O mapeamento de ambientes é um dos maiores desafios para pesquisadores na área de navegação autônoma. As técnicas existentes estão divididas em dois importantes paradigmas, o mapeamento métrico e o topológico. Diversos métodos de mapeamento que combinam as vantagens de cada um desses paradigmas têm sido propostos. Este projeto consiste na adaptação e extensão de um sistema integrado para navegação autônoma de robôs móveis através do aperfeiçoamento da interface e também da incorporação de uma técnica de mapeamento topológico. Para isso, a técnica conhecida como Grade de Ocupação, utilizada em geral para mapeamento métrico é combinada com um método de esqueletização de imagens para a realização do mapeamento topológico. Além disso, transformações morfológicas de erosão e abertura, adequadas a ambientes reais, foram utilizadas, visando reduzir a influência de ruídos na abordagem proposta, uma vez que devido a ruídos inerentes as leituras sensoriais obtidas pelo robô, o mapa topológico gerado apresenta diversas linhas topológicas desnecessárias, dificultando consequentemente a tarefa de navegação autônoma. Vários experimentos foram executados para verificar a eficiência da combinação de técnicas proposta, tanto em nível de simulação quanto em um robô real. Os resultados obtidos demonstraram que a técnica de esqueletização de imagens combinada ao mapeamento métrico do ambiente é uma forma simples e viável de se obter as linhas topológicas do espaço livre do ambiente. A aplicação das transformações morfológicas demonstrou ser eficiente para a criação de mapas topológicos livres de ruído, uma vez que elimina grande parte das linhas topológicas geradas em conseqüência dos ruídos dos sensores do robô / Environment mapping has been a great challenge for many researchers in the autonomous navigation area. There are two important paradigms for mapping, metric and topological mapping. Several mapping methods that combine the advantages of each paradigm have been proposed. This project consists to the adaptation and extension of a mobile robots autonomous navigation integrated system by improving the interface and incorporation of a topological mapping technique. For this, the technique known as Occupation Grid for metric mapping is combined with an image skeletonization method used for topological mapping. This work also aims to propose a set of morphology transformations to generation of topological maps suitable for real environments, seeking to reduce influence of noise in performed mapping. The topological map generated through this combination presents several unnecessary topological lines, due noise inherent to the own robot ability of capturing sensor signals, hindering consequently the task of autonomous navigation. Several experiments have been performed to verify the efficiency of the proposed approach. The results obtained demonstrate that image skeletonization technique combined with the metric mapping is a simple and feasible method for obtaining the topological lines corresponding to free space of the environment. The application of the morphology transformations demonstrated to be a useful method to the creation of topological maps considerably less noise, since it eliminates most of the topological lines generated in consequence of noise in the sensors

The study of particle morphology plays an important role in understanding the micromechanical behavior of cohesionless soil. Shear strength and liquefaction characteristics of granular soil depend on various morphological characteristics of soil grains such as their particle size, shape and surface texture. Therefore, accurate characterization and quantification of particle shape is necessary to study the effect of grain shape on mechanical behavior of granular assembly. However, the theoretical and practical developments of quantification of particle morphology and its influence on the mechanical response of granular assemblies has been very limited due to the lack of quantitative information about particle geometries, the experimental and numerical difficulties in characterizing and modeling irregular particle morphology. Motivated by the practical relevance of these challenges, this research presents a comprehensive approach to model irregular particle shape accurately both in two and three dimensions. To facilitate the research goal, a variety of natural and processed sand samples is collected from various locations around the world. A series of experimental and analytical studies are performed following the sample collection effort to characterize and quantify particle shapes of various sand samples by using Fourier shape descriptors. As part of the particle shape quantification and modeling, a methodology is developed to determine an optimum sample size for each sand sample used in the analysis. Recently, Discrete Element Method (DEM) has gained attention to model irregular particle morphology in two and three dimensions. In order to generate and reconstruct particle assemblies of highly irregular geometric shapes of a particular sand sample in the DEM environment, the relationship between grain size and shape is explored and no relationship is found between grain size and shape for the sand samples analyzed. A skeletonization algorithm is developed in this study in order to automate the Overlapping Discrete Element Cluster (ODEC) technique for modeling irregular particle shape in two and three dimensions. Finally, the two-dimensional and three-dimensional particle shapes are implemented within discrete element modeling software, PFC2D and PFC3D, to evaluate the influence of grain shape on shear strength behavior of granular soil by using discrete simulation of direct shear test.

