Nous nous intéressons au problème de la reconstruction tridimensionnelle d'objets complexes à partir de coupes sériées. Le premier chapitre du mémoire s'attache à montrer l'intérêt de mettre à la disposition de la modélisation géologique 3D un ensemble d'outils variés et notamment des méthodes d'interpolation et de reconstruction adaptées. Le second chapitre pose la problématique générale de la reconstruction 3D et propose un état de l'art sur les méthodes existantes. Ces deux chapitres composent la première partie du manuscrit. Dans la deuxième partie du mémoire nous proposons une nouvelle méthode de reconstruction 3D qui permet de traiter de manière simple et automatique l'ensemble des problèmes de topologie (trous, branchements multiples, contours isolés). Elle s'appuie sur la construction adaptative de coupes intermédiaires par interpolation entre les sections initiales (chapitre 3). Ce processus utilise un diagramme de Voronoï généralisé simplifié, le réseau bissecteur, comme outil d'interpolation 2D. Nous fournissons une description géométrique complète du réseau bissecteur 2D et nous montrons que sa complexité algébrique est la même que celle des éléments qui permettent de le calculer (segments en 2D, portions de plans en 3D). Nous proposons ensuite deux algorithmes de construction des réseaux bissecteurs interne et externe de formes polygonales éventuellement trouées, dont la complexité en temps est respectivement en O(n2 log n) et O(n2), et la mémoire en O(n2) et O(n) respectivement (chapitre 4). La mise en correspondance des contours est abordée dans le chapitre 5 et nous suggérons quelques solutions pour traiter certains problèmes délicats. La construction du réseau bissecteur permet ensuite d'obte~ir une surface valide de l'objet en guidant de manière directe la triangulation entre les points des différentes sections. Il n'y a donc pas besoin de post-traitements. De plus, l'ajout automatique de portions de coupes intermédiaires dans les zones de changements de topologie ou de variations de morphologie permet une meilleure définition des surfaces générées (chapitre 6). Dans la dernière partie du mémoire nous discutons les résultats obtenus et nous les comparons avec ceux de deux méthodes existantes (chapitre 7).

Tradicionalment, la reproducció del mon real se'ns ha mostrat a traves d'imatges planes. Aquestes imatges se solien materialitzar mitjançant pintures sobre tela o be amb dibuixos. Avui, per sort, encara podem veure pintures fetes a ma, tot i que la majoria d'imatges s'adquireixen mitjançant càmeres, i es mostren directament a una audiència, com en el cinema, la televisió o exposicions de fotografies, o be son processades per un sistema computeritzat per tal d'obtenir un resultat en particular. Aquests processaments s'apliquen en camps com en el control de qualitat industrial o be en la recerca mes puntera en intel·ligència artificial. Aplicant algorismes de processament de nivell mitja es poden obtenir imatges 3D a partir d'imatges 2D, utilitzant tècniques ben conegudes anomenades Shape From X, on X es el mètode per obtenir la tercera dimensió, i varia en funció de la tècnica que s'utilitza a tal nalitat. Tot i que l'evolució cap a la càmera 3D va començar en els 90, cal que les tècniques per obtenir les formes tridimensionals siguin mes i mes acurades. Les aplicacions dels escàners 3D han augmentat considerablement en els darrers anys, especialment en camps com el lleure, diagnosi/cirurgia assistida, robòtica, etc. Una de les tècniques mes utilitzades per obtenir informació 3D d'una escena, es la triangulació, i mes concretament, la utilització d'escàners laser tridimensionals. Des de la seva aparició formal en publicacions científiques al 1971 [SS71], hi ha hagut contribucions per solucionar problemes inherents com ara la disminució d'oclusions, millora de la precisió, velocitat d'adquisició, descripció de la forma, etc. Tots i cadascun dels mètodes per obtenir punts 3D d'una escena te associat un procés de calibració, i aquest procés juga un paper decisiu en el rendiment d'un dispositiu d'adquisició tridimensional. La nalitat d'aquesta tesi es la d'abordar el problema de l'adquisició de forma 3D, des d'un punt de vista total, reportant un estat de l'art sobre escàners laser basats en triangulació, provant