This thesis addresses a number of problems in computer vision, image processing, and geometry processing, and presents novel solutions to these problems. The overarching theme of the techniques presented here is a multi-scale approach, leveraging mathematical tools to represent images and surfaces at different scales, and methods that can be adapted from one type of domain (eg., the plane) to another (eg., the sphere). The main problem addressed in this thesis is known as stereo reconstruction: reconstructing the geometry of a scene or object from two or more images of that scene. We develop novel algorithms to do this, which work for both planar and spherical images. By developing a novel way to formulate the notion of disparity for spherical images, we are able effectively adapt our algorithms from planar to spherical images. Our stereo reconstruction algorithm is based on a novel application of distance transforms to multi-scale matching. We use matching information aggregated over multiple scales, and enforce consistency between these scales using distance transforms. We then show how multiple spherical disparity maps can be efficiently and robustly fused using visibility and other geometric constraints. We then show how the reconstructed point clouds can be used to synthesize a realistic sequence of novel views, images from points of view not captured in the input images, in real-time. Along the way to this result, we address some related problems. For example, multi-scale features can be detected in spherical images by convolving those images with a filterbank, generating an overcomplete spherical wavelet representation of the image from which the multiscale features can be extracted. Convolution of spherical images is much more efficient in the spherical harmonic domain than in the spatial domain. Thus, we develop a GPU implementation for fast spherical harmonic transforms and frequency domain convolutions of spherical images. This tool can also be used to detect multi-scale features on geometric surfaces. When we have a point cloud of a surface of a particular class of object, whether generated by stereo reconstruction or by some other modality, we can use statistics and machine learning to more robustly estimate the surface. If we have at our disposal a database of surfaces of a particular type of object, such as the human face, we can compute statistics over this database to constrain the possible shape a new surface of this type can take. We show how a statistical spherical wavelet shape prior can be used to efficiently and robustly reconstruct a face shape from noisy point cloud data, including stereo data.

Devant les difficultés croissantes liées au coût en développement, en consommation, en surface de silicium, nécessaires aux nouvelles optimisations des architectures monocœur, on assiste au retour en force du parallélisme et des coprocesseurs spécialisés dans les architectures. Cette technique apporte le meilleur compromis entre puissance de calcul élevée et utilisations des ressources. Afin d'exploiter efficacement toutes ces architectures, il faut partitionner le code en tâches, appelées codelet, avant de les distribuer aux différentes unités de calcul. Ce partionnement est complexe et l'espace des solutions est vaste. Il est donc nécessaire de développer des outils d'automatisation efficaces pour le partitionnement du code séquentiel. Les travaux présentés dans cette thèse portent sur l'élaboration d'un tel processus de partitionnement. L'approche d'Astex est basée sur la spéculation, en effet les codelets sont construits à partir des profils d'exécution de l'application. La spéculation permet un grand nombre d'optimisations inexistantes ou impossibles statiquement. L'élaboration, la gestion dynamique et l'usage que l'on peut faire de la spéculation sont un vaste sujet d'étude. La deuxième contribution de cette thèse porte sur l'usage de la spéculation dans l'optimisation des communications entre processeur et coprocesseur et traite en particulier du cas du GPGPU, i.e. l'utilisation d'un processeur graphique comme coprocesseur de calcul intensif.

A parallel GPU compatible Lagrangian mesh free particle solver for multiphase fluid flow based on SPH scheme is developed and used to capture the interface evolution during droplet impact. Surface tension is modeled employing the multiphase scheme of Hu et al. (2006). In order to precisely simulate the wetting phenomena, a method based on the work of Šikalo et al. (2005) is jointly used with the model proposed by Afkhami et al. (2009) to ensure accurate dynamic contact angle calculations. Accurate predictions were obtained for droplet contact angle during spreading. A two-dimensional analytical model is developed as an expansion to the work of Chandra et al. (1991). Results obtain from the solver agrees well to this analytical results. Effects of memory management techniques along with a variety of task assigning algorithms on GPU are studied. GPU speedups of up to 120 times faster than a single processor CPU were obtained.

