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Communication pour le congrès ISPRS du 4 au 10 Juillet 2021; International audience; In this paper, we present a methodology to fusion 3D visible and thermal infrared (TIR) information on a coastal landslide area located in Normandy, France. A reflex and TIR camera on-board an Unmanned Aerial Vehicle are utilized to generate a 3D visible and a thermal model using Photogrammetry. A Python-written algorithm is then used to associate the thermal scalar on the TIR model to the closest point on the visible point cloud, before applying α-blending to ease the visualization of both data sets. This methodology leads to the generation of an integrated 3D thermo-visible model, allowing the direct analysis of the surface temperatures, visible data and geometric configuration of the landslide.

In this paper, we perform a numerical study for the solution of optimal constrained optimization problems for linear convection–diffusion PDEs by local and global radial basis function techniques. To the best of our knowledge, these control problems have not been treated in the literature by RBFs methods. It is well-known that the algebraic system of RBFs methods presents a larger condition number and a higher numerical complexity as the number of nodes (or shape parameter), increases. In this work, and in the context of optimal constrained optimization problems, we explore a possible answer to both problems. Specifically, we introduce a local RBF method (denoted as LAM-DQ), based on the combination of an asymmetric RBFs local method (LAM), inspired in local Hermite interpolation (LHI), combined with the differential quadrature method (DQ). We also propose a preconditioning technique that in combination with extended arithmetic precision let us treat the ill-conditioning problem. We numerically prove that as the number of nodes increases, then for errors of the same order, the condition number remains tractable, in quad-precision, and the numerical complexity of the local method remains bounded.

The industrial growth introduced the Industry 4.0 revolution, which uses several IoT-based technologies to manage the huge amount of data generated by its connected systems. This revolution aims to exchange data between the different parts and improve the performance of the manufacturing process. Facing several limitations, this paradigm needs the Fog Computing to ameliorate the Cloud services and the distribution of real-time decision-making and the secure and interoperable data analysis. The internal logistics presents the need to transmit and treat the data in real-time to take a more efficient decisions in a shorter delay. The Fog-based architecture is composed of terminal devices, Edge, Fog and Gateway devices. A model is presented to optimize the Fog integration (The cost of the links and nodes). Experimental results of an exact method optimization using Fico Xpress show a reduction of the Fog Computing integration cost in an internal logistic center.

International audience; The problem of concern in this work is the construction of free divergence fields given scattered horizontal components. As customary, the problem is formulated as a PDE constrained least squares problem. The novelty of our approach is to construct the so-called adjusted field, as the unique solution along an appropriately chosen descent direction. The latter is obtained by the adjoint equation technique. It is shown that the classical adjusted field of Sasaki’s is a particular case. On choosing descent directions, the underlying mass consistent model leads to the solution of an elliptic problem which is solved by means of a radial basis functions method. Finally, some numerical results for wind field adjustment are presented.

International audience; The numerical simulation of time-harmonic waves in heterogeneous media is a tricky task which consists in reproducing oscillations. These oscillations become stronger as the frequency increases, and high-order finite element methods have demonstrated their capability to reproduce the oscilla-tory behavior. However, they keep coping with limitations in capturing fine scale heterogeneities. We propose a new approach which can be applied in highly heterogeneous propagation media. It consists in constructing an approximate medium in which we can perform computations for a large variety of frequencies. The construction of the approximate medium can be understood as applying a quadrature formula locally. We establish estimates which generalize existing estimates formerly obtained for homogeneous Helmholtz problems. We then provide numerical results which illustrate the good level of accuracy of our solution methodology.

International audience; We study a spline-based approximation of vector fields in the conservative case (the gradient vector field derives from a potential function). We introduce a minimization problem on a Hilbert space for which the existence and uniqueness of the solution is given. We apply this approach to a registration process in image processing.