el funcionament i rendiment de diferents sistemes, i fent aportacions per millorar la precisió en la detecció del feix laser, especialment en condicions adverses, i solucionant el problema de la calibració a partir de mètodes geomètrics projectius. / Traditionally, the reproduction of the real world has been shown to us by means of at images. These images used to be materialised by means of paint on canvas, drawings or the like. Today, we still see hand made pictures, by fortune, although most of the images are acquired by cameras and they are either directly shown to an audience, like in the cinema, television or photographs, or they are processed by a computer system in order to obtain a particular result, like in industrial quality assurance or bleeding edge artificial intelligence research. Applying mid-level processing algorithms, 3D images can be obtained from 2D ones, using well known techniques called Shape From X, where X is the method for obtaining the 3rd dimension. While the evolution to the 3D camera begun in the 90s, the techniques for obtaining the most accurate 3D shape need to be continuously improving. The application of 3D scanners has spread signi cantly in the recent years, specially in elds like entertainment, assisted diagnosis/ surgery, robotics, etc. One of the most used techniques to obtain 3D information from a scene is triangulation, and more concretely, triangulationbased laser scanners. Since their formal appearance in scienti c publications, in 1971 [SS71], there have been contributions for solving inherent problems like occlusion avoidance, accuracy improvement, acquisition speed, shape description, etc. All of the methods for obtaining 3D points of a scene is accompained with a calibration procedure, and this procedure plays a decisive role in the performance of the acquisition device. The goal of this thesis is to provide a holistic approach to the problem of shape acquisition, giving a wide survey of triangulation laser scanners, testing the performance of di erent systems, and to give contributions for both improving acquisition accuracy under adverse conditions and solving the calibration problem. In addition, the calibration approach is based on previous works that used projective geometry to this end.

Aquesta tesi tracta el problema del posicionament de robots mòbils quan, en el decurs del moviment, es realitzen mesures angulars relatives al robot de l'orientació de la recta entre un dels seus punts i punts de l'entorn de posició coneguda. Es considera que les mesures angulars són fetes per un sensor làser giratori que detecta diferents reflectors catadiòptrics fixos.La contribució principal és el desenvolupament d'un algorisme dinàmic, basat en un filtre de Kalman estès (EKF), que estima a cada instant de temps l'estat format pels angles associats als reflectors. La simulació hodomètrica dels angles entre mesures directes del sensor làser garanteix l'ús consistent i continuat dels mètodes de triangulació per a determinar la posició i l'orientació del robot.Inclou simulacions informàtiques i experiments per a validar la precisió del mètode de posicionament proposat. En l'experimentació s'utilitza un robot mòbil omnidireccional amb tres rodes de lliscament direccional de corrons esfèrics. / This thesis focuses on mobile robot positioning methods based on angular measurements, relative to the robot frame and made during its motion, of the orientation of the straight lines between one of its points and known artificial landmarks. The angular measurements are assumed to be done by a rotating laser scanner that detects different catadioptric landmarks on the workspace.Its main contribution is the development of a dynamic algorithm based on an extended Kalman filter (EKF) that estimates at any time the state-vector of the landmark relative angles. The odometric simulation of landmark angles between actual measurements guarantees the consistent and continuous use of the triangulation methods to determine the robot position and orientation.It includes computer simulations and experiments in order to validate the accuracy of the proposed positioning method. In the experiments, an omnidirectional mobile robot with three directionally sliding wheels made of spherical rollers has been used.

