitésimales possède une sous-algèbre de Lie presque abélienne. Troisièmement, nous étudions et proposons une caractérisation des systèmes affines triviaux sur des variétés à $3$ dimensions et avec un contrôle scalaire. En particulier, nous donnons une nouvelle preuve de la caractérisation précédemment obtenue par Serres. Notre caractérisation est basée sur les propriétés de deux invariants fonctionnels du bouclage : la courbure (introduite par Agrachev) et la courbure centro-affine (utilisée par Wilkens). Enfin, nous donnons plusieurs formes normales de systèmes affine, pour lesquelles la courbure et la courbure centro-affine ont des propriétés particulières.
Published: 2023

15. High order numerical methods for Vlasov-Poisson models of plasma sheaths

Author: Ayot, Valentin, Badsi, Mehdi, Barsamian, Yann, Crestetto, Anaïs, Crouseilles, Nicolas, Mehrenberger, Michel, Prost, Averil, Tayou-Fotso, Christian, Université de Bordeaux (UB), Équipe Calcul scientifique et Modélisation, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ), École Européenne de Bruxelles, Multi-scale numerical geometric schemes (MINGUS), École normale supérieure - Rennes (ENS Rennes)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut de Recherche Mathématique de Rennes (IRMAR), Aix Marseille Université (AMU), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), COmplex Flows For Energy and Environment (COFFEE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), Centre de Calcul Intensif d’Aix-Marseille is acknowledged for granting access to its high performancecomputing resources. This project has been supported by the French Federation for Magnetic FusionStudies (FR-FCM) and by the French ANR project MUFFIN ANR-19-CE46-0004. This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200 EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them. Finally, authors would like to thanks the CEMRACS organizers, Pierre Navaro for the computational support and the CIRM’s boards., ANR-19-CE46-0004,MUFFIN,Multiéchelle et Trefftz pour le transport numérique(2019), European Project: 101052200,Implementation of activities described in the Roadmap to Fusion during Horizon Europe through a joint programme of the members of the EUROfusion consortium,EUROfusion, Crouseilles, Nicolas, Multiéchelle et Trefftz pour le transport numérique - - MUFFIN2019 - ANR-19-CE46-0004 - AAPG2019 - VALID, and EUROfusion - EUROfusion - - Implementation of activities described in the Roadmap to Fusion during Horizon Europe through a joint programme of the members of the EUROfusion consortium0000-00-00 - 0000-00-00 - 101052200 - VALID
Subjects: [PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph], [PHYS.PHYS.PHYS-COMP-PH] Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: This article is a report of the CEMRACS 2022 project, called HIVLASHEA, standing for "High order methods for Vlasov-Poisson models for sheaths". A two-species Vlasov-Poisson model is described together with some numerical simulations, permitting to exhibit the formation of a plasma sheath. The numerical simulations are performed with two different methods: a first order classical finite difference (FD) scheme and a high order semi-Lagrangian (SL) scheme with Strang splitting; for the latter one, the implementation of (non-periodic) boundary conditions is discussed. The codes are first evaluated on a one-species case, where an analytical solution is known. For the two-species case, cross comparisons and the influence of the numerical parameters for the SL method are performed in order to have an idea of a reference numerical simulation. Aknowledgements Centre de Calcul Intensif d'Aix-Marseille is acknowledged for granting access to its high performance computing resources.
Published: 2023

16. RELATIONSHIP BETWEEN THE MAXIMUM PRINCIPLE AND DYNAMIC PROGRAMMING FOR MINIMAX PROBLEMS

Author: Cristopher Hermosilla, Hasnaa Zidani, Departamento de Matematica, Universidad Tecnica Federico Santa Maria, Universidad Tecnica Federico Santa Maria [Valparaiso] (UTFSM), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Optimisation et commande (OC), Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris), This work was supported by ECOS-ANID (Grant Number ECOS200064). C. Hermosilla has received research support from FONDECYT Grant Number 11190456 and H. Zidani received research support from Région Normandie and EU through ERDF program (Chaire COPTI)., and European Project: ERDF
Subjects: Control and Optimization, Applied Mathematics, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract: International audience; This paper is concerned with the relationship between the maximum principle and dynamic programming for a large class of optimal control problems with maximum running cost. Inspired by a technique introduced by Vinter in the 1980s, we are able to obtain jointly a global and a partial sensitivity relation that link the coextremal with the value function of the problem at hand. One of the main contributions of this work is that these relations are derived by using a single perturbed problem, and therefore, both sensitivity relations hold, at the same time, for the same coextremal. As a by-product, and thanks to the level-set approach, we obtain a new set of sensitivity relations for Mayer problems with state constraints. One important feature of this last result is that it holds under mild assumptions, without the need of imposing strong compatibility assumptions between the dynamics and the state constraints set. Minimax optimal control problems and Maximum principle and Dynamic programming and Sensitivity analysis and State constraints
Published: 2023

17. Construction and analysis of a HDG solution for the total-flux-formulation of the convected Helmholtz equation

Author: Hélène Barucq, Nathan Rouxelin, Sébastien Tordeux, Modélisation et simulation de la propagation des ondes fondées sur des mesures expérimentales pour caractériser des milieux géophysiques et héliophysiques et concevoir des objets complexes (MAKUTU), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Polytechnique de Bordeaux (Bordeaux INP), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Nathan Rouxelin is supported by a grant from e2s-UPPA.
Subjects: Computational Mathematics, Algebra and Number Theory, error estimates, Applied Mathematics, convected helmholtz, aeroacoustic, HDG, Riemann solver, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: We introduce a hybridizable discontinuous Galerkin (HDG) method for the convected Helmholtz equation based on the total flux formulation, in which the vector unknown represents both diffusive and convective phenomena. This HDG method is constricted with the same interpolation degree for all the unknowns and a physically informed value for the penalization parameter is computed. A detailed analysis including local and global well-posedness as well as a super-convergence result is carried out. We then provide numerical experiments to illustrate the theoretical results.
Published: 2023

18. VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS IN PROPER CAT(0) SPACES

Author: JERHAOUI, Othmane, Zidani, Hasnaa, Optimisation et commande (OC), Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris), École Nationale Supérieure de Techniques Avancées (ENSTA Paris), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), This word was partially supported by grant from the Foundation of mathematics Jacques Hadamard (FMJH), ANR-22-CE40-0010,COSS,COntrôle sur des Structures Stratifiées(2022), and European Project: ERDF
Subjects: [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract: In this article, we develop a novel notion of viscosity solutions for first order Hamilton-Jacobi equations in proper CAT(0) spaces. The notion of viscosity is defined by taking test functions that are directionally differentiable and can be represented as a difference of two semiconvex functions. Under mild assumptions on the Hamiltonian, we recover the main features of viscosity theory for both the stationary and the time-dependent cases in this setting: the comparison principle and Perron's method. Finally, we show that this notion of viscosity coincides with classical one in R N and we give several examples of Hamilton-Jacobi equations in more general CAT(0) spaces covered by this setting.
Published: 2022