International audience; In many problems of geophysical interest, one has to deal with data that exhibit complex fault structures. This occurs, for instance, when describing the topography of seafloor surfaces, mountain ranges, volcanoes, islands, or the shape of geological entities, as well as when dealing with reservoir characterization and modelling. In all these circumstances, due to the presence of large and rapid variations in the data, attempting a fitting using conventional approximation methods necessarily leads to instability phenomena or undesirable oscillations which can locally and even globally hinder the approximation. As will be shown in this paper, the right approach to get a good approximant consists, in effect, in applying first a segmentation process to precisely define the locations of large variations and faults, and exploiting then a discrete approximation technique. To perform the segmentation step, we propose a quasi-automatic algorithm that uses a level set method to obtain from the given (gridded or scattered) Lagrange data several patches delimited by large gradients (or faults). Then, with the knowledge of the location of the discontinuities of the surface, we generate a triangular mesh (which takes into account the identified set of discontinuities) on which a $D^m$ -spline approximant is constructed. To show the efficiency of this technique, we will present the results obtained by its application to synthetic datasets as well as real gridded datasets in Oceanography and Geosciences.

International audience; Cet article aborde le problème de l'extraction semi-automatique de régularités dans des dialogues sous la forme de motifs dialogiques. Nous présentons un algorithme de program-mation dynamique en O(mA × n × mB) permettant d'extraire de manière non supervisée des motifs récurrents de tableaux bidimensionnels d'annotations représentant des dialogues (mA et mB correspondent au nombre de lignes des deux tableaux considérés et n à leur nombre de colonnes). Cet algorithme, combiné à une méthode de partitionnement, permet d'obtenir des régularités caractéristiques d'un corpus annoté. Les paramètres de la méthode et les résultats obtenus (i.e., les motifs dialogiques et les partitions de motifs) sont évalués manuellement par un expert lors d'une expérimentation. ABSTRACT. This article addresses the problem of semi-automatic regularity extraction in dialogues in the shape of dialogical patterns. We present a dynamic programming algorithm which runs in O(mA × n × mB) that enables to perform an unsupervised extraction of recurrent patterns from two-dimensional dialogue annotations (with mA and mB the number of lines in the two considered arrays and n their number of columns). We show how it can be combined to a clustering heuristique in order to extract relevant regularities from an annotated corpus. The parameters of the method and the results obtained (i.e., dialogical patterns and pattern clustering solutions) are evaluated manually by an expert through an experiment. MOTS-CLÉS : extraction de régularités, motifs dialogiques, modélisation du dialogue.

Let I :Ω→ℜ be a given bounded image function, where Ω is an open and bounded domain which belongs to ℜn. Let us consider n=2 for the purpose of illustration. Also, let S={xi}i∈Ω be a finite set of given points. We would like to find a contour Γ⊂Ω, such that Γ is an object boundary interpolating the points from S. We combine the ideas of the geodesic active contour (cf. Caselles et al. [7,8]) and of interpolation of points (cf. Zhao et al. [40]) in a level set approach developed by Osher and Sethian [33]. We present modelling of the proposed method, both theoretical results (viscosity solution) and numerical results are given.

International audience; We study a spline-based approximation of vector fields in the conservative case. This problem appears for instance when approximating current or wind velocity fields, the data deriving in those cases from a potential (pressure for the wind, etc.). In the modeling, we introduce a minimization problem on an Hilbert space for which the existence and uniqueness of the solution are provided. A convergence result in the introduced Sobolev space is established using norm equivalence and compactness arguments, as well as an approximation error estimate of the involved smoothing Dm-splines.

