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3. Variational, geometric, and statistical methods for modeling brain anatomy and function

Author

Faugeras, Olivier, Adde, Geoffray, Charpiat, Guillaume, ChefdʼHotel, Christophe, Clerc, Maureen, Deneux, Thomas, Deriche, Rachid, Hermosillo, Gerardo, Keriven, Renaud, Kornprobst, Pierre, Kybic, Jan, Lenglet, Christophe, Lopez-Perez, Lucero, Papadopoulo, Théo, Pons, Jean-Philippe, Segonne, Florent, Thirion, Bertrand, Tschumperlé, David, Viéville, Thierry, and Wotawa, Nicolas

Published
2004
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4. Control Theory and Fast Marching Methods for Brain Connectivity Mapping

Author

Prados, Emmanuel, Lenglet, Christophe, Pons, Jean-Philippe, Wotawa, Nicolas, Deriche, Rachid, Faugeras, Olivier, Soatto, Stefano, UCLA Vision Lab, University of California [Los Angeles] (UCLA), University of California-University of California, 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, University of California (UC)-University of California (UC), 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), 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), Département d'informatique de l'École normale supérieure (DI-ENS), École normale supérieure - Paris (ENS Paris), and 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)

Subjects
[INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], RIEMANIAN MANIFOLD, CONTROL THEORY, PDE, BRAIN CONNECTIVITY MAPPING, CONNECTIVITY MEASURES, FAST MARCHING METHODS, HAMILTON-JACOBI-BELLMAN EQUATIONS
Abstract

We propose a novel, fast and robust technique for the computation of anatomical connectivity in the brain. Our approach exploits the information provided by Diffusion Tensor Magnetic Resonance Imaging (or DTI) and models the white matter by using Riemannian geometry and control theory. We show that it is possible, from a region of interest, to compute the geodesic distance to any other point and the associated optimal vector field. The latter can be used to trace shortest paths coinciding with neural fiber bundles. We also demonstrate that no explicit computation of those 3D curves is necessary to assess the degree of connectivity of the region of interest with the rest of the brain. We finally introduce a general local connectivity measure whose statistics along the optimal paths may be used to evaluate the degree of connectivity of any pair of voxels. All those quantities can be computed simultaneously in a Fast Marching framework, directly yielding the connectivity maps. Apart from being extremely fast, this method has other advantages such as the strict respect of the convoluted geometry of white matter, the fact that it is parameter-free, and its robustness to noise. We illustrate our technique by showing results on real and synthetic datasets. Our GCM (Geodesic Connectivity Mapping) algorithm is implemented in C++ and will be soon available on the web.

Published
2006

5. Contributions méthodologiques et appliquées à la méthode des modèles déformables

Author

Pons, Jean-Philippe, 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), Ecole des Ponts ParisTech, Olivier Faugeras, 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), and Nivault, Estelle

Subjects
topology, active contour, deformable model, brain, méthode variationnelle, segmentation, mouvement, point correspondence, correspondance ponctuelle, dépliement, variational method, stéréovision, cortex, motion, ensembles de niveau, cerveau, contour actif, [INFO.INFO-HC]Computer Science [cs]/Human-Computer Interaction [cs.HC], [INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC], level set, unfolding, modèle déformable, topologie
Abstract

