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11 results on '"Shape gradient"'

1. Modeling and optimization of hourglass-shaped aquaporins

Author

Florian Omnès, Yannick Privat, Matthieu Bonnivard, Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), and The authors were partially supported by the Project 'Analysis and simulation of optimal shapes - application to lifesciences' of the Paris City Hall.

Subjects
slip/flow rate boundary condition, Computer science, Applied Mathematics, Numerical analysis, 010102 general mathematics, Boundary (topology), Topology, 01 natural sciences, law.invention, 010101 applied mathematics, Navier-Stokes system, law, Modeling and Simulation, shape optimization, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Point (geometry), Shape optimization, Shape gradient, Hourglass, 0101 mathematics, extension-regularization procedure, Energy (signal processing), Communication channel
Abstract

This paper is concerned with aquaporins (AQPs), that are proteins playing the role of water-selective channels also called nanopores, involved in many biological systems. From a technological point of view, it is relevant to design systems enjoying as good filtration properties. Inspired by [S. Gravelle, L. Joly, C. Ybert and L. Bocquet, Large permeabilities of hourglass nanopores: From hydrodynamics to single file transport, J. Chem. Phys. 141 (2014) 18C526], we investigate in a quite general framework shape optimization issues related to the improvement of hourglass-shaped aquaporins performances, in terms of energy dissipated by the fluid through the channel. After modeling this problem mathematically, we show that it is well-posed in some sense, and compute the so-called shape derivative of the cost functional in view of numerical simulations. Noting that our framework requires regularity properties of the free boundary, we introduce a dedicated numerical method, using in particular a proper shape gradient extension-regularization to adapt the mesh at each iteration, in an adequate way. Optimal shapes of aquaporins are then provided for relevant values of parameters, and we finally discuss the observed performances with respect to the existing results/literature.

Published
2017

2. A mutual reference shape based on information theory

Author

Stéphanie Jehan-Besson, Laurent Sarry, J. Lebenberg, Régis Clouard, Mireille Garreau, Christophe Tilmant, Laurent Najman, Muriel Lefort, Jean Cousty, Alexandre Cochet, Patrick Clarysse, Alain Lalande, Frédérique Frouin, A. De Cesare, Equipe Image - Laboratoire GREYC - UMR6072, 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 ), Institut Pascal ( IP ), Université Blaise Pascal - Clermont-Ferrand 2 ( UBP ) -Sigma CLERMONT ( Sigma CLERMONT ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire d'Imagerie Fonctionnelle ( LIF ), Université Pierre et Marie Curie - Paris 6 ( UPMC ) -IFR14-IFR49-Institut National de la Santé et de la Recherche Médicale ( INSERM ), 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 d'Informatique Gaspard-Monge ( LIGM ), Université Paris-Est Marne-la-Vallée ( UPEM ) -École des Ponts ParisTech ( ENPC ) -ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique ( CNRS ), 1 - Imagerie et modélisation Vasculaires, Thoraciques et Cérébrales ( MOTIVATE ), Centre de Recherche en Acquisition et Traitement de l'Image pour la Santé ( CREATIS ), Hospices Civils de Lyon ( HCL ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Université de Lyon-Institut National des Sciences Appliquées de Lyon ( INSA Lyon ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Hospices Civils de Lyon ( HCL ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ), Image Science for Interventional Techniques ( ISIT ), Université d'Auvergne - Clermont-Ferrand I ( UdA ) -Clermont Université-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire Traitement du Signal et de l'Image ( LTSI ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ), 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), Institut Pascal (IP), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-SIGMA Clermont (SIGMA Clermont)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Imagerie Fonctionnelle (LIF), Université Pierre et Marie Curie - Paris 6 (UPMC)-IFR14-IFR49-Institut National de la Santé et de la Recherche Médicale (INSERM), Laboratoire Electronique, Informatique et Image [UMR6306] (Le2i), Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS)-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, Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Imagerie et modélisation Vasculaires, Thoraciques et Cérébrales (MOTIVATE), Centre de Recherche en Acquisition et Traitement de l'Image pour la Santé (CREATIS), Université Jean Monnet [Saint-Étienne] (UJM)-Hospices Civils de Lyon (HCL)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Jean Monnet [Saint-Étienne] (UJM)-Hospices Civils de Lyon (HCL)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM), Image Science for Interventional Techniques (ISIT), Université d'Auvergne - Clermont-Ferrand I (UdA)-Clermont Université-Centre National de la Recherche Scientifique (CNRS), Laboratoire Traitement du Signal et de l'Image (LTSI), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de la Santé et de la Recherche Médicale (INSERM), 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), Université de Bourgogne (UB)-École Nationale Supérieure d'Arts et Métiers (ENSAM), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-Arts et Métiers Sciences et Technologies, HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement-Centre National de la Recherche Scientifique (CNRS), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Université de Rennes (UR)-Institut National de la Santé et de la Recherche Médicale (INSERM), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Hospices Civils de Lyon (HCL)-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Hospices Civils de Lyon (HCL)-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Lalande, Alain, Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Hospices Civils de Lyon (HCL)-Université Jean Monnet - Saint-Étienne (UJM)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Hospices Civils de Lyon (HCL)-Université Jean Monnet - Saint-Étienne (UJM)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
average shape, [INFO.INFO-IM] Computer Science [cs]/Medical Imaging, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Scale-space segmentation, Information theory, Joint entropy, Active shape model, segmentation evalua-tion, [ INFO.INFO-TI ] Computer Science [cs]/Image Processing, [INFO.INFO-IM]Computer Science [cs]/Medical Imaging, cardiac MRI, Mathematics, ComputingMethodologies_COMPUTERGRAPHICS, Active contour model, [ INFO.INFO-IM ] Computer Science [cs]/Medical Imaging, business.industry, Active contours, Pattern recognition, Mutual information, [INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV], Point distribution model, shape gradient, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], Artificial intelligence, business, Shape analysis (digital geometry)
Abstract

