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Optical Tomography is a medical imaging modality that can be used to non- invasively image functional changes within the body. As near-infrared light is highly scattered by biological tissue, the process of image reconstruction is ill-posed and, in general is also under-determined. As such, model based iterative image reconstruction methods are used. These methods require an accurate model of light propagation through tissue, also known as the forward model. The diffusion approximation (DA) to the radiative transport equation is one of the most widely used forward models. It is based on the assumption that scattering events dominate over absorption events resulting in a diffuse light distribution. This is valid in cases with low absorption coefficients or large geometries (greater than a few scattering lengths). In many cases, however, such as in small animal imaging where the source-detector separation is small, this assumption is not valid and so a higher-ordered approximation is required. In this thesis, a three-dimensional frequency domain forward model based on the simplified spherical harmonics (SPN) approximation to the radiative transport equation is introduced. By comparison with a Monte- Carlo model, the SPN approximation is shown to be more accurate than the DA, especially in regions near to the sources and detectors and the increase in accuracy is greater in cases with stronger absorption. This is particularly important for bioluminescent imaging of small animals which involve both small geometries and strong absorption. Due to the asymptotic nature of the 3 SPN approximation, the highest ordered model was not necessarily the most accurate, but all models with N>1 were more accurate than the DA. The SPN based forward model has also been implemented into an image reconstruction algorithm. Despite the fact that the SPN approximation does not combine the scattering coefficient and anisotropy factor into a single variable, as is the case in the DA, it was found that it is not possible to reconstruct them uniquely. The SPN based models were shown to be able to reconstruct optical maps with greater accuracy than the DA. However, due to the increased number of unknowns to be recovered, the SP7 based reconstructed images contained significant artefact and cross-talk. Finally, a SPN-Diffusion hybrid model was developed in which the SPN model was used in the regions near to the source and the DA elsewhere. This model provides the increase of accuracy of the SPN models in the regions where the DA is insufficient, whilst retaining the computational efficiency of the DA. It was shown that the hybrid model leads to increased accuracy not only in the regions solved using the SPN model, but also in the DA based regions where as in a pure DA model, the errors near the source were propagated throughout the domain. It is also shown that the hybrid model can be solved in half the time of the full SPN model.

Optical coherence tomography (OCT) imaging is used in an increasing number of biomedical and industrial applications. A massively parallel simulator of OCT of inhomogeneous turbid media, e.g., biological tissue, could be used as a practical tool to expedite and expand the study of the physical phenomena involving such imaging technique, as well as, to design OCT systems with enhanced performance. Our work presents the open-source implementation of this massively parallel simulator of OCT to satisfy the ever-increasing need for prompt computation of OCT signals with accuracy and flexibility. Our Monte Carlo-based simulator uses graphic processing units (GPUs) to accelerate the intensive computation of processing tens of millions of photon packets undergoing a random walk through a sample. It provides computation of both Class I diffusive reflectance due to ballistic and quasi-ballistic scattered photons and Class II diffusive reflectance due to multiple scattered photons. Our implementation was tested by comparing results with previously validated OCT simulators in multilayered and inhomogeneous (arbitrary spatial distributions) turbid media configurations. It models the objects as a tetrahedron-based mesh and implements and advanced importance sampling technique. Our massively parallel simulator of OCT speeds up the simulation of OCT signals by a factor of 40 times when compared to it central processing unit (CPU)-based sequential implementation.

This dissertation addresses the problem of inferring scene depth information from a collection of calibrated images taken from different viewpoints via stereo matching. Although it has been heavily investigated for decades, depth from stereo remains a long-standing challenge and popular research topic for several reasons. First of all, in order to be of practical use for many real-time applications such as autonomous driving, accurate depth estimation in real-time is of great importance and one of the core challenges in stereo. Second, for applications such as 3D reconstruction and view synthesis, high-quality depth estimation is crucial to achieve photo realistic results. However, due to the matching ambiguities, accurate dense depth estimates are difficult to achieve. Last but not least, most stereo algorithms rely on identification of corresponding points among images and only work effectively when scenes are Lambertian. For non-Lambertian surfaces, the "brightness constancy" assumption is no longer valid. This dissertation contributes three novel stereo algorithms that are motivated by the specific requirements and limitations imposed by different applications. In addressing high speed depth estimation from images, we present a stereo algorithm that achieves high quality results while maintaining real-time performance. We introduce an adaptive aggregation step in a dynamic-programming framework. Matching costs are aggregated in the vertical direction using a computationally expensive weighting scheme based on color and distance proximity. We utilize the vector processing capability and parallelism in commodity graphics hardware to speed up this process over two orders of magnitude. In addressing high accuracy depth estimation, we present a stereo model that makes use of constraints from points with known depths - the Ground Control Points (GCPs) as referred to in stereo literature. Our formulation explicitly models the influences of GCPs in a Markov Random Field. A novel regularization prior is naturally integrated into a global inference framework in a principled way using the Bayes rule. Our probabilistic framework allows GCPs to be obtained from various modalities and provides a natural way to integrate information from various sensors. In addressing non-Lambertian reflectance, we introduce a new invariant for stereo correspondence which allows completely arbitrary scene reflectance (bidirectional reflectance distribution functions - BRDFs). This invariant can be used to formulate a rank constraint on stereo matching when the scene is observed by several lighting configurations in which only the lighting intensity varies.