Deformable models constitute a flexible framework to address various shape reconstruction problems in image processing. They have been initially proposed for the purpose of image segmentation, but they have also proven successful in many other contexts in computer vision and in medical imaging,including region tracking, stereovision, shape from shading and shape from unstructured point sets. The key elements of this framework are the design of an energy functional, the choice of a minimization procedure and of a geometric representation. In this thesis, we tackle these three elements, with the objective of increasing the applicability and efficiency of deformable models. With regard to the geometric representation, we overcome the loss of the point correspondence and the inability to control topology changes with the level set method. We propose two associated applications in the field of medical imaging: the generation of unfolded area preserving representations of the cerebral cortex, and the segmentation of several head tissues from anatomical magnetic resonance images. With regard to the minimization procedure, we show that the robustness to local minima can be improved by substituting a spatially coherent minimizing flow to a traditional gradient descent. Finally, with regard to the design of the energy functional, we propose a novel modeling of multi-view stereovision and scene flow estimation with deformable models, relying on a global image-based matching score., Les modèles déformables fournissent un cadre flexible pour traiter divers problèmes de reconstruction de forme en traitement d'images. Ils ont été proposés initialement pour la segmentation d'images, mais ils se sont aussi révélés adaptés dans de nombreux autres contextes en vision par ordinateur et en imagerie médicale, notamment le suivi de régions, la stéréovision, le "shape from shading" et la reconstruction à partir d'un nuage de points. Les éléments clés de cette méthodologie sont l'élaboration d'une fonctionnelle d'énergie, le choix d'une procédure de minimisation et d'une représentation géométrique. Dans cette thèse, nous abordons ces trois éléments, avec pour but d'élargir le champ d'application des modèles déformables et d'accroître leur performance. En ce qui concerne la représentation géométrique, nous venons à bout de la perte de la correspondance ponctuelle et de l'impossibilité de contrôler les changements de topologie avec la méthode des ensembles de niveau. Nous proposons deux applications associées dans le domaine de l'imagerie médicale: la génération de représentations dépliées du cortex cérébral avec préservation de l'aire, et la segmentation de plusieurs tissus de la tête à partir d'images par résonance magnétique anatomiques. En ce qui concerne la procédure de minimisation, nous montrons que la robustesse aux minima locaux peut être améliorée en remplaçant une descente de gradient traditionnelle par un flot de minimisation spatialement cohérent. Enfin, en ce qui concerne l'élaboration de la fonctionnelle d'énergie, nous proposons une nouvelle modélisation de la stéréovision multi-caméras et de l'estimation du mouvement tridimensionnel non-rigide, fondée sur un critère de mise en correspondance global et basé image.

Published
2005

6. Realistic numerical modeling of human head tissues exposure to electromagnetic waves from mobiles phones

Author

Scarella, Gilles, Clatz, Olivier, Lanteri, Stéphane, Beaume, Grégory, Oudot, Steve, Pons, Jean-Philippe, Piperno, Serge, Joly, Patrick, Wiart, Joe, Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS), Institut National de Recherche en Informatique et en Automatique (Inria)-École des Ponts ParisTech (ENPC), Analysis and Simulation of Biomedical Images (ASCLEPIOS), 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), Medical imaging and robotics (EPIDAURE), Scientific computing, modeling and numerical analysis (CAIMAN), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS), Centre de Mise en Forme des Matériaux (CEMEF), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Geometric computing (GEOMETRICA), Geometric Computation Group [Stanford], Computer Science Department [Stanford], Stanford University-Stanford University, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria), Département de Mathématiques et Applications - ENS Paris (DMA), École normale supérieure - Paris (ENS-PSL), Centre d'Enseignement et de Recherche en Technologies de l'Information et Systèmes (CERTIS), École des Ponts ParisTech (ENPC), Centre Scientifique et Technique du Bâtiment (CSTB), imagine [Marne-la-Vallée], 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)-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)-Centre Scientifique et Technique du Bâtiment (CSTB), Computer and biological vision (ODYSSEE), Département d'informatique - ENS Paris (DI-ENS), 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), 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, Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media (NACHOS), 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), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), Modeling, analysis and simulation of wave propagation phenomena (ONDES), Inria Paris-Rocquencourt, 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), Dynamic graphs and the web graph (IDENT), Propagation des Ondes : Étude Mathématique et Simulation (POEMS), Inria Saclay - Ile de France, France Télécom Recherche & Développement (FT R&D), France Télécom, France Telecom Division R&D [Issy-les-Moulineaux], Orange Labs [Issy les Moulineaux], MINES ParisTech - École nationale supérieure des mines de Paris, 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), 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)-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)-Centre Scientifique et Technique du Bâtiment (CSTB), 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), 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), Centre Scientifique et Technique du Bâtiment (CSTB)-École des Ponts ParisTech (ENPC)-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)-Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-Université Paris-Est Marne-la-Vallée (UPEM), 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), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Inria Sophia Antipolis - Méditerranée (CRISAM)

