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3D scanner for educational purposes
Romanovský, Jiří ; Navrátil, Robert (referee) ; Koutecký, Tomáš (advisor)
This diploma thesis deals with the design of a 3D optical scanner using the structured light projection method. The aim of this thesis is to demonstrate the principles and processes of 3D scanning by using the DLP LightCrafter projector and the ImagingSource camera. The individual stages of the measurement process will be implemented to the Matlab software environment to describe the various principles and methods which can be used for digitizing the objects.
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Optimizing the calibration of the cameras of photogrammetric system designed for the measurement of rotationally symmetric forgings
Hurník, Jakub ; Navrátil, Robert (referee) ; Zatočilová, Aneta (advisor)
At present, there are only a few systems in the world, that allow measurement of the dimensional accuracy of hot forgings directly in the manufacturing process. This work deals with the development of the calibration method of the cameras for the developed photogrammetric system, intended for the mentioned purposes. The conditions of measurement are very specific - high temperature and large dimensions of measured semi-finished products, environment of heavy industry. Employed methods are chosen with the emphasis on reliability of the system, taking into account the demanding conditions in the industrial premises. Calibration is designed for a large field of view, utilizing coded reference points in a scene with known spatial coordinates. The result of the work is the calibration software created in the MATLAB environment.
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Lossless Light Field Compression
Navrátil, Robert ; Šolony, Marek (referee) ; Bařina, David (advisor)
This thesis is focused on lossless light-field images compression, where it could be viable to extend common predictors into more dimensions. First chapter is regarding to essential theory about light-field images and 4D light-field, which is followed by description of every predictor and coder. With this is connected description of used compression pipeline. Last chapters contains description of solution and differences between every predictor result and theirs dimensional variant. At the end the results are compared with PNG. The result is that some 4D variants of implemented predictors have better compression rate than PNG.
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On Market Efficiency, Optimal Distributional Trading Gain, and Utility Maximization
Navrátil, Robert ; Večeř, Jan (advisor)
On Market Efficiency, Optimal Distributional Trading Gain, and Utility Maximization Robert Navr'atil The aim of this thesis is multifold. First, using results from the optimal distributional trading gain problem, we determine a utility-maximizing portfolio that optimizes the benefit an agent may receive by trading the difference between his perceived future distribution of a security price and the risk-neutral density provided by the corresponding option market. Moreover, we show how one can fit the risk-neutral density directly from option market data using the SVI parameterization. We use integer programming with kernel search heuristics to statically replicate the optimal payoff. Second, we show that the United States equity market was inefficient during the weeks following the initiation of the COVID-19 pandemic. This is demonstrated by showing that utility-maximizing agents over the period ranging from mid-February to late March 2020 could generate statistically significant profits by utilizing historical price and virus- related data to forecast future equity ETF returns. Finally, we focus on the passport option. We present a version of insurance of a traded account that symmetrically treats both of its underlying assets. In our approach, we impose a natural symmetric limit in which the agent can...
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On Market Efficiency, Optimal Distributional Trading Gain, and Utility Maximization
Navrátil, Robert ; Večeř, Jan (advisor) ; Witzany, Jiří (referee) ; Pospíšil, Jan (referee)
On Market Efficiency, Optimal Distributional Trading Gain, and Utility Maximization Robert Navr'atil The aim of this thesis is multifold. First, using results from the optimal distributional trading gain problem, we determine a utility-maximizing portfolio that optimizes the benefit an agent may receive by trading the difference between his perceived future distribution of a security price and the risk-neutral density provided by the corresponding option market. Moreover, we show how one can fit the risk-neutral density directly from option market data using the SVI parameterization. We use integer programming with kernel search heuristics to statically replicate the optimal payoff. Second, we show that the United States equity market was inefficient during the weeks following the initiation of the COVID-19 pandemic. This is demonstrated by showing that utility-maximizing agents over the period ranging from mid-February to late March 2020 could generate statistically significant profits by utilizing historical price and virus- related data to forecast future equity ETF returns. Finally, we focus on the passport option. We present a version of insurance of a traded account that symmetrically treats both of its underlying assets. In our approach, we impose a natural symmetric limit in which the agent can...