Consider distinct latin squares, L and M, of order n. Then the pair (T1, T2) where T1 = L \M and T2 = M \ L is called a latin bitrade. Furthermore T1 and T2 are referred to as latin trades, in which T2 is said to be a disjoint mate of T1 (and vice versa). Drápal (1991) showed that, under certain conditions, a partition of an equilateral triangle of side length n, where n is some integer, into smaller, integer length sided equilateral triangles gives rise to a latin trade within the latin square based on the addition table for the integers modulo n. A partial latin square P of order n is said to be completable if there exists a latin square L of order n such that P ⊆ L. If there is only one such possible latin square, L, of order n then P is said to be uniquely completable and P is called a defining set of L. Furthermore, if C is a uniquely completable partial latin square such that no proper subset of C is uniquely completable, C is said to be a critical set or a minimal defining set. These concepts, namely latin trades and defining sets in latin squares, are intimately connected by the following observation. If L is a latin square and D ⊆ L is a defining set, then D intersects all latin bitrades for which one mate is contained in L. In Part I of this thesis Dr´apal’s result is applied to investigate the structure of certain defining sets in latin squares. The results that are obtained are interesting in themselves; furthermore, the geometric approach to the problem yields additional appealing results. These geometric results are discussed in Chapters 3, 4, 5 and 6. They pertain to partitioning regions (polygons in R2 that satisfy certain obvious conditions) into equilateral, integer length sided, triangles, such that no point, in the region, is a corner of more than three distinct triangles. In Chapter 2 one of the main two theorems on defining sets is established, as is a method for using the above geometric results to prove the nonexistence of certain types of defining sets. In Part II of this thesis, intersection problems, for latin squares and Steiner triple systems, are considered. The seminal works, for problems of these types, are due to Lindner and Rosa (1975) and Fu (1980). A natural progression, from the established literature, for intersection problems between elements in a pair of latin squares or Steiner triple systems is to problems in which the intersection is composed of a number of disjoint configurations (isomorphic copies of some specified partial triple system). In this thesis solutions to two intersection problems for disjoint configurations are detailed. An m-flower, (F,F), is a partial triple system/configuration, such that: F = {{x, yi, zi} | {yi, zi} ∩ {yj , zj} = ∅, for 0 ≤ i, j ≤ m − 1, i 6= j}; and F = UX∈FX. The first such problem considered in this thesis asks for necessary and sufficient conditions for integers k and m ≥ 2 such that a pair of latin squares of order n exists that intersect precisely in k disjoint m-flowers. The necessary terminology, constructions, lemmas and proof for this result are contained in Chapters 7, 8 and 9. The second such problem considered in this thesis asks for necessary and sufficient conditions for integers k such that a pair of Steiner triple systems of order u exists that intersect precisely in k disjoint 2-flowers. This result relies on the solution to the latin square problem and an additional result from Chapter 9. The further constructions and lemmas used to prove this result are detailed in Chapter 10.

Consider distinct latin squares, L and M, of order n. Then the pair (T1, T2) where T1 = L \M and T2 = M \ L is called a latin bitrade. Furthermore T1 and T2 are referred to as latin trades, in which T2 is said to be a disjoint mate of T1 (and vice versa). Drápal (1991) showed that, under certain conditions, a partition of an equilateral triangle of side length n, where n is some integer, into smaller, integer length sided equilateral triangles gives rise to a latin trade within the latin square based on the addition table for the integers modulo n. A partial latin square P of order n is said to be completable if there exists a latin square L of order n such that P ⊆ L. If there is only one such possible latin square, L, of order n then P is said to be uniquely completable and P is called a defining set of L. Furthermore, if C is a uniquely completable partial latin square such that no proper subset of C is uniquely completable, C is said to be a critical set or a minimal defining set. These concepts, namely latin trades and defining sets in latin squares, are intimately connected by the following observation. If L is a latin square and D ⊆ L is a defining set, then D intersects all latin bitrades for which one mate is contained in L. In Part I of this thesis Dr´apal’s result is applied to investigate the structure of certain defining sets in latin squares. The results that are obtained are interesting in themselves; furthermore, the geometric approach to the problem yields additional appealing results. These geometric results are discussed in Chapters 3, 4, 5 and 6. They pertain to partitioning regions (polygons in R2 that satisfy certain obvious conditions) into equilateral, integer length sided, triangles, such that no point, in the region, is a corner of more than three distinct triangles. In Chapter 2 one of the main two theorems on defining sets is established, as is a method for using the above geometric results to prove the nonexistence of certain types of defining sets. In Part II of this thesis, intersection problems, for latin squares and Steiner triple systems, are considered. The seminal works, for problems of these types, are due to Lindner and Rosa (1975) and Fu (1980). A natural progression, from the established literature, for intersection problems between elements in a pair of latin squares or Steiner triple systems is to problems in which the intersection is composed of a number of disjoint configurations (isomorphic copies of some specified partial triple system). In this thesis solutions to two intersection problems for disjoint configurations are detailed. An m-flower, (F,F), is a partial triple system/configuration, such that: F = {{x, yi, zi} | {yi, zi} ∩ {yj , zj} = ∅, for 0 ≤ i, j ≤ m − 1, i 6= j}; and F = UX∈FX. The first such problem considered in this thesis asks for necessary and sufficient conditions for integers k and m ≥ 2 such that a pair of latin squares of order n exists that intersect precisely in k disjoint m-flowers. The necessary terminology, constructions, lemmas and proof for this result are contained in Chapters 7, 8 and 9. The second such problem considered in this thesis asks for necessary and sufficient conditions for integers k such that a pair of Steiner triple systems of order u exists that intersect precisely in k disjoint 2-flowers. This result relies on the solution to the latin square problem and an additional result from Chapter 9. The further constructions and lemmas used to prove this result are detailed in Chapter 10.

