Em Computação Gráfica, campos vetoriais possuem diversas aplicações desde a síntese e mapeamento de texturas à animações de fluidos, produzindo efeitos amplamente utilizados na indústria do entretenimento. Para produzir tais campos, é preferível o uso de ferramentas de design em vez de simulações numéricas não só devido ao menor custo computacional mas, principalmente, por prover liberdade ao artista ao sintetizar o campo de acordo com a sua necessidade. Atualmente, na literatura, existem bons métodos de design de campos vetoriais em superfícies de objetos tridimensionais porém, o design no interior desses objetos ainda é pouco estudado, principalmente quando o campo de interesse possui propriedades específicas. O objetivo deste trabalho é desenvolver uma técnica para sintetizar campos vetoriais, com características do movimento de fluidos incompressíveis, no interior de domínios. Em uma primeira etapa, o método consiste na interpolação dos vetores de controle, com uma certa propriedade desejada, em todo o domínio. Posteriormente, o campo obtido é modificado para respeitar a geometria do contorno. / Vector fields are important to an wide range of applications on the field of Computer Graphics, from the synthesis and mapping of textures to fluid animation, producing effects widely used on the entertainment industry. To produce such fields, design tools are prefered over numerical simulations not only for its lower computational cost, but mainly by providing freedom to the artist in the creation process. Nowadays, good methods of vector field design over surfaces exist in literature, however there is only a few studies on the synthesis of vector fields of the interior of objects and even fewer when specific properties of the field are required. This work presents a technique to synthesize vector fields with properties of imcompressible fluids motion in the interior of objects. On a first step, the method consists in interpolating control vectors with a certain desired property throughout the whole domain and later the resulting field is modified to properly fit the boundary geometry of the object.

This thesis proposes machine learning algorithms for processing geometry by example. Each algorithm takes as input a collection of shapes along with exemplar values of target properties related to shape processing tasks. The goal of the algorithms is to output a function that maps from the shape data to the target properties. The learned functions can be applied to novel input shape data in order to synthesize the target properties with style similar to the training examples. Learning such functions is particularly useful for two different types of geometry processing problems. The first type of problems involves learning functions that map to target properties required for shape interpretation and understanding. The second type of problems involves learning functions that map to geometric attributes of animated shapes required for real-time rendering of dynamic scenes. With respect to the first type of problems involving shape interpretation and understanding, I demonstrate learning for shape segmentation and line illustration. For shape segmentation, the algorithms learn functions of shape data in order to perform segmentation and recognition of parts in 3D meshes simultaneously. This is in contrast to existing mesh segmentation methods that attempt segmentation without recognition based only on low-level geometric cues. The proposed method does not require any manual parameter tuning and achieves significant improvements in results over the state-of-the-art. For line illustration, the algorithms learn functions from shape and shading data to hatching properties, given a single exemplar line illustration of a shape. Learning models of such artistic-based properties is extremely challenging, since hatching exhibits significant complexity as a network of overlapping curves of varying orientation, thickness, density, as well as considerable stylistic variation. In contrast to existing algorithms that are hand-tuned or hand-designed from insight and intuition, the proposed technique offers a largely automated and potentially natural workflow for artists. With respect to the second type of problems involving fast computations of geometric attributes in dynamic scenes, I demonstrate algorithms for learning functions of shape animation parameters that specifically aim at taking advantage of the spatial and temporal coherence in the attribute data. As a result, the learned mappings can be evaluated very efficiently during runtime. This is especially useful when traditional geometric computations are too expensive to re-estimate the shape attributes at each frame. I apply such algorithms to efficiently compute curvature and high-order derivatives of animated surfaces. As a result, curvature-dependent tasks, such as line drawing, which could be previously performed only offline for animated scenes, can now be executed in real-time on modern CPU hardware.

