Avec l'avènement du « big data », de nombreuses répercussions ont eu lieu dans tous les domaines de la technologie de l'information, préconisant des solutions innovantes remportant le meilleur compromis entre coûts et précision. En théorie des graphes, où les graphes constituent un support de modélisation puissant qui permet de formaliser des problèmes allant des plus simples aux plus complexes, la recherche pour des problèmes NP-complet ou NP-difficils se tourne plutôt vers des solutions approchées, mettant ainsi en avant les algorithmes d'approximations et les heuristiques alors que les solutions exactes deviennent extrêmement coûteuses et impossible d'utilisation.Nous abordons dans cette thèse deux problématiques principales: dans un premier temps, le problème du partitionnement des graphes est abordé d'une perspective « big data », où les graphes massifs sont partitionnés en streaming. Nous étudions et proposons plusieurs modèles de partitionnement en streaming et nous évaluons leurs performances autant sur le plan théorique qu'empirique. Dans un second temps, nous nous intéressons au requêtage des graphes distribués/partitionnés. Dans ce cadre, nous étudions la problématique de la « recherche agrégative dans les graphes » qui a pour but de répondre à des requêtes interrogeant plusieurs fragments de graphes et qui se charge de la reconstruction de la réponse finale tel que l'on obtient un « matching approché » avec la requête initiale / With the advent of the "big data", many repercussions have taken place in all fields of information technology, advocating innovative solutions with the best compromise between cost and accuracy. In graph theory, where graphs provide a powerful modeling support for formalizing problems ranging from the simplest to the most complex, the search for NP-complete or NP-difficult problems is rather directed towards approximate solutions, thus Forward approximation algorithms and heuristics while exact solutions become extremely expensive and impossible to use. In this thesis we discuss two main problems: first, the problem of partitioning graphs is approached from a perspective big data, where massive graphs are partitioned in streaming. We study and propose several models of streaming partitioning and we evaluate their performances both theoretically and empirically. In a second step, we are interested in querying distributed / partitioned graphs. In this context, we study the problem of aggregative search in graphs, which aims to answer queries that interrogate several fragments of graphs and which is responsible for reconstructing the final response such that a Matching approached with the initial query

Dans cette thèse, nous nous intéressons à la recherche d’images similaires avec des descripteurs structurés par découpages d’images sur les graphes.Nous proposons une nouvelle approche appelée “bag-of-bags of words” (BBoW) pour la recherche d’images par le contenu (CBIR). Il s’agit d’une extension du modèle classique dit sac-de-mots (bag of words - BoW). Dans notre approche, une image est représentée par un graphe placé sur une grille régulière de pixels d’image. Les poids sur les arêtes dépendent de caractéristiques locales de couleur et texture. Le graphe est découpé en un nombre fixe de régions qui constituent une partition irrégulière de l’image. Enfin, chaque partition est représentée par sa propre signature suivant le même schéma que le BoW. Une image est donc décrite par un ensemble de signatures qui sont ensuite combinées pour la recherche d’images similaires dans une base de données. Contrairement aux méthodes existantes telles que Spatial Pyramid Matching (SPM), le modèle BBoW proposé ne repose pas sur l’hypothèse que des parties similaires d’une scène apparaissent toujours au même endroit dans des images d’une même catégorie. L’extension de cette méthode ` a une approche multi-échelle, appelée Irregular Pyramid Matching (IPM), est ´ également décrite. Les résultats montrent la qualité de notre approche lorsque les partitions obtenues sont stables au sein d’une même catégorie d’images. Une analyse statistique est menée pour définir concrètement la notion de partition stable.Nous donnons nos résultats sur des bases de données pour la reconnaissance d’objets, d’indexation et de recherche d’images par le contenu afin de montrer le caractère général de nos contributions / Image representation is a fundamental question for several computer vision tasks. The contributions discussed in this thesis extend the basic bag-of-words representations for the tasks of object recognition and image retrieval.In the present thesis, we are interested in image description by structural graph descriptors. We propose a model, named bag-of-bags of words (BBoW), to address the problems of object recognition (for object search by similarity), and especially Content-Based Image Retrieval (CBIR) from image databases. The proposed BBoW model, is an approach based on irregular pyramid partitions over the image. An image is first represented as a connected graph of local features on a regular grid of pixels. Irregular partitions (subgraphs) of the image are further built by using graph partitioning methods. Each subgraph in the partition is then represented by its own signature. The BBoW model with the aid of graphs, extends the classical bag-of-words (BoW) model by embedding color homogeneity and limited spatial information through irregular partitions of an image. Compared to existing methods for image retrieval, such as Spatial Pyramid Matching (SPM), the BBoW model does not assume that similar parts of a scene always appear at the same location in images of the same category. The extension of the proposed model to pyramid gives rise to a method we named irregular pyramid matching (IPM).The experiments demonstrate the strength of our approach for image retrieval when the partitions are stable across an image category. The statistical analysisof subgraphs is fulfilled in the thesis. To validate our contributions, we report results on three related computer vision datasets for object recognition, (localized)content-based image retrieval and image indexing. The experimental results in a database of 13,044 general-purposed images demonstrate the efficiency and effectiveness of the proposed BBoW framework.