Consider distinct latin squares, L and M, of order n. Then the pair (T1, T2) where T1 = L \M and T2 = M \ L is called a latin bitrade. Furthermore T1 and T2 are referred to as latin trades, in which T2 is said to be a disjoint mate of T1 (and vice versa). Drápal (1991) showed that, under certain conditions, a partition of an equilateral triangle of side length n, where n is some integer, into smaller, integer length sided equilateral triangles gives rise to a latin trade within the latin square based on the addition table for the integers modulo n. A partial latin square P of order n is said to be completable if there exists a latin square L of order n such that P ⊆ L. If there is only one such possible latin square, L, of order n then P is said to be uniquely completable and P is called a defining set of L. Furthermore, if C is a uniquely completable partial latin square such that no proper subset of C is uniquely completable, C is said to be a critical set or a minimal defining set. These concepts, namely latin trades and defining sets in latin squares, are intimately connected by the following observation. If L is a latin square and D ⊆ L is a defining set, then D intersects all latin bitrades for which one mate is contained in L. In Part I of this thesis Dr´apal’s result is applied to investigate the structure of certain defining sets in latin squares. The results that are obtained are interesting in themselves; furthermore, the geometric approach to the problem yields additional appealing results. These geometric results are discussed in Chapters 3, 4, 5 and 6. They pertain to partitioning regions (polygons in R2 that satisfy certain obvious conditions) into equilateral, integer length sided, triangles, such that no point, in the region, is a corner of more than three distinct triangles. In Chapter 2 one of the main two theorems on defining sets is established, as is a method for using the above geometric results to prove the nonexistence of certain types of defining sets. In Part II of this thesis, intersection problems, for latin squares and Steiner triple systems, are considered. The seminal works, for problems of these types, are due to Lindner and Rosa (1975) and Fu (1980). A natural progression, from the established literature, for intersection problems between elements in a pair of latin squares or Steiner triple systems is to problems in which the intersection is composed of a number of disjoint configurations (isomorphic copies of some specified partial triple system). In this thesis solutions to two intersection problems for disjoint configurations are detailed. An m-flower, (F,F), is a partial triple system/configuration, such that: F = {{x, yi, zi} | {yi, zi} ∩ {yj , zj} = ∅, for 0 ≤ i, j ≤ m − 1, i 6= j}; and F = UX∈FX. The first such problem considered in this thesis asks for necessary and sufficient conditions for integers k and m ≥ 2 such that a pair of latin squares of order n exists that intersect precisely in k disjoint m-flowers. The necessary terminology, constructions, lemmas and proof for this result are contained in Chapters 7, 8 and 9. The second such problem considered in this thesis asks for necessary and sufficient conditions for integers k such that a pair of Steiner triple systems of order u exists that intersect precisely in k disjoint 2-flowers. This result relies on the solution to the latin square problem and an additional result from Chapter 9. The further constructions and lemmas used to prove this result are detailed in Chapter 10.