19. Interactive Narration Requires Interaction and Emotion

Author: Pauchet , Alexandre, Rioult , François, Chanoni , Emilie, Alès , Zacharie, Serban , Ovidiu, Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), Normandie Université (NU), Equipe CODAG - Laboratoire GREYC - UMR6072, Groupe de Recherche en Informatique, Image et Instrumentation de Caen (GREYC), Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Normandie Université (NU)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Psychologie et Neurosciences de la Cognition et de l'affectivité (PSY-NCA), Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Normandie Université (NU), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes ( LITIS ), Université Le Havre Normandie ( ULH ), Normandie Université ( NU ) -Normandie Université ( NU ) -Université de Rouen Normandie ( UNIROUEN ), Normandie Université ( NU ) -Institut national des sciences appliquées Rouen Normandie ( INSA Rouen Normandie ), Normandie Université ( NU ), Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen ( GREYC ), Université de Caen Normandie ( UNICAEN ), Normandie Université ( NU ) -Normandie Université ( NU ) -Ecole Nationale Supérieure d'Ingénieurs de Caen ( ENSICAEN ), Normandie Université ( NU ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Caen Normandie ( UNICAEN ), Normandie Université ( NU ) -Centre National de la Recherche Scientifique ( CNRS ), Psychologie et Neurosciences de la Cognition et de l'affectivité ( PSY-NCA ), Université de Rouen Normandie ( UNIROUEN ), Normandie Université ( NU ) -Normandie Université ( NU ), Laboratoire de Mathématiques de l'INSA de Rouen Normandie ( LMI ), Institut national des sciences appliquées Rouen Normandie ( INSA Rouen Normandie ), and Référent, Greyc
Subjects: [INFO.INFO-AI] Computer Science [cs]/Artificial Intelligence [cs.AI], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], [ INFO.INFO-AI ] Computer Science [cs]/Artificial Intelligence [cs.AI], [ INFO.INFO-LG ] Computer Science [cs]/Machine Learning [cs.LG], ComputingMilieux_MISCELLANEOUS, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract: International audience
Published: 2013

20. Mixture of linear regression models for short term PM10 forecasting in Haute Normandie (France)

Author: Misiti, Michel, Misiti, Yves, Poggi, Jean-Michel, Portier, Bruno, Laboratoire de Mathématiques d'Orsay (LM-Orsay), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Model selection in statistical learning (SELECT), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Institut Universitaire de Technologie Paris Descartes (IUT - Paris Descartes), Université Paris Descartes - Paris 5 (UPD5), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Laboratoire de Mathématiques d'Orsay ( LM-Orsay ), Université Paris-Sud - Paris 11 ( UP11 ) -Centre National de la Recherche Scientifique ( CNRS ), Model selection in statistical learning ( SELECT ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Laboratoire de Mathématiques d'Orsay ( LMO ), Université Paris-Saclay-Centre National de la Recherche Scientifique ( CNRS ) -Université Paris-Saclay-Centre National de la Recherche Scientifique ( CNRS ) -Centre National de la Recherche Scientifique ( CNRS ), Institut Universitaire de Technologie Paris Descartes ( IUT - Paris Descartes ), Université Paris Descartes - Paris 5 ( UPD5 ), Laboratoire de Mathématiques de l'INSA de Rouen Normandie ( LMI ), Institut national des sciences appliquées Rouen Normandie ( INSA Rouen Normandie ), Normandie Université ( NU ) -Normandie Université ( NU ), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Poggi, Jean-Michel, Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)
Subjects: PM10, [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Mixture of linear models, 62M10, 62P12, 62H30, Air quality, [ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST], [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Particulate matter, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], [ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH], Forecasting
Abstract: Mixture of linear regression models is used for the short-term statistical forecasting of the daily mean PM10 concentration. Hourly concentrations of PM10 have been measured in three cities in Haute-Normandie (France): Rouen, Le Havre and Dieppe. The Haute-Normandie region is located at northwest of Paris, near the south side of Manche sea and is heavily industrialized. We consider six monitoring stations reflecting the diversity of situations: urban background, traffic, rural and industrial stations. We have focused our attention on recent data from 2007 to 2011. We forecast the daily mean PM10 concentration by modeling it as a mixture of linear regression models involving meteorological predictors and the average concentration measured on the previous day. The values of observed meteorological variables are used for fitting the models but the corresponding predictions are considered for the test data, leading to realistic evaluations of forecasting performances, which are calculated through a leave-one-out scheme on the four years. We discuss in this paper several methodological issues including estimation schemes, introduction of the deterministic predictions of meteorological models and how to handle the forecasting at various horizons from some hours to one day ahead.
Published: 2013

21. Depth reconstruction by means of defocused light from incomplete measurements

Author: Zakharova, Anastasia, Laligant, Olivier, Stolz, Christophe, Stolz, Christophe, Laboratoire de Mathématiques de l'INSA de Rouen Normandie ( LMI ), Institut national des sciences appliquées Rouen Normandie ( INSA Rouen Normandie ), Normandie Université ( NU ) -Normandie Université ( NU ), Laboratoire Electronique, Informatique et Image ( Le2i ), Université de Bourgogne ( UB ) -AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Laboratoire Electronique, Informatique et Image [UMR6306] (Le2i), Université de Bourgogne (UB)-École Nationale Supérieure d'Arts et Métiers (ENSAM), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Arts et Métiers Sciences et Technologies, and HESAM Université (HESAM)-HESAM Université (HESAM)-AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement-Centre National de la Recherche Scientifique (CNRS)
Subjects: [SPI.OPTI] Engineering Sciences [physics]/Optics / Photonic, [SPI.OPTI]Engineering Sciences [physics]/Optics / Photonic, [ SPI.OPTI ] Engineering Sciences [physics]/Optics / Photonic, ComputingMilieux_MISCELLANEOUS
Abstract: National audience
Published: 2013

