pastProjects.html

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                    href="#projCOMEDIC" role="tab" aria-controls="home">ANR Project COMEDIC </a>
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                    href="#projdigitalSnow" role="tab" aria-controls="home">ANR Project digitalSnow </a>
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                    href="#projGeoDib" role="tab" aria-controls="home">ANR Project GeoDIB</a>
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                <h5>CoMeDiC: Convergent Metrics for Digital Calculus</h5>
                <ul>
                <li><b>Project Type</b>: ANR  (French founding)</li>
                <li><b>Project coordinator</b>:<b>Jacques-Olivier Lachaud (LAMA)</b></li>
                <li><b>Period:</b> Sept 2015 - Sept 2020 </li>
                <li><b>Partners:</b>
                    <ul>
                    <li> LAMA, Chambéry, France: partner coordinator: <b>Jacques-Olivier Lachaud</b>, participants: Dorin Bucur, Xavier Provençal, Marion Foare
                    Thomas Caissard,  Daniel Antunes  </li>
                    <li> LIRIS, Lyon, France: partner coordinator: <b>David Coeurjolly</b>, participants: Tristan Roussillon, Nicolas Bonneel, Pierre Gueth, Thomas Caissard  </li>
                    <li> ESIEE Paris, France: Partners coordinator: <b>Hugues Talbot </b>, participants: Laurent Najman, Pascal Romon, Yukiko Kenmochi, Kacper Pluta, Daniel Antunes  </li>
                    <li> LJK (Grenoble), France; Partners coordinator: <b>Edouard Oudet</b> participants: Bozhidar Velichkov, Boris Thibert  </li>
                    <li> Associated members: Elie Bretin (ICJ, Lyon), Roland Denis (ICJ, Lyon), Yan Gérard (LIMOS, Clermont)  </li>
                </ul>
                <li><b>Website </b>: from <a href="https://anr.fr/Projet-ANR-15-CE40-0006">anr</a>
                    and official project page <a href="https://lama.univ-savoie.fr/comedic/teams/">here</a>
                </li>
                <li><b>Summary</b>: 
                    Discrete exterior calculus has emerged in the last decade as a powerful framework for solving discrete variational problems in image and geometry processing. It simplifies both the formulation of variational problems and their numerical resolution, and is able to extract global optima in many cases. However nothing guarantees that, on digital data like 2D or 3D images, digital curves and surfaces, it approaches the expected result of standard calculus, even when refining the discrete domain toward the limit continuous domain. 
                    The CoMeDiC project aims at filling the gap between discrete calculus and standard calculus for subsets of the digital space Z^n. The general idea is to define well-chosen metrics for discrete calculus that make it converge toward continuous values. This approach is now possible due to recent advances in digital geometry on multigrid convergent estimators. Digital calculus then addresses variational problems involving domains such as digital surfaces, curves, graphs living in a higher dimensional ambient space, as well as problems involving discontinuities or subtle boundary conditions. 
                    This project addresses theoretical problems like the definition of a sound digital calculus, the study of appropriate estimators for metrics, the statement of convergence properties. It is also concerned with its efficient numerical implementation. It studies also variational problems that present difficulties to standard numerical methods, like problems with discontinuities or free boundaries, or problems involving domains of codimension greater or equal to one as surfaces or curves. Last, this project focuses on three domains of application for digital calculus --- image analysis, digital geometry processing and shape optimisation --- both to guide and nourish theoretical developments, as well as to serve as testbed for digital calculus.
                </li>
                </ul>
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                <h5>digitalSnow: Digital Geometry and Applied Mathematics for Snow Metamorphism</h5>
                <ul>
                    <li><b>Project Type</b>: ANR (French founding)</li>
                    <li><b>Project coordinator</b>: <b>David Coeurjolly (LIRIS)</b>
                    <li><b>Period:</b> 08/2011 - 2015 (48 Months)</li>
                    <li><b>Partners:</b>
                        <ul>
                            <li> LIRIS, Lyon, France: partner coordinator: <b>David Coeurjolly</b>, participants:
                                G. Damiand, J.-C. Iehl, V. Ostromoukhov, T. Roussillon, I. Sivignon, X. Wang, J.
                                Levallois </li>

