Vision 3D multi-images : contribution à l’obtention de solutions globales par optimisation polynomiale et théorie des moments

L’objectif général de cette thèse est d’appliquer une méthode d’optimisation polynomiale basée sur la théorie des moments à certains problèmes de vision artificielle. Ces problèmes sont en général non convexes et classiquement résolus à l’aide de méthodes d’optimisation locales Ces techniques ne convergent généralement pas vers le minimum global et nécessitent de fournir une estimée initiale proche de la solution exacte. Les méthodes d’optimisation globale permettent d’éviter ces inconvénients. L’optimisation polynomiale basée sur la théorie des moments présente en outre l’avantage de prendre en compte des contraintes. Dans cette thèse nous étendrons cette méthode aux problèmes de minimisation d’une somme d’un grand nombre de fractions rationnelles. De plus, sous certaines hypothèses de "faible couplage" ou de "parcimonie" des variables du problème, nous montrerons qu’il est possible de considérer un nombre important de variables tout en conservant des temps de calcul raisonnables. Enfin nous appliquerons les méthodes proposées aux problèmes de vision par ordinateur suivants : minimisation des distorsions projectives induites par le processus de rectification d’images, estimation de la matrice fondamentale, reconstruction 3D multi-vues avec et sans distorsions radiales. ABSTRACT : The overall objective of this thesis is to apply a polynomial optimization method, based on moments theory, on some vision problems. These problems are often nonconvex and they are classically solved using local optimization methods. Without additional hypothesis, these techniques don’t converge to the global minimum and need to provide an initial estimate close to the exact solution. Global optimization methods overcome this drawback. Moreover, the polynomial optimization based on moments theory could take into account particular constraints. In this thesis, we extend this method to the problems of minimizing a sum of many rational functions. In addition, under particular assumptions of "sparsity", we show that it is possible to deal with a large number of variables while maintaining reasonable computation times. Finally, we apply these methods to particular computer vision problems: minimization of projective distortions due to image rectification process, Fundamental matrix estimation, and multi-view 3D reconstruction with and without radial distortions

Optimization of BEM-Based Cooling Channels Injection Moulding Using Model Reduction

Issu de : ESAFORM 2008 - 11th International ESAFORM conference on material forming, Lyon, FRANCE, April 23-25 2008International audienceToday, around 30% of manufactured plastic goods rely on injection moulding. The cooling time can represent more than 70% of the injection cycle. In this process, heat transfer during the cooling step has a great influence both on the quality of the final parts that are produced, and on the moulding cycle time. Models based on a full 3D finite element method renders unpractical the use of optimization of the design and placement of the cooling channel in injection moulds. We have extended the use of boundary element method (BEM) to this process. We introduce in this paper a practical methodology to optimize both the position and the shape of the cooling channels in injection moulding processes. We couple the direct computation with an optimization algorithm such as SQP (Sequential Quadratic Programming). First, we propose an implementation of the model reduction in the BEM solver. This technique permits to reduce considerably the computing time during the linear system resolution (unsteady case). Secondly, we couple it with an optimization algorithm to evaluate its potentiality. For example, we can minimize the maximal temperature on the cavity surface subject to a temperature uniformity constraint. Thirdly, we present encouraging computational results on plastic parts that show that our optimization methodology is viable

Vision 3D multi-images (contribution à l'obtention de solutions globales par optimisation polynomiale et théorie des moments)

L objectif général de cette thèse est d appliquer une méthode d optimisation polynomiale basée sur la théorie des moments à certains problèmes de vision artificielle. Ces problèmes sont en général non convexes et classiquement résolus à l aide de méthodes d optimisation locales Ces techniques ne convergent généralement pas vers le minimum global et nécessitent de fournir une estimée initiale proche de la solution exacte. Les méthodes d optimisation globale permettent d éviter ces inconvénients. L optimisation polynomiale basée sur la théorie des moments présente en outre l avantage de prendre en compte des contraintes. Dans cette thèse nous étendrons cette méthode aux problèmes de minimisation d une somme d un grand nombre de fractions rationnelles. De plus, sous certaines hypothèses de "faible couplage" ou de "parcimonie" des variables du problème, nous montrerons qu il est possible de considérer un nombre important de variables tout en conservant des temps de calcul raisonnables. Enfin nous appliquerons les méthodes proposées aux problèmes de vision par ordinateur suivants : minimisation des distorsions projectives induites par le processus de rectification d images, estimation de la matrice fondamentale, reconstruction 3D multi-vues avec et sans distorsions radiales.The overall objective of this thesis is to apply a polynomial optimization method, based on moments theory, on some vision problems. These problems are often nonconvex and they are classically solved using local optimization methods. Without additional hypothesis, these techniques don t converge to the global minimum and need to provide an initial estimate close to the exact solution. Global optimization methods overcome this drawback. Moreover, the polynomial optimization based on moments theory could take into account particular constraints. In this thesis, we extend this method to the problems of minimizing a sum of many rational functions. In addition, under particular assumptions of "sparsity", we show that it is possible to deal with a large number of variables while maintaining reasonable computation times. Finally, we apply these methods to particular computer vision problems: minimization of projective distortions due to image rectification process, Fundamental matrix estimation, and multi-view 3D reconstruction with and without radial distortions.TOULOUSE-ENSIACET (315552325) / SudocSudocFranceF

