Jerome Pousin | Université Lyon (original) (raw)
Papers by Jerome Pousin
2018 14th IEEE International Conference on Signal Processing (ICSP), 2018
We investigate the problem of constructing statistical atlas of human cardiac fiber structure fro... more We investigate the problem of constructing statistical atlas of human cardiac fiber structure from limited number of datasets. We introduced a Parzen-Gaussian model to construct the probabilistic atlas of human cardiac fiber structure due to the fact that it can generate a general atlas using very small number of samples. Experimental results showed that atlas using Parzen-Gaussian model can avoid FA/MD collapse, which can be introduced by atlas from registered DW images and registered tensor fields.
On considere une barre elastique homogene vibrant longitudinalement dont une de ses extremites es... more On considere une barre elastique homogene vibrant longitudinalement dont une de ses extremites est libre de bouger, tant qu'elle ne touche pas un obstacle rigide et l'autre extremite est fixee. Le probleme mathematique peut etre formule comme une equation des ondes monodimentionnelles soumise a une condition limite unilaterale. La methode de redistribution de masse ponderee est introduite et sa convergence est prouvee. Ensuite, differents choix de redistribution de masse sont presentes et analyses.
Issued by Sandia National Laboratmies, operated for the United States Department of Energy by San... more Issued by Sandia National Laboratmies, operated for the United States Department of Energy by Sandia Corpration. NOTICE. This report was p r e p a d as an account of work sponsored by an agency of the United States Government Neither theunited States Government, nor any agency thereor nm any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Referenm herein to any specific commercial product, pmceas. m service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof, or any of their contractors or subcontractors The views and opinions expressed herein do not necessarily state or ratlect those of the United States Government, any agency thomot m any of their contractors. Printed in the United States of America. Thia report has been reproduced directly fmm the best available copy.
Irbm, Mar 1, 2015
ABSTRACT The aim of this project is to design a generic formalism for parietal and regional track... more ABSTRACT The aim of this project is to design a generic formalism for parietal and regional tracking of the left ventricle (LV) and to adapt it to cardiac imaging modalities used in clinical routine (echocardiography, gated-SPECT, cine-MRI). The estimated displacement field must be reliable enough and insensitive to various artifacts to assess regional myocardial function in 3D from the accurate and precise computation of strain. The strain has recently proved to be of great interest for diagnosis and prognostic in cardiology, but its interpretation remains difficult because of the relative nature of the indices. The clinical objective of the 3DStrain project is to bring answers about the knowledge of normality.
Research Square (Research Square), Apr 19, 2023
Generally, meshless interpolations are not polynomial, in this paper, we propose a meshless polyn... more Generally, meshless interpolations are not polynomial, in this paper, we propose a meshless polynomial local interpolator. This interpolator uses Lagrange polynomials P 1 and a nearest neighbors strategy, and have yet been introduced in a previous work [1] investigating the relation between an artificial neural network and the transport of the identity towards a given function to be interpolated. Unfortunately, it has been reported in [1] that the order of convergence of the interpolation deteriorates when the size of the d-simplexe becomes too small, because the built d-simplexe does not necessary contain the point at which interpolation is computed. The aim of this note is to remedy this difficulty. Here, we study the problem of interpolating d-dimensional data with P 1 polynomials by minimizing a data-fidelity cost function, involving the barycentric coordinates of the d + 1-nearest neighbors. Data points distributions are not required to be structured, and the nearest neighbors are computed through a penalized minimization process in order to get a no degenerate d-simplex containing the point at which the interpolation is computed. The proposed interpolation operator is local, and a global one can be built which will be no more polynomial. Some numerical results are provided showing the efficiency of the proposed method.
Journal of Magnetic Resonance, 2020
We investigate the problem of constructing statistical atlas of human cardiac fiber structure fro... more We investigate the problem of constructing statistical atlas of human cardiac fiber structure from limited number of datasets. We introduced a Parzen-Gaussian model to construct the probabilistic atlas of human cardiac fiber structure due to the fact that it can generate a general atlas using very small number of samples. Experimental results showed that atlas using Parzen-Gaussian model can avoid FA/MD collapse, which can be introduced by atlas from registered DW images and registered tensor fields.
