Modélisation, Analyse, Représentation des Images Numériques Approche combinatoire de l’imagerie

My research are focused on combinatorial image processing. My approach is to propose mathematical models to abstract physical reality. This abstraction allows to define new techniques leading to original solutions for some problems. In this context, I propose a topological model of image, regions segmentation based on statistical criteria and combinatorial algorithms, and a bound representation based on combinatorial maps.Mes travaux de recherche sont basés sur une approche combinatoire et discrète de l’imagerie. Ma démarche est de proposer des définitions de modèles mathématiques fournissant une abstraction de la réalité physique, cette abstraction permettant de définir des nouvelles techniques amenant des solutions originales à des problèmes posés. Dans ce cadre, je me suis plus particulièrement intéressé à la définition d’un modèle formel d’image, à la segmentation en régions par des techniques algorithmiques et statistiques, et à la structuration du résultat à l’aide d’une représentation combinatoire

2L-CONVEX POLYOMINOES: GEOMETRICAL ASPECTS

International audienceA polyomino P is called 2L-convex if for every two cells there exists a monotone path included in P with at most two changes of direction. This paper studies the geometrical aspects of a sub-class of 2L-convex polyominoes called I0,0 and states a characterization of 2L it in terms of monotone paths. In a second part, four geometries are introduced and the tomographical point of view is investigated using the switching components (that is, the elements of this sub-class that have the same projections). Finally, some unicity results are given for the reconstruction of these polyominoes according to their projections

Reconnaissance de morceaux de plans discrets bruités

mémoire de DEA, 37 pagesLa reconnaissance d'objets discrets est un sujet important en géométrie discrète et de nombreux travaux concernant les droites et les plans ont été réalisés. Nous nous intéressons à la notion d'objets discrets flous, correspondant à des objets discrets bruités, et à leur détection. Ces objets sont définis analytiquement et les algorithmes développés à partir de ceux-ci s'adaptent aux données bruitées par les méthodes d'acquisition, par exemple les données médicales issues de scanners, d'échographie, d'IRM... Dans ce mémoire nous nous intéresserons plus particulièrement aux plans discrets bruités. En introduisant la définition d'un morceau de plan discret flou, nous montrerons que le problème de le reconnaissance d'un tel objet est équivalent à celui du calcul de l'épaisseur d'un ensemble de points en dimension 3. Après une étude des méthodes existantes résolvant le calcul de l'épaisseur, un algorithme connu sera alors adapté pour résoudre le problème de la reconnaissance incrémentale des morceaux de plans discrets flous

The number of directed k-convex polyominoes

We present a new method to obtain the generating functions for directed convex polyominoes according to several different statistics including: width, height, size of last column/row and number of corners. This method can be used to study different families of directed convex polyominoes: symmetric polyominoes, parallelogram polyominoes. In this paper, we apply our method to determine the generating function for directed k-convex polyominoes. We show it is a rational function and we study its asymptotic behavior

Tie-zone : the bridge between watershed transforms and fuzzy connectedness

Orientador: Roberto de Alencar LotufoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: Esta tese introduz o novo conceito de transformada de zona de empate que unifica as múltiplas soluções de uma transformada de watershed, conservando apenas as partes comuns em todas estas, tal que as partes que diferem constituem a zona de empate. A zona de empate aplicada ao watershed via transformada imagem-floresta (TZ-IFT-WT) se revela um elo inédito entre transformadas de watershed baseadas em paradigmas muito diferentes: gota d'água, inundação, caminhos ótimos e floresta de peso mínimo. Para todos esses paradigmas e os algoritmos derivados, é um desafio se ter uma solução única, fina, e que seja consistente com uma definição. Por isso, propõe-se um afinamento da zona de empate, único e consistente. Além disso, demonstra-se que a TZ-IFT-WT também é o dual de métodos de segmentação baseados em conexidade nebulosa. Assim, a ponte criada entre as abordagens morfológica e nebulosa permite aproveitar avanços de ambas. Em conseqüência disso, o conceito de núcleo de robustez para as sementes é explorado no caso do watershed.Abstract: This thesis introduces the new concept of tie-zone transform that unifies the multiple solutions of a watershed transform, by conserving only the common parts among them such that the differing parts constitute the tie zone. The tie zone applied to the watershed via image-foresting transform (TZ-IFTWT) proves to be a link between watershed transforms based on very different paradigms: drop of water, flooding, optimal paths and forest of minimum weight. For all these paradigms and the derived algorithms, it is a challenge to get a unique and thin solution which is consistent with a definition. That is why we propose a unique and consistent thinning of the tie zone. In addition, we demonstrate that the TZ-IFT-WT is also the dual of segmentation methods based on fuzzy connectedness. Thus, the bridge between the morphological and the fuzzy approaches allows to take benefit from the advance of both. As a consequence, the concept of cores of robustness for the seeds is exploited in the case of watersheds.DoutoradoEngenharia de ComputaçãoDoutor em Engenharia Elétric