22. DC programming and DCA for solving some classes of problems in transportation and communication systemes

Author: Ta, Anh Son, Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), INSA de Rouen, Tao Pham Dinh, Hoai An Lê Thi, and STAR, ABES
Subjects: Routing problems, Car pooling problems, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], Méthode de décomposition proximale, Méthode d'étiquetage des graphes, Problèmes de routage, Proximal decomposition method, [INFO.INFO-OH] Computer Science [cs]/Other [cs.OH], Power control problems, DC programming and DCA, Programmation DC et DCA, Labeling algorithms in graph theory, Problèmes de contrôle de l'alimentation, Optimal spectrum balancing problems, Problèmes de covoiturage, Problèmes d'équilibrage du spectre
Abstract: In this thesis, we focus on developing deterministic and heuristic approaches for solving some classes of optimization problems in Telecommunication and Mobility & Transport domain: Routing problems, Car pooloing problems, Power control problems in wireless network, Optimal spectrum balancing problems in DSL networks. They are large-scale nonconvex optimization problems. Our methodologies are focus on DC programming and DCA, Proximal decomposition method and Labeling method in graph theory. They are well-known as powerful tools in optimization. The considered problems were reformulated using the DC formulation/reformulation and exact penalty techniques and the DCA was used to obtain the solution. Also, depending on the structure of considered problems, we can provide appropriate DE decompositions or good initial points for DCA. All these proposed methods have been implemented with MATLAB, C/C++ to confirm the practical aspects and enhance our research works., Cette thèse a pour but de développer des approches déterministes et heuristiques pour résoudre certaines classes des problèmes d'optimisation en télécommunication et la mobilité d'un réseau de transport : problèmes de routage, problèmes de covoiturage, problèmes de contrôle de l'alimentation dans un réseau sans fil, problèmes d'équilibrage du spectre dans les réseaux DSL. Il s'agit des problèmes d'optimisation non convexe de très grande taille. Nos approches sont basées sur la programmation DC&DCA, méthode de décomposition proximale et la méthode d'étiquetage des graphes. Grâce aux techniques de formulation/reformulation et de pénalité exacte, nous avons établi des programmes DC équivalents en vue de leur résolution par DCA. Selon la structure de ces problèmes, on peut fournir des décompositions DC appropriées ou de bons points initiaux de DCA. Nos méthodes ont été programmées sous MATLAB, C/C++. Ils montrent la performance de nos algorithmes par rapport à des méthodes existantes.
Published: 2012

23. Quantifying local and background contributions to PM10 concentrations in Haute-Normandie, using random forests

Author: Bobbia, Michel, Jollois, François-Xavier, Poggi, Jean-Michel, Portier, Bruno, Université Paris Descartes - Paris 5 (UPD5), Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Model selection in statistical learning (SELECT), Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Université Paris Descartes - Paris 5 ( UPD5 ), Laboratoire de Mathématiques d'Orsay ( LM-Orsay ), Université Paris-Sud - Paris 11 ( UP11 ) -Centre National de la Recherche Scientifique ( CNRS ), Model selection in statistical learning ( SELECT ), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Laboratoire de Mathématiques d'Orsay ( LMO ), Université Paris-Saclay-Centre National de la Recherche Scientifique ( CNRS ) -Université Paris-Saclay-Centre National de la Recherche Scientifique ( CNRS ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques de l'INSA de Rouen Normandie ( LMI ), Institut national des sciences appliquées Rouen Normandie ( INSA Rouen Normandie ), Normandie Université ( NU ) -Normandie Université ( NU ), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)
Subjects: [STAT.AP]Statistics [stat]/Applications [stat.AP], [ STAT.AP ] Statistics [stat]/Applications [stat.AP], ComputingMilieux_MISCELLANEOUS
Abstract: International audience
Published: 2011

24. Modal computation for openwaveguides

Author: Leclerc, Augustin, Tonnoir, Antoine, Barucq, Hélène, Durufle, Marc, Gout, Christian, Modélisation et simulation de la propagation des ondes fondées sur des mesures expérimentales pour caractériser des milieux géophysiques et héliophysiques et concevoir des objets complexes (MAKUTU), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Polytechnique de Bordeaux (Bordeaux INP), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), and Institut Polytechnique de Bordeaux (Bordeaux INP)
Subjects: [MATH]Mathematics [math], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience
Published: 2022

25. Numerics for finite-dimensional optimal control problems

Author: Caillau, Jean-Baptiste, Ferretti, Roberto, Trélat, Emmanuel, Zidani, Hasnaa, Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Université Côte d'Azur (UCA), Mathematics for Control, Transport and Applications (McTAO), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Università degli Studi Roma Tre = Roma Tre University (ROMA TRE), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Control And GEometry (CaGE ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Sorbonne Université (SU), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), and Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)
Subjects: Direct and indirect methods, Pontryagin maximum principle, Optimistic planning, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Hamilton-Jacobi-Bellman equation, Optimal control
Abstract: We survey on numerics for finite-dimensional nonlinear optimal control. The chapter is written as a guide to practitioners who wish to get rapidly acquainted with the main numerical methods used to efficiently solve an optimal control problem. We consider throughout two classical examples, quite simple but representative enough to be complexified and generalized to other problems: the Zermelo and the Goddard problems. We provide their solving codes that are available on the web and make the point on the most up-to-date and efficient methods existing nowadays. We range on direct and indirect methods, on Hamilton-Jacobi approaches and we end with optimistic planning. Our examples illustrate the pros and cons of the methods and we also show how those various approaches can be combined in view of augmenting the efficiency of the numerical solving.
Published: 2022

26. Programmation DC et DCA en optimisation combinatoire et optimisation polynomiale via les techniques de SDP : codes et simulations numériques

Author: Niu, Yi Shuai, Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), INSA de Rouen, and Tao Pham Dinh
Subjects: Qmi, Local and Global Optimization, Relaxation DC, Polynomial optimization, DC programming, Software implementation, Mixed-integer programming, Relaxation SDP, Homogeneous polynomial function, Branch and Bound (B&B), Bmi, B&b, Sdp, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], Programmation DC, Optimisation polynomiale, Semi-definite relaxation, Dca, Optimisation combinatoire
Abstract: The main objective of this thesis focuses on theoretical and algorithmic researches of local and global optimization techniques to DC programming & DCA with Branch and Bound (B&B) and the DC/SDP relaxation techniques to solve several types of non-convex optimization problems (including Combinatorial Optimization and Polynomial Optimization). This thesis is divided into four parts :We present in the first part some fondamental theorems and essential techniques in DC programming & DC Algorithm (DCA), the SDP Relaxation techniques, as well as the Branch and Bound methods (B&B).In the second part, we are interested in solving mixed integer quadratic and linear programs. We propose new local and global approaches based on DCA, B&B and SDP. The implementation of software and numerical simulations have also been investigated.The third part explores the DC programming approaches & DCA combined with a B&B technique and SDP for locally and globally solving a class of polynomial programming. The polynomial program with homogeneous polynomial functionsand its application to portfolio selection problem involving higher order moments in financial optimization have been deeply studied in this part.Finally, in the last part, we present our research on optimization problems under constraints of semi-definite matrices via our DC programming approaches. This part is dedicated to the resolution of the BMI and QMI feasibility problems in the field of optimal control.All these proposed methods have been implemented with MATLAB, C++ etc., that allowing us to confirm the practical use and enrich our research works.; L’objectif de cette thèse porte sur des recherches théoriques et algorithmiques d’optimisation locale et globale via les techniques de programmation DC & DCA, Séparation et Evaluation (SE) ainsi que les techniques de relaxation DC/SDP, pour résoudre plusieurs types de problèmes d’optimisation non convexe (notamment en Optimisation Combinatoire et Optimisation Polynomiale). La thèse comporte quatre parties :La première partie présente les outils fondamentaux et les techniques essentielles en programmation DC & l’Algorithme DC (DCA), ainsi que les techniques de relaxation SDP, et les méthodes de séparation et évaluation (SE).Dans la deuxième partie, nous nous intéressons à la résolution de problèmes de programmation quadratique et linéaire mixte en variables entières. Nous proposons de nouvelles approches locales et globales basées sur DCA, SE et SDP. L’implémentation de logiciel et des simulations numériques sont aussi étudiées.La troisième partie explore des approches de la programmation DC & DCA en les combinant aux techniques SE et SDP pour la résolution locale et globale de programmes polynomiaux. Le programme polynomial avec des fonctions polynomiales homogènes et son application à la gestion de portefeuille avec moments d’ordre supérieur en optimisation financière ont été discutés de manière approfondie dans cette partie.Enfin, nous étudions dans la dernière partie un programme d’optimisation sous contraintes de type matrices semi-définies via nos approches de la programmation DC. Nous nous consacrons à la résolution du problème de réalisabilité des contraintes BMI et QMI en contrôle optimal.L’ensemble de ces travaux a été implémenté avec MATLAB, C/C++ ... nous permettant de confirmer l’utilisation pratique et d’enrichir nos travaux de recherche.
Published: 2010