Issued by Sandia National Laboratmies, operated for the United States Department of Energy by San... more Issued by Sandia National Laboratmies, operated for the United States Department of Energy by Sandia Corpration. NOTICE. This report was p r e p a d as an account of work sponsored by an agency of the United States Government Neither theunited States Government, nor any agency thereor nm any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Referenm herein to any specific commercial product, pmceas. m service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof, or any of their contractors or subcontractors The views and opinions expressed herein do not necessarily state or ratlect those of the United States Government, any agency thomot m any of their contractors. Printed in the United States of America. Thia report has been reproduced directly fmm the best available copy.
HAL (Le Centre pour la Communication Scientifique Directe), Jun 18, 2013
Finite element methods are known to produce spurious oscillations when the transport equation is ... more Finite element methods are known to produce spurious oscillations when the transport equation is solved. In this paper, a variational formulation for the transport equation is proposed, and by introducing a positivity constraint combined with a penalization of the total variation of the solution, a discrete maximum principle is verified for lagrange first order finite element methods. Moreover, the oscillations are cancelled.
International Conference on Industrial Engineering and Systems Management, Oct 1, 2013
In the process of image restoration, the denoising is an important step. Several models of non-li... more In the process of image restoration, the denoising is an important step. Several models of non-linear diffusive filters requiring solving partial differential equations have been proposed in the literature [1], [2], [3], [4], [5], [6], [7] during the last decades. The existence and uniqueness of a solution in Hilbert space has been established under suitable conditions on the filtering function for the Perona Malik model [5] considering Dirichlet homogeneous and inhomogeneous boundary conditions [1], [2]. In this work, we propose a nonlinear diffusion model inspired by the Perona-Malik one taking into account the Neumann boundary condition. The existence, uniqueness and regularity of the solution to the mathematical problem are established in a Hilbert space. The numerical simulation of the discretized problem is performed using the finite elements method. The effectiveness of this model has been tested on many noisy images with noises of different natures. A comparison of signal to noise ratio (SNR) is used to estimate the quality of the restored images by this model and the Perona-Malik one.
Moroccan Journal of Condensed Matter, 2004
The aim of this work is to study a mathematical model, based on the pseudo-concentration function... more The aim of this work is to study a mathematical model, based on the pseudo-concentration function model, for the filling of shallow molds with polymers. The proposed model is 2-D, the chemical reactivity of the fluid is accounted with the conversion rate satisfying a Kamal-Sourour model, and the temperature is not considered. We prove the existence of a solution of the proposed mathematical model.
Journal of Computational and Applied Mathematics, 2024
Asymptotic Analysis, 2015
The result presented in this article is an adaptation of the gradient flow technique applied to a... more The result presented in this article is an adaptation of the gradient flow technique applied to a periodic problem combined with a singular perturbation method. The motivation for considering such a question originates from problems of cardiac images segmentation and of tracking cardiac images in medical image analysis. The 'elastic deformable template' model introduced previously for image segmentation is improved and adapted to the image tracking problem. A result of convergence is proved, for a periodic linear elastic model, the elastic tensor of which vanishes, when the parameter associated to the quasi-static technique goes to infinity.
HAL (Le Centre pour la Communication Scientifique Directe), 2011
International audienc
HAL (Le Centre pour la Communication Scientifique Directe), May 18, 2015
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Ima Journal of Numerical Analysis, Jun 19, 2017
We introduce a residual-based a posteriori error estimator for contact problems in two and three ... more We introduce a residual-based a posteriori error estimator for contact problems in two and three dimensional linear elasticity, discretized with linear and quadratic finite elements and Nitsche's method. Efficiency and reliability of the estimator are proved under a saturation assumption. Numerical experiments illustrate the theoretical properties and the good performance of the estimator.
arXiv (Cornell University), Jan 5, 2016
This paper deals with a one-dimensional wave equation being subjected to a unilateral boundary co... more This paper deals with a one-dimensional wave equation being subjected to a unilateral boundary condition. An approximation of this problem combining the finite element and mass redistribution methods is proposed. The mass redistribution method is based on a redistribution of the body mass such that there is no inertia at the contact node and the mass of the contact node is redistributed on the other nodes. The convergence as well as an error estimate in time are proved. The analytical solution associated with a benchmark problem is introduced and it is compared to approximate solutions for different choices of mass redistribution. However some oscillations for the energy associated with approximate solutions obtained for the second order schemes can be observed after the impact. To overcome this difficulty, an new unconditionally stable and a very lightly dissipative scheme is proposed.
