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Image Inpainting Methods
Kovacs, Jan ; Špiřík, Jan (referee) ; Průša, Zdeněk (advisor)
This thesis deals with an overview of modern Image Inpainting Methods. There are several best-known methods selected and described in the theoretical part of this work. Each of the selected methods is described and evaluated according to the informations available in literature. Among the methods that were selected and subsequently described in this work are Image Inpainting, Fragment-Based Image Completion, Exemplar-Based Image Inpainting, Gradient-Based Image Completion by Solving Poisson Equation and Inpainting by Flexible Haar-Wavelet Shrinkage. The MATLAB implementation of the Framelet-Based Image Inpainting algorithm forms practical part of the thesis. The Framelet transform was created for the purposes of the algorithm. The user interaction provides GUI, which was also implemented in MATLAB. The GUI allows setting input images, algorithm parameters and interaction with the output. The user is always informed about the current state of the computation, and the current result of image completion is shown to him. Moreover, it was created a tool that allows the user to define the areas to be supplemented, using the mouse. Finally, the algorithm performance is evaluated and compared using both Framelet and Contourlet transform.
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Partial Differential Equations Parallel Solutions
Nečasová, Gabriela ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This thesis deals with the topic of partial differential equations parallel solutions. First, it focuses on ordinary differential equations (ODE) and their solution methods using Taylor polynomial. Another part is devoted to partial differential equations (PDE). There are several types of PDE, there are parabolic, hyperbolic and eliptic PDE. There is also explained how to use TKSL system for PDE computing. Another part focuses on solution methods of PDE, these methods are forward, backward and combined methods. There was explained, how to solve these methods in TKSL and Matlab systems. Computing accuracy and time complexity are also discussed. Another part of thesis is PDE parallel solutions. Thanks to the possibility of PDE convertion to ODE systems it is possible to represent each ODE equation by independent operation unit. These units enable parallel computing. The last chapter is devoted to implementation. Application enables generation of ODE systems for TKSL system. These ODE systems represent given hyperbolic PDE.
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Water hammer theory
Šíblová, Kamila ; Habán, Vladimír (referee) ; Fialová, Simona (advisor)
The thesis is a well-arranged text, which deals with the theory, solution and use of water hammer. For solution is used the method of charakteristic, the Lax-Wendroff method and the methods of FTCS. The thesis is a synthesis of all available information about the watter hammer and its use in practice.
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Telegraph Equation
Továrek, Tomáš ; Nechvátal, Luděk (referee) ; Franců, Jan (advisor)
Telegraph equations simulate propagation of the electric signal in an electrical transmission line. This pair of partial diferential equations is derived from physical laws. Behaviour of their solution,. especially effect of impedance match of transmission line on signal distortion is studied. The results are illustrated by numerical experiments.
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Solving of partial differential equations by Fourier method
Barvenčík, Oldřich ; Opluštil, Zdeněk (referee) ; Nechvátal, Luděk (advisor)
Bachelor thesis is a survey text which deals with solving partial deferential equations by Fourier method, i.e. method when we look for a solution of (initial) boundary value problem in form of the infinite Fourier series. The key step is a hypothesis that the solution can be expressed in form with separated variables, therefore the method is sometimes called separation of variables method. The essence can be demonstrated on parabolic and hyperbolic homogeneous problems. In the thesis both types in one (space) dimension are systematically analyzed, at first homogeneous problem, then homogeneous one with non-homogeneous boundary conditions and finally completely non-homogeneous problem.
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