Angiography is an invasive procedure since contrast medium is injected into circulatory system of patients and the mostly preferred technique is X-ray angiography. For diagnosis, treatment planning, and risk assessment purposes, interventional radiologists utilize visual inspection to determine connectivity relations between vessels. This situation leads angiography to be more invasive, since it requires additional injection of contrast medium and X-ray dose. This thesis work presents a 3-D vascular connectivity tracking toolkit for automated extraction of vascular networks in 3-D medical images. The proposed method automatically extracts the vascular network connected to a user-defined point in a user-defined direction, and requires no further user interaction. The toolkit prevents additional injection of contrast agent and X-ray dose, saves time for the interventional radiologist. While the algorithm is applicable on all 3-D angiography images, performance of the method is observed on 3-D catheter angiography image of cerebrovascular structures. The algorithm iteratively tracks gravity centers of vascular branches in the user-defined direction, preserving connection to the user-defined point. Curvy branches are tracked even if they have discontinuous portions. Since this tracking method does not depend on lumen diameter and intensity differences, branches with stenoses and branches having large intensity difference can be successfully tracked. Skeletonization and junction detection methods are described, which are used to detect the sub branches, indirectly connected to the point. These methods are capable of handling bifurcations, trifurcations, and junctions having more branches. However, false junctions occurring due to superposition of vessels are not eliminated.

Research on forest ecosystems receives high attention, especially nowadays with regard to sustainable management of renewable resources and the climate change. In particular, accurate information on the 3D structure of a tree is important for forest science and bioclimatology, but also in the scope of commercial applications. Conventional methods to measure geometric plant features are labor- and time-intensive. For detailed analysis, trees have to be cut down, which is often undesirable. Here, Terrestrial Laser Scanning (TLS) provides a particularly attractive tool because of its contactless measurement technique. The object geometry is reproduced as a 3D point cloud. The objective of this thesis is the automatic retrieval of the spatial structure of trees from TLS data. We focus on forest scenes with comparably high stand density and with many occlusions resulting from it. The varying level of detail of TLS data poses a big challenge. We present two fully automatic methods to obtain skeletal structures from scanned trees that have complementary properties. First, we explain a method that retrieves the entire tree skeleton from 3D data of co-registered scans. The branching structure is obtained from a voxel space representation by searching paths from branch tips to the trunk. The trunk is determined in advance from the 3D points. The skeleton of a tree is generated as a 3D line graph. Besides 3D coordinates and range, a scan provides 2D indices from the intensity image for each measurement. This is exploited in the second method that processes individual scans. Furthermore, we introduce a novel concept to manage TLS data that facilitated the researchwork. Initially, the range image is segmented into connected components. We describe a procedure to retrieve the boundary of a component that is capable of tracing inner depth discontinuities. A 2D skeleton is generated from the boundary information and used to decompose the component into sub components. A Principal Curve is computed from the 3D point set that is associated with a sub component. The skeletal structure of a connected component is summarized as a set of polylines. Objective evaluation of the results remains an open problem because the task itself is ill-defined: There exists no clear definition of what the true skeleton should be w.r.t. a given point set. Consequently, we are not able to assess the correctness of the methods quantitatively, but have to rely on visual assessment of results and provide a thorough discussion of the particularities of both methods. We present experiment results of both