International audience; In this paper, we propose to consider the estimation of a refer-ence shape from a set of different segmentation results using both active contours and information theory. The reference shape is defined as the minimum of a criterion that benefits from both the mutual information and the joint entropy of the input segmentations and called a mutual shape. This energy criterion is here justified using similarities between informa-tion theory quantities and area measures, and presented in a continuous variational framework. This framework brings out some interesting evaluation measures such as the speci-ficity and sensitivity. In order to solve this shape optimization problem, shape derivatives are computed for each term of the criterion and interpreted as an evolution equation of an active contour. Some synthetical examples allow us to cast the light on the difference between our mutual shape and an average shape. Our framework has been considered for the estimation of a mutual shape for the evaluation of cardiac segmentation methods in MRI.

Published
2014
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3. Shape sensitivity analysis of the work functional for the compressible Navier–Stokes equations

Author

Plotnikov, Pavel I., Sokolowski, Jan, Lavryentyev Institute of Hydrodynamics, Russian Academy of Sciences [Moscow] (RAS), Institut Élie Cartan de Lorraine (IECL), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Nonhomogeneous Dirichlet boundary value problem for nonstationary, Work functional, Shape functional, Shape derivative, Drag functional, Compressible Navier–Stokes equations, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Shape gradient, Rigid obstacle
Abstract

International audience; The compressible Navier–Stokes equations with nonhomogeneous Dirichlet conditions in a bounded domain with an obstacle are considered (P.I. Plotnikov, J. Sokolowski, Compressible Navier-Stokes Equations. Theory and Shape Optimization, Birkhäuser, Basel, 2012). The dependence of local solutions on the shape of an obstacle is analyzed (P.I. Plotnikov, E.V. Ruban, J. Sokołowski, SIAM J. Math. Anal. 40:1152–1200, 2008; P.I. Plotnikov, E.V. Ruban, J. Sokołowski, J. Math. Pures Appl. 92:113–162, 2009; P.I. Plotnikov, J. Sokołowski, Dokl. Akad. Nauk 397:166–169, 2004; P.I. Plotnikov, J. Sokołowski, J. Math. Fluid Mech. 7:529–573, 2005; P.I. Plotnikov, J. Sokołowski, Comm. Math. Phys. 258:567–608, 2005; P.I. Plotnikov, J. Sokołowski, SIAM J. Control Optim. 45:1165–1197, 2006; P.I. Plotnikov, J. Sokołowski, Uspekhi Mat. Nauk 62:117–148, 2007; P.I. Plotnikov, J. Sokołowski, Stationary boundary value problems for compressible Navier-Stokes equations, in Handbook of Differential Equations: Stationary Partial Differential Equations, vol. VI, Elsevier/North-Holland, Amsterdam, 2008, pp. 313–410; P.I. Plotnikov, J. Sokołowski, SIAM J. Control Optim. 48:4680–4706, 2010; P.I. Plotnikov, J. Sokołowski, J. Math. Sci. 170:34–130, 2010). The shape derivatives (J. Sokołowski, J.-P. Zolésio, Introduction to Shape Optimization. Shape Sensitivity Analysis, Springer, Berlin/Heidelberg/New York, 1992) of solutions to the compressible Navier–Stokes equations are derived. The shape gradient (J. Sokołowski, J.-P. Zolésio, Introduction to Shape Optimization. Shape Sensitivity Analysis, Springer, Berlin/Heidelberg/New York, 1992) of the work functional is obtained. In this way the framework for numerical methods of shape optimization (P. Plotnikov, J. Sokołowski, A. Żochowski, Numerical experiments in drag minimization for compressible Navier-Stokes flows in bounded domains, in Proceedings of the 14th International IEEE/IFAC Conference on Methods and Models in Automation and Robotics, MMAR’09, 2009, 4 pp; A. Kaźmierczak, P.I. Plotnikov, J. Sokołowski, A. Żochowski, Numerical method for drag minimization in compressible flows, in 15th International Conference on Methods and Models in Automation and Robotics (MMAR), pp. 97–101, 2009.