Consider distinct latin squares, L and M, of order n. Then the pair (T1, T2) where T1 = L \M and T2 = M \ L is called a latin bitrade. Furthermore T1 and T2 are referred to as latin trades, in which T2 is said to be a disjoint mate of T1 (and vice versa). Drápal (1991) showed that, under certain conditions, a partition of an equilateral triangle of side length n, where n is some integer, into smaller, integer length sided equilateral triangles gives rise to a latin trade within the latin square based on the addition table for the integers modulo n. A partial latin square P of order n is said to be completable if there exists a latin square L of order n such that P ⊆ L. If there is only one such possible latin square, L, of order n then P is said to be uniquely completable and P is called a defining set of L. Furthermore, if C is a uniquely completable partial latin square such that no proper subset of C is uniquely completable, C is said to be a critical set or a minimal defining set. These concepts, namely latin trades and defining sets in latin squares, are intimately connected by the following observation. If L is a latin square and D ⊆ L is a defining set, then D intersects all latin bitrades for which one mate is contained in L. In Part I of this thesis Dr´apal’s result is applied to investigate the structure of certain defining sets in latin squares. The results that are obtained are interesting in themselves; furthermore, the geometric approach to the problem yields additional appealing results. These geometric results are discussed in Chapters 3, 4, 5 and 6. They pertain to partitioning regions (polygons in R2 that satisfy certain obvious conditions) into equilateral, integer length sided, triangles, such that no point, in the region, is a corner of more than three distinct triangles. In Chapter 2 one of the main two theorems on defining sets is established, as is a method for using the above geometric results to prove the nonexistence of certain types of defining sets. In Part II of this thesis, intersection problems, for latin squares and Steiner triple systems, are considered. The seminal works, for problems of these types, are due to Lindner and Rosa (1975) and Fu (1980). A natural progression, from the established literature, for intersection problems between elements in a pair of latin squares or Steiner triple systems is to problems in which the intersection is composed of a number of disjoint configurations (isomorphic copies of some specified partial triple system). In this thesis solutions to two intersection problems for disjoint configurations are detailed. An m-flower, (F,F), is a partial triple system/configuration, such that: F = {{x, yi, zi} | {yi, zi} ∩ {yj , zj} = ∅, for 0 ≤ i, j ≤ m − 1, i 6= j}; and F = UX∈FX. The first such problem considered in this thesis asks for necessary and sufficient conditions for integers k and m ≥ 2 such that a pair of latin squares of order n exists that intersect precisely in k disjoint m-flowers. The necessary terminology, constructions, lemmas and proof for this result are contained in Chapters 7, 8 and 9. The second such problem considered in this thesis asks for necessary and sufficient conditions for integers k such that a pair of Steiner triple systems of order u exists that intersect precisely in k disjoint 2-flowers. This result relies on the solution to the latin square problem and an additional result from Chapter 9. The further constructions and lemmas used to prove this result are detailed in Chapter 10.