Pour construire le lien entre l'organisation structurale des milieux dispersés concentrés et leurs propriétés mécaniques, il est nécessaire de pourvoir identifier leur structure à l'échelle microscopique. En particulier, il faut être capable mesurer la taille des particules ou des amas de particules, leur concentration et les éventuelles anisotropies liées à une déformation ou une orientation (globale ou partielle) dans le cas de particules anisotropes (fibres par exemple) ou déformables (émulsions, globules rouges,...). La difficulté majeure est que ces systèmes composés de particules micrométriques sont généralement opaques à la lumière visible (produits agroalimentaires tels que les laitages, fluides biologiques tels que le sang, matériaux liés au bâtiment tels que les ciments, les argiles ou les peintures,...). Nous avons ainsi mis au point une technique optique basée sur la diffusion multiple de la lumière. Dans le cadre de cette thèse, nous nous intéressons plus particulièrement à la caractérisation des milieux constitués d'objets anisotropes. Sous l'action d'un champ de cisaillement, on observe une orientation privilégiée ou une déformation globale des particules. L'objectif de cette thèse est donc à la fois d'étudier les mécanismes qui sont à l'origine de la déformation et/ou l'orientation des particules et également de mesurer ces anisotropies à l'échelle microscopique. On s'appuie pour mener cette étude sur un dispositif développé au laboratoire basé sur le transport incohérent de lumière couplé à un rhéomètre. Il s'agit d'un dispositif constitué d'une source laser focalisée à la surface d'un échantillon et d'une caméra CCD permettant l'acquisition d'une image rétrodiffusée loin du point d'impacte du laser. Parallèlement, une base de données de simulation de Monte Carlo est en cours de réalisation permettant par analyse des images rétrodiffusées anisotropes, de remonter à l'information sur l'anisotropie réelle des particules (facteur de forme) leur champ d'orientation (paramètre d'ordre). En effet, en confrontant les données expérimentales aux données numériques, nous sommes en mesure de déterminer le taux d'orientation moyen de particules très anisotropes ou de caractériser la déformation des particules. Une application à la déformation des rouges sous cisaillement pour du sang en concentration physiologique (40 à 50% en volume) sera présentée. D'autres applications, notamment à l'endommagement des plastiques et à l'orientation de suspensions de fibres seront discutées / To build the link between the structural organization between concentrated dispersions and their mechanical properties, you have to be able to identify their microscopic structure. In particular, for anisotropic particles (fibbers for example) or deformable particles (emulsions, red blood cells...), the knowledge of the particle size, the concentration, the deformation or the orientation of particles (partial or global) are very important. Most of concentrated dispersions are generally opaque to visible light (biological fluids as blood, clays...). An optical diffusing method based on multiple diffusion light has been developed in the laboratory to study this kind of materials. In this thesis, we are interested in the general problem of characterizing concentrated dispersions with anisotropic objects. Under shear rate, a preferential orientation or a global deformation of particles has been observed. The objective of this thesis is to study the mechanisms which involve deformation and/or orientation of anisotropic particles. An experimental device based on the incoherent light transport has been developed at the laboratory in order to determine the orientation or the deformation. The experimental device is composed of a focused laser diode and a CCD camera to acquire the backscattered images. A data base of Monte Carlo simulation has been created in order to get the form factor or the orientation of particles by analyse of anisotropic backscattered images. By comparing the numerical data with the experimental data, we are able to determine the average rate of orientated particles. Thanks to this optical diffusing method, the deformation of red blood cells in physiological concentration (40 to 50% volume fraction) and the orientation of fibbers dispersion has been study

Light transport simulation aims at the numerical computation of the propagation of visible electromagnetic energy in macroscopic environments. In this thesis, we develop the foundations for a modern theory of light transport simulation, unveiling the geometric structure of the continuous theory and providing a formulation of computational techniques that furnishes remarkably efficacy with only local information. Utilizing recent results from various communities, we develop the physical and mathematical structure of light transport from Maxwell's equations by studying a lifted representation of electromagnetic theory on the cotangent bundle. At the short wavelength limit, this yields a Hamiltonian description on six-dimensional phase space, with the classical formulation over the space of "positions and directions" resulting from a reduction to the five-dimensional cosphere bundle. We establish the connection between light transport and geometrical optics by a non-canonical Legendre transform, and we derive classical concepts from radiometry, such as radiance and irradiance, by considering measurements of the light energy density. We also show that in idealized environments light transport is a Lie-Poisson system for the group of symplectic diffeomorphisms, unveiling a tantalizing similarity between light transport and fluid dynamics. Using Stone's theorem, we also derive a functional analytic description of light transport. This bridges the gap to existing formulations in the literature and naturally leads to computational questions. We then address one of the central challenges for light transport simulation in everyday environments with scattering surfaces: how are efficient computations possible when the light energy density can only be evaluated pointwise? Using biorthogonal and possibly overcomplete bases formed by reproducing kernel functions, we develop a comprehensive theory for computational techniques that are restricted to pointwise information, subsuming for example sampling theorems, interpolation formulas, quadrature rules, density estimation schemes, and Monte Carlo integration. The use of overcomplete representations makes us thereby robust to imperfect information, as is often unavoidable in practical applications, and numerical optimization of the sampling locations leads to close to optimal techniques, providing performance which considerably improves over the state of the art in the literature.

