Sparse variational regularization for visual motion estimation

The computation of visual motion is a key component in numerous computer vision tasks such as object detection, visual object tracking and activity recognition. Despite exten- sive research effort, efficient handling of motion discontinuities, occlusions and illumina- tion changes still remains elusive in visual motion estimation. The work presented in this thesis utilizes variational methods to handle the aforementioned problems because these methods allow the integration of various mathematical concepts into a single en- ergy minimization framework. This thesis applies the concepts from signal sparsity to the variational regularization for visual motion estimation. The regularization is designed in such a way that it handles motion discontinuities and can detect object occlusions

Assisting digital volume correlation with mechanical image-based modeling: application to the measurement of kinematic fields at the architecture scale in cellular materials

La mesure de champs de déplacement et de déformation aux petites échelles dans des microstructures complexes représente encore un défi majeur dans le monde de la mécanique expérimentale. Ceci est en partie dû aux acquisitions d'images et à la pauvreté de la texture à ces échelles. C'est notamment le cas pour les matériaux cellulaires lorsqu'ils sont imagés avec des micro-tomographes conventionnels et qu'ils peuvent être sujets à des mécanismes de déformation complexes. Comme la validation de modèles numériques et l'identification des propriétés mécaniques de matériaux se base sur des mesures précises de déplacements et de déformations, la conception et l'implémentation d'algorithmes robustes et fiables de corrélation d'images semble nécessaire. Lorsque l'on s'intéresse à l'utilisation de la corrélation d'images volumiques (DVC) pour les matériaux cellulaires, on est confronté à un paradoxe: l'absence de texture à l'échelle du constituant conduit à considérer l'architecture comme marqueur pour la corrélation. Ceci conduit à l'échec des techniques ordinaires de DVC à mesurer des cinématiques aux échelles subcellulaires en lien avec des comportements mécaniques locaux complexes tels que la flexion ou le flambement de travées. L'objectif de cette thèse est la conception d'une technique de DVC pour la mesure de champs de déplacement dans des matériaux cellulaires à l'échelle de leurs architectures. Cette technique assiste la corrélation d'images par une régularisation élastique faible en utilisant un modèle mécanique généré automatiquement et basé sur les images. La méthode suggérée introduit une séparation d'échelles au dessus desquelles la DVC est dominante et en dessous desquelles elle est assistée par le modèle mécanique basé sur l'image. Une première étude numérique consistant à comparer différentes techniques de construction de modèles mécaniques basés sur les images est conduite. L'accent est mis sur deux méthodes de calcul particulières: la méthode des éléments finis (FEM) et la méthode des cellules finies (FCM) qui consiste à immerger la géométrie complexe dans une grille régulière de haut ordre sans utiliser de mailleurs. Si la FCM évite une première phase délicate de discrétisation, plusieurs paramètres restent néanmoins délicats à fixer. Dans ce travail, ces paramètres sont ajustés afin d'obtenir (a) la meilleure précision (bornée par les erreurs de pixellisation) tout en (b) assurant une complexité minimale. Pour l'aspect mesure par corrélation d'images régularisée, plusieurs expérimentations virtuelles à partir de différentes simulations numériques (en élasticité, en plasticité et en non-linéarité géométrique) sont d'abord réalisées afin d'analyser l'influence des paramètres de régularisation introduits. Les erreurs de mesures peuvent dans ce cas être quantifiées à l'aide des solutions de référence éléments finis. La capacité de la méthode à mesurer des cinématiques complexes en absence de texture est démontrée pour des régimes non-linéaires tels que le flambement. Finalement, le travail proposé est généralisé à la corrélation volumique des différents états de déformation du matériau et à la construction automatique de la micro-architecture cellulaire en utilisant soit une grille B-spline d'ordre arbitraire (FCM) soit un maillage éléments finis (FEM). Une mise en évidence expérimentale de l'efficacité et de la justesse de l'approche proposée est effectuée à travers de la mesure de cinématiques complexes dans une mousse polyuréthane sollicitée en compression lors d'un essai in situ.Measuring displacement and strain fields at low observable scales in complex microstructures still remains a challenge in experimental mechanics often because of the combination of low definition images with poor texture at this scale. The problem is particularly acute in the case of cellular materials, when imaged by conventional micro-tomographs, for which complex highly non-linear local phenomena can occur. As the validation of numerical models and the identification of mechanical properties of materials must rely on accurate measurements of displacement and strain fields, the design and implementation of robust and faithful image correlation algorithms must be conducted. With cellular materials, the use of digital volume correlation (DVC) faces a paradox: in the absence of markings of exploitable texture on/or in the struts or cell walls, the available speckle will be formed by the material architecture itself. This leads to the inability of classical DVC codes to measure kinematics at the cellular and a fortiori sub-cellular scales, precisely because the interpolation basis of the displacement field cannot account for the complexity of the underlying kinematics, especially when bending or buckling of beams or walls occurs. The objective of the thesis is to develop a DVC technique for the measurement of displacement fields in cellular materials at the scale of their architecture. The proposed solution consists in assisting DVC by a weak elastic regularization using an automatic image-based mechanical model. The proposed method introduces a separation of scales above which DVC is dominant and below which it is assisted by image-based modeling. First, a numerical investigation and comparison of different techniques for building automatically a geometric and mechanical model from tomographic images is conducted. Two particular methods are considered: the finite element method (FEM) and the finite-cell method (FCM). The FCM is a fictitious domain method that consists in immersing the complex geometry in a high order structured grid and does not require meshing. In this context, various discretization parameters appear delicate to choose. In this work, these parameters are adjusted to obtain (a) the best possible accuracy (bounded by pixelation errors) while (b) ensuring minimal complexity. Concerning the ability of the mechanical image-based models to regularize DIC, several virtual experimentations are performed in two-dimensions in order to finely analyze the influence of the introduced regularization lengths for different input mechanical behaviors (elastic, elasto-plastic and geometrically non-linear) and in comparison with ground truth. We show that the method can estimate complex local displacement and strain fields with speckle-free low definition images, even in non-linear regimes such as local buckling. Finally a three-dimensional generalization is performed through the development of a DVC framework. It takes as an input the reconstructed volumes at the different deformation states of the material and constructs automatically the cellular micro-architeture geometry. It considers either an immersed structured B-spline grid of arbitrary order or a finite-element mesh. An experimental evidence is performed by measuring the complex kinematics of a polyurethane foam under compression during an in situ test