27. Géométrie et classification des systèmes de contact : applications du contrôle des systèmes mécaniques non holonomes

Author: Li, Shunjie, Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), INSA de Rouen, and Witold Respondek
Subjects: Contact system, Platitude, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], Système nonholonome, Système de contact, Système de contrôle, Flatness, Nonholonomic system, Control system
Abstract: In the first part of the Ph.D thesis, we characterize all x-flat outputs and their singular loci of any 2-inputs driftless control system wich is equivalent to the chained system. Then we apply that result to the n-trailer system in order to calculate all its x-flats outputs. In the second part, we establish a new model of the n-bar system in (m+1)-dimensional space. With the help of this model, we show that the system is locally equivalent to the m-chained system and also describe its singular locus. Furthermore we analyse its flatness property and determine its minimal flat outputs. In the third part, we give necessary and sufficient conditions for a distribution to be lacally equivalent to the Cartan distribution for surfaces. Finally, in the fourth part, we give necessary and sufficient verifiable conditions for a multi-input affine control system to be orbital feedback linearizable.; Dans la première partie de cette thèse, nous caractérisons complètement toutes les x-sorties plates et leurs lieux singuliers pour un système avec deux contrôles qui est équivalent au système chaîné. Nous appliquons aussi ce résultat au système de robot mobile avec des remorques pour calculer toutes ses x-sorties plates. Dans la deuxième partie, nous présentons un nouveau modèle pour le système à n-barres dans l'espace de dimension m+1. Nous montrons que ce système est localement équivalent au système m-chaîné et caractérisons aussi ses lieux singuliers. Ensuite, nous analysons sa propriété de platitude et donnons ses sorties plates minimales. Dans la troisième partie, nous donnons des conditions nécessaires et suffisantes pour qu'une distribution soit équivalente à la distribution de Cartan pour des surfaces. Finalement, dans la quatrième partie, nous donnons des conditions nécessaires et suffisantes vérifiables pour qu'un système multi-entrées soit linéarisable par bouclage orbital.
Published: 2010

28. Geometry and classification of contact systems : applications to control of nonholomic mechanical systems

Author: Li, Shunjie, Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), INSA de Rouen, Witold Respondek, and STAR, ABES
Subjects: Contact system, Platitude, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], Système nonholonome, Système de contact, Système de contrôle, [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], Flatness, Nonholonomic system, Control system
Abstract: In the first part of the Ph.D thesis, we characterize all x-flat outputs and their singular loci of any 2-inputs driftless control system wich is equivalent to the chained system. Then we apply that result to the n-trailer system in order to calculate all its x-flats outputs. In the second part, we establish a new model of the n-bar system in (m+1)-dimensional space. With the help of this model, we show that the system is locally equivalent to the m-chained system and also describe its singular locus. Furthermore we analyse its flatness property and determine its minimal flat outputs. In the third part, we give necessary and sufficient conditions for a distribution to be lacally equivalent to the Cartan distribution for surfaces. Finally, in the fourth part, we give necessary and sufficient verifiable conditions for a multi-input affine control system to be orbital feedback linearizable., Dans la première partie de cette thèse, nous caractérisons complètement toutes les x-sorties plates et leurs lieux singuliers pour un système avec deux contrôles qui est équivalent au système chaîné. Nous appliquons aussi ce résultat au système de robot mobile avec des remorques pour calculer toutes ses x-sorties plates. Dans la deuxième partie, nous présentons un nouveau modèle pour le système à n-barres dans l'espace de dimension m+1. Nous montrons que ce système est localement équivalent au système m-chaîné et caractérisons aussi ses lieux singuliers. Ensuite, nous analysons sa propriété de platitude et donnons ses sorties plates minimales. Dans la troisième partie, nous donnons des conditions nécessaires et suffisantes pour qu'une distribution soit équivalente à la distribution de Cartan pour des surfaces. Finalement, dans la quatrième partie, nous donnons des conditions nécessaires et suffisantes vérifiables pour qu'un système multi-entrées soit linéarisable par bouclage orbital.
Published: 2010

29. Three-dimensional atomic mapping of hydrogenated polymorphous silicon solar cells

Author: Pareige, Philippe [GPM, CNRS, Université et INSA de Rouen, Normandie Université, 76801 Saint Etienne du Rouvray (France)]
Published: 2016
Full Text: View/download PDF

30. Segmentation of complex geophysical structures with well data

Author: Christian Gout, Carole Le Guyader, Laboratoire de Mathématiques de l'INSA de Rouen Normandie ( LMI ), Institut national des sciences appliquées Rouen Normandie ( INSA Rouen Normandie ), Normandie Université ( NU ) -Normandie Université ( NU ), Department of Mathematics [Hawaii], University of Hawai`i, Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015 ( LAMAV ), Université de Valenciennes et du Hainaut-Cambresis ( UVHC ) -Centre National de la Recherche Scientifique ( CNRS ), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), University of Hawai‘i [Mānoa] (UHM), Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015 (LAMAV), Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Centre National de la Recherche Scientifique (CNRS)-INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France), Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Centre National de la Recherche Scientifique (CNRS), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)
Subjects: Level set method, Image (category theory), Boundary (topology), [SDU.STU]Sciences of the Universe [physics]/Earth Sciences, [ SDU.STU ] Sciences of the Universe [physics]/Earth Sciences, 010103 numerical & computational mathematics, 02 engineering and technology, Function (mathematics), Geophysics, [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA], 01 natural sciences, Domain (mathematical analysis), Computer Science Applications, Computational Mathematics, Level set, Computational Theory and Mathematics, Computer Science::Computer Vision and Pattern Recognition, Bounded function, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, 0101 mathematics, Computers in Earth Sciences, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Interpolation, Mathematics
Abstract: In many problems of geophysical interest, when trying to segment images (i.e., to locate interfaces between different regions on the images), one has to deal with data that exhibit very complex structures. This occurs, for instance, when describing complex geophysical images (with layers, faults,...); in that case, segmentation is very difficult. Moreover, the segmentation process requires to take into account well data to interpolate, which implies integrating interpolation condition in the mathematical model. More precisely, let $I:\Omega\rightarrow\Re$ be a given bounded image function, where Ω is an open and bounded domain that belongs to $\Re^{n}$ . Let $S=\left\{ x_{i}\right\} _{i}\in\Omega$ be a finite set of given points (well data). The aim is to find a contour Γ⊂Ω such that Γ is an object boundary interpolating the points from S. To do that, we combine the ideas of the geodesic active contour (Caselles et al., Int. J. Comput. Vision 22-1:61-87, 1997) and of interpolation of points (Zhao et al., Comput. Vis. Image Understand. 80:295-314, 1986) in a Level Set approach developed by Osher and Sethian (J. Comput. Phys. 79:12-49, 1988). We present modelling of the proposed method. Both theoretical results (viscosity solution) and numerical results (on a velocity model for a real seismic line) are given.
Published: 2006