Published
2014
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4. Topological and shape gradient strategy for solving geometrical inverse problems

Author

S. Chaabane, Houcine Meftahi, Mohamed Masmoudi, Faculté des Sciences de Sfax, Université de Sfax - University of Sfax, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Informatique et Applications (LMIA), Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA)), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), and Laboratoire de Mathématiques Informatique et Applications [UHA] (LMIA)

Subjects
Applied Mathematics, 010102 general mathematics, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Inverse, Function (mathematics), Inverse problem, Topology, 01 natural sciences, Domain (mathematical analysis), 010101 applied mathematics, Superposition principle, Shape gradient, 0101 mathematics, Shape reconstruction, Analysis, Topological quantum number, ComputingMilieux_MISCELLANEOUS, Mathematics, 35R30 (35J25 65N21)
Abstract

In this paper we present a technique for shape reconstruction based on the topological and shape gradients. The shape in consideration is a solution of an inverse conductivity problem. To solve such a problem numerically, we compute the topological gradient of a Kohn–Vogelius-type cost function when the domain under consideration is perturbed by the introduction of a small inclusion instead of a hole. The reconstruction is done by considering the shape as a superposition of very thin elliptic inclusions to get a first approximation. Then, we use a gradient-type algorithm to perform a good reconstruction. Various numerical experiments of single and multiple inclusions demonstrate the viability of the designed algorithm.

Published
2013
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5. Topological Derivatives in Shape Optimization

Author

Novotny, A.A., Sokolowski, Jan, Laboratorio Nacional de Computação Cientifica [Rio de Janeiro] (LNCC / MCT), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), and Sokolowski, Jan

Subjects
topological derivative, shape gradient, topological gradient, crack identification, shape optimization, polarization tensor, [MATH] Mathematics [math], multiple eigenvalues, [MATH]Mathematics [math], defect modeling, spectral problem
Abstract

International audience; The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intended for researchers and graduate students in applied mathematics and computational mechanics interested in any aspect of topological asymptotic analysis. In particular, it can be adopted as a textbook in advanced courses on the subject and shall be useful for readers interested on the mathematical aspects of topological asymptotic analysis as well as on applications of topological derivatives in computation mechanics.

Published
2012

6. Gradient Flows for Optimizing Triangular Mesh-based Surfaces: Applications to 3D Reconstruction Problems dealing with Visibility

Author

Emmanuel Prados, Amaël Delaunoy, Interpretation and Modelling of Images and Videos (PERCEPTION), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), and ANR-06-MDCA-0007,FLAMENCO,Modélisation de scène spatio-temporelle(2006)

Subjects
Surface (mathematics), ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Geometry, 02 engineering and technology, Shape gradient, Variational methods, Artificial Intelligence, Triangle mesh, 0202 electrical engineering, electronic engineering, information engineering, 3D reconstruction, Mathematics, ComputingMethodologies_COMPUTERGRAPHICS, Visibility (geometry), Process (computing), 020207 software engineering, Surface evolution, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Pattern recognition (psychology), Gradient descent flow, Visibility, 020201 artificial intelligence & image processing, Computer Vision and Pattern Recognition, Triangle mesh-based surface, Gradient descent, Multi-view stereovision, Software, Energy (signal processing)
Abstract

International audience; This article tackles the problem of using variational methods for evolving 3D deformable surfaces. We give an overview of gradient descent flows when the surface is represented by a triangular mesh-based surface, and we detail the gradients of two generic energy functionals which embody a number of energies used in mesh processing and computer vision. In particular, we show how to rigorously account for visibility in the surface optimization process. We present different applications including 3D reconstruction from multiple views for which the visibility is fundamental. The gradient correctly takes into account the visibility changes that occur when a surface moves; this forces the contours generated by the reconstructed surface to perfectly match with the apparent contours in the input images.