2018 14th IEEE International Conference on Signal Processing (ICSP), 2018
We investigate the problem of constructing statistical atlas of human cardiac fiber structure fro... more We investigate the problem of constructing statistical atlas of human cardiac fiber structure from limited number of datasets. We introduced a Parzen-Gaussian model to construct the probabilistic atlas of human cardiac fiber structure due to the fact that it can generate a general atlas using very small number of samples. Experimental results showed that atlas using Parzen-Gaussian model can avoid FA/MD collapse, which can be introduced by atlas from registered DW images and registered tensor fields.
On considere une barre elastique homogene vibrant longitudinalement dont une de ses extremites es... more On considere une barre elastique homogene vibrant longitudinalement dont une de ses extremites est libre de bouger, tant qu'elle ne touche pas un obstacle rigide et l'autre extremite est fixee. Le probleme mathematique peut etre formule comme une equation des ondes monodimentionnelles soumise a une condition limite unilaterale. La methode de redistribution de masse ponderee est introduite et sa convergence est prouvee. Ensuite, differents choix de redistribution de masse sont presentes et analyses.
Issued by Sandia National Laboratmies, operated for the United States Department of Energy by San... more Issued by Sandia National Laboratmies, operated for the United States Department of Energy by Sandia Corpration. NOTICE. This report was p r e p a d as an account of work sponsored by an agency of the United States Government Neither theunited States Government, nor any agency thereor nm any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Referenm herein to any specific commercial product, pmceas. m service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof, or any of their contractors or subcontractors The views and opinions expressed herein do not necessarily state or ratlect those of the United States Government, any agency thomot m any of their contractors. Printed in the United States of America. Thia report has been reproduced directly fmm the best available copy.
Irbm, Mar 1, 2015
ABSTRACT The aim of this project is to design a generic formalism for parietal and regional track... more ABSTRACT The aim of this project is to design a generic formalism for parietal and regional tracking of the left ventricle (LV) and to adapt it to cardiac imaging modalities used in clinical routine (echocardiography, gated-SPECT, cine-MRI). The estimated displacement field must be reliable enough and insensitive to various artifacts to assess regional myocardial function in 3D from the accurate and precise computation of strain. The strain has recently proved to be of great interest for diagnosis and prognostic in cardiology, but its interpretation remains difficult because of the relative nature of the indices. The clinical objective of the 3DStrain project is to bring answers about the knowledge of normality.
Research Square (Research Square), Apr 19, 2023
Generally, meshless interpolations are not polynomial, in this paper, we propose a meshless polyn... more Generally, meshless interpolations are not polynomial, in this paper, we propose a meshless polynomial local interpolator. This interpolator uses Lagrange polynomials P 1 and a nearest neighbors strategy, and have yet been introduced in a previous work [1] investigating the relation between an artificial neural network and the transport of the identity towards a given function to be interpolated. Unfortunately, it has been reported in [1] that the order of convergence of the interpolation deteriorates when the size of the d-simplexe becomes too small, because the built d-simplexe does not necessary contain the point at which interpolation is computed. The aim of this note is to remedy this difficulty. Here, we study the problem of interpolating d-dimensional data with P 1 polynomials by minimizing a data-fidelity cost function, involving the barycentric coordinates of the d + 1-nearest neighbors. Data points distributions are not required to be structured, and the nearest neighbors are computed through a penalized minimization process in order to get a no degenerate d-simplex containing the point at which the interpolation is computed. The proposed interpolation operator is local, and a global one can be built which will be no more polynomial. Some numerical results are provided showing the efficiency of the proposed method.
Journal of Magnetic Resonance, 2020
We investigate the problem of constructing statistical atlas of human cardiac fiber structure fro... more We investigate the problem of constructing statistical atlas of human cardiac fiber structure from limited number of datasets. We introduced a Parzen-Gaussian model to construct the probabilistic atlas of human cardiac fiber structure due to the fact that it can generate a general atlas using very small number of samples. Experimental results showed that atlas using Parzen-Gaussian model can avoid FA/MD collapse, which can be introduced by atlas from registered DW images and registered tensor fields.