31. Image Segmentation with a Priori Conditions: Applications to Medical and Geophysical Imaging

Author: Guzel Khayretdinova, Christian Gout, Théophile Chaumont-Frelet, Sergei Kuksenko, Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Tomsk State University of Control Systems and Radioelectronics (TUSUR), Modélisation et méthodes numériques pour le calcul d'interactions onde-matière nanostructurée (ATLANTIS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Laboratoire Jean Alexandre Dieudonné (LJAD), and ANR-21-CE23-0013,MEDISEG,Nouveaux challenges en segmentation d'images médicales par apprentissage profond(2021)
Subjects: Computational Mathematics, image segmentation, a priori segmentation, level set method, geodesic active contour, Applied Mathematics, General Engineering, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, [MATH]Mathematics [math]
Abstract: International audience; In this paper, we propose a method for semi-supervised image segmentation based on geometric active contours. The main novelty of the proposed method is the initialization of the segmentation process, which is performed with a polynomial approximation of a user defined initialization (for instance, a set of points or a curve to be interpolated). This work is related to many potential applications: the geometric conditions can be useful to improve the quality the segmentation process in medicine and geophysics when it is required (weak contrast of the image, missing parts in the image, non-continuous contour…). We compare our method to other segmentation algorithms, and we give experimental results related to several medical and geophysical applications.
Published: 2022

32. Limits and consistency of non-local and graph approximations to the Eikonal equation

Author: Jalal Fadili, Nicolas Forcadel, Thi Tuyen Nguyen, Rita Zantout, Equipe Image - Laboratoire GREYC - UMR6072, Groupe de Recherche en Informatique, Image et Instrumentation de Caen (GREYC), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), Normandie Université (NU), École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), This work was supported by the Normandy Region grant MoNomads and partly by the European Union’sHorizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 777826 (NoMADS)., European Project: 777826,NoMADS(2018), Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Normandie Université (NU)-Université de Caen Normandie (UNICAEN), and Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN)
Subjects: Computational Mathematics, Error bounds, Continuum limits, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Viscosity solution, Applied Mathematics, General Mathematics, MSC: 70H20, 49L25, 65N15, 58J32, 60D05, 05C90, Weighted graphs, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Eikonal equation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Non-local
Abstract: In this paper, we study a nonlocal approximation of the time-dependent (local) Eikonal equation with Dirichlet-type boundary conditions, where the kernel in the nonlocal problem is properly scaled. Based on the theory of viscosity solutions, we prove existence and uniqueness of the viscosity solutions of both the local and nonlocal problems, as well as regularity properties of these solutions in time and space. We then derive error bounds between the solution to the nonlocal problem and that of the local one, both in continuous time and forward Euler time discretization. We then turn to studying continuum limits of nonlocal problems defined on random weighted graphs with $n$ vertices. In particular, we establish that if the kernel scale parameter decreases at an appropriate rate as $n$ grows then, almost surely, the solution of the problem on graphs converges uniformly to the viscosity solution of the local problem as the time step vanishes and the number vertices $n$ grows large.
Published: 2022

33. A HDG Framework For Convected Wave Equations. Applications In Heliosesimology

Author: Rouxelin, Nathan, Barucq, Hélène, Tordeux, Sébastien, Rouxelin, Nathan, Modélisation et simulation de la propagation des ondes fondées sur des mesures expérimentales pour caractériser des milieux géophysiques et héliophysiques et concevoir des objets complexes (MAKUTU), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Polytechnique de Bordeaux (Bordeaux INP), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), and Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)
Subjects: [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience
Published: 2022

34. Vibrational and electronic collisional-radiative model in air for Earth entry problems

Author: Bultel, Arnaud [CORIA - UMR 6614, Normandie Université, CNRS - Université et INSA de Rouen, Campus Universitaire du Madrillet, 76800 Saint-Etienne du Rouvray Cedex (France)]
Published: 2014
Full Text: View/download PDF

35. Construction of flat inputs for mechanical systems

Author: Jean-Pierre Barbot, Witold Respondek, Florentina Nicolau, Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire QUARTZ (QUARTZ ), Université Paris 8 Vincennes-Saint-Denis (UP8)-SUPMECA - Institut supérieur de mécanique de Paris (SUPMECA)-Ecole Nationale Supérieure de l'Electronique et de ses Applications (ENSEA)-Ecole Internationale des Sciences du Traitement de l'Information (EISTI), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)
Subjects: 0209 industrial biotechnology, mechanical flat inputs, Flatness (systems theory), Degrees of freedom, Mathematical analysis, Mechanical systems, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Structure (category theory), 02 engineering and technology, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Mechanical system, 020901 industrial engineering & automation, 020401 chemical engineering, Control and Systems Engineering, [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], flat inputs, 0204 chemical engineering, Mathematics, flatness
Abstract: International audience; For observed mechanical systems, we study the problem of constructing flat inputs that are consistent with the mechanical structure of the systems. Such inputs will be called mechanical flat inputs. We show that contrary to flat inputs, that exist (almost) everywhere, in general, for the existence of mechanical flat inputs, additional structural conditions are needed. We provide necessary and sufficient conditions for the existence of mechanical inputs for observed mechanical systems with n degrees of freedom, where n is arbitrary, and n − 1 measurements.
Published: 2021

36. Generalized Nesterov's accelerated proximal gradient algorithms with convergence rate of order o(1/k 2 )

Author: Huynh, van Ngai, Ta, Anh Son, Department of Mathematics, Pedagogical University of Quynhon, Pedagogical University of Quynhon, Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), and Huynh, Van Ngai
Subjects: convex optimization, proximal mapping, subdifferential Mathematics Subject Classification: 49J52, 49M37, Nesterov accelerated gradient method, 90C30, 65K05, [MATH] Mathematics [math], [MATH]Mathematics [math], forward-backward method, 90C25, 90C26
Abstract: The accelerated gradient method initiated by Nesterov is now recognized to be one of the most powerful tools for solving smooth convex optimization problems. This method improves significantly the convergence rate of function values from O(1/k) of the standard gradient method down to O(1/k 2). In this paper, we present two generalized variants of Nesterov's accelerated proximal gradient method for solving composition convex optimization problems in which the objective function is represented by the sum of a smooth convex function and a nonsmooth convex part. We show that with suitable ways to pick the sequences of parameters, the convergence rate for the function values of this proposed method is actually of order o(1/k 2). Especially, when the objective function is p−uniformly convex for p > 2, the convergence rate is of order O ln k/k 2p/(p−2) , and the convergence is linear if the objective function is strongly convex. By-product, we derive a forward-backward algorithm generalizing the one by Attouch-Peypouquet [1], which produces a convergence sequence with a convergence rate of the function values of order o(1/k 2).
Published: 2021

