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Les ombres sont un élément important pour la compréhension d'une scène. Grâce à elles, il est possible de résoudre des situations autrement ambigües, notamment concernant les mouvements, ou encore les positions relatives des objets de la scène. Il y a principalement deux types d'ombres: des ombres dures, aux limites très nettes, qui résultent souvent de lumières ponctuelles ou directionnelles; et des ombres douces, plus floues, qui contribuent à l'atmosphère et à la qualité visuelle de la scène. Les ombres douces résultent de grandes sources de lumière, comme des cartes environnementales, et sont difficiles à échantillonner efficacement en temps réel. Lorsque l'interactivité est prioritaire sur la qualité, des méthodes d'approximation peuvent être utilisées pour améliorer le rendu d'une scène à moindre coût en temps de calcul. Nous calculons interactivement les ombres douces résultant de sources de lumière environnementales, pour des scènes composées d'objets en mouvement et d'un champ de hauteurs dynamique. Notre méthode enrichit la méthode d'exponentiation des harmoniques sphériques, jusque là limitée aux bloqueurs sphériques, pour pouvoir traiter des champs de hauteurs. Nous ajoutons également une représentation pour les BRDFs diffuses et glossy. Nous pouvons ainsi combiner les visibilités et BRDFs dans un même espace, afin de calculer efficacement les ombres douces et les réflexions de scènes complexes. Un algorithme hybride, qui associe les visibilités en espace écran et en espace objet, permet de découpler la complexité des ombres de la complexité de la scène. / Shadows provide important visual cues to a viewer about the relative positions of objects in a scene, as well as certain properties of the lighting in an environment, such as orientation, size, and intensity. The importance of shadows in visual simulations is even more striking when any element of an environment, such as characters in a scene or the light sources themselves, are animated over time. The simulation of so-called "hard" shadows from small point or directional light sources is a very mature field in computer graphics, with many concrete and well-established solutions. On the other hand, efficiently approximating the shadowing effects from larger "area" light sources, such as ceiling lights or environment maps captured from the real world, remains an open problem. Indeed, in many applications, the availability of a high-performance solution to this problem trumps the need for an accurate solution. Our work aims to solve the problem of approximating soft shadows interactively, in scenes where the geometric elements and lighting are both allowed to be animated over time. We decompose dynamic scene elements into deformable objects, approximated with a collection of non-deformable animated spheres, and height field geometry. By leveraging a novel spherical harmonic basis-space exponentiation formulation, we are able to very quickly accumulate the shadowing effects from these many dynamic blockers, while also encoding their local reflectance behaviour in a similar reduced basis representation. Our proof-of-concept implementation uses a hybrid, multi-resolution image- and object-space visibility marching algorithm that decouples geometric complexity from radiometric complexity. We demonstrate our method on several scenes with dynamic blockers and complex illumination.

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.

<p>New methods for global shape description of three-dimensional digital objects are presented. The shape of an object is first represented by a digital surface where the faces are either triangles or quadrilaterals. Techniques for computing a high-quality parameterization of the surface are developed and this parameterization is used to approximate the shape of the object. Spherical harmonics are used as basis functions for approximations of the coordinate functions. Information about the global shape is then captured by the coefficients in the spherical harmonics expansions.</p><p>For a starshaped object it is shown how a parameterization can be computed by a projection from its surface onto the unit sphere. An algorithm for computing the position at which the centre of the sphere should be placed, is presented. This algorithm is suited for digital voxel objects. Most of the work is concerned with digital objects whose surfaces are homeomorphic to the sphere. The standard method for computing parameterizations of such surfaces is shown to fail on many objects. This is due to the large distortions of the geometric properties of the surface that often occur with this method. Algorithms to handle this problem are suggested. Non-linear optimization methods are used to find a mapping between a surface and the sphere that minimizes geometric distortion and is useful as a parameterization of the surface. </p><p>The methods can be applied, for example, in medical imaging for shape recognition, detection of shape deformations and shape comparisons of three-dimensional objects.</p>

New methods for global shape description of three-dimensional digital objects are presented. The shape of an object is first represented by a digital surface where the faces are either triangles or quadrilaterals. Techniques for computing a high-quality parameterization of the surface are developed and this parameterization is used to approximate the shape of the object. Spherical harmonics are used as basis functions for approximations of the coordinate functions. Information about the global shape is then captured by the coefficients in the spherical harmonics expansions. For a starshaped object it is shown how a parameterization can be computed by a projection from its surface onto the unit sphere. An algorithm for computing the position at which the centre of the sphere should be placed, is presented. This algorithm is suited for digital voxel objects. Most of the work is concerned with digital objects whose surfaces are homeomorphic to the sphere. The standard method for computing parameterizations of such surfaces is shown to fail on many objects. This is due to the large distortions of the geometric properties of the surface that often occur with this method. Algorithms to handle this problem are suggested. Non-linear optimization methods are used to find a mapping between a surface and the sphere that minimizes geometric distortion and is useful as a parameterization of the surface. The methods can be applied, for example, in medical imaging for shape recognition, detection of shape deformations and shape comparisons of three-dimensional objects.

This thesis examines the advantages to nonlinear least-squares (NLS) fitting of diffusion-weighted MRI data over the commonly used linear least-squares (LLS) approach. A modified fitting algorithm is proposed which accounts for the positive bias experienced in magnitude images at low SNR. For b-values in the clinical range (~1000 s/mm2), the increase in precision of FA and fibre orientation estimates is almost negligible, except at very high anisotropy. The optimal b-value for estimating tensor parameters was slightly higher for NLS. The primary advantage to NLS was improved performance at high b-values, for which complex fibre architectures were more easily resolved. This was demonstrated using a model-selection classifier based on higher-order diffusion models. Using a b-value of 3000 s/mm2 and magnitude-corrected NLS fitting, at least 10% of voxels in the brain exhibited diffusion profiles which could not be represented by the tensor model.

This thesis examines the advantages to nonlinear least-squares (NLS) fitting of diffusion-weighted MRI data over the commonly used linear least-squares (LLS) approach. A modified fitting algorithm is proposed which accounts for the positive bias experienced in magnitude images at low SNR. For b-values in the clinical range (~1000 s/mm2), the increase in precision of FA and fibre orientation estimates is almost negligible, except at very high anisotropy. The optimal b-value for estimating tensor parameters was slightly higher for NLS. The primary advantage to NLS was improved performance at high b-values, for which complex fibre architectures were more easily resolved. This was demonstrated using a model-selection classifier based on higher-order diffusion models. Using a b-value of 3000 s/mm2 and magnitude-corrected NLS fitting, at least 10% of voxels in the brain exhibited diffusion profiles which could not be represented by the tensor model.