Cette thèse se situe à l’intersection de deux domaines de recherche scientifique la Reconnaissance d’Objets Structurels (ROS) et la Recherche Opérationnelle (RO). Le premier consiste à rendre la machine plus intelligente et à reconnaître les objets, en particulier ceux basés sur les graphes. Alors que le second se focalise sur la résolution de problèmes d’optimisation combinatoire difficiles. L’idée principale de cette thèse est de combiner les connaissances de ces deux domaines. Parmi les problèmes difficiles existants en ROS, le problème de la distance d’édition entre graphes (DEG) a été sélectionné comme le cœur de ce travail. Les contributions portent sur la conception de méthodes adoptées du domaine RO pour la résolution du problème de DEG. Explicitement, des nouveaux modèles linéaires en nombre entiers et des matheuristiques ont été développé à cet effet et de très bons résultats ont été obtenus par rapport à des approches existantes. / This thesis is focused on Graph Matching (GM) problems and in particular the Graph Edit Distance (GED) problems. There is a growing interest in these problems due to their numerous applications in different research domains, e.g. biology, chemistry, computer vision, etc. However, these problems are known to be complex and hard to solve, as the GED is a NP-hard problem. The main objectives sought in this thesis, are to develop methods for solving GED problems to optimality and/or heuristically. Operations Research (OR) field offers a wide range of exact and heuristic algorithms that have accomplished very good results when solving optimization problems. So, basically all the contributions presented in thesis are methods inspired from OR field. The exact methods are designed based on deep analysis and understanding of the problem, and are presented as Mixed Integer Linear Program (MILP) formulations. The proposed heuristic approaches are adapted versions of existing MILP-based heuristics (also known as matheuristics), by considering problem-dependent information to improve their performances and accuracy.

In this thesis, we propose many developments in the context of Structural Similarity. We address both node (local) similarity and graph (global) similarity. Concerning node similarity, we focus on improving the diffusive process leading to compute this similarity (e.g. Commute Times) by means of modifying or rewiring the structure of the graph (Graph Densification), although some advances in Laplacian-based ranking are also included in this document. Graph Densification is a particular case of what we call graph rewiring, i.e. a novel field (similar to image processing) where input graphs are rewired to be better conditioned for the subsequent pattern recognition tasks (e.g. clustering). In the thesis, we contribute with an scalable an effective method driven by Dirichlet processes. We propose both a completely unsupervised and a semi-supervised approach for Dirichlet densification. We also contribute with new random walkers (Return Random Walks) that are useful structural filters as well as asymmetry detectors in directed brain networks used to make early predictions of Alzheimer's disease (AD). Graph similarity is addressed by means of designing structural information channels as a means of measuring the Mutual Information between graphs. To this end, we first embed the graphs by means of Commute Times. Commute times embeddings have good properties for Delaunay triangulations (the typical representation for Graph Matching in computer vision). This means that these embeddings can act as encoders in the channel as well as decoders (since they are invertible). Consequently, structural noise can be modelled by the deformation introduced in one of the manifolds to fit the other one. This methodology leads to a very high discriminative similarity measure, since the Mutual Information is measured on the manifolds (vectorial domain) through copulas and bypass entropy estimators. This is consistent with the methodology of decoupling the measurement of graph similarity in two steps: a) linearizing the Quadratic Assignment Problem (QAP) by means of the embedding trick, and b) measuring similarity in vector spaces. The QAP problem is also investigated in this thesis. More precisely, we analyze the behaviour of $m$-best Graph Matching methods. These methods usually start by a couple of best solutions and then expand locally the search space by excluding previous clamped variables. The next variable to clamp is usually selected randomly, but we show that this reduces the performance when structural noise arises (outliers). Alternatively, we propose several heuristics for spanning the search space and evaluate all of them, showing that they are usually better than random selection. These heuristics are particularly interesting because they exploit the structure of the affinity matrix. Efficiency is improved as well. Concerning the application domains explored in this thesis we focus on object recognition (graph similarity), clustering (rewiring), compression/decompression of graphs (links with Extremal Graph Theory), 3D shape simplification (sparsification) and early prediction of AD. / Ministerio de Economía, Industria y Competitividad (Referencia TIN2012-32839 BES-2013-064482)