Subjects
[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, [INFO.INFO-IM]Computer Science [cs]/Medical Imaging, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Abstract

International audience; The ever-rising diffusion of cellular phones has brought about an increased concern for the possible consequences of electromagnetic radiation on human health. Possible thermal effects have been investigated, via experimentation or simulation, by several research projects in the last decade. Concerning numerical modeling, the power absorption in a user's head is generally computed using discretized models built from clinical MRI data. The vast majority of such numerical studies have been conducted using Finite Differences Time Domain methods, although strong limitations of their accuracy are due to heterogeneity, poor definition of the detailed structures of head tissues (staircasing effects), etc. In order to propose numerical modeling using Finite Element or Discontinuous Galerkin Time Domain methods, reliable automated tools for the unstructured discretization of human heads are also needed. Results presented in this article aim at filling the gap between human head MRI images and the accurate numerical modeling of wave propagation in biological tissues and its thermal effects.

Published
2005

7. Modelling Dynamic Scenes by Registrating Multi-View Image Sequences

Author

Pons, Jean-Philippe, Keriven, Renaud, Faugeras, Olivier, Inria, Rapport De Recherche, 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), INRIA, Département d'informatique - ENS Paris (DI-ENS), 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), 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), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Inria Sophia Antipolis - Méditerranée (CRISAM)

Subjects
VARIATIONAL METHOD, NON-RIGID 3D MOTION, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], SCENE FLOW, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, MUTUAL INFORMATION, CROSS CORRELATION, [INFO.INFO-OH] Computer Science [cs]/Other [cs.OH], REGISTRATION, NON-LAMBERTIAN, PREDICTION ERROR, LEVEL SETS, ComputingMethodologies_COMPUTERGRAPHICS, STEREOVISION
Abstract

We present a new variational method for multi-view stereovision and non-rigid three-dimensional motion estimation from multiple video sequences. Our method minimizes the prediction error of the estimated shape and motion. Both problems then translate into a generic image registration task. The latter is entrusted to a similarity measure chosen depending on imaging conditions and scene properties. In particular, our method can be made robust to appearance changes due to non-Lambertian materials and illumination changes. Our method results in a simpler, more flexible, and more efficient implementation than existing deformable surface approaches. The computation time on large datasets does not exceed thirty minutes. Moreover, our method is compliant with a hardware implementation with graphics processor units. Our stereovision algorithm yields very good results on a variety of datasets including specularities and translucency. We have successfully tested our scene flow algorithm on a very challenging multi-view video sequence of a non-rigid event.

Published
2004

8. How to deal with point correspondences and tangential velocities in the level set framework

Author

Pons, Jean-Philippe, Hermosillo, Gerardo, Keriven, Renaud, Faugeras, Olivier, Inria, Rapport De Recherche, 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), INRIA, 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), École normale supérieure - Paris (ENS-PSL), and 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)

Subjects
[INFO.INFO-OH] Computer Science [cs]/Other [cs.OH], POINT CORRESPONDENCES, INTRINSIC HEAT FLOW, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], CORTEX UNFOLDING, DIFFEOMORPHISMS, MEAN CURVATURE FLOW, AREA PRESERVATION, LEVEL SETS, SURFACE DIFFUSION FLOW, LAPLACE-BELTRAMI OPERATOR
Abstract

