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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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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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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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