International audience; Reservoir engineers have to predict the behavior of a hydrocarbon reservoir by building a simulation model which can best reproduce the data collected in the field. These data fall into two types: static data, which are invariable in time, and dynamic data, which evolve according to fluid motions in the reservoir. In this paper, we focus on the integration of dynamic data related to four-dimensional (4D) inverted seismic data. Such seismic data constitute an invaluable source of information on fluid displacement and geology over extensive areas of the reservoir. However, incorporating them in the reservoir model through a matching process is a challenging task. Classical formulations of the objective function, which computes the misfit between observed data and responses computed by the reservoir model, are not adapted to 4D inverted seismic data. For example, a least square based mismatch is not representative of the visual difference between two seismic images. In this paper, we define a new formulation of the objective function based on simplification of seismic data in order to extract relevant information. This simplification involves filtering and segmentation techniques, as well as image comparison methods rooted in image analysis. More precisely, we focus on the non-local means algorithm for filtering, on the level-set framework for segmentation and on the local modified Hausdorff distance for image comparison. We investigate the efficiency of such techniques in the context of seismic data, and illustrate their potential on a synthetic history matching reservoir example.

This introductory paper describes the main topics of this special issue, dedicated to Leonardo Traversoni, known at the international level as the promoter of the conference series "Multivariate Approximation: Theory and Applications", to celebrate his 60th birthday. © 2012 Elsevier B.V. All rights reserved.

cited By (since 1996)1; International audience; In this paper, we investigate a new method to enforce topology preservation on deformation fields. The method is composed of two steps. The first one consists in correcting the gradient vector fields of the deformation at the discrete level, in order to fulfill a set of conditions ensuring topology preservation in the continuous domain after bilinear interpolation. This part, although related to prior works by Karaçali and Davatzikos, proposes a new approach based on interval analysis. The second one aims to reconstruct the deformation, given its full set of discrete gradient vectors. The problem is phrased as a functional minimization problem on the convex subset K of the Hilbert space V. The existence and uniqueness of the solution of the problem are established, and the use of Lagrange's multipliers allows to obtain the variational formulation of the problem on the Hilbert space V. Experimental results demonstrate the efficiency of the method. © 2011 IEEE.

In many problems of geophysical interest, when trying to segment images (i.e., to locate interfaces between different regions on the images), one has to deal with data that exhibit very complex structures. This occurs, for instance, when describing complex geophysical images (with layers, faults,...); in that case, segmentation is very difficult. Moreover, the segmentation process requires to take into account well data to interpolate, which implies integrating interpolation condition in the mathematical model. More precisely, let $I:\Omega\rightarrow\Re$ be a given bounded image function, where Ω is an open and bounded domain that belongs to $\Re^{n}$ . Let $S=\left\{ x_{i}\right\} _{i}\in\Omega$ be a finite set of given points (well data). The aim is to find a contour Γ⊂Ω such that Γ is an object boundary interpolating the points from S. To do that, we combine the ideas of the geodesic active contour (Caselles et al., Int. J. Comput. Vision 22-1:61-87, 1997) and of interpolation of points (Zhao et al., Comput. Vis. Image Understand. 80:295-314, 1986) in a Level Set approach developed by Osher and Sethian (J. Comput. Phys. 79:12-49, 1988). We present modelling of the proposed method. Both theoretical results (viscosity solution) and numerical results (on a velocity model for a real seismic line) are given.

International audience; We study the problem of constructing a smooth approximant from a finite set of patches given on a surface defined by an equation x3 = f(x1, x2). As an approximant of f, a discrete smoothing spline belonging to a suitable piecewise polynomial space is proposed. Error results and numerical results are given.

Starting from two sequences {Ĝa,c,n} and {Ĝd,b,n} of ordinary Gauss quadrature formulae with an orthogonality measure dσ on the open intervals (a,c) and (d,b), respectively. We construct a new sequence {Ĝa,b,e(n)} of extended Gaussian quadrature formulae for dσ on (a,b), which is based on some preassigned points, the nodes of Ĝa,c,n, Ĝd,b,n and the e(n) zeros contained in (c,d) of a nonclassical orthogonal polynomial on [a,b] with respect to a linear functional. The principal result gives explicit formulae relating these polynomials and shows how their recurrence coefficients in the three-term recurrence formulae are related. Thus, a new class of Gaussian quadratures, having some nodes contained in a given interior interval, can be computed directly by standard software for ordinary Gauss quadrature formulae.