37. The early stage of formation of self-organized nanocolumns in thin films: Monte Carlo simulations versus atomic-scale observations in Ge-Mn

Author: Blavette, D. [Groupe de Physique des Matériaux (GPM) UMR 6634, Normandie Université, Université et INSA de Rouen - CNRS, Av. de l'Université, BP 12, 76801 Saint Etienne du Rouvray (France)]
Published: 2014
Full Text: View/download PDF

38. Micro to macro traffic model: the case of a convergent junction

Author: El Khatib, Nader, Forcadel, Nicolas, Zaydan, Mamdouh, Lebanese American University (LAU), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), and Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)
Subjects: viscosity solutions, Slepčev formulation, non-local operators, 90B20, 35B27, 35F20, Condensed Matter::Mesoscopic Systems and Quantum Hall Effect, traffic flow, AMS Classification: 35D40, 90B20, 35B27, 35F20, 45K05, Condensed Matter::Superconductivity, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], microscopic model on junction, 45K05 specified homogenization, AMS Classification: 35D40, Hamilton-Jacobi equations, specified homogenization
Abstract: In this paper, we establish a rigorous connection between a microscopic and a macroscopic traffic model on a convergent junction. At the microscopic scale, we assume that each driver satisfies the "follow the leader" model before the junction point and, a priori, knows its turn to enter the junction. At the macroscopic scale, we obtain a Hamilton-Jacobi equation with a flux limiting condition at the junction point as in [27]. The novelty of this model is that we are able to treat the case of a convergent junction, which wasn't covered in [18]. We explain in the Appendix how to treat the general case with several incoming and outgoing roads.
Published: 2021

39. DCA-based algorithms for DC Fitting

Author: Tao Pham Dinh, Vinh Thanh Ho, Hoai An Le Thi, Laboratoire de Génie Informatique, de Production et de Maintenance (LGIPM), Université de Lorraine (UL), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), and Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)
Subjects: Scheme (programming language), Applied Mathematics, Computer Science::Neural and Evolutionary Computation, 010103 numerical & computational mathematics, Function (mathematics), 01 natural sciences, 010101 applied mathematics, Set (abstract data type), Euclidean distance, Computational Mathematics, Data point, Decomposition (computer science), [INFO]Computer Science [cs], 0101 mathematics, Convex function, computer, Algorithm, ComputingMilieux_MISCELLANEOUS, Mathematics, computer.programming_language
Abstract: We investigate a nonconvex, nonsmooth optimization approach based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) for the so-called DC fitting problem, which aims to fit a given set of data points by a DC function. The problem is tackled as minimizing the squared Euclidean norm fitting error. It is formulated as a DC program for which a standard DCA scheme is developed. Furthermore, a modified DCA scheme with successive DC decomposition is proposed. These standard/modified versions of DCA are applied for solving the continuous piecewise-linear fitting problem. Numerical experiments on many synthetic and real datasets with small-to-large sizes show the efficiency of our DCA-based approach in comparison with the existing approaches for constructing continuous piecewise-linear models.
Published: 2021

40. Limits and consistency of non-local and graph approximations to the Eikonal equation

Author: FADILI, Jalal M., FORCADEL, Nicolas, TUYEN NGUYEN, Thi, Equipe Image - Laboratoire GREYC - UMR6072, Groupe de Recherche en Informatique, Image et Instrumentation de Caen (GREYC), Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Normandie Université (NU)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU), École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), This work was supported by the Normandy Region grant MoNomads and partly by the European Union’sHorizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 777826 (NoMADS)., and European Project: 777826,NoMADS(2018)
Subjects: Error bounds, Continuum limits, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Viscosity solution, MSC: 70H20, 49L25, 65N15, 58J32, 60D05, 05C90, Weighted graphs, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Eikonal equation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Non-local
Abstract: In this paper, we study a non-local approximation of the time-dependent (local) Eikonal equation with Dirichlet-type boundary conditions, where the kernel in the non-local problem is properly scaled. Based on the theory of viscosity solutions, we prove existence and uniqueness of the viscosity solutions of both the local and non-local problems, as well as regularity properties of these solutions in time and space. We then derive error bounds between the solution to the non-local problem and that of the local one, both in continuous-time and Backward Euler time discretization. We then turn to studying continuum limits of non-local problems defined on random weighted graphs with $n$ vertices. In particular, we establish that if the kernel scale parameter decreases at an appropriate rate as $n$ grows, then almost surely, the solution of the problem on graphs converges uniformly to the viscosity solution of the local problem as the time step vanishes and the number vertices $n$ grows large.
Published: 2021

41. Multiscale Registration

Author: Noémie Debroux, Carole Le Guyader, Luminita A. Vese, Institut Pascal (IP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), Université Clermont Auvergne (UCA)-Université Clermont Auvergne (UCA), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), and Department of Mathematics, University of California Los Angeles
Subjects: nonlinear elasticity, Γ -convergence, bi-Lipschitz homeomorphisms, Ogden materials, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, 030218 nuclear medicine & medical imaging, 010101 applied mathematics, 03 medical and health sciences, 0302 clinical medicine, registration, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], 0101 mathematics, Multiscale analysis
Abstract: International audience; In the seminal paper E. Tadmor, S. Nezzar and L. Vese, A multiscale image representation using hierarchical (BV, L 2) decompositions, Multiscale Model. Simul., 2(4), 554-579, (2004), the authors introduce a multiscale image decomposition model providing a hierarchical decomposition of a given image into the sum of scale-varying components. In line with this framework, we extend the approach to the case of registration, task which consists of mapping salient features of an image onto the corresponding ones in another, the underlying goal being to obtain such a kind of hierarchical decomposition of the deformation relating the two considered images (-from the coarser one that encodes the main structural/geometrical deformation, to the more refined one-). To achieve this goal, we introduce a functional minimisation problem in a hyperelasticity setting by viewing the shapes to be matched as Ogden materials. This approach is complemented by hard constraints on the L ∞-norm of both the Jacobian and its inverse, ensuring that the deformation is a bi-Lipschitz homeomorphism. Theoretical results emphasising the mathematical soundness of the model are provided, among which the existence of minimisers, a Γ-convergence result and an analysis of a suitable numerical algorithm, along with numerical simulations demonstrating the ability of the model to produce accurate hierarchical representations of deformations.
Published: 2021