This thesis proposes machine learning algorithms for processing geometry by example. Each algorithm takes as input a collection of shapes along with exemplar values of target properties related to shape processing tasks. The goal of the algorithms is to output a function that maps from the shape data to the target properties. The learned functions can be applied to novel input shape data in order to synthesize the target properties with style similar to the training examples. Learning such functions is particularly useful for two different types of geometry processing problems. The first type of problems involves learning functions that map to target properties required for shape interpretation and understanding. The second type of problems involves learning functions that map to geometric attributes of animated shapes required for real-time rendering of dynamic scenes. With respect to the first type of problems involving shape interpretation and understanding, I demonstrate learning for shape segmentation and line illustration. For shape segmentation, the algorithms learn functions of shape data in order to perform segmentation and recognition of parts in 3D meshes simultaneously. This is in contrast to existing mesh segmentation methods that attempt segmentation without recognition based only on low-level geometric cues. The proposed method does not require any manual parameter tuning and achieves significant improvements in results over the state-of-the-art. For line illustration, the algorithms learn functions from shape and shading data to hatching properties, given a single exemplar line illustration of a shape. Learning models of such artistic-based properties is extremely challenging, since hatching exhibits significant complexity as a network of overlapping curves of varying orientation, thickness, density, as well as considerable stylistic variation. In contrast to existing algorithms that are hand-tuned or hand-designed from insight and intuition, the proposed technique offers a largely automated and potentially natural workflow for artists. With respect to the second type of problems involving fast computations of geometric attributes in dynamic scenes, I demonstrate algorithms for learning functions of shape animation parameters that specifically aim at taking advantage of the spatial and temporal coherence in the attribute data. As a result, the learned mappings can be evaluated very efficiently during runtime. This is especially useful when traditional geometric computations are too expensive to re-estimate the shape attributes at each frame. I apply such algorithms to efficiently compute curvature and high-order derivatives of animated surfaces. As a result, curvature-dependent tasks, such as line drawing, which could be previously performed only offline for animated scenes, can now be executed in real-time on modern CPU hardware.

La modélisation géométrique et la sémantisation de scènes intérieures à partir d'échantillon de points et un sujet de recherche qui prend de plus en plus d'importance. Cependant, le traitement d'un ensemble volumineux de données est rendu difficile d'une part par le nombre élevé d'objets parasitant la scène et d'autre part par divers défauts d'acquisitions comme par exemple des données manquantes ou un échantillonnage de la scène non isotrope. Cette thèse s'intéresse de près à de nouvelles méthodes permettant de modéliser géométriquement un nuage de point non structuré et d’y donner de la sémantique. Dans le chapitre 2, nous présentons deux méthodes permettant de transformer le nuage de points en un ensemble de formes. Nous proposons en premier lieu une méthode d'extraction de lignes qui détecte des segments à partir d'une coupe horizontale du nuage de point initiale. Puis nous introduisons une méthode par croissance de régions qui détecte et renforce progressivement des régularités parmi les formes planaires. Dans la première partie du chapitre 3, nous proposons une méthode basée sur de l'analyse statistique afin de séparer de la structure de la scène les objets la parasitant. Dans la seconde partie, nous présentons une méthode d'apprentissage supervisé permettant de classifier des objets en fonction d'un ensemble de formes planaires. Nous introduisons dans le chapitre 4 une méthode permettant de modéliser géométriquement le volume d'une pièce (sans meubles). Une formulation énergétique est utilisée afin de labelliser les régions d’une partition générée à partir de formes élémentaires comme étant intérieur ou extérieur de manière robuste au bruit et aux données. / Geometric modeling and semantization of indoor scenes from sampled point data is an emerging research topic. Recent advances in acquisition technologies provide highly accurate laser scanners and low-cost handheld RGB-D cameras for real-time acquisition. However, the processing of large data sets is hampered by high amounts of clutter and various defects such as missing data, outliers and anisotropic sampling. This thesis investigates three novel methods for efficient geometric modeling and semantization from unstructured point data: Shape detection, classification and geometric modeling. Chapter 2 introduces two methods for abstracting the input point data with primitive shapes. First, we propose a line extraction method to detect wall segments from a horizontal cross-section of the input point cloud. Second, we introduce a region growing method that progressively detects and reinforces regularities of planar shapes. This method utilizes regularities common to man-made architecture, i.e. coplanarity, parallelism and orthogonality, to reduce complexity and improve data fitting in defect-laden data. Chapter 3 introduces a method based on statistical analysis for separating clutter from structure. We also contribute a supervised machine learning method for object classification based on sets of planar shapes. Chapter 4 introduces a method for 3D geometric modeling of indoor scenes. We first partition the space using primitive shapes detected from permanent structures. An energy formulation is then used to solve an inside/outside labeling of a space partitioning, the latter providing robustness to missing data and outliers.