A parallel GPU compatible Lagrangian mesh free particle solver for multiphase fluid flow based on SPH scheme is developed and used to capture the interface evolution during droplet impact. Surface tension is modeled employing the multiphase scheme of Hu et al. (2006). In order to precisely simulate the wetting phenomena, a method based on the work of Šikalo et al. (2005) is jointly used with the model proposed by Afkhami et al. (2009) to ensure accurate dynamic contact angle calculations. Accurate predictions were obtained for droplet contact angle during spreading. A two-dimensional analytical model is developed as an expansion to the work of Chandra et al. (1991). Results obtain from the solver agrees well to this analytical results. Effects of memory management techniques along with a variety of task assigning algorithms on GPU are studied. GPU speedups of up to 120 times faster than a single processor CPU were obtained.

Since the introduction of programmable Graphics Processing Units (GPUs) and procedural shaders, hardware vendors have each developed their own individual real-time shading language standard. None of these shading languages is fully platform independent. Although this real-time programmable shader technology could be developed into 3D application on a single system, this platform dependent limitation keeps the shader technology away from 3D Internet applications. The primary purpose of this dissertation is to design a framework for translating different shader formats to platform independent shaders and embed them into the eXtensible 3D (X3D) scene for 3D web applications. This framework includes a back-end core shader converter, which translates shaders among different shading languages with a middle XML layer. Also included is a shader library containing a basic set of shaders that developers can load and add shaders to. This framework will then be applied to some applications in Biomolecular Visualization.

Cette thèse apporte des solutions pour exploiter efficacement les nouvelles architectures hautement parallèles, dans le contexte des simulations d'objets déformables en temps réel. Les premières contributions de ce document, se concentrent sur le calcul de la déformation des objets. Pour cela nous proposerons des solutions de parallélisations de solveurs linéaires, couplées à des techniques de preconditionnement asynchrone. Le second ensemble de contributions, repose sur le processeur graphique pour produire une nouvelle méthode de détection des collisions, basée sur le volume d'intersection entre les objets déformables. Enfin les derniers travaux apportent des solutions pour produire une réponse précise aux contacts, et compatible avec le temps réel. Nous aborderons notamment les problèmes liés à la découpe des organes, et à la prise en compte du couplage mécanique entre les contacts. Pour terminer, nous illustrerons nos contributions dans un ensemble d'applications médicales, qui tirent parti des contributions de ce document.

Trends in computer engineering place renewed emphasis on increasing parallelism and heterogeneity. The rise of parallelism adds an additional dimension to the challenge of portability, as different processors support different notions of parallelism, whether vector parallelism executing in a few threads on multicore CPUs or large-scale thread hierarchies on GPUs. Thus, software experiences obstacles to portability and efficient execution beyond differences in instruction sets; rather, the underlying execution models of radically different architectures may not be compatible. Dynamic compilation applied to data-parallel heterogeneous architectures presents an abstraction layer decoupling program representations from optimized binaries, thus enabling portability without encumbering performance. This dissertation proposes several techniques that extend dynamic compilation to data-parallel execution models. These contributions include: - characterization of data-parallel workloads - machine-independent application metrics - framework for performance modeling and prediction - execution model translation for vector processors - region-based compilation and scheduling We evaluate these claims via the development of a novel dynamic compilation framework, GPU Ocelot, with which we execute real-world workloads from GPU computing. This enables the execution of GPU computing workloads to run efficiently on multicore CPUs, GPUs, and a functional simulator. We show data-parallel workloads exhibit performance scaling, take advantage of vector instruction set extensions, and effectively exploit data locality via scheduling which attempts to maximize control locality.

Dans cette thèse, nous montrons que les optimisations source-à-source sont un moyen efficace pour générer des programmes irréguliers ou parallèles performants à partir d'une implémentation. Après avoir présenté l'évolution des architectures des processeurs, nous proposons deux méthodes distinctes. La première pour extraire des codelets d'un programme irréguliers, les optimiser et prédire les performances du programme modifié. L'autre pour limiter l'impact des problèmes d'alignements dus à la vectorisation ou aux conflits de bancs. Nous présentons aussi différentes techniques de parallélisation, l'une générant des codelets parallèles, l'autre ordonnançant un graphe de taches sur un système hétérogène.