Text in Afrikaans / Die doel van die navorsing is om die individu se aanpassing tydens integrasie te ondersoek. 'n Gedragsprofiel vir aanpassing word in die literatuuroorsig voorgestel volgens sin van koherensie as konstruk van die salutogenese paradigma. Empiries word die lewensorientasievraelys as psigometriese instrument gebruik om sterkte van sin van koherensie te bepaal. K walitatiewe onderhoude, gegrond op fenomenologiese beginsels, word gebruik om aanpassing kwalitatief te evalueer. In die navorsingsontwerp is daar sprake van verkennende, beskrywende en verklarende navorsing en nie-waarskynlikheidsteekproeftrekking word gebruik. Kwantitatiewe en kwalitatiewe resultate word gekoppel ten einde inteme geldigheid op kontekstuele vlak te verseker. Bevindinge toon dat betekenisvolheid van die integrasieproses die vemaamste verskil maak tussen aanpassing en nie-aanpassing. Verstaanbaarheid binne grense van die onmiddellike omgewing en hantering van instrumentele eise sonder om die fokus op emosionele parameters te plaas, fasiliteer verdere aanpassing. Relevante sleutelwoorde is aanpassing, stres, patogenese, salutogenese, sin van koherensie, verstaanbaarheid, hanteerbaarheid, betekenisvolheid, fenomenologie en triangulasie. / The aim of this research is to study individual coping during integration. A behavioural profile for coping is proposed in the literature study based on sense of coherence, a construct of the salutogenesis paradigm. Empirically the psychometric instrument, orientation to life questionnaire, is used to determine the strength of sense of coherence. Qualitative interviewing, based on phenomenological principles, is used to evaluate coping qualitatively. In the research design there are signs of exploratory, descriptive and explanatory research and nonprobability sampling is used. Quantitative and qualitative results are combined to ensure internal validity on a contextual level. Findings showed that meaningfulness of the integration process is the major difference between coping and not coping. Comprehensibility within the boundaries of the immediate environment and the management of instrumental demands without focusing on the emotional parameters, facilitate further coping. / Industrial Psychology / M.A. (Industrial Psychology)

Fundação de Amparo a Pesquisa do Estado de Minas Gerais / The aim of this work is to develop a non-contact 3D scanning robot to measure surfaces from objects of small sizes. The 3D scanner is shaped for a mechanical structure and an optic lecture system. The mechanical structure has 5 degrees of freedom. Such system is composed by two kinematic chains used to move the laser sensor and the workpiece respectively. The lecture system is derived from a laser sensor, based on 3D active triangulation technique that acquires the surface workpiece data. This technique assurance the scanning of the workpiece surface with reduced dimensional errors and consequently it makes possible the use less data points. Therefore it is achievable the fast data processing to reverse engineering method. In order to analyze its kinematics and dynamic model, its workspace, error analysis, and efforts at the joints, methods for reading the surface coordinates were proposed. For the analysis were considered the resolution and mechanical characteristics of the components used for the construction of a prototype. / O objetivo deste trabalho consiste no estudo e desenvolvimento de um digitalizador tridimensional robótico que será empregado para adquirir as dimensões superficiais de objetos de tamanho reduzido. O digitalizador é composto por uma estrutura mecânica e um sistema de leitura ótico. A estrutura mecânica do digitalizador possui 5 graus de liberdade e é composta por duas cadeias cinemáticas acopladas cinematicamente, onde uma delas é utilizada para movimentar o sensor laser e a outra para movimentar o objeto. O sistema de leitura é composto por um sensor laser que é baseado no método da triangulação ativa espacial para adquirir as medidas superficiais do objeto. Neste trabalho é utilizado o método da triangulação espacial porque ele garante o acompanhamento superficial do objeto para diminuir os erros nas medições, facilita a redução da quantidade de dados, facilitando o processamento de dados nas tarefas de engenharia reversa. Para permitir analisar os modelos cinemático e dinâmico, com o conseqüente estudo de seu espaço de trabalho de leitura, análise de erros, e dos esforços nas articulações, foram propostas metodologias de leitura da superfície do objeto. Para as análises foram consideradas as características mecânicas e de resolução dos componentes utilizados para a construção de um protótipo. / Doutor em Engenharia Mecânica

This thesis presents a complete and fully automatic method for estimating the volume of an airbag, through all stages of its inflation, with multiple synchronized high-speed cameras. Using recorded contours of the inflating airbag, its visual hull is reconstructed with a novel method: The intersections of all back-projected contours are first identified with an accelerated epipolar algorithm. These intersections, together with additional points sampled from concave surface regions of the visual hull, are then Delaunay triangulated to a connected set of tetrahedra. Finally, the visual hull is extracted by carving away the tetrahedra that are classified as inconsistent with the contours, according to a voting procedure. The volume of an airbag's visual hull is always larger than the airbag's real volume. By projecting a known synthetic model of the airbag into the cameras, this volume offset is computed, and an accurate estimate of the real airbag volume is extracted. Even though volume estimates can be computed for all camera setups, the cameras should be specially posed to achieve optimal results. Such poses are uniquely found for different airbag models with a separate, fully automatic, simulated annealing algorithm. Satisfying results are presented for both synthetic and real-world data.