The objective of this thesis is to demonstrate how to do theoretical analyses of fatigue and fracture mechanics in a structure for horizontal axis wind turbine. The chain of calculations required to reach this objective is particularly long for two reasons : firstly, the wind speed varies randomly with time , secondly, the vibration amplitude of the mast is amplified due to its natural frequencies of vibration. A whole chapter is dedicated to modeling the wind speed in space and time. The same chapter shows how to synthesize a random signal by employing a power spectral density function (PSD). The axial force of the rotor is the most important loading on a structure for horizontal axis wind turbine. This force has a non linear relation with the wind speed. This implies the need to determine the PSD of the axial force from its signal, by employing a spectral estimation method. The Thomson Multitaper method revealed to be the most satisfactory for this application. The PSD of displacement of the mast is determined by associating the receptance of the structural system and the PSD of the force representing all loadings. Finally, a signal of stress can be synthesized from its PSD. The fatigue cycle counting method known as rainflow is discussed and employed. The fact that the signal of stress has a variable amplitude implies the need of a more sophisticated method to simulate a crack propagation. The method chosen in this thesis is called strip-yield., L'objectif de cette thèse est de démontrer comment faire une analyse théorique de fatigue et de mécanique de la rupture d'une structure éolienne à l'axe horizontal. La chaîne des calculs nécessaires pour atteindre cet objectif s'avère être particulièrement longue pour deux raisons : d'abord, la vitesse du vent varie aléatoirement avec le temps ; deuxièmement, l'amplitude de vibration du mât est amplifié en raison des ses fréquences naturelles de vibration. Un chapitre entier est consacré à la modélisation de la vitesse du vent dans l'espace et dans le temps. Ce même chapitre démontre comment synthétiser un signal aléatoire à partir d'une fonction de densité spectrale de puissance (DSP). La force axiale du rotor est le chargement le plus important sur une structure éolienne à l'axe horizontal. Cette force a un rapport non linéaire avec la vitesse du vent. Cela implique la nécessité de déterminer la DSP de la force axiale à partir de son signal, en se servant d'une technique d'estimation spectrale. La méthode Thomson Multitaper s'est avéré la plus satisfaisante pour cette application. La DSP des déplacements du mât est déterminée en associant la réceptance du système structurel avec la DSP de la force qui représente tous les chargements. Un signal de contrainte peut finalement être synthétisé à partir de sa DSP. La technique de comptage de cycles de chargement connue sous le nom de rainflow est abordée et appliquée. Le fait que le signal de contraintes a une amplitude variable implique la nécessité d'employer une technique plus avancée de simulation de propagation de fissures. La technique choisie pour cette thèse est connue sous le nom de strip-yield (bande d'écoulement).

This work focuses on the modelling of problems related to image registration. Image registration consists in finding an optimal deformation such that a deformed image is aligned with a reference image. It is an important task encountered in a large range of applications such as medical imaging, comparison of data or shape tracking. The first chapter concerns the problem of topology preservation. This condition of topology preservation is important when the sought deformation reflects physical properties of the objects to be distorted. The following chapters propose several methods of image registration based on the nonlinear elasticity theory. Indeed, the objects to be matched are modelled as hyperelastic materials. Different fidelity terms have been investigated as well as two joint segmentation/registration models., Ce travail porte sur la modélisation de problèmes liés au recalage d'images. Le recalage consiste à trouver une déformation optimale de sorte qu'une image déformée s'aligne sur une image de référence. Il s'agit d'une technique que l'on rencontre dans de nombreux domaines, comme l'imagerie médicale, la comparaison de données ou le suivi de formes. Le premier chapitre se concentre sur le problème de préservation de la topologie. Cette condition de préservation de la topologie est importante lorsque la déformation recherchée traduit des propriétés physiques des objets soumis à la déformation. Les chapitres suivants proposent la construction de différentes méthodes de recalage d'images fondées sur la théorie de l'élasticité non linéaire. En effet, les objets à apparier sont supposés être des matériaux hyper-élastiques. Différents termes d'attaches aux données ont été explorés ainsi que deux modèles conjoints de segmentation et recalage.