Em Computação Gráfica, campos vetoriais possuem diversas aplicações desde a síntese e mapeamento de texturas à animações de fluidos, produzindo efeitos amplamente utilizados na indústria do entretenimento. Para produzir tais campos, é preferível o uso de ferramentas de design em vez de simulações numéricas não só devido ao menor custo computacional mas, principalmente, por prover liberdade ao artista ao sintetizar o campo de acordo com a sua necessidade. Atualmente, na literatura, existem bons métodos de design de campos vetoriais em superfícies de objetos tridimensionais porém, o design no interior desses objetos ainda é pouco estudado, principalmente quando o campo de interesse possui propriedades específicas. O objetivo deste trabalho é desenvolver uma técnica para sintetizar campos vetoriais, com características do movimento de fluidos incompressíveis, no interior de domínios. Em uma primeira etapa, o método consiste na interpolação dos vetores de controle, com uma certa propriedade desejada, em todo o domínio. Posteriormente, o campo obtido é modificado para respeitar a geometria do contorno. / Vector fields are important to an wide range of applications on the field of Computer Graphics, from the synthesis and mapping of textures to fluid animation, producing effects widely used on the entertainment industry. To produce such fields, design tools are prefered over numerical simulations not only for its lower computational cost, but mainly by providing freedom to the artist in the creation process. Nowadays, good methods of vector field design over surfaces exist in literature, however there is only a few studies on the synthesis of vector fields of the interior of objects and even fewer when specific properties of the field are required. This work presents a technique to synthesize vector fields with properties of imcompressible fluids motion in the interior of objects. On a first step, the method consists in interpolating control vectors with a certain desired property throughout the whole domain and later the resulting field is modified to properly fit the boundary geometry of the object.

This thesis extends the utility of the Monte Carlo approach to PDE-based methods presented in the paper Monte Carlo Geometry Processing. In particular, we implement this method on the GPU using CUDA, and investigate more viable methods of estimating the source integral when solving Poisson’s equation with intricate source terms. This is the case for a large group of gradient-domain methods in computer graphics, where source terms are represented by discrete volumetric data on regular grids. We develop unbiased source integral estimators like image-based importance sampling (IBIS) and biased estimators like source integral caching (SIC) and evaluate these against existing GPU-accelerated finite difference solvers for gradient-domain applications. By decoupling the source integration step from the WoS-algorithm, we find that the SIC method can improve performance by several orders of magnitude, making it competitive with existing finite difference solvers in many cases. We further investigate the viability of distance fields for accelerated distance queries and find that these can provide significant performance improvements compared to BVHs without meaningfully affecting bias. / <p>Examensarbetet är utfört vid Institutionen för teknik och naturvetenskap (ITN) vid Tekniska fakulteten, Linköpings universitet</p>