In this report, we overcome a major drawback of the level set framework: the lack of point correspondences. We maintain explicit backward correspondences from the evolving interface to the initial one by advecting the initial point coordinates with the same velocity as the level set function. Our method leads to a system of coupled Eulerian partial differential equations. We show in a variety of numerical experiments that it can handle both normal and tangential velocities, large deformations, shocks, rarefactions and topological changes. Applications are many since our method can upgrade virtually any level set evolution. We complement our work with the design of non zero tangential velocities that preserve the relative area of interface patches; this feature may be crucial in such applications as computational geometry, grid generation or unfolding of the organs' surfaces, e.g. brain, in medical imaging. This report also tackles a diffeomorphic approach to level set evolution, a family of volume-preserving smoothing flows, and some numerical aspects of the intrinsic heat flow on implicit surfaces.

Published
2003

9. Globally Optimal Spatio-temporal Reconstruction from Cluttered Videos.

Author

Aganj, Ehsan, Pons, Jean-Philippe, and Keriven, Renaud

Abstract

We propose a method for multi-view reconstruction from videos adapted to dynamic cluttered scenes under uncontrolled imaging conditions. Taking visibility into account and being based on a global optimization of a true spatio-temporal energy, it offers several desirable properties: no need for silhouettes, robustness to noise, independent from any initialization, no heuristic force, reduced flickering results, etc. Results on real-world data proves the potential of what is, to our knowledge, the only globally optimal spatio-temporal multi-view reconstruction method. [ABSTRACT FROM AUTHOR]

Published
2010
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10. Dense and Accurate Spatio-temporal Multi-view Stereovision.

Author

Courchay, Jérôme, Pons, Jean-Philippe, Monasse, Pascal, and Keriven, Renaud

Abstract

In this paper, we propose a novel method to simultaneously and accurately estimate the 3D shape and 3D motion of a dynamic scene from multiple-viewpoint calibrated videos. We follow a variational approach in the vein of previous work on stereo reconstruction and scene flow estimation. We adopt a representation of a dynamic scene by an animated mesh, i.e. a polygonal mesh with fixed connectivity whose time-varying vertex positions sample the trajectories of material points. Interestingly, this representation ensures a consistent coding of shape and motion by construction. Our method accurately recovers 3D shape and 3D motion by optimizing the positions of the vertices of the animated mesh. This optimization is driven by an energy function which incorporates multi-view and inter-frame photo-consistency, smoothness of the spatio-temporal surface and of the velocity field. Central to our work is an image-based photo-consistency score which can be efficiently computed and which fully handles projective distortion and partial occlusions. We demonstrate the effectiveness of our method on several challenging real-world dynamic scenes. [ABSTRACT FROM AUTHOR]

Published
2010
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11. Transductive Segmentation of Textured Meshes.

Author

Chauve, Anne-Laure, Pons, Jean-Philippe, Audibert, Jean-Yves, and Keriven, Renaud

Abstract

This paper addresses the problem of segmenting a textured mesh into objects or object classes, consistently with user-supplied seeds. We view this task as transductive learning and use the flexibility of kernel-based weights to incorporate a various number of diverse features. Our method combines a Laplacian graph regularizer that enforces spatial coherence in label propagation and an SVM classifier that ensures dissemination of the seeds characteristics. Our interactive framework allows to easily specify classes seeds with sketches drawn on the mesh and potentially refine the segmentation. We obtain qualitatively good segmentations on several architectural scenes and show the applicability of our method to outliers removing. [ABSTRACT FROM AUTHOR]

Published
2010
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12. From Segmented Images to Good Quality Meshes Using Delaunay Refinement.

Author

Boissonnat, Jean-Daniel, Pons, Jean-Philippe, and Yvinec, Mariette

Abstract

This paper surveys Delaunay-based meshing techniques for curved objects, and their application in medical imaging and in computer vision to the extraction of geometric models from segmented images. We show that the so-called Delaunay refinement technique allows to mesh surfaces and volumes bounded by surfaces, with theoretical guarantees on the quality of the approximation, from a geometrical and a topological point of view. Moreover, it offers extensive control over the size and shape of mesh elements, for instance through a (possibly non-uniform) sizing field. We show how this general paradigm can be adapted to produce anisotropic meshes, i.e. meshes elongated along prescribed directions. Lastly, we discuss extensions to higher dimensions, and especially to space-time for producing time-varying 3D models. This is also of interest when input images are transformed into data points in some higher dimensional space as is common practice in machine learning. [ABSTRACT FROM AUTHOR]

Published
2009
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13. 3D Reconstruction of Large Scale City Models as a Support to Sustainable Development.