methods. The first method efficiently retrieves full skeletons of trees, which approximate the branching structure. The level of detail is mainly governed by the voxel space and therefore, smaller branches are reproduced inadequately. The second method retrieves partial skeletons of a tree with high reproduction accuracy. The method is sensitive to noise in the boundary, but the results are very promising. There are plenty of possibilities to enhance the method’s robustness. The combination of the strengths of both presented methods needs to be investigated further and may lead to a robust way to obtain complete tree skeletons from TLS data automatically. / Die Erforschung des ÖkosystemsWald spielt gerade heutzutage im Hinblick auf den nachhaltigen Umgang mit nachwachsenden Rohstoffen und den Klimawandel eine große Rolle. Insbesondere die exakte Beschreibung der dreidimensionalen Struktur eines Baumes ist wichtig für die Forstwissenschaften und Bioklimatologie, aber auch im Rahmen kommerzieller Anwendungen. Die konventionellen Methoden um geometrische Pflanzenmerkmale zu messen sind arbeitsintensiv und zeitaufwändig. Für eine genaue Analyse müssen Bäume gefällt werden, was oft unerwünscht ist. Hierbei bietet sich das Terrestrische Laserscanning (TLS) als besonders attraktives Werkzeug aufgrund seines kontaktlosen Messprinzips an. Die Objektgeometrie wird als 3D-Punktwolke wiedergegeben. Basierend darauf ist das Ziel der Arbeit die automatische Bestimmung der räumlichen Baumstruktur aus TLS-Daten. Der Fokus liegt dabei auf Waldszenen mit vergleichsweise hoher Bestandesdichte und mit zahlreichen daraus resultierenden Verdeckungen. Die Auswertung dieser TLS-Daten, die einen unterschiedlichen Grad an Detailreichtum aufweisen, stellt eine große Herausforderung dar. Zwei vollautomatische Methoden zur Generierung von Skelettstrukturen von gescannten Bäumen, welche komplementäre Eigenschaften besitzen, werden vorgestellt. Bei der ersten Methode wird das Gesamtskelett eines Baumes aus 3D-Daten von registrierten Scans bestimmt. Die Aststruktur wird von einer Voxelraum-Repräsentation abgeleitet indem Pfade von Astspitzen zum Stamm gesucht werden. Der Stamm wird im Voraus aus den 3D-Punkten rekonstruiert. Das Baumskelett wird als 3D-Liniengraph erzeugt. Für jeden gemessenen Punkt stellt ein Scan neben 3D-Koordinaten und Distanzwerten auch 2D-Indizes zur Verfügung, die sich aus dem Intensitätsbild ergeben. Bei der zweiten Methode, die auf Einzelscans arbeitet, wird dies ausgenutzt. Außerdem wird ein neuartiges Konzept zum Management von TLS-Daten beschrieben, welches die Forschungsarbeit erleichtert hat. Zunächst wird das Tiefenbild in Komponenten aufgeteilt. Es wird eine Prozedur zur Bestimmung von Komponentenkonturen vorgestellt, die in der Lage ist innere Tiefendiskontinuitäten zu verfolgen. Von der Konturinformation wird ein 2D-Skelett generiert, welches benutzt wird um die Komponente in Teilkomponenten zu zerlegen. Von der 3D-Punktmenge, die mit einer Teilkomponente assoziiert ist, wird eine Principal Curve berechnet. Die Skelettstruktur einer Komponente im Tiefenbild wird als Menge von Polylinien zusammengefasst. Die objektive Evaluation der Resultate stellt weiterhin ein ungelöstes Problem dar, weil die Aufgabe selbst nicht klar erfassbar ist: Es existiert keine eindeutige Definition davon was das wahre Skelett in Bezug auf eine gegebene Punktmenge sein sollte. Die Korrektheit der Methoden kann daher nicht quantitativ beschrieben werden. Aus diesem Grund, können die Ergebnisse nur visuell beurteiltwerden. Weiterhinwerden die Charakteristiken beider Methoden eingehend diskutiert. Es werden Experimentresultate beider Methoden vorgestellt. Die erste Methode bestimmt effizient das Skelett eines Baumes, welches die Aststruktur approximiert. Der Detaillierungsgrad wird hauptsächlich durch den Voxelraum bestimmt, weshalb kleinere Äste nicht angemessen reproduziert werden. Die zweite Methode rekonstruiert Teilskelette eines Baums mit hoher Detailtreue. Die Methode reagiert sensibel auf Rauschen in der Kontur, dennoch sind die Ergebnisse vielversprechend. Es gibt eine Vielzahl von Möglichkeiten die Robustheit der Methode zu verbessern. Die Kombination der Stärken von beiden präsentierten Methoden sollte weiter untersucht werden und kann zu einem robusteren Ansatz führen um vollständige Baumskelette automatisch aus TLS-Daten zu generieren.