Issued by Sandia National Laboratmies, operated for the United States Department of Energy by San... more Issued by Sandia National Laboratmies, operated for the United States Department of Energy by Sandia Corpration. NOTICE. This report was p r e p a d as an account of work sponsored by an agency of the United States Government Neither theunited States Government, nor any agency thereor nm any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Referenm herein to any specific commercial product, pmceas. m service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof, or any of their contractors or subcontractors The views and opinions expressed herein do not necessarily state or ratlect those of the United States Government, any agency thomot m any of their contractors. Printed in the United States of America. Thia report has been reproduced directly fmm the best available copy.
HAL (Le Centre pour la Communication Scientifique Directe), Jun 18, 2013
Finite element methods are known to produce spurious oscillations when the transport equation is ... more Finite element methods are known to produce spurious oscillations when the transport equation is solved. In this paper, a variational formulation for the transport equation is proposed, and by introducing a positivity constraint combined with a penalization of the total variation of the solution, a discrete maximum principle is verified for lagrange first order finite element methods. Moreover, the oscillations are cancelled.
International Conference on Industrial Engineering and Systems Management, Oct 1, 2013
In the process of image restoration, the denoising is an important step. Several models of non-li... more In the process of image restoration, the denoising is an important step. Several models of non-linear diffusive filters requiring solving partial differential equations have been proposed in the literature [1], [2], [3], [4], [5], [6], [7] during the last decades. The existence and uniqueness of a solution in Hilbert space has been established under suitable conditions on the filtering function for the Perona Malik model [5] considering Dirichlet homogeneous and inhomogeneous boundary conditions [1], [2]. In this work, we propose a nonlinear diffusion model inspired by the Perona-Malik one taking into account the Neumann boundary condition. The existence, uniqueness and regularity of the solution to the mathematical problem are established in a Hilbert space. The numerical simulation of the discretized problem is performed using the finite elements method. The effectiveness of this model has been tested on many noisy images with noises of different natures. A comparison of signal to noise ratio (SNR) is used to estimate the quality of the restored images by this model and the Perona-Malik one.
Moroccan Journal of Condensed Matter, 2004
The aim of this work is to study a mathematical model, based on the pseudo-concentration function... more The aim of this work is to study a mathematical model, based on the pseudo-concentration function model, for the filling of shallow molds with polymers. The proposed model is 2-D, the chemical reactivity of the fluid is accounted with the conversion rate satisfying a Kamal-Sourour model, and the temperature is not considered. We prove the existence of a solution of the proposed mathematical model.
Journal of Computational and Applied Mathematics, 2024
Asymptotic Analysis, 2015
The result presented in this article is an adaptation of the gradient flow technique applied to a... more The result presented in this article is an adaptation of the gradient flow technique applied to a periodic problem combined with a singular perturbation method. The motivation for considering such a question originates from problems of cardiac images segmentation and of tracking cardiac images in medical image analysis. The 'elastic deformable template' model introduced previously for image segmentation is improved and adapted to the image tracking problem. A result of convergence is proved, for a periodic linear elastic model, the elastic tensor of which vanishes, when the parameter associated to the quasi-static technique goes to infinity.
HAL (Le Centre pour la Communication Scientifique Directe), 2011
International audienc
HAL (Le Centre pour la Communication Scientifique Directe), May 18, 2015
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Ima Journal of Numerical Analysis, Jun 19, 2017
We introduce a residual-based a posteriori error estimator for contact problems in two and three ... more We introduce a residual-based a posteriori error estimator for contact problems in two and three dimensional linear elasticity, discretized with linear and quadratic finite elements and Nitsche's method. Efficiency and reliability of the estimator are proved under a saturation assumption. Numerical experiments illustrate the theoretical properties and the good performance of the estimator.
arXiv (Cornell University), Jan 5, 2016
This paper deals with a one-dimensional wave equation being subjected to a unilateral boundary co... more This paper deals with a one-dimensional wave equation being subjected to a unilateral boundary condition. An approximation of this problem combining the finite element and mass redistribution methods is proposed. The mass redistribution method is based on a redistribution of the body mass such that there is no inertia at the contact node and the mass of the contact node is redistributed on the other nodes. The convergence as well as an error estimate in time are proved. The analytical solution associated with a benchmark problem is introduced and it is compared to approximate solutions for different choices of mass redistribution. However some oscillations for the energy associated with approximate solutions obtained for the second order schemes can be observed after the impact. To overcome this difficulty, an new unconditionally stable and a very lightly dissipative scheme is proposed.