Published
2011
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7. Shape gradients, shape warping and medical application to facial expression analysis

Author

Maurel, Pierre, Computer and biological vision (ODYSSEE), Département d'informatique de l'École normale supérieure (DI-ENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-École des Ponts ParisTech (ENPC), Université Paris-Diderot - Paris VII, Olivier Faugeras(Olivier.Faugeras@inria.fr), and Maurel, Pierre

Subjects
minimisation, shape matching, imagerie médicale, medical imaging, forme, shape warping, recalage, mise en correspondance, computer vision, expressions faciales, shape gradient, vision par ordinateur, minimization, image, [INFO.INFO-HC]Computer Science [cs]/Human-Computer Interaction [cs.HC], [INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC], facial expression
Abstract

In this document, we start by investigating shape warping and shape matching (planar curves in 2D or surfaces in 3D). We define and minimize distances between shapes. In order to be able to introduce a priori information on the kind of path we want to follow during the minimization, we present a generalisation of the shape gradient notion and then different way to add constraints on the gradient form.The second part focuses on the application side of our work. We developed a method for facial expression analysis under uncontrolled imaging conditions and used it in the concrete case of the study of epilepsy seizures., Dans ce travail, nous commençons par étudier le recalage et la mise en correspondance de formes 2D ou 3D (courbes ou surfaces). Nous définissons et minimisons des distances entre ces formes. Afin d'avoir un certain contrôle sur le chemin suivi lors de la minimisation, nous introduisons une généralisation du gradient de forme permettant d'ajouter une contrainte sur la forme du gradient de différentes manières.Dans une seconde partie plus applicative, nous présentons nos travaux sur l'analyse automatique d'expressions faciales appliquée à des patients épileptiques et explorons la possibilité d'utiliser cet outil pour l'aide au diagnostic.

Published
2008

8. Shape Gradient for Image and Video Segmentation

Author

Stéphanie Jehan-Besson, Michel Barlaud, Ariane Herbulot, Gilles Aubert, 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), Équipe Robotique, Action et Perception (LAAS-RAP), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe IMAGES-CREATIVE, Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (... - 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 (... - 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 d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), 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 (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 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), Paragios Nikos, Chen Yunmei, Faugeras, Olivier, 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), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), 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), and Laboratoire Jean Alexandre Dieudonné (LJAD)

Subjects
Kernel density estimation, Probability density function, parzen window, 02 engineering and technology, Topology, Joint entropy, 030218 nuclear medicine & medical imaging, 03 medical and health sciences, 0302 clinical medicine, Image statistics, 0202 electrical engineering, electronic engineering, information engineering, Entropy (information theory), Segmentation, Shape optimization, Parametric statistics, Mathematics, Active contour model, active regions, region functionals, segmentation, distance between pdfs, tracking, active contours, shape gradient, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], shape optimization, 020201 artificial intelligence & image processing, boundary functionals, non parametric statistics, entropy, Algorithm
Abstract

International audience; In this chapter, we propose to concentrate on the research of an optimal domain with regards to a global criterion including region andboundary functionals. A local shape minimizer is obtained through the evolution of a deformable domain in the direction of the shape gradient. Shape derivation tools, coming from shape optimization theory, allow us to easily differentiate region and boundary functionals. We more particularly focus on region functionals involving region-dependent features that are globally attached to the region. A general framework is proposed and illustrated by many examples involving functions of parametric or non parametric probability density functions (pdfs) of image features. Among these functions, we notably study the minimization of information measures such as the entropy for the segmentation of homogeneous regions or the minimization of the distance between pdfs for tracking or matching regions of interest.

Published
2006
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9. Inhomogeneous boundary value problems for compressible Navier-Stokes equation: well-posedness and sensitivity analysis

Author

Plotnikov, Pavel I., Ruban, Evgenya V., Sokolowski, Jan, Sokolowski, Jan, Lavryentyev Institute of Hydrodynamics, Russian Academy of Sciences [Moscow] (RAS), Institut Élie Cartan de Nancy (IECN), and Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
shape sensitivity analysis, Mathematics::Analysis of PDEs, transport equations, drag minimization, approximate solutions, Physics::Fluid Dynamics, necessary optimality conditions, Shape optimization, shape gradient, 76N10, 35Q30, 76N25, 35A15, 35Q35, 76N15, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], compressible Navier-Stokes equations, shape derivative, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]
Abstract

