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Photorealistic Rendering of 3D Scenes
Vlnas, Michal ; Milet, Tomáš (referee) ; Zemčík, Pavel (advisor)
This thesis proposes a concept of sampling, especially for path tracing like algorithms, for faster convergence of the scene, using a local radiance approximation in the scene with hemispherical harmonics, which allows more effective way of ray casting on the given surface. In the first part, the basics of photorealistic rendering are introduced together with commonly used algorithms for image synthesis. The mathematical apparatus used in this thesis is defined in the second part of the thesis. Subsequently, existing solutions in this area are presented. The following chapter summarizes state-of-the-art methods in this branch. The rest of this thesis is focused on proposal and implementation of already mentioned extension.
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Ray-tracing Using IPP Library
Kukla, Michal ; Havel, Jiří (referee) ; Hradiš, Michal (advisor)
Master thesis is dealing with design and implementation of ray-tracing and path-tracing using IPP library. Theoretical part discusses current trends in acceleration of selected algorithms and also possibilities of parallelization. Design of ray-tracing and path-tracing algorithm and form of parallelization are described in proposal. This part also discusses implementation of adaptive sampling and importance sampling with Monte Carlo method to accelerate path-tracing algorithm. Next part is dealing with particular steps in implementation of selected rendering methods regarding IPP library. Implementation of network interface using Boost library is also discussed. At the end, implemented methods are subjected to performance and quality test. Final product of this thesis is server aplication capable of handling multiple connections which provides visualisation and client application which implements ray-tracing and path-tracing.
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Advanced simulation methods for reliability analysis of structures
Gerasimov, Aleksei ; Lehký, David (referee) ; Vořechovský, Miroslav (advisor)
The thesis apply to reliability problems approach of Voronoi tessellation, typically used in the field of samples designs evaluation and for Monte Carlo samples reweighing. It is shown, this general technique estimation converges to that of Importance Sampling method despite it does not rely on Importance Sampling's auxiliary density. Consequently, reliability analysis could be divided into sampling itself and assessment of simulation results. As an extension of this idea, adaptive statistical sampling using QHull library was attempted.
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Guiding a Path Tracer with Local Radiance Estimates
Berger, Martin ; Wilkie, Alexander (advisor) ; Křivánek, Jaroslav (referee)
Path tracing is a basic, statistically unbiased method for calculating the global illumination in 3D scenes. For practical purposes, the algorithm is too slow, so it is used mainly for theoretical purposes or as a base for more advanced algorithms. This thesis explores the possibility of improving this algorithm by augmenting the sampling part, which computes outgoing directions during ray traversal through the scene. This optimization is accomplished by creating a special data structure in a preprocess step, which describes approximate light distribution in the scene and which then aids the sampling process. The presented algorithm is implemented in the PBRT library.
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Sequential Monte Carlo Methods
Sobková, Eva ; Zikmundová, Markéta (advisor) ; Prokešová, Michaela (referee)
Monte Carlo methods are used for stochastic systems simulations. Sequential Monte Carlo methods take advantage of the fact that observations are coming sequentially. This allows us to refine our estimate sequentially in time We introduce a State Space Model as a Hidden Markov Model. We describe Perfect Monte Carlo Sampling, Importance Sampling, Sequential Importance Sampling and discuss advantages and disadvantages of these methods. This discussion brings us to add a resampling step in Sequential Importance Sampling and introduce Particle Filter and Particle Marginal Metropolis-Hastings algorithm. We choose a Hidden Markov Model used for stochastic volatility modeling and make a simulation study in Wolfram Mathematica, version 8.
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Importance Sampling methods in solving optimization problems
Zavřel, Lukáš ; Kozmík, Václav (advisor) ; Kopa, Miloš (referee)
Present work deals with the portfolio selection problem using mean-risk models where analysed risk measures include variance, VaR and CVaR. The main goal is to approximate solution of optimization problems using simulation techniques like Monte Carlo and Importance Sampling. For both simulation techniques we present a numerical study of their variance and efficiency with respect to optimal solution. For normal distribution with particular expected value and variance the values of parameters for sampling using Importance Sampling method are empirically deduced and they are consequently used for solving a practical problem of choice of optimal portfolio from ten stocks, when their weekly historical prices are available. All optimization problems are solved in Wolfram Mathematica program. Powered by TCPDF (www.tcpdf.org)
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Photorealistic Rendering of 3D Scenes
Vlnas, Michal ; Milet, Tomáš (referee) ; Zemčík, Pavel (advisor)
This thesis proposes a concept of sampling, especially for path tracing like algorithms, for faster convergence of the scene, using a local radiance approximation in the scene with hemispherical harmonics, which allows more effective way of ray casting on the given surface. In the first part, the basics of photorealistic rendering are introduced together with commonly used algorithms for image synthesis. The mathematical apparatus used in this thesis is defined in the second part of the thesis. Subsequently, existing solutions in this area are presented. The following chapter summarizes state-of-the-art methods in this branch. The rest of this thesis is focused on proposal and implementation of already mentioned extension.
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Advanced simulation methods for reliability analysis of structures
Gerasimov, Aleksei ; Lehký, David (referee) ; Vořechovský, Miroslav (advisor)
The thesis apply to reliability problems approach of Voronoi tessellation, typically used in the field of samples designs evaluation and for Monte Carlo samples reweighing. It is shown, this general technique estimation converges to that of Importance Sampling method despite it does not rely on Importance Sampling's auxiliary density. Consequently, reliability analysis could be divided into sampling itself and assessment of simulation results. As an extension of this idea, adaptive statistical sampling using QHull library was attempted.
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Importance Sampling methods in solving optimization problems
Zavřel, Lukáš ; Kozmík, Václav (advisor) ; Kopa, Miloš (referee)
Present work deals with the portfolio selection problem using mean-risk models where analysed risk measures include variance, VaR and CVaR. The main goal is to approximate solution of optimization problems using simulation techniques like Monte Carlo and Importance Sampling. For both simulation techniques we present a numerical study of their variance and efficiency with respect to optimal solution. For normal distribution with particular expected value and variance the values of parameters for sampling using Importance Sampling method are empirically deduced and they are consequently used for solving a practical problem of choice of optimal portfolio from ten stocks, when their weekly historical prices are available. All optimization problems are solved in Wolfram Mathematica program. Powered by TCPDF (www.tcpdf.org)
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Multi-Stage Stochastic Programming with CVaR: Modeling, Algorithms and Robustness
Kozmík, Václav ; Dupačová, Jitka (advisor) ; Morton, David (referee) ; Kaňková, Vlasta (referee)
Multi-Stage Stochastic Programming with CVaR: Modeling, Algorithms and Robustness RNDr. Václav Kozmík Abstract: We formulate a multi-stage stochastic linear program with three different risk measures based on CVaR and discuss their properties, such as time consistency. The stochastic dual dynamic programming algorithm is described and its draw- backs in the risk-averse setting are demonstrated. We present a new approach to evaluating policies in multi-stage risk-averse programs, which aims to elimi- nate the biggest drawback - lack of a reasonable upper bound estimator. Our approach is based on an importance sampling scheme, which is thoroughly ana- lyzed. A general variance reduction scheme for mean-risk sampling with CVaR is provided. In order to evaluate robustness of the presented models we extend con- tamination technique to the case of large-scale programs, where a precise solution cannot be obtained. Our computational results are based on a simple multi-stage asset allocation model and confirm usefulness of the presented procedures, as well as give additional insights into the behavior of more complex models. Keywords: Multi-stage stochastic programming, stochastic dual dynamic programming, im- portance sampling, contamination, CVaR
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