O mapeamento de ambientes é um dos maiores desafios para pesquisadores na área de navegação autônoma. As técnicas existentes estão divididas em dois importantes paradigmas, o mapeamento métrico e o topológico. Diversos métodos de mapeamento que combinam as vantagens de cada um desses paradigmas têm sido propostos. Este projeto consiste na adaptação e extensão de um sistema integrado para navegação autônoma de robôs móveis através do aperfeiçoamento da interface e também da incorporação de uma técnica de mapeamento topológico. Para isso, a técnica conhecida como Grade de Ocupação, utilizada em geral para mapeamento métrico é combinada com um método de esqueletização de imagens para a realização do mapeamento topológico. Além disso, transformações morfológicas de erosão e abertura, adequadas a ambientes reais, foram utilizadas, visando reduzir a influência de ruídos na abordagem proposta, uma vez que devido a ruídos inerentes as leituras sensoriais obtidas pelo robô, o mapa topológico gerado apresenta diversas linhas topológicas desnecessárias, dificultando consequentemente a tarefa de navegação autônoma. Vários experimentos foram executados para verificar a eficiência da combinação de técnicas proposta, tanto em nível de simulação quanto em um robô real. Os resultados obtidos demonstraram que a técnica de esqueletização de imagens combinada ao mapeamento métrico do ambiente é uma forma simples e viável de se obter as linhas topológicas do espaço livre do ambiente. A aplicação das transformações morfológicas demonstrou ser eficiente para a criação de mapas topológicos livres de ruído, uma vez que elimina grande parte das linhas topológicas geradas em conseqüência dos ruídos dos sensores do robô / Environment mapping has been a great challenge for many researchers in the autonomous navigation area. There are two important paradigms for mapping, metric and topological mapping. Several mapping methods that combine the advantages of each paradigm have been proposed. This project consists to the adaptation and extension of a mobile robots autonomous navigation integrated system by improving the interface and incorporation of a topological mapping technique. For this, the technique known as Occupation Grid for metric mapping is combined with an image skeletonization method used for topological mapping. This work also aims to propose a set of morphology transformations to generation of topological maps suitable for real environments, seeking to reduce influence of noise in performed mapping. The topological map generated through this combination presents several unnecessary topological lines, due noise inherent to the own robot ability of capturing sensor signals, hindering consequently the task of autonomous navigation. Several experiments have been performed to verify the efficiency of the proposed approach. The results obtained demonstrate that image skeletonization technique combined with the metric mapping is a simple and feasible method for obtaining the topological lines corresponding to free space of the environment. The application of the morphology transformations demonstrated to be a useful method to the creation of topological maps considerably less noise, since it eliminates most of the topological lines generated in consequence of noise in the sensors

No description available.

The aim of this thesis is automatic alignment of head CT scan. Currently, the alignment is performed manually by an expert, however this process is time consuming. Therefore, methods for automatization of this process are being developed. Two algorithms for alignment in axial and coronal plane were designed based on bilateral symmetry of head. Following an algorithm for alignment in sagittal plane which uses CG-TOB reference line for rotation angle detection. Algorithms were implemented in MATLAB and tested and validated using a database of manually annotated head CT scans.

In the past years the so-called body-centered cubic grid (bcc) has been examined and proved to be superior over Cartesian lattices for certain applications. Our work deals with parallel thinning on these bcc grids. We introduce conditions which are sufficient for retaining topology and suggest additional conditions to influence the shape of the resulting skeleton. We further developed an algorithm to extract curve skeletons out of 3d objects in parallel which we also present here. We show in our results that the developed thinning approach on bcc grids is extremely efficient.