Casamento de padrões de pontos é um problema fundamental em reconhecimento de padrões. O objetivo é encontrar uma correspondência entre dois conjuntos de pontos, associados a características relevantes de objetos ou entidades, mapeando os pontos de um conjunto no outro. Este problema está associado a muitas aplicações, como por exemplo, reconhecimento de objetos baseado em modelos, imagens estéreo, registro de imagens, biometria, entre outros. Para encontrar um mapeamento, os objetos são codificados por representações abstratas, codificando as características relevantes consideradas na comparação entre pares de objetos. Neste trabalho, objetos são representados por grafos, codificando tanto as características `locais\' quanto as relações espaciais entre estas características. A comparação entre objetos é guiada por uma formulação de atribuição quadrática, que é um problema NP-difícil. Para estimar uma solução, duas técnicas de casamento entre grafos são propostas: uma baseada em grafos auxiliares, chamados de grafos deformados; e outra baseada em representações `esparsas\', campos aleatórios de Markov e propagação de crenças. Devido as suas respectivas limitações, as abordagens são adequadas para situações específicas, conforme mostrado neste documento. Resultados envolvendo as duas abordagens são ilustrados em quatro importantes aplicações: casamento de imagens de gel eletroforese 2D, segmentação interativa de imagens naturais, casamento de formas, e colorização assistida por computador. / Point set matching is a fundamental problem in pattern recognition. The goal is to match two sets of points, associated to relevant features of objects or entities, by finding a mapping, or a correspondence, from one set to another set of points. This issue arises in many applications, e.g. model-based object recognition, stereo matching, image registration, biometrics, among others. In order to find a mapping, the objects can be encoded by abstract representations, carrying relevant features which are taken into account to compare pairs of objects. In this work, graphs are adopted to represent the objects, encoding their `local\' features and the spatial relations between these features. The comparison of two given objects is guided by a quadratic assignment formulation, which is NP-hard. In order to estimate the optimal solution, two approximations techniques, via graph matching, are proposed: one is based on auxiliary graphs, called deformed graphs; the other is based on `sparse\' representations, Markov random fields and belief propagation. Due to their respective limitations, each approach is more suitable to each specific situation, as shown in this document. The quality of the two approaches is illustrated on four important applications: 2D electrophoresis gel matching, interactive natural image segmentation, shape matching, and computer-assisted colorization.

Casamento de padrões de pontos é um problema fundamental em reconhecimento de padrões. O objetivo é encontrar uma correspondência entre dois conjuntos de pontos, associados a características relevantes de objetos ou entidades, mapeando os pontos de um conjunto no outro. Este problema está associado a muitas aplicações, como por exemplo, reconhecimento de objetos baseado em modelos, imagens estéreo, registro de imagens, biometria, entre outros. Para encontrar um mapeamento, os objetos são codificados por representações abstratas, codificando as características relevantes consideradas na comparação entre pares de objetos. Neste trabalho, objetos são representados por grafos, codificando tanto as características `locais\' quanto as relações espaciais entre estas características. A comparação entre objetos é guiada por uma formulação de atribuição quadrática, que é um problema NP-difícil. Para estimar uma solução, duas técnicas de casamento entre grafos são propostas: uma baseada em grafos auxiliares, chamados de grafos deformados; e outra baseada em representações `esparsas\', campos aleatórios de Markov e propagação de crenças. Devido as suas respectivas limitações, as abordagens são adequadas para situações específicas, conforme mostrado neste documento. Resultados envolvendo as duas abordagens são ilustrados em quatro importantes aplicações: casamento de imagens de gel eletroforese 2D, segmentação interativa de imagens naturais, casamento de formas, e colorização assistida por computador. / Point set matching is a fundamental problem in pattern recognition. The goal is to match two sets of points, associated to relevant features of objects or entities, by finding a mapping, or a correspondence, from one set to another set of points. This issue arises in many applications, e.g. model-based object recognition, stereo matching, image registration, biometrics, among others. In order to find a mapping, the objects can be encoded by abstract representations, carrying relevant features which are taken into account to compare pairs of objects. In this work, graphs are adopted to represent the objects, encoding their `local\' features and the spatial relations between these features. The comparison of two given objects is guided by a quadratic assignment formulation, which is NP-hard. In order to estimate the optimal solution, two approximations techniques, via graph matching, are proposed: one is based on auxiliary graphs, called deformed graphs; the other is based on `sparse\' representations, Markov random fields and belief propagation. Due to their respective limitations, each approach is more suitable to each specific situation, as shown in this document. The quality of the two approaches is illustrated on four important applications: 2D electrophoresis gel matching, interactive natural image segmentation, shape matching, and computer-assisted colorization.