In the context of dialogue analysis, a corpus of dialogues can be represented as a set of arrays of annotations encoding the dialogue utterances. In order to identify the frequently used dialogue schemes, we design a two-step methodology in which recurrent patterns are first extracted and then partitioned into homogenous classes constituting the regularities. Two methods are developed to extract recurrent patterns: LPCA-DC and SABRE. The former is an adaptation of a dynamic programming algorithm whereas the latter is obtained from a formal modeling of the extraction of local alignment problem in annotations arrays.The partitioning of recurrent patterns is realised using various heuristics from the literature as well as two original formulations of the K-partitioning problem in the form of mixed integer linear programs. Throughout a polyhedral study of a polyhedron associated to these formulations, facets are characterized (in particular: 2-chorded cycle inequalities, 2-partition inequalities and general clique inequalities). These theoretical results allow the establishment of an efficient cutting plane algorithm.We developed a decision support software called VIESA which implements these different methods and allows their evaluation during two experiments realised by a psychologist. Thus, regularities corresponding to dialogical strategies that previous manual extractions failed to identify are obtained., Dans le cadre de l’aide à l’analyse de dialogues, un corpus de dialogues peut être représenté par un ensemble de tableaux d’annotations encodant les différents énoncés des dialogues. Afin d’identifier des schémas dialogiques mis en oeuvre fréquemment, nous définissons une méthodologie en deux étapes : extraction de motifs récurrents, puis partitionnement de ces motifs en classes homogènes constituant ces régularités. Deux méthodes sont développées afin de réaliser l’extraction de motifs récurrents : LPCADC et SABRE. La première est une adaptation d’un algorithme de programmation dynamique tandis que la seconde est issue d’une modélisation formelle du problème d’extraction d’alignements locaux dans un couple de tableaux d’annotations.Le partitionnement de motifs récurrents est réalisé par diverses heuristiques de la littérature ainsi que deux formulations originales du problème de K-partitionnement sous la forme de programmes linéaires en nombres entiers. Lors d’une étude polyèdrale, nous caractérisons des facettes d’un polyèdre associé à ces formulations (notamment les inégalités de 2-partitions, les inégalités 2-chorded cycles et les inégalités de clique généralisées). Ces résultats théoriques permettent la mise en place d’un algorithme de plans coupants résolvant efficacement le problème.Nous développons le logiciel d’aide à la décision VIESA, mettant en oeuvre ces différentes méthodes et permettant leur évaluation au cours de deux expérimentations réalisées par un expert psychologue. Des régularités correspondant à des stratégies dialogiques que des extractions manuelles n’avaient pas permis d’obtenir sont ainsi identifiées.

International audience; The aim of our work is to specify and develop a geometric modeler, based on the formalism of iterated function systems with the following objectives: access to a new universe of original, various, aesthetic shapes, modeling of conventional shapes (smooth surfaces, solids) and unconventional shapes (rough surfaces, porous solids) by defining and controlling the relief (surface state) and lacunarity (size and distribution of holes). In this context we intend to develop differential calculus tools for fractal curves and surfaces defined by IFS. Using local fractional derivatives, we show that, even if most fractal curves are nowhere differentiable, they admit a left and right half-tangents, what gives us an additional parameter to characterize shapes.