42. A GEOMETRICALLY-CONSTRAINED DEEP NETWORK FOR CT IMAGE SEGMENTATION

Author: Caroline Petitjean, Zoe Lambert, Carole Le Guyader, Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Equipe Quantification en Imagerie Fonctionnelle (QuantIF-LITIS), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Normandie Université (NU), and Equipe Apprentissage (DocApp - LITIS)
Subjects: 0209 industrial biotechnology, Computer science, Boundary (topology), Context (language use), 02 engineering and technology, Convolutional neural network, Convexity, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], 020901 industrial engineering & automation, Douglas-Rachford algorithm, 0202 electrical engineering, electronic engineering, information engineering, Segmentation, ADMM algorithm, image segmentation, business.industry, Deep learning, deep learning, [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], Image segmentation, proximal operator, Piecewise, 020201 artificial intelligence & image processing, CT scans, Artificial intelligence, business, Algorithm, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Abstract: International audience; Incorporating prior knowledge into a segmentation process, whether it be geometrical constraints such as volume penalisation, (partial) convexity enforcement, or topological prescriptions to preserve the contextual relations between objects, proves to improve accuracy in medical image segmentation, in particular when addressing the issue of weak boundary definition. Motivated by this observation, the proposed contribution aims to include geometrical constraints in the training of convolutional neural networks in the form of a penalty in the loss function. These geometrical constraints take several forms and encompass level curve alignment through the weighted total variation component, an area penalisation phrased as a hard constraint in the modelling, and an intensity homogeneity criterion based on a combination of the standard Dice loss with the piecewise constant Mumford-Shah model. The mathematical formulation yields a non-smooth non-convex optimisation problem, which rules out conventional smooth optimisation techniques and leads us to adopt a Lagrangian setting. The application falls within the scope of organ-at-risk segmentation in CT (Computed Tomography) images, in the context of radiotherapy planning. Experiments demonstrate that our method provides significant improvements over existing non-constrained approaches.
Published: 2021

43. A non-local macroscopic model for traffic flow

Author: Ioana Ciotir, Nicolas Forcadel, Rim Fayad, Antoine Tonnoir, Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), North Carolina State University [Raleigh] (NC State), and University of North Carolina System (UNC)
Subjects: Work (thermodynamics), viscosity solutions, Macroscopic model, homogenization, macroscopic models, 01 natural sciences, Homogenization (chemistry), Traffic flow, AMS Classification: 76A30, Applied mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Limit (mathematics), Uniqueness, Hamilton–Jacobi equations, 0101 mathematics, [MATH]Mathematics [math], Mathematics, 35D40, Numerical Analysis, Continuous solution, 35F21 Keywords: Traffic flow, Applied Mathematics, 010102 general mathematics, 35B27, Non local, 010101 applied mathematics, Computational Mathematics, Modeling and Simulation, Hamilton-Jacobi equations, Analysis, non-local model
Abstract: International audience; In this work, we propose a non-local Hamilton–Jacobi model for traffic flow and we prove the existence and uniqueness of the solution of this model. This model is justified as the limit of a rescaled microscopic model. We also propose a numerical scheme and we prove an estimate error between the continuous solution of this problem and the numerical one. Finally, we provide some numerical illustrations.
Published: 2021

44. Nonlinear Fokker-Planck equation with reflecting boundary conditions

Author: Ciotir, Ioana, Fayad, Rim, Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), and Ciotir, Ioana
Subjects: [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Applied Mathematics, secondary 35Q84, Fokker-Planck equation, 35D99, m-accretive operator, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], McKean-Vlasov stochastic differential equation AMS [2020] Primary 60H30, mild solution, 60G46, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 60H10, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Analysis
Abstract: We study the existence and uniqueness of a mild solution to a nonlinear Fokker-Planck equation with reflecting boundary conditions, by using a monotonicity approach. Then we prove that the mild solution is also a distributional one.
Published: 2021

45. Variational multi-task MRI reconstruction: Joint reconstruction, registration and super-resolution

Author: Carola-Bibiane Schönlieb, Noémie Debroux, Angelica I. Aviles-Rivero, Veronica Corona, Carole Le Guyader, Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge [UK] (CAM), Department of Pure Mathematics and Mathematical Statistics (DPMMS), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), Institut Pascal (IP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), Université Clermont Auvergne (UCA)-Université Clermont Auvergne (UCA), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Corona, Veronica [0000-0003-2160-5482], and Apollo - University of Cambridge Repository
Subjects: math.NA, Image Registration, Computer science, media_common.quotation_subject, Physics::Medical Physics, Motion Correction, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, MRI Reconstruction, Image registration, Fidelity, CPU time, Health Informatics, Motion (physics), 030218 nuclear medicine & medical imaging, Set (abstract data type), Motion, 03 medical and health sciences, Imaging, Three-Dimensional, 0302 clinical medicine, Image Super-resolution, Image Processing, Computer-Assisted, FOS: Electrical engineering, electronic engineering, information engineering, FOS: Mathematics, [INFO.INFO-IM]Computer Science [cs]/Medical Imaging, Humans, Radiology, Nuclear Medicine and imaging, Computer vision, Mathematics - Numerical Analysis, Representation (mathematics), cs.NA, media_common, ComputingMethodologies_COMPUTERGRAPHICS, Radiological and Ultrasound Technology, business.industry, Image and Video Processing (eess.IV), Numerical Analysis (math.NA), Electrical Engineering and Systems Science - Image and Video Processing, Magnetic Resonance Imaging, Computer Graphics and Computer-Aided Design, Term (time), Task (computing), eess.IV, Computer Vision and Pattern Recognition, Artificial intelligence, business, Algorithms, 030217 neurology & neurosurgery
Abstract: Motion degradation is a central problem in Magnetic Resonance Imaging (MRI). This work addresses the problem of how to obtain higher quality, super-resolved motion-free reconstructions from highly undersampled MRI data. In this work, we present for the first time a variational multi-task framework that allows joining three relevant tasks in MRI: reconstruction, registration and super-resolution. Our framework takes a set of multiple undersampled MR acquisitions corrupted by motion into a novel multi-task optimisation model, which is composed of an L2 fidelity term that allows sharing representation between tasks, super-resolution foundations and hyperelastic deformations to model biological tissue behaviors. We demonstrate that this combination yields significant improvements over sequential models and other bi-task methods. Our results exhibit fine details and compensate for motion producing sharp and highly textured images compared to state of the art methods while keeping low CPU time. Our improvements are appraised on both clinical assessment and statistical analysis.
Published: 2021