Computer Aided Design (CAD) models often need to be processed due to data translation issues and requirements of the downstream applications like computational field simulation, rapid rototyping, computer graphics,computational manufacturing, and real-time rendering before they can be used. Automatic CAD model processing tools can significantly reduce the amount of time and cost associated with the manual processing.In this dissertaion, automated topology generation and feature removal techniques are developed to prepare suitable models with mimunum user interaction. A topology generation algorithm, commonly known as CAD repairing/healing, is presented to detect commonly found geometrical and topological issues like cracks, gaps, overlaps, intersections, T-connections, and no/invalid topology in the model, process them and build correct topological information. The present algorithm is based on the iterative vertex pair contraction and expansion operations called stitching and filling respectively. The algorithm closes small gaps/overlaps via the stitching operation and fills larger gaps by adding faces through the filling operation to process the model accurately. Processed models are guaranteed to be free of intersecting faces or surfaces. Moreover, the topology generation algorithm can process manifold as well as non-manifold models, which makes the procedure more general and flexible. This algorithm uses an automatic and adaptive distance threshold that enhances reliability of the process and preserves small features in the model. In addition, a spatial data structure, the octree, is used for searching and neighbor finding to process large models efficiently. In this way, the combination of generality, accuracy, reliability, and efficiency of this algorithm seems to be a significant improvement over existing techniques. Results are presented showing the effectiveness of the algorithm to process two- and three-dimensional configurations. Feature detection and removal and feature collapse algorithms are presented to detect and remove small features from CAD models automatically. The feature detection and removal algorithm uses a feature size measure based on the surface area and perimeter to detect small features accurately and remove them from the model. Small feature removal may create holes in the model that are post-processed using the stitching and/or filling operations of the topology generation algorithm. The feature collapse algorithm is based on the iterative vertex pair contraction operation, which is a generalization of an edge-collapse operation, to collapse small features. Unlike previous efforts that use edge-collapse as a dimension reduction operator, the feature collapse algorithm can pair up any arbitrary vertices and perform iterative vertex pair contraction to collapse small features as well as glue unconnected regions. Results showing the automatic detection and removal of most commonly found small features like small edges/faces, fillets, chamfers, nuts, and bolts from real mechanical parts are presented.

L'analyse et la reconstruction automatique de scène urbaine 3D est un problème fondamental dans le domaine de la vision par ordinateur et du traitement numérique de la géométrie. Cette thèse présente des méthodologies pour résoudre le problème complexe de la reconstruction d'éléments urbains en 3D à partir de données aériennes Lidar ou bien de maillages générés par imagerie Multi-View Stereo (MVS). Nos approches génèrent une représentation précise et compacte sous la forme d'un maillage 3D comportant une sémantique de l'espace urbain. Deux étapes sont nécessaires ; une identification des différents éléments de la scène urbaine, et une modélisation des éléments sous la forme d'un maillage 3D. Le Chapitre 2 présente deux méthodes de classifications des éléments urbains en classes d'intérêts permettant d'obtenir une compréhension approfondie de la scène urbaine, et d'élaborer différentes stratégies de reconstruction suivant le type d'éléments urbains. Cette idée, consistant à insérer à la fois une information sémantique et géométrique dans les scènes urbaines, est présentée en détails et validée à travers des expériences. Le Chapitre 3 présente une approche pour détecter la 'Végétation' incluses dans des données Lidar reposant sur les processus ponctuels marqués, combinée avec une nouvelle méthode d'optimisation. Le Chapitre 4 décrit à la fois une approche de maillage 3D pour les 'Bâtiments' à partir de données Lidar et de données MVS. Des expériences sur des structures urbaines larges et complexes montrent les bonnes performances de nos systèmes. / Analysis and 3D reconstruction of urban scenes from physical measurements is a fundamental problem in computer vision and geometry processing. Within the last decades, an important demand arises for automatic methods generating urban scenes representations. This thesis investigates the design of pipelines for solving the complex problem of reconstructing 3D urban elements from either aerial Lidar data or Multi-View Stereo (MVS) meshes. Our approaches generate accurate and compact mesh representations enriched with urban-related semantic labeling.In urban scene reconstruction, two important steps are necessary: an identification of the different elements of the scenes, and a representation of these elements with 3D meshes. Chapter 2 presents two classification methods which yield to a segmentation of the scene into semantic classes of interests. The beneath is twofold. First, this brings awareness of the scene for better understanding. Second, deferent reconstruction strategies are adopted for each type of urban elements. Our idea of inserting both semantical and structural information within urban scenes is discussed and validated through experiments. In Chapter 3, a top-down approach to detect 'Vegetation' elements from Lidar data is proposed using Marked Point Processes and a novel optimization method. In Chapter 4, bottom-up approaches are presented reconstructing 'Building' elements from Lidar data and from MVS meshes. Experiments on complex urban structures illustrate the robustness and scalability of our systems.