3D is emerging as a new media. Its widespread adoption requires the implementation of userfriendly tools to create and manipulate three-dimensional shapes. Current softwares heavily rely on underlying shape modeling, usually a surfacic one, and are then often counter-intuitive orlimiting. Our objective is the design of an approach alleviating those limitations and allowing the user to only focus on the process of creating forms. Drawing inspiration from the ancient use of clay,we propose to model a material in a lagrangian description. A shape is described by a particles system, where each particle represents a small fraction of the total volume of the shape. In this framework, the Smoothed Particle Hydrodynamics method enables to approximate physical values anywhere in space. Relying on this method, we propose a modeling of material with two levels, one level representing the topology and the other one describing local geometry of the shape.The SPH method especially enables to evaluate a density of matter. We use this property todefine an implicit surface based on the physical properties of the particles system to reproduce the continuous aspect of matter. Those virtual materials can then be manipulated locally through interactions reproducing the handling of dough in the real world or through global shape deformation. Our approach is demonstrated by several prototypes running either on typical desktop workstation or in immersive environment system., La 3D s'impose comme un nouveau média dont l'adoption généralisée passe par la conception d'outils, accessibles au grand public, de création et de manipulation de formes tridimensionnelles quelconques. Les outils actuels reposent fortement sur la modélisation sous-jacente des formes, généralement surfacique, et sont alors peu intuitifs ou limitatifs dans l'expressivité offerte à l'utilisateur.Nous souhaitons, dans ces travaux, définir une approche ne présentant pas ces défauts et permettant à l'utilisateur de se concentrer sur le processus créatif. En nous inspirant de l'utilisation séculaire de l'argile, nous proposons une approche modélisant la matière sous forme lagrangienne.Une forme est ainsi décrite par un système de particules, où chaque particule représente un petit volume du volume global.Dans ce cadre lagrangien, la méthode Smoothed Particle Hydrodynamics (SPH) permet l'approximation de grandeurs physiques en tout point de l'espace. Nous proposons alors une modélisation de matériaux à deux couches, l'une décrivant la topologie et l'autre décrivant la géométrie du système global.La méthode SPH permet, entre autres, d'évaluer la densité de matière. Ceci nous permet de définir une surface implicite basée sur les propriétés physiques du système de particules pour redonner un aspect continu à la matière.Ces matériaux peuvent alors être manipulés au moyen d'interactions locales reproduisant le maniement de la pâte à modeler, et de déformations globales. L'intérêt de notre approche est démontrée par plusieurs prototypes fonctionnant sur des stations de travail standard ou dans des environnements immersifs.

International audience; This paper deals with the Helmholtz-Hodge decomposition of a vector field in bounded domain. We present a practical algorithm to compute this decomposition in the context of divergence-free and curl- free wavelets satisfying suitable boundary conditions. The method requires the inversion of divergence-free and curl-free wavelet Gram matrices. We propose an optimal preconditioning which allows to solve the systems with a small number of iterations. Finally, numerical examples prove the accuracy and the efficiency of the method.

In this dissertation, we are interested in several issues related to 3D data processing. The first one concerns people detection and tracking in depth map sequences. We propose an improvement of an existing method based on a segmentation stage followed by a tracking module. The second issue is head detection and modelling in 3D point clouds. In order to do this, we adopt a probabilistic approach based on a new spherical mixture model. The last considered application deals with the restoration of deteriorated depth maps. To solve this problem, we propose to use a surface approximation method based on interpolation Dm-splines with scale transforms to approximate and restore the image. Presented results illustrate the efficiency of the developed algorithms., Dans le cadre de cette thèse, nous nous intéressons à plusieurs problématiques liées au traitement de données 3D. La première concerne la détection et le suivi de personnes dans des séquences d'images de profondeur. Nous proposons une amélioration d'une méthode existante basée sur une étape de segmentation, puis de suivi des personnes. La deuxième problématique abordée est la détection et la modélisation de têtes dans un nuage de points 3D. Pour cela, nous adoptons une approche probabiliste basée sur un nouveau modèle de mélange sphérique. La dernière application traitée est liée à la restauration d'images de profondeur présentant des données manquantes. Nous proposons pour cela d'utiliser une méthode d'approximation de surface par Dm-splines d'interpolation avec changements d'échelle pour approximer et restaurer les données. Les résultats présentés illustrent l'efficacité des algorithmes développés.