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Lossless Light Field Compression
Navrátil, Robert ; Šolony, Marek (referee) ; Bařina, David (advisor)
This thesis is focused on lossless light-field images compression, where it could be viable to extend common predictors into more dimensions. First chapter is regarding to essential theory about light-field images and 4D light-field, which is followed by description of every predictor and coder. With this is connected description of used compression pipeline. Last chapters contains description of solution and differences between every predictor result and theirs dimensional variant. At the end the results are compared with PNG. The result is that some 4D variants of implemented predictors have better compression rate than PNG.
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Portfolio Management with Multiple Benchmarks
Navrátil, Robert ; Večeř, Jan (advisor) ; Pešta, Michal (referee)
Portfolio Management with Multiple Benchmarks Bc. Robert Navrátil Abstract: In this thesis, we study a maximal volatility portfolio that treats all assets in a symmetric way and related option contract. To preserve symmetry we need numeraire that treats all assets symmetrically. We choose market index with equal weights. In case of two assets we focus on a variation of a passport option on the portfolio. The optimal strategy for the investor is the mentioned maximal volatility portfolio. We extend the known optimal strategy for the option to a richer class of convex payoff functions. We also show a modification of the optimal strategy for maximizing the probability of ending above or at a desired level. We later extend the symmetric market model to case of three assets, which can be even further extended to an arbitrary number of assets. The three asset model requires more parameters than are observable from the data, however we show indistinguishably of the model on the choice of parameters under very natural conditions. Both numerical simulations and an application on real data is provided. 1
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Girsanov Theorem
Navrátil, Robert ; Šnupárková, Jana (advisor) ; Maslowski, Bohdan (referee)
Girsanov Theorem Bachelor's thesis - Robert Navrátil Abstract Modern theory of probability and financial mathematics require the theory of stochastic calculus. Its foundations contain Wiener process (Brownian motion) and the integral of stochastic process with respect to another stochastic process. This thesis deals with building the mathematical theory needed to construct the stochastic integral, with the construction itself, the Girsanov Theorem and its applications. The Girsanov Theorem uses equivalent probability measure to transform Wiener process with drift to Wiener process without drift. Using the Girsanov Theorem, we change our measure to the equivalent risk neutral measure and we deduce Black-Scholes formula which estimates the prize of European call option with underlying stock asset. The stock prize is modelled using the geometric Brownian motion. Finally, we demonstrate, on real life data, how this model works and what are its outcomes. 1
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Optimizing the calibration of the cameras of photogrammetric system designed for the measurement of rotationally symmetric forgings
Hurník, Jakub ; Navrátil, Robert (referee) ; Zatočilová, Aneta (advisor)
At present, there are only a few systems in the world, that allow measurement of the dimensional accuracy of hot forgings directly in the manufacturing process. This work deals with the development of the calibration method of the cameras for the developed photogrammetric system, intended for the mentioned purposes. The conditions of measurement are very specific - high temperature and large dimensions of measured semi-finished products, environment of heavy industry. Employed methods are chosen with the emphasis on reliability of the system, taking into account the demanding conditions in the industrial premises. Calibration is designed for a large field of view, utilizing coded reference points in a scene with known spatial coordinates. The result of the work is the calibration software created in the MATLAB environment.
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3D scanner for educational purposes
Romanovský, Jiří ; Navrátil, Robert (referee) ; Koutecký, Tomáš (advisor)
This diploma thesis deals with the design of a 3D optical scanner using the structured light projection method. The aim of this thesis is to demonstrate the principles and processes of 3D scanning by using the DLP LightCrafter projector and the ImagingSource camera. The individual stages of the measurement process will be implemented to the Matlab software environment to describe the various principles and methods which can be used for digitizing the objects.
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