                            <li>LAMA, Chambéry: partner coordinator: <b>Jacques-Olivier Lachaud</b>, participants:
                                C. Acary-Robert, D. Bucur, E. Oudet, X. Provençal </li>
                            <li> CEN/ CNRM-GAME, France: partner coordinator: <b>F. Flin</b>, participants: N.
                                Calonne, A. Dufour, B. Lesaffre </li>
                        </ul>
                    <li><b>Website </b>: from <a href="https://anr.fr/Projet-ANR-11-BS02-0009">anr</a> and official
                        project page <a href="https://projet.liris.cnrs.fr/dsnow">here</a></li>
                    <li><b>Abstract</b>: 
                            During a snowfall, the snow crystals accumulate on the ground and gradually form a
                            complex porous medium constituted of air, water vapor, ice and sometimes liquid water.
                            This ground-lying snow transforms with time, depending on the physical parameters of the
                            environment. This process, called metamorphism, can be divided into three main types of
                            metamorphisms: the wet snow metamorphism, the isothermal metamorphism, and the
                            temperature gradient (TG) metamorphism. In polar or mountainous conditions, these
                            processes are followed by compaction of snow into ice under the load of the upper snow
                            layers. Although the general effects of theses various types of metamorphism are roughly
                            well-known, the physical mechanisms that lead to these transformations are not perfectly
                            well understood. A better microscale simulation of these mechanisms would help to
                            understand how snow changes its microstructure depending on the applied physical
                            conditions and has major impacts on the studies of snow behavior and properties at
                            larger scale.

                            The main purpose of this project is to provide efficient computational tools to study
                            the snow metamorphism from 3D images of real snow microstructures acquired using X-ray
                            tomography techniques. In particular, our work will focus on the development of 3D
                            image-based numerical models that can simulate the shape evolution of the snow
                            microstructure during its metamorphism. It will be completed by other tools designed to
                            extract physical properties from the computed microstructures.

                            The resolution of these problems requires a strong interaction between three
                            disciplines: Snow Physics, Applied Mathematics and Computer Science, which justifies
                            the collaboration between the CEN, the LAMA and the LIRIS respectively. To achieve our
                            objectives, three key points are required: obtaining 3D images of snow microstructures,
                            representing the digital objects with adapted data structures in order to perform
                            numerical measurements, and evolving the digital objects according to physical laws.
                            Last but not least, experimental validations of the proposed tools and models are
                            required. The project is composed of the four following tasks:
                            <ul>

                                <li>Snow metamorphism modelling</li>
                                <li>HP digital toolbox for volumetric and surface analysis</li>
                                <li>Dynamic digital structures for evolving regions</li>
                                <li>Physical rendering for snow radiative transfer</li>

                            </ul>

                            This project has several impacts in Snow Physics, Applied Mathematics and Computer
                            Science. The main results will be made available to the scientific community using the
                            DGtal open source library.
                    </li>
                </ul>
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                <h5>GeoDib: Discrete Geometry for noisy Digital objects</h5>
                <ul>
                    <li><b>Project Type</b>: ANR  (French founding)</li>
                    <li><b>Project coordinator</b>: <b>Isabelle Debled-Rennesson (LORIA)</b></li>
                    <li><b>Period:</b> September 2016 - September 2020 </li>
                    <li><b>Partners:</b>
                        <ul>
                            <li> LORIA, Nancy, France: partner coordinator: <b>Isabelle Debled-Rennesson</b>, 
                                participants: Bertrand Kerautret, Philippe Even, Jean-Luc Rémy, Laurent Provot
                                </li>
                                <li> LaBRI, Nancy, France: partner coordinator: <b>Jacques-Olivier Lachaud</b>, 
                                participants: Anne Vialard, François de VieilleVille, Martin Braure de Calignon
                                </li>
                                <li> LAIC, Nancy, France: partner coordinator: <b>Fabien Feschet </b>, 
                                participants: Yan Gérard, Remy Malgouyres, Jean-Pierre Reveilles, Alexandre Faure
                                </li>
                                <li> LIRIS, Nancy, France: partner coordinator: <b>Isabelle Sivignon</b>, 
                                participants: David Coeurjolly, Laure Tougne, Tristan Roussillon, Antoine Vacavant
                                </li>
                            