On continuous maximum ow image segmentation algorithm

Ces dernières années avec les progrès matériels, les dimensions et le contenu des images acquises se sont complexifiés de manière notable. Egalement, le différentiel de performance entre les architectures classiques mono-processeur et parallèles est passé résolument en faveur de ces dernières. Pourtant, les manières de programmer sont restées largement les mêmes, instituant un manque criant de performance même sur ces architectures. Dans cette thèse, nous explorons en détails un algorithme particulier, les flots maximaux continus. Nous explicitons pourquoi cet algorithme est important et utile, et nous proposons plusieurs implémentations sur diverses architectures, du mono-processeur à l'architecture SMP et NUMA, ainsi que sur les architectures massivement parallèles des GPGPU. Nous explorons aussi des applications et nous évaluons ses performances sur des images de grande taille en science des matériaux et en biologie à l'échelle nanoIn recent years, with the advance of computing equipment and image acquisition techniques, the sizes, dimensions and content of acquired images have increased considerably. Unfortunately as time passes there is a steadily increasing gap between the classical and parallel programming paradigms and their actual performance on modern computer hardware. In this thesis we consider in depth one particular algorithm, the continuous maximum flow computation. We review in detail why this algorithm is useful and interesting, and we propose efficient and portable implementations on various architectures. We also examine how it performs in the terms of segmentation quality on some recent problems of materials science and nano-scale biologyPARIS-EST-Université (770839901) / SudocSudocFranceF

Enumeration of polyominoes defined in terms of pattern avoidance or convexity constraints

In this thesis, we consider the problem of characterizing and enumerating sets of polyominoes described in terms of some constraints, defined either by convexity or by pattern containment. We are interested in a well known subclass of convex polyominoes, the k-convex polyominoes for which the enumeration according to the semi-perimeter is known only for k=1,2. We obtain, from a recursive decomposition, the generating function of the class of k-convex parallelogram polyominoes, which turns out to be rational. Noting that this generating function can be expressed in terms of the Fibonacci polynomials, we describe a bijection between the class of k-parallelogram polyominoes and the class of planted planar trees having height less than k+3. In the second part of the thesis we examine the notion of pattern avoidance, which has been extensively studied for permutations. We introduce the concept of pattern avoidance in the context of matrices, more precisely permutation matrices and polyomino matrices. We present definitions analogous to those given for permutations and in particular we define polyomino classes, i.e. sets downward closed with respect to the containment relation. So, the study of the old and new properties of the redefined sets of objects has not only become interesting, but it has also suggested the study of the associated poset. In both approaches our results can be used to treat open problems related to polyominoes as well as other combinatorial objects.Comment: PhD thesi

Gaze-Based Human-Robot Interaction by the Brunswick Model

We present a new paradigm for human-robot interaction based on social signal processing, and in particular on the Brunswick model. Originally, the Brunswick model copes with face-to-face dyadic interaction, assuming that the interactants are communicating through a continuous exchange of non verbal social signals, in addition to the spoken messages. Social signals have to be interpreted, thanks to a proper recognition phase that considers visual and audio information. The Brunswick model allows to quantitatively evaluate the quality of the interaction using statistical tools which measure how effective is the recognition phase. In this paper we cast this theory when one of the interactants is a robot; in this case, the recognition phase performed by the robot and the human have to be revised w.r.t. the original model. The model is applied to Berrick, a recent open-source low-cost robotic head platform, where the gazing is the social signal to be considered