Author

Pons, Jean-Philippe and Soubra, Souheil

Abstract

No part of the economic community can now escape from the urgent issues related to global warming, carbon footprint and reducing energy consumption. Nevertheless, the construction sector is particularly under pressure. Indeed, it is one of the biggest consumers of energy. It also largely contributes to the massive use of some critical resources (such as energy, water, materials and space...) and is responsible for a large portion of greenhouse gas emissions. In that context, the paper explores new approaches for urban planning by combining Virtual Environments and Simulations to address sustainability issues. These approaches are based on the possibilities of reconstructing 3D models of the built environment using standard photographs taken with off-the shelf hand-held digital cameras. The 3D models can then be combined with simulations in order to address sustainable urban development issues. [ABSTRACT FROM AUTHOR]

Published
2008
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14. A GPU Implementation of Level Set Multiview Stereo.

Author

Alexandrov, Vassil N., Albada, Geert Dick, Sloot, Peter M. A., Dongarra, Jack, Labatut, Patrick, Keriven, Renaud, and Pons, Jean-Philippe

Abstract

Variational methods that evolve surfaces according to PDEs have been quite successful for solving the multiview stereo shape reconstruction problem since [1]. However just like every other algorithm that tackles this problem, their running time is quite high (from dozens of minutes to several hours). Fortunately graphics hardware has shown a great potential for speeding up many low-level computer vision tasks. In this paper, we present the analysis of the different bottlenecks of the original implementation of [2] and show how to efficently port it to GPUs using well-known GPGPU techniques. We finally present some results and discuss the improvements. [ABSTRACT FROM AUTHOR]

Published
2006
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15. Active Contours Under Topology Control Genus Preserving Level Sets.

Author

Yanxi Liu, Tianzi Jiang, Changshui Zhang, Ségonne, Florent, Pons, Jean-Philippe, Grimson, Eric, and Fischl, Bruce

Abstract

We present a novel framework to exert topology control over a level set evolution. Level set methods offer several advantages over parametric active contours, in particular automated topological changes. In some applications, where some a priori knowledge of the target topology is available, topological changes may not be desirable. This is typically the case in biomedical image segmentation, where the topology of the target shape is prescribed by anatomical knowledge. However, topologically constrained evolutions often generate topological barriers that lead to large geometric inconsistencies. We introduce a topologically controlled level set framework that greatly alleviates this problem. Unlike existing work, our method allows connected components to merge, split or vanish under some specific conditions that ensure that no topological defects are generated. We demonstrate the strength of our method on a wide range of numerical experiments and illustrate its performance on the segmentation of cortical surfaces and blood vessels. [ABSTRACT FROM AUTHOR]

Published
2005
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16. Brain Connectivity Mapping Using Riemannian Geometry, Control Theory, and PDEs.

Author

Lenglet, Christophe, Prados, Emmanuel, Pons, Jean-Philippe, Deriche, Rachid, and Faugeras, Olivier

Subjects
BRAIN mapping, RIEMANNIAN geometry, DIFFUSION tensor imaging, HAMILTON-Jacobi equations, WIENER processes, PARTIAL differential equations
Abstract