In the paper compressible, stationary Navier-Stokes equations are considered. A framework for analysis of such equations is established. In particular, the well-posedness for inhomogeneous boundary value problems of elliptic-hyperbolic type is shown. Analysis is performed for small perturbations of the so-called approximate solutions, i.e., the solutions take form (1.12). The approximate solutions are determined from Stokes problem (1.11). The small perturbations are given by solutions to (1.13). The uniqueness of solutions for problem (1.13) is proved, and in addition, the differentiability of solutions with respect to the coefficients of differential operators in shown. The results on the well-posedness of nonlinear problem are interesting on its own, and are used to obtain the shape differentiability of the drag functional for incompressible Navier-Stokes equations. The shape gradient of the drag functional is derived in the classical and useful for computations form, an appropriate adjoint state is introduced to this end. The shape derivatives of solutions to the Navier-Stokes equations are given by smooth functions, however the shape differentiability is shown in a weak norm. The method of analysis proposed in the paper is general, and can be used to establish the well-posedness for distributed and boundary control problems a well as for inverse problems in the case of the state equations in the form of compressible Navier-Stokes equations. The differentiability of solutions to the Navier-Stokes equations with respect to the date leads to the first order necessary conditions for a broad class of optimization problems.

Published
2006

10. Image Segmentation Using Active Contours: Calculus of Variations or Shape Gradients?

Author

Gilles Aubert, Olivier Faugeras, Stéphanie Jehan-Besson, Michel Barlaud, Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 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), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (... - 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), Computer and biological vision (ODYSSEE), Département d'informatique - ENS Paris (DI-ENS), Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-École des Ponts ParisTech (ENPC), INRIA, Département d'informatique de l'École normale supérieure (DI-ENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Inria Sophia Antipolis - Méditerranée (CRISAM), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), and Inria, Rapport De Recherche

Subjects
Gâteaux derivative, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], Boundary (topology), 02 engineering and technology, 030218 nuclear medicine & medical imaging, Image (mathematics), 03 medical and health sciences, 0302 clinical medicine, Parzen window estimation, 0202 electrical engineering, electronic engineering, information engineering, Segmentation, Shape optimization, Equivalence (measure theory), image segmentation, Mathematics, region segmentation, active regions, region functionals, Applied Mathematics, Mathematical analysis, calculus of variations, Image segmentation, [INFO.INFO-OH] Computer Science [cs]/Other [cs.OH], active contours, AMS : 35, 35K, 49, 49Q10, 68U10, image statistics, shape gradient, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], shape optimization, 020201 artificial intelligence & image processing, boundary functionals, level set methods, Calculus of variations, Euler-Lagrange equations
Abstract

International audience; We consider the problem of segmenting an image through the minimization of an energy criterion involving region and boundary functionals. We show that one can go from one class to the otherb y solving Poisson's orHelmholtz's equation with well-chosen boundary conditions. Using this equivalence, we study the case of a large class of region functionals by standard methods of the calculus of variations and derive the corresponding Euler-Lagrange equations. We revisit this problem using the notion of a shape derivative and show that the same equations can be elegantly derived without going through the unnatural step of converting the region integrals into boundary integrals. We also define a larger class of region functionals based on the estimation and comparison to a prototype of the probability density distribution of image features and show how the shape derivative tool allows us to easily compute the corresponding Gˆateaux derivatives and Euler-Lagrange equations. Finally we apply this new functional to the problem of regions segmentation in sequences of color images. We briefly describe our numerical scheme and show some experimental results.

Published
2003
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11. Set Weak Evolution and Transverse Field , Variational Applications and Shape Differential Equation

Author

Zolésio, Jean-Paul, Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE (OPALE), 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 (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 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 (... - 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), INRIA, 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), and 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)

Subjects
TRANSVERSE FIELD, SHAPE DIFFERENTIAL EQUATION, CONVECTION, SHAPE GRADIENT, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], LEVEL SET
Abstract

We consider weak eulerian evolution of domains through the convection of a measurable set by a nonsmooth vector field V. The transverse variation leads to derivative of functional associated to the evolutiontube and we propose eulerian variational formulation for several classical problems such as incompressible euler flow ( in \cite{chemnitz}, \cite{cambridge} minimal curves...which turn to be governed by a geometrical adjoint state lambda which is backward and is obtained with the use of the so-called tranvserse field Z introduced in \cite{washingtown}. We also re-visit the shape different- ial equation introduced in 1976 () and extend it to the level set approach whose speed vector approach was contained in the free boundary modeling in 1980 (\cite{iowa2}).

Published
2002

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