Light transport simulation aims at the numerical computation of the propagation of visible electromagnetic energy in macroscopic environments. In this thesis, we develop the foundations for a modern theory of light transport simulation, unveiling the geometric structure of the continuous theory and providing a formulation of computational techniques that furnishes remarkably efficacy with only local information. Utilizing recent results from various communities, we develop the physical and mathematical structure of light transport from Maxwell's equations by studying a lifted representation of electromagnetic theory on the cotangent bundle. At the short wavelength limit, this yields a Hamiltonian description on six-dimensional phase space, with the classical formulation over the space of "positions and directions" resulting from a reduction to the five-dimensional cosphere bundle. We establish the connection between light transport and geometrical optics by a non-canonical Legendre transform, and we derive classical concepts from radiometry, such as radiance and irradiance, by considering measurements of the light energy density. We also show that in idealized environments light transport is a Lie-Poisson system for the group of symplectic diffeomorphisms, unveiling a tantalizing similarity between light transport and fluid dynamics. Using Stone's theorem, we also derive a functional analytic description of light transport. This bridges the gap to existing formulations in the literature and naturally leads to computational questions. We then address one of the central challenges for light transport simulation in everyday environments with scattering surfaces: how are efficient computations possible when the light energy density can only be evaluated pointwise? Using biorthogonal and possibly overcomplete bases formed by reproducing kernel functions, we develop a comprehensive theory for computational techniques that are restricted to pointwise information, subsuming for example sampling theorems, interpolation formulas, quadrature rules, density estimation schemes, and Monte Carlo integration. The use of overcomplete representations makes us thereby robust to imperfect information, as is often unavoidable in practical applications, and numerical optimization of the sampling locations leads to close to optimal techniques, providing performance which considerably improves over the state of the art in the literature.

The development of predictive appearance models for organic tissues is a challenging task due to the inherent complexity of these materials. In this thesis, we closely examine the biophysical processes responsible for the appearance attributes of whole blood, one the most fundamental of these materials. We describe a new appearance model that simulates the mechanisms of light propagation and absorption within the cellular and fluid portions of this specialized tissue. The proposed model employs a comprehensive, and yet flexible first principles approach based on the morphological, optical and biochemical properties of blood cells. This approach allows for environment driven changes in the cells' anatomy and orientation to be appropriately included into the light transport simulations. The correctness and predictive capabilities of the proposed model are quantitatively and qualitatively evaluated through comparisons of modeled results with actual measured data and experimental observations reported in the scientific literature. Its incorporation into rendering systems is illustrated through images of blood samples depicting appearance variations controlled by physiologically meaningful parameters. Besides the contributions to the modeling of material appearance, the research presented in this thesis is also expected to have applications in a wide range of biomedical areas, from optical diagnostics to the visualization and noninvasive imaging of blood-perfused tissues.

The development of predictive appearance models for organic tissues is a challenging task due to the inherent complexity of these materials. In this thesis, we closely examine the biophysical processes responsible for the appearance attributes of whole blood, one the most fundamental of these materials. We describe a new appearance model that simulates the mechanisms of light propagation and absorption within the cellular and fluid portions of this specialized tissue. The proposed model employs a comprehensive, and yet flexible first principles approach based on the morphological, optical and biochemical properties of blood cells. This approach allows for environment driven changes in the cells' anatomy and orientation to be appropriately included into the light transport simulations. The correctness and predictive capabilities of the proposed model are quantitatively and qualitatively evaluated through comparisons of modeled results with actual measured data and experimental observations reported in the scientific literature. Its incorporation into rendering systems is illustrated through images of blood samples depicting appearance variations controlled by physiologically meaningful parameters. Besides the contributions to the modeling of material appearance, the research presented in this thesis is also expected to have applications in a wide range of biomedical areas, from optical diagnostics to the visualization and noninvasive imaging of blood-perfused tissues.

Realistic Image synthesis, usually, requires long computations and the simulation of the light interacting with a virtual scene. One of the most computationally intensive simulation in this area is the visualization of solid participating media. This media can describe many different types of object with the same physical parameters (e.g. marble, air, fire, skin, wax ...). Simulating the light interacting with it requires the computation of many independent photons interactions inside the medium. However, those interactions can be computed in parallel, using the power of modern Graphic Processor Unit, or GPU, computing. This work present an overview over different methodologies, that can affect the performance of this type of simulations on the GPU. Different existing ideas are analyzed, compared and modified with the scope of speeding up the computation respect to the classic CPU implementation. 1