We introduce an original approach for the cerebral white matter connectivity mapping from diffusion tensor imaging (DTI). Our method relies on a global modeling of the acquired magnetic resonance imaging volume as a Riemannian manifold whose metric directly derives from the diffusion tensor. These tensors will be used to measure physical three-dimensional distances between different locations of a brain diffusion tensor image. The key concept is the notion of geodesic distance that will allow us to find optimal paths in the white matter. We claim that such optimal paths are reasonable approximations of neural fiber bundles. The geodesic distance function can be seen as the solution of two theoretically equivalent but, in practice, significantly different problems in the partial differential equation framework: an initial value problem which is intrinsically dynamic, and a boundary value problem which is, on the contrary, intrinsically stationary. The two approaches have very different properties which make them more or less adequate for our problem and more or less computationally efficient. The dynamic formulation is quite easy to implement but has several practical drawbacks. On the contrary, the stationary formulation is much more tedious to implement; we will show, however, that it has many virtues which make it more suitable for our connectivity mapping problem. Finally, we will present different possible measures of connectivity, reflecting the degree of connectivity between different regions of the brain. We will illustrate these notions on synthetic and real DTI datasets. [ABSTRACT FROM AUTHOR]

Published
2009
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17. High Accuracy and Visibility-Consistent Dense Multiview Stereo.

Author

Vu, Hoang-Hiep, Labatut, Patrick, Pons, Jean-Philippe, and Keriven, Renaud

Subjects
STEREOSCOPIC cameras, ACCURACY, IMAGE reconstruction, MATHEMATICAL optimization, IMAGE processing, IMAGING systems
Abstract

Since the initial comparison of Seitz et al. [48], the accuracy of dense multiview stereovision methods has been increasing steadily. A number of limitations, however, make most of these methods not suitable to outdoor scenes taken under uncontrolled imaging conditions. The present work consists of a complete dense multiview stereo pipeline which circumvents these limitations, being able to handle large-scale scenes without sacrificing accuracy. Highly detailed reconstructions are produced within very reasonable time thanks to two key stages in our pipeline: a minimum s-t cut optimization over an adaptive domain that robustly and efficiently filters a quasidense point cloud from outliers and reconstructs an initial surface by integrating visibility constraints, followed by a mesh-based variational refinement that captures small details, smartly handling photo-consistency, regularization, and adaptive resolution. The pipeline has been tested over a wide range of scenes: from classic compact objects taken in a laboratory setting, to outdoor architectural scenes, landscapes, and cultural heritage sites. The accuracy of its reconstructions has also been measured on the dense multiview benchmark proposed by Strecha et al. [59], showing the results to compare more than favorably with the current state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Published
2012
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18. Realistic numerical modelling of human head tissue exposure to electromagnetic waves from cellular phones

Author

Scarella, Gilles, Clatz, Olivier, Lanteri, Stéphane, Beaume, Grégory, Oudot, Steve, Pons, Jean-Philippe, Piperno, Sergo, Joly, Patrick, and Wiart, Joe

Subjects
*CELL phones, *ELECTROMAGNETIC waves, *PHYSIOLOGICAL effects of electromagnetism, *MATHEMATICAL models, *MAGNETIC resonance imaging, *FINITE element method, *GALERKIN methods
Abstract

Abstract: The ever-rising diffusion of cellular phones has brought about an increased concern for the possible consequences of electromagnetic radiation on human health. Possible thermal effects have been investigated, via experimentation or simulation, by several research projects in the last decade. Concerning numerical modeling, the power absorption in a user''s head is generally computed using discretized models built from clinical MRI data. The vast majority of such numerical studies have been conducted using Finite Differences Time Domain methods, although strong limitations of their accuracy are due to heterogeneity, poor definition of the detailed structures of head tissues (staircasing effects), etc. In order to propose numerical modeling using Finite Element or Discontinuous Galerkin Time Domain methods, reliable automated tools for the unstructured discretization of human heads are also needed. Results presented in this article aim at filling the gap between human head MRI images and the accurate numerical modeling of wave propagation in biological tissues and its thermal effects. To cite this article: G. Scarella et al., C. R. Physique 7 (2006). [Copyright &y& Elsevier]

Published
2006
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