An analytical model taking feed rate effect into consideration for scallop height calculation in milling with torus-end cutter

International audienceFeed rate effect on scallop height in complex surface milling by torus-end mill is rarely studied. In a previous paper, an analytical predictive model of scallop height based on transverse step over distance has been established. However, this model doesn’t take feed rate effect into consideration. In the present work an analytical expression of scallop height, including feed rate effect, is detailed in order to quantify feed rate effect and thus to estimate more precisely the surface quality. Then, an experimental validation is conducted, comparing the presented model predictions with experimental results. Actually, the share of the scallop height due to feed effect is highly dependent on the machining configuration. However, most of time, the feed effect on total scallop height values is far from being negligible

Stéréo corrélation d'images numériques et régularisation mécanique

Cette étude a pour but de mesurer des conditions aux limites en rotation et en déplacement pour un modèle plaque à l'aide de la Stéréo Corrélation d'Images Numérique. Une approche de type Éléments-Finis est alors utilisée ainsi qu'une approche intégrée de corrélation. La détermination de la courbure de la plaque s'effectue ainsi à l'aide d'une Régularisation cinématique de type plaque afin de prendre en compte les rotations dans la mesure et non par dérivation d'une mesure

Contribution to the global resolution of minimization problems in computer vision by polynomial optimization and moments theory

L’objectif général de cette thèse est d’appliquer une méthode d’optimisation polynomiale basée sur la théorie des moments à certains problèmes de vision artificielle. Ces problèmes sont en général non convexes et classiquement résolus à l’aide de méthodes d’optimisation locales Ces techniques ne convergent généralement pas vers le minimum global et nécessitent de fournir une estimée initiale proche de la solution exacte. Les méthodes d’optimisation globale permettent d’éviter ces inconvénients. L’optimisation polynomiale basée sur la théorie des moments présente en outre l’avantage de prendre en compte des contraintes. Dans cette thèse nous étendrons cette méthode aux problèmes de minimisation d’une somme d’un grand nombre de fractions rationnelles. De plus, sous certaines hypothèses de "faible couplage" ou de "parcimonie" des variables du problème, nous montrerons qu’il est possible de considérer un nombre important de variables tout en conservant des temps de calcul raisonnables. Enfin nous appliquerons les méthodes proposées aux problèmes de vision par ordinateur suivants : minimisation des distorsions projectives induites par le processus de rectification d’images, estimation de la matrice fondamentale, reconstruction 3D multi-vues avec et sans distorsions radiales.The overall objective of this thesis is to apply a polynomial optimization method, based on moments theory, on some vision problems. These problems are often nonconvex and they are classically solved using local optimization methods. Without additional hypothesis, these techniques don’t converge to the global minimum and need to provide an initial estimate close to the exact solution. Global optimization methods overcome this drawback. Moreover, the polynomial optimization based on moments theory could take into account particular constraints. In this thesis, we extend this method to the problems of minimizing a sum of many rational functions. In addition, under particular assumptions of "sparsity", we show that it is possible to deal with a large number of variables while maintaining reasonable computation times. Finally, we apply these methods to particular computer vision problems: minimization of projective distortions due to image rectification process, Fundamental matrix estimation, and multi-view 3D reconstruction with and without radial distortions

Trichromatic thermoreflectometry for an improved accuracy of true temperature field measurement on a multi-material part

International audienceThis article addresses the problem of measuring an accurate temperature field on a multi-material part which exhibits spatial, temporal, spectral and thermal emissivity variations. The article analyses the contribution of trichromatic thermoreflectometry method compared to bichromatic thermoreflectometry method. Thermoreflectometry, an active thermography method, measures in-situ the emissivity, together with the temperature. The emissivity is measured indirectly by measuring the bidirectional reflectivity of the sample and by estimating its diffusion function. The bichromatic thermoreflectometry assumes an independent diffusion function with wavelength. For trichromatic thermoreflectometry, the diffusion function varies linearly with the wavelength. This article demonstrates the benefit of trichromatic thermoreflectometry on both simulated and experimental data. The simulated data come from measurements of emissivity and diffusion function of six different materials (metallic and dielectric) performed with a FTIR (Fourier Transform InfraRed) spectrometer. The addition of noise on these estimated values enables the propagation of uncertainties, which shows that the bias on temperature estimation is lower with trichromatic thermoreflectometry. Finally, an experimental demonstration on three of the six materials confirms a lower temperature measurement error (difference between the measured temperature and a reference temperature) with trichromatic thermoreflectometry

Optimization of structures under buckling constraints using frame elements

International audiencetructural optimization is of increasing interest in a wide variety of application fields. In this article, structural optimization under stress and buckling constraints is investigated. A structure comprised of a set of frame elements is considered. The aim is to obtain the minimal mass structure, by optimizing the number of frame elements and their cross sectional dimensions. A formulation as a mixed-integer nonlinear optimization problem with a tailored objective function is introduced. This cost function is a combination of the structural mass and the sum of the second moments of inertia of each structural element. Moreover, a new algorithm, tailored to the considered problem, is proposed. Numerical results show that the proposed approach provides interesting structural mass savings

Truss-like structures optimization under buckling constraints using frame elements with anisotropic cross sections

International audienc