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Free algebraic structures and their application for segmentation of a digital image
Čambalová, Kateřina ; Solovjovs, Sergejs (referee) ; Pavlík, Jan (advisor)
The thesis covers methods for image segmentation. Fuzzy segmentation is based on the thresholding method. This is generalized to accept multiple criteria. The whole process is mathematically based on the free algebra theory. Free distributive lattice is created from poset of elements based on image properties and the lattice members are represented by terms used by the threshoding. Possible segmentation results compose the equivalence classes distribution. The thesis also contains description of resulting algorithms and methods for their optimization. Also the method of area subtracting is introduced.
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Quantum logic and projective spaces
Peksová, Lada ; Krýsl, Svatopluk (advisor) ; Cejnar, Pavel (referee)
A set of statements about the properties of a quantum system is looked at as at a partially ordered set of subspaces of finite or infinite dimensional Hilbert space. The operation of ordering is performed on a set of propositions comparing the truth values of these propositions and on the set of subspaces as the opera- tion of inclusion. Based on the required properties these structures are translated into operations on the lattice. The correspondence with Heisenberg uncertainty principle is shown there. Furthermore, it is shown that the lattices correspond- ing to the subspaces of infinite dimensional Hilbert space are not modular. This property is replaced with weaker property of orthomodularity, when operation of the negation is added. Following the work of G. Birkhoff and J. von Neumann, the structure of quantum logic is looked for in projective spaces, which are in- troduced either arithmetically or axiomatically. The examples of quantum logic, their physical implementation and eventual implementation in projective spaces are analysed. 1
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Free algebraic structures and their application for segmentation of a digital image
Čambalová, Kateřina ; Solovjovs, Sergejs (referee) ; Pavlík, Jan (advisor)
The thesis covers methods for image segmentation. Fuzzy segmentation is based on the thresholding method. This is generalized to accept multiple criteria. The whole process is mathematically based on the free algebra theory. Free distributive lattice is created from poset of elements based on image properties and the lattice members are represented by terms used by the threshoding. Possible segmentation results compose the equivalence classes distribution. The thesis also contains description of resulting algorithms and methods for their optimization. Also the method of area subtracting is introduced.
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Národnostní konflikty a jejich možné řešení na území bývalého Sovětského svazu
Sidko, Evgenia ; Veselý, Zdeněk (advisor) ; Krines, Vlastimil (referee)
Hlavním úkolem této diplomové práce je analyzovat příčiny a vyčlenit jednotlivé typy národnostních konfliktů na území bývalého Sovětského svazu; vytyčit způsoby prevence, prognózování a řešení národnostních konfliktů na příkladech podněsterského, gruzínsko-abchazského a rusko ? čečenského konfliktů. Ve své práce se snažím analyzovat možné způsoby urovnání konfliktů v daných regionech. Teoretická a praktická významnost mé diplomové práce spočívá v možném použití výsledků při rozhodování o nejlepším způsobu urovnání národnostních konfliktů na území bývalého Sovětského svazu.
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