En aquesta tesi es solucionen problemes de visibilitat i proximitat sobre superfícies triangulades considerant elements generalitzats. Com a elements generalitzats considerem:punts, segments, poligonals i polígons. Les estrategies que proposem utilitzen algoritmesde geometria computacional i hardware gràfic. Comencem tractant els problemes de visibilitat sobre models de terrenys triangulats considerant un conjunt d'elements de visió generalitzats. Es presenten dos mètodes per obtenir, de forma aproximada, mapes de multi-visibilitat. Un mapa de multi-visibilitat és la subdivisió del domini del terreny que codifica la visibilitat d'acord amb diferents criteris. El primer mètode, de difícil implementació, utilitza informació de visibilitat exacte per reconstruir de forma aproximada el mapa de multi-visibilitat. El segon, que va acompanyat de resultats d'implementació, obté informació de visibilitat aproximada percalcular i visualitzar mapes de multi-visibilitat discrets mitjançant hardware gràfic. Coma aplicacions es resolen problemes de multi-visibilitat entre regions i es responen preguntessobre la multi-visibilitat d'un punt o d'una regió. A continuació tractem els problemes de proximitat sobre superfícies polièdriques triangulades considerant seus generalitzades. Es presenten dos mètodes, amb resultats d'implementació, per calcular distàncies des de seus generalitzades sobre superfícies polièdriques on hi poden haver obstacles generalitzats. El primer mètode calcula, de forma exacte, les distàncies definides pels camins més curts des de les seus als punts del poliedre. El segon mètode calcula, de forma aproximada, distàncies considerant els camins més curts sobre superfícies polièdriques amb pesos. Com a aplicacions, es calculen diagrames de Voronoi d'ordre k, i es resolen, de forma aproximada, alguns problemes de localització de serveis. També es proporciona un estudi teòric sobre la complexitat dels diagrames de Voronoi d'ordre k d'un conjunt de seus generalitzades en un poliedre sense pesos. / In this thesis, we solve visibility and proximity problems on triangulated surfaces concerning generalized elements. As generalized elements, we consider: points, segments, polygonal chains and polygonal regions. The proposed strategies use algorithms of Computational Geometry and Graphics Hardware. We start by studying multi-visibility problems on triangulated terrain models concerning a set of generalized view elements. We present two methods to obtain approximate multi-visibility maps. A multi-visibility map is a subdivision of the terrain domain encoding visibility according to different criteria. The first method, of complex implementation, uses exactly computed visibility information to approximately reconstruct the unknown multi-visibility map. The second, from which implementation results are provided, uses approximate visibility information to compute and visualize discrete multi-visibility maps by exploiting graphics hardware capabilities. As applications, we compute multi-visibility maps, solve inter-region multi-visibility problems and approximately answer point and polygonal region multi-visibility queries. Next, we tackle proximity problems on triangulated polyhedral surfaces, where generalized obstacles are allowed, considering generalized sources. We present two methods, with implementation results, to compute distances on polyhedral surfaces from a generalized source. The first method computes exact shortest path distances from generalized sources. The second provides approximate weighted shortest path distances from generalized sites on weighted polyhedral surfaces. Both methods are posteriorly extended to handle the multiple-site problem where the corresponding distance field is obtained. As applications, we compute discrete order-k Voronoi diagrams and approximately solve some facility location problems. We also provide a theoretical study on the order-k Voronoi diagram complexity of a set of generalized sources for the non-weighted case.

Aquesta tesi presenta un nou mètode pel disseny invers de reflectors. Ens hem centrat en tres temes principals: l’ús de fonts de llum reals i complexes, la definició d’un algoritme ràpid pel càlcul de la il•luminació del reflector, i la definició d’un algoritme d’optimització per trobar més eficientment el reflector desitjat. Les fonts de llum estan representades per models near-field, que es comprimeixen amb un error molt petit, fins i tot per fonts de llum amb milions de raigs i objectes a il•luminar molt propers. Llavors proposem un mètode ràpid per obtenir la distribució de la il•luminació d’un reflector i la seva comparació amb la il•luminació desitjada, i que treballa completament en la GPU. Finalment, proposem un nou mètode d’optimització global que permet trobar la solució en menys passos que molts altres mètodes d’optimització clàssics, i alhora evitant mínims locals. / This thesis presents new methods for the inverse reflector design problem. We have focused on three main topics: the use of real and complex light sources, the definition of a fast lighting simulation algorithm to compute the reflector lighting, and the definition of an optimization algorithm to more efficiently find the desired reflector. The light sources are represented by near-field datasets, that are compressed with a low error, even with millions of rays and for very close objects. Then, we propose a fast method to obtain the outgoing light distribution of a reflector and the comparison with the desired one, working completely in the GPU. Finally, a new global optimization method is proposed to search the solution in less steps than most other classic optimization methods, also avoiding local minima.