46. How to minimally modify a dynamical system when constructing flat inputs?

Author: Nicolau, Florentina, Respondek, Witold, Barbot, Jean-Pierre, Laboratoire QUARTZ (QUARTZ ), Université Paris 8 Vincennes-Saint-Denis (UP8)-SUPMECA - Institut supérieur de mécanique de Paris (SUPMECA)-Ecole Nationale Supérieure de l'Electronique et de ses Applications (ENSEA)-Ecole Internationale des Sciences du Traitement de l'Information (EISTI), Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Université Paris 8 Vincennes-Saint-Denis (UP8)-Ecole Nationale Supérieure de l'Electronique et de ses Applications (ENSEA)-SUPMECA - Institut supérieur de mécanique de Paris (SUPMECA)-Ecole Internationale des Sciences du Traitement de l'Information (EISTI), and Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)
Subjects: [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract: International audience; In this paper, we study the problem of constructing flat inputs for multi-output dynamical systems, in particular, we address the issue of the minimal modification of the initial dynamical system (the measure of modification being the number of equations that have to be changed by adding flat inputs). We show that in the observable case, control vector fields that distort m equations only (where m is the number of measurements) can always be constructed (and this is the minimal possible number of equations that have to be modified by adding flat inputs), while in the unobservable case, the best that we can hope for is that m + 1 equations only are modified such that they involve flat inputs. We discuss when the original output is a flat output of minimal possible differential weight for the minimally modified control system (where by differential weight, we mean the minimal number of derivatives of components of a flat output needed to express all states and controls). We propose a solution for constructing flat inputs leading to a minimally modified control system consistent with the minimal differential weight and, moreover, for which the observable part is affected by the minimal possible number of controls (this last property being important in applications). We show that, in that case, at least 2m − 1 equations have to be affected by the flat inputs.
Published: 2021

47. DC programming and DCA for enhancing physical layer security via relay beamforming strategies

Author: Thi Thuy Tran, Hoai An Pham Thi, Tao Pham Dinh, Nhu Tuan Nguyen, FPT University, Laboratoire de Génie Informatique, de Production et de Maintenance (LGIPM), Université de Lorraine (UL), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), and Vietnam Information Security Journal
Subjects: 021103 operations research, Control and Optimization, 0211 other engineering and technologies, Business, Management and Accounting (miscellaneous), [INFO]Computer Science [cs], 010103 numerical & computational mathematics, 02 engineering and technology, 0101 mathematics, 01 natural sciences, ComputingMilieux_MISCELLANEOUS
Abstract: International audience
Published: 2021

48. On a surprising instability result of Perfectly Matched Layers for Maxwell's equations in 3D media with diagonal anisotropy

Author: Sonia Fliss, Maryna Kachanovska, Maria Kazakova, Eliane Bécache, Propagation des Ondes : Étude Mathématique et Simulation (POEMS), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), and ANR-11-LABX-0056,LMH,LabEx Mathématique Hadamard(2011)
Subjects: Perfectly Matched Layers, backward waves, Wave propagation, General Mathematics, 010102 general mathematics, Diagonal, Mathematical analysis, Context (language use), 01 natural sciences, Instability, law.invention, Anisotropic Maxwell's equation, symbols.namesake, Maxwell's equations, law, 0103 physical sciences, symbols, Cartesian coordinate system, 010307 mathematical physics, 0101 mathematics, Anisotropy, Scalar field, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract: International audience; The analysis of Cartesian Perfectly Matched Layers (PMLs) in the context of time-domain electromagnetic wave propagation in a 3D unbounded anisotropic homogeneous medium modelled by a diagonal dielectric tensor is presented. Contrary to the 3D scalar wave equation or 2D Maxwell's equations some diagonal anisotropies lead to the existence of backward waves giving rise to instabilities of the PMLs. Numerical experiments confirm the presented result.; Dans cette note nous nous intéressons à l’analyse de stabilité de la méthode de couches absorbantesparfaitement adaptées (PMLs) pour la propagation d’ondes électromagnétiques en régime transitoiredans un milieu anisotrope décrit par un tenseur diélectrique diagonal. Contrairement aux cas de l’équationd’ondes scalaire 3D et des équations de Maxwell 2D, certaines anisotropies diagonales mènent à l’existenced’ondes inverses qui provoquent des instabilités de la méthode PML. Ce résultat est illustré par des simulationsnumériques.
Published: 2021

49. Preface to the special issue dedicated to the 6th World Congress on Global Optimization held in Metz, France, July 8–10, 2019

Author: Hoai An Le Thi, Yaroslav D. Sergeyev, Tao Pham Dinh, Laboratoire de Génie Informatique, de Production et de Maintenance (LGIPM), Université de Lorraine (UL), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), and University of Calabria
Subjects: Engineering, 021103 operations research, Control and Optimization, business.industry, 0211 other engineering and technologies, Library science, Computational intelligence, 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, [INFO]Computer Science [cs], 0101 mathematics, business, Global optimization, ComputingMilieux_MISCELLANEOUS
Abstract: International audience
Published: 2021

50. Learning discontinuous piecewise affine fitting functions using mixed integer programming over lattice

Author: Ruobing Shen, Stéphane Canu, Claudia D’Ambrosio, Leo Liberti, Bo Tang, Department of Mathematics and Computer Science [Heidelberg], Universität Heidelberg [Heidelberg], University of Toronto (Department of Mechanical and Industrial Engineering), Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), and Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)
Subjects: 021103 operations research, Control and Optimization, Continuous function, Applied Mathematics, 0211 other engineering and technologies, Integer lattice, Lattice (group), 02 engineering and technology, Image segmentation, Function (mathematics), [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO], Management Science and Operations Research, Computer Science Applications, 0202 electrical engineering, electronic engineering, information engineering, Business, Management and Accounting (miscellaneous), Applied mathematics, 020201 artificial intelligence & image processing, Integer programming, Cutting-plane method, ComputingMilieux_MISCELLANEOUS, Integer (computer science), Mathematics
Abstract: Piecewise affine functions are widely used to approximate nonlinear and discontinuous functions. However, most, if not all existing models, only deal with fitting a continuous function. In this paper, we investigate the problem of fitting a discontinuous piecewise affine function to a given function defined on an arbitrary subset of an integer lattice, where no restriction on the partition of the domain is enforced (i.e., its geometric shape can be nonconvex). This is useful for segmentation and denoising when the given function corresponds to a mapping from pixels of a bitmap image to their color depth values. We propose a novel Mixed Integer Program (MIP) formulation for the piecewise affine fitting problem, where binary edge variables determine the boundary between two partitions of the function domain. To obtain a consistent partitioning (e.g., image segmentation), we include multicut constraints in the formulation. The resulting problem is $$\mathcal {NP}$$ -hard, and two techniques are introduced to improve the computation. One is to adopt a cutting plane method to add the exponentially many multicut inequalities on-the-fly. The other is to provide initial feasible solutions using a tailored heuristic algorithm. We show that the MIP formulation on grid graphs is approximate, while on king’s graph, it is exact under certain circumstances. We conduct initial experiments on synthetic images as well as real depth images, and discuss the advantages and drawbacks of the two models.
Published: 2021

Catalog

Books, media, physical & digital resources

See catalog results

Searchworks

Select search scope, currently: Articles Catalog books, media & more in Jio Institute collections Articles journal articles & other e-resources

Search

Search Constraints

Refine your results

Search Limiters

Topic

Publication Year Range

Publication Type

Journal

Region

Database

Publisher

621 results on '"INSA de Rouen"'

Search Results

Catalog

Select search scope, currently: Articles

Catalog

books, media & more in Jio Institute collections

Articles

journal articles & other e-resources