This work addresses the end-to-end virtual automation of structural optimization up to the derivation of a parametric geometry model that can be used for application areas such as additive manufacturing or the verification of the structural optimization result with the finite element method. A holistic design in structural optimization can be achieved with the weighted sum method, which can be automatically parameterized with curve skeletonization and cross-section regression to virtually verify the result and control the local size for additive manufacturing. is investigated in general. In this paper, a holistic design is understood as a design that considers various compliances as an objective function. This parameterization uses the automated determination of beam parameters by so-called curve skeletonization with subsequent cross-section shape parameter estimation based on moments of area, especially for multi-objective optimized shapes. An essential contribution is the linking of the parameterization with the results of the structural optimization, e.g., to include properties such as boundary conditions, load conditions, sensitivities or even density variables in the curve skeleton parameterization. The parameterization focuses on guiding the skeletonization based on the information provided by the optimization and the finite element model. In addition, the cross-section detection considers circular, elliptical, and tensor product spline cross-sections that can be applied to various shape descriptors such as convolutional surfaces, subdivision surfaces, or constructive solid geometry. The shape parameters of these cross-sections are estimated using stiffness distributions, moments of area of 2D images, and convolutional neural networks with a tailored loss function to moments of area. Each final geometry is designed by extruding the cross-section along the appropriate curve segment of the beam and joining it to other beams by using only unification operations. The focus of multi-objective structural optimization considering 1D, 2D and 3D elements is on cases that can be modeled using equations by the Poisson equation and linear elasticity. This enables the development of designs in application areas such as thermal conduction, electrostatics, magnetostatics, potential flow, linear elasticity and diffusion, which can be optimized in combination or individually. Due to the simplicity of the cases defined by the Poisson equation, no experts are required, so that many conceptual designs can be generated and reconstructed by ordinary users with little effort. Specifically for 1D elements, a element stiffness matrices for tensor product spline cross-sections are derived, which can be used to optimize a variety of lattice structures and automatically convert them into free-form surfaces. For 2D elements, non-local trigonometric interpolation functions are used, which should significantly increase interpretability of the density distribution. To further improve the optimization, a parameter-free mesh deformation is embedded so that the compliances can be further reduced by locally shifting the node positions. Finally, the proposed end-to-end optimization and parameterization is applied to verify a linear elasto-static optimization result for and to satisfy local size constraint for the manufacturing with selective laser melting of a heat transfer optimization result for a heat sink of a CPU. For the elasto-static case, the parameterization is adjusted until a certain criterion (displacement) is satisfied, while for the heat transfer case, the manufacturing constraints are satisfied by automatically changing the local size with the proposed parameterization. This heat sink is then manufactured without manual adjustment and experimentally validated to limit the temperature of a CPU to a certain level.:TABLE OF CONTENT III I LIST OF ABBREVIATIONS V II LIST OF SYMBOLS V III LIST OF FIGURES XIII IV LIST OF TABLES XVIII 1. INTRODUCTION 1 1.1 RESEARCH DESIGN AND MOTIVATION 6 1.2 RESEARCH THESES AND CHAPTER OVERVIEW 9 2. PRELIMINARIES OF TOPOLOGY OPTIMIZATION 12 2.1 MATERIAL INTERPOLATION 16 2.2 TOPOLOGY OPTIMIZATION WITH PARAMETER-FREE SHAPE OPTIMIZATION 17 2.3 MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION WITH THE WEIGHTED SUM METHOD 18 3. SIMULTANEOUS SIZE, TOPOLOGY AND PARAMETER-FREE SHAPE OPTIMIZATION OF WIREFRAMES WITH B-SPLINE CROSS-SECTIONS 21 3.1 FUNDAMENTALS IN WIREFRAME OPTIMIZATION 22 3.2 SIZE AND TOPOLOGY OPTIMIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 27 3.3 PARAMETER-FREE SHAPE OPTIMIZATION EMBEDDED IN SIZE OPTIMIZATION 32 3.4 WEIGHTED SUM SIZE AND TOPOLOGY OPTIMIZATION 36 3.5 CROSS-SECTION COMPARISON 39 4. NON-LOCAL TRIGONOMETRIC INTERPOLATION IN TOPOLOGY OPTIMIZATION 41 4.1 FUNDAMENTALS IN MATERIAL INTERPOLATIONS 43 4.2 NON-LOCAL TRIGONOMETRIC SHAPE FUNCTIONS 45 4.3 NON-LOCAL PARAMETER-FREE SHAPE OPTIMIZATION WITH