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.

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

Fluorescence is a common effect in nature, it re-emits light by absorbing photons, caus- ing a wavelength shift from a shorter wavelength to a longer one. In recent years, there is an increased interest in including fluorescence in physically-based rendering. Fluorescence behavior is properly represented as a re-radiation matrix: for a given input wavelength, this matrix indicates how much energy is re-emitted at all other wavelengths. However, such a 2D representation has a significant memory footprint, especially when a scene con- tains a high number of fluorescent objects or fluorescent textures. This thesis proposes using Gaussian Mixture Domain to model re-radiation, which allows us to significantly reduce the memory footprint. Instead of storing the full matrix, we work with a set of Gaussian parameters that also allow direct importance sampling. When accuracy is a concern, one can still use the re-radiation matrix data and just benefit from impor- tance sampling provided by the Gaussian Mixture. Our method is useful when numerous fluorescent materials are present in a scene, particularly for textures with fluorescent components. 1

Title: Adjoint-Driven Importance Sampling in Light Transport Simulation Author: RNDr. Jiří Vorba Department: Department of Software and Computer Science Education Supervisor: doc. Ing. Jaroslav Křivánek, Ph.D., Department of Software and Computer Science Education Abstract: Monte Carlo light transport simulation has recently been adopted by the movie industry as a standard tool for producing photo realistic imagery. As the industry pushes current technologies to the very edge of their possibilities, the unprecedented complexity of rendered scenes has underlined a fundamental weakness of MC light transport simulation: slow convergence in the presence of indirect illumination. The culprit of this poor behaviour is that the sam- pling schemes used in the state-of-the-art MC transport algorithms usually do not adapt to the conditions of rendered scenes. We base our work on the ob- servation that the vast amount of samples needed by these algorithms forms an abundant source of information that can be used to derive superior sampling strategies, tailored for a given scene. In the first part of this thesis, we adapt general machine learning techniques to train directional distributions for biasing scattering directions of camera paths towards incident illumination (radiance). Our approach allows progressive...

Light transport simulation is used in realistic image synthesis to create physically plausible images of virtual scenes. Important components of the scenes are participating media (e.g. air, water, skin etc.). Efficient computation of light transport in participating media robust to their large diversity is still an open problem. We implemented the UPBP algorithm recently developed by Křivánek et al. It addresses the problem by combining several complementary previous methods using multiple importance sampling, and excels at rendering scenes where the previous methods alone fail. The implementation is available online, we focused on its thorough description to facilitate and support further research in this field. Powered by TCPDF (www.tcpdf.org)

Monte Carlo light transport simulation has become a de-facto standard tool for photorealistic rendering. However, the algorithms used by the current rendering systems are often ineffective, especially in scenes featuring light transport due to multiple highly glossy or specular interactions and complex visibility between the camera and light sources. It is therefore desirable to adopt more robust algorithms in practice. Light transport algorithms based on Markov chain Monte Carlo (MCMC) are known to be effective at sampling many different kinds of light transport paths even in the presence of complex visibility. However, the current MCMC algorithms often over-sample some of the paths while under-sampling or completely missing other paths. We attribute this behavior to insufficient global exploration of path space which leads to their unpredictable convergence and causes the occurrence of image artifacts. This in turn prohibits adoption of MCMC algorithms in practice. In this thesis we therefore focus on improving global exploration in MCMC algorithms for light transport simulation. First, we present a new MCMC algorithm that utilizes replica exchange to improve global exploration. To maximize efficiency of replica exchange we introduce tempering of the path space, which allows easier discovery of important...

Photorealistic rendering has a wide variety of applications, and so there are many rendering algorithms and their variations tailored for specific use cases. Even though practically all of them do physically-based simulations of light transport, their results on the same scene are often different - sometimes because of the nature of a given algorithm or in a worse case because of bugs in their implementation. It is difficult to compare these algorithms, especially across different rendering frameworks, because there is not any standardized testing software or dataset available. Therefore, the only way to get an unbiased comparison of algorithms is to create and use your dataset or reimplement the algorithms in one rendering framework of choice, but both solutions can be difficult and time-consuming. We address these problems with our test suite based on a rigorously defined methodology of evaluation of light transport algorithms. We present a scripting framework for automated testing and fast comparison of rendering results and provide a documented set of non-volumetric test scenes for most popular research-oriented render- ing frameworks. Our test suite is easily extensible to support additional renderers and scenes. 1