                        </ul>
                    <li><b>Website </b>: official project page <a
                            href="https://projet.liris.cnrs.fr/geodib/">here</a>.
                    </li>
                    <li><b>Summary</b>: 
                            Le projet proposé se situe dans le cadre de la Géométrie discrète. Cette branche
                            d'études, apparue dans les années 70 a pour objectif de définir un cadre théorique pour
                            transposer pour des objets définis sur la grille régulière les bases de la géométrie
                            euclidienne.

                            Plusieurs questions clés ressortent des dernières conférences du domaine (IWCIA 04 et
                            DGCI 05) et des journées nationales organisées dans le cadre d'une action spécifique
                            Géométrie Discrète et Géométrie Algorithmique. En particulier, un intérêt croissant est
                            apparu ces dernières années pour l'étude de la géométrie des objets discrets bruités. En
                            effet, les champs d'applications des travaux de la géométrie discrète se trouvent
                            principalement en informatique géométrique et graphique, en particulier en synthèse
                            d'image, traitement d'image, analyse de documents et imagerie médicale. Dans ces
                            domaines, les données sont quelquefois bruitées et les algorithmes classiques de la
                            géométrie discrète ne fournissent pas dans ce cas de résultats satisfaisants.

                            Ce projet regroupe des membres de la communauté française de géométrie discrète, issus
                            de 4 laboratoires (LABRI, LIRIS, LLAIC, LORIA), qui souhaitent développer une géométrie
                            des objets discrets bruités en utilisant de nouvelles techniques issues de la géométrie
                            discrète et en se détachant des méthodes classiques comme la logique floue ou encore les
                            techniques de filtrage utilisées en traitement d' image. Plus spécifiquement, les
                            membres de ce projet s'intéressent à l'étude des courbes et surfaces discrètes bruitées
                            correspondant aux contours et bords d' objets discrets. Notre objectif est d'élaborer,
                            dans le cadre de la géométrie discrète, un formalisme adapté à ces objets tenant compte
                            du bruit inhérent aux outils et méthodes d'acquisition en contrôlant les approximations
                            effectuées.

                            Plusieurs façons d'aborder l'étude de la géométrie discrète ont été développées, nous
                            utilisons dans ce projet le point de vue arithmétique définissant analytiquement les
                            primitives discrètes. L'étude des courbes et des surfaces discrètes bruitées portera sur
                            les 3 axes suivants :
                            <ul>
                                <li>Définitions de primitives géométriques adaptées aux objets discrets bruités :
                                    Des premiers travaux ont été réalisés par des membres du projet qui généralisent
                                    les notions de segments de droites discrètes et de morceaux de plans discrets,
                                    nous souhaitons approfondir cette voie mais aussi définir de nouvelles
                                    primitives géométriques.</li>
                                <li>Extraction de paramètres géométriques sur les objets bruités : L'étude des
                                    propriétés arithmétiques, géométriques et combinatoires des primitives discrètes
                                    permettra d'obtenir des algorithmes performants (par exemple de reconnaissance
                                    ou de parcours) et d'extraire des paramètres géométriques (périmètre, courbure,
                                    normale, aire, ...) sur les courbes et surfaces bruitées.</li>
                                <li>Analyse et modélisation des objets discrets bruités : En utilisant les
                                    définitions et algorithmes proposés dans les deux premiers axes, nous souhaitons
                                    développer des outils pour analyser ces objets et reconstruire des objets
                                    continus correspondant aux structures discrètes étudiées.</li>
                            </ul>
                    </li>
                </ul>
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