TRIGONOMETRIC SHAPE FUNCTIONS 49 4.4 NON-LOCAL AND PARAMETER-FREE MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION 54 5. FUNDAMENTALS IN SKELETON GUIDED SHAPE PARAMETRIZATION IN TOPOLOGY OPTIMIZATION 58 5.1 SKELETONIZATION IN TOPOLOGY OPTIMIZATION 61 5.2 CROSS-SECTION RECOGNITION FOR IMAGES 66 5.3 SUBDIVISION SURFACES 67 5.4 CONVOLUTIONAL SURFACES WITH META BALL KERNEL 71 5.5 CONSTRUCTIVE SOLID GEOMETRY 73 6. CURVE SKELETON GUIDED BEAM PARAMETRIZATION OF TOPOLOGY OPTIMIZATION RESULTS 75 6.1 FUNDAMENTALS IN SKELETON SUPPORTED RECONSTRUCTION 76 6.2 SUBDIVISION SURFACE PARAMETRIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 78 6.3 CURVE SKELETONIZATION TAILORED TO TOPOLOGY OPTIMIZATION WITH PRE-PROCESSING 82 6.4 SURFACE RECONSTRUCTION USING LOCAL STIFFNESS DISTRIBUTION 86 7. CROSS-SECTION SHAPE PARAMETRIZATION FOR PERIODIC B-SPLINES 96 7.1 PRELIMINARIES IN B-SPLINE CONTROL GRID ESTIMATION 97 7.2 CROSS-SECTION EXTRACTION OF 2D IMAGES 101 7.3 TENSOR SPLINE PARAMETRIZATION WITH MOMENTS OF AREA 105 7.4 B-SPLINE PARAMETRIZATION WITH MOMENTS OF AREA GUIDED CONVOLUTIONAL NEURAL NETWORK 110 8. FULLY AUTOMATED COMPLIANCE OPTIMIZATION AND CURVE-SKELETON PARAMETRIZATION FOR A CPU HEAT SINK WITH SIZE CONTROL FOR SLM 115 8.1 AUTOMATED 1D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINED SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 118 8.2 AUTOMATED 2D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINT SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 120 8.3 USING THE HEAT SINK PROTOTYPES COOLING A CPU 123 9. CONCLUSION 127 10. OUTLOOK 131 LITERATURE 133 APPENDIX 147 A PREVIOUS STUDIES 147 B CROSS-SECTION PROPERTIES 149 C CASE STUDIES FOR THE CROSS-SECTION PARAMETRIZATION 155 D EXPERIMENTAL SETUP 158

L'analyse d'images est devenue ces dernières années une discipline de plus en plus riche de l'informatique. La topologie discrète propose un panel d'outils incontournables dans le traitement d'images, notamment grâce à l'outil du squelette, qui permet de simplifier des objets tout en conservant certaines informations intactes. Cette thèse étudie comment certains outils de la topologie discrète, notamment les squelettes, peuvent être utilisés pour le traitement d'images de matériaux.Le squelette d'un objet peut être vu comme une simplification d'un objet, possédant certaines caractéristiques identiques à celles de l'objet original. Il est alors possible d'étudier un squelette et de généraliser certains résultats à l'objet entier. Dans une première partie, nous proposons une nouvelle méthode pour conserver, dans un squelette, certaines caractéristiques géométriques de l'objet original (méthode nécessitant un paramètre de filtrage de la part de l'utilisateur) et obtenir ainsi un squelette possédant la même apparence que l'objet original. La seconde partie propose de ne plus travailler avec des objets constitués de voxels, mais avec des objets constitués de complexes cubiques. Dans ce nouveau cadre, nous proposons de nouveaux algorithmes de squelettisation, dont certains permettent de conserver certaines caractéristiques géométriques de l'objet de départ dans le squelette, de façon automatique (aucun paramètre de filtrage ne doit être donné par l'utilisateur). Nous montrerons ensuite comment un squelette, dans le cadre des complexes cubiques, peut être décomposé en différentes parties. Enfin, nous montrerons nos résultats sur différentes applications, allant de l'étude des matériaux à l'imagerie médicale / These last years, the domain of image analysis has drastically evolved. Digital topology offer a set of tools adapted to image analysis, especially the skeletonization process (also called homotopic thinning) which can simplify input data while keeping specific information untouched. In this thesis, we focus on how digital topology, especially skeletons, can help material image analysis.The goal of a skeletonization process is to remove unnecessary information from an input, and provide a simplified object, called the skeleton, having the same characteristics than the original data. It is then possible to perform some computations on the skeleton and generalise their results to the original data. In the first part of this thesis, we propose some new tools for preserving, during skeletonization, important geometrical features of the original data, and obtain a skeleton with the same visual appearance than the input.In the second part, we present the cubical complex framework, where objects are no more made only of voxels. We propose in this framework new skeletonization algorithms, some of them preserving automatically the visual aspect of the input during the thinning process (no filtering parameter from the user is required). We then show how a skeleton, in the cubical complexes framework, can be decomposed into basic parts, and we show some applications of these algorithms to material image analysis and medical image analysis