Variational methods and its applications to computer vision

Many computer vision applications such as image segmentation can be formulated in a ''variational'' way as energy minimization problems. Unfortunately, the computational task of minimizing these energies is usually difficult as it generally involves non convex functions in a space with thousands of dimensions and often the associated combinatorial problems are NP-hard to solve. Furthermore, they are ill-posed inverse problems and therefore are extremely sensitive to perturbations (e.g. noise). For this reason in order to compute a physically reliable approximation from given noisy data, it is necessary to incorporate into the mathematical model appropriate regularizations that require complex computations. The main aim of this work is to describe variational segmentation methods that are particularly effective for curvilinear structures. Due to their complex geometry, classical regularization techniques cannot be adopted because they lead to the loss of most of low contrasted details. In contrast, the proposed method not only better preserves curvilinear structures, but also reconnects some parts that may have been disconnected by noise. Moreover, it can be easily extensible to graphs and successfully applied to different types of data such as medical imagery (i.e. vessels, hearth coronaries etc), material samples (i.e. concrete) and satellite signals (i.e. streets, rivers etc.). In particular, we will show results and performances about an implementation targeting new generation of High Performance Computing (HPC) architectures where different types of coprocessors cooperate. The involved dataset consists of approximately 200 images of cracks, captured in three different tunnels by a robotic machine designed for the European ROBO-SPECT project.Open Acces

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Atlas to Image-with-Tumor Registration based on Demons and Deformation Inpainting

International audienceThis paper presents a method for nonlinear registration of images, where there exists no one-to-one correspondence in parts of the image. Such a situation occurs for instance in the case where an atlas of normal anatomy shall be matched to pathological data, such as tumors, resections or lesions. Our idea is to use local con dence weights and to model pathological regions with zero con dence. We integrate this concept into the e cient and publicly available di eomorphic demons registration framework. Finally, we show that this process better captures deformations in high-con dence regions than without using the proposed modi cation. Furthermore, it is easy to implement and runs faster than previous approaches

Broad chemical transferability in structure-based coarse-graining

Compared to top-down coarse-grained (CG) models, bottom-up approaches are capable of offering higher structural fidelity. This fidelity results from the tight link to a higher-resolution reference, making the CG model chemically specific. Unfortunately, chemical specificity can be at odds with compound-screening strategies, which call for transferable parametrizations. Here we present an approach to reconcile bottom-up, structure-preserving CG models with chemical transferability. We consider the bottom-up CG parametrization of 3,441 C$_7$O$_2$ small-molecule isomers. Our approach combines atomic representations, unsupervised learning, and a large-scale extended-ensemble force-matching parametrization. We first identify a subset of 19 representative molecules, which maximally encode the local environment of all gas-phase conformers. Reference interactions between the 19 representative molecules were obtained from both homogeneous bulk liquids and various binary mixtures. An extended-ensemble parametrization over all 703 state points leads to a CG model that is both structure-based and chemically transferable. Remarkably, the resulting force field is on average more structurally accurate than single-state-point equivalents. Averaging over the extended ensemble acts as a mean-force regularizer, smoothing out both force and structural correlations that are overly specific to a single state point. Our approach aims at transferability through a set of CG bead types that can be used to easily construct new molecules, while retaining the benefits of a structure-based parametrization.Comment: 15 pages, 7 figure