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Clifford algebras in colour theory and image analysis
Tichý, Radek ; Vašík, Petr (referee) ; Hrdina, Jaroslav (advisor)
This thesis deals with conformal geometric algebra CGA for colour image processing, particularly with colour segmentation. For this reason it is not sufficient to work in RGB colour space. It is more convenient to use a colour space called CIELAB. CIELAB is endowed by Euclidean metric corresponding with human perception of colours. Afterwards an algorithm for an object detection via CGA based on colour differences is included. The final part of the thesis deals with least squares fitting of sphere to points using CGA. The sphere fitting is then used to adjust colour differences in an image to improve the algorithm for an object detection.
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Rigid body motion from the geometric viewpoint
Karas, Jakub ; Hrdina, Jaroslav (referee) ; Návrat, Aleš (advisor)
Cílem této práce je odvodit rovnice levo-invariantních Hamiltonovských systémů na Lieových grupách. Naše motivace je následující. Pohyb tuhého tělesa v 3D prostoru lze formulovat jako úlohu optimálního řízení na $\R^3$. Pro takto formulovanou úlohu lze využít Pontryaginův princip maxima (PMP). Nicméně pohyb tuhého tělesa lze také chápat jako úlohu na Lieově grupě SE(3). Tato úloha patří do skupiny tzv. levo-invariantních úloh. Jako další zjednodušení volíme také levo-invariantní Hamiltoniány. Běžný postup při studiu takových úloh je, že formulujeme Lagrangián této úlohy, odvodíme Hamiltonián a následně formulujeme Hamiltonovy rovnice. Náš postup je opačný. Odvodíme Hamiltonovy rovnice pro obecnou Lieovu grupu a obecný levo-invariantní Hamiltonián a následně zkoumáme, jaké typy úloh můžeme popsat volbou konkrétní Lieovy grupy a konkrétního Hamiltoniánu. Teoretické výsledky poté využijeme k vytvoření simulačního skriptu pohybu tuhého a pružného tělesa, který využije konformní geometrickou algebru (CGA) jako své výpočetní jádro. CGA je totiž nesmírně silný nástroj pro popis této problematiky, jelikož využitím CGA lze vyvinout kód, který je nezávislý na dimenzi uvažovaného prostoru bez větší námahy.
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The process of city block modeling using a procedural programming language
Koucká, Lucie ; Štych, Přemysl (advisor) ; Brůha, Lukáš (referee)
The master thesis deals with a block subdivision into parcels using procedural modeling. The main goal focuses on improving of the existing method called OBB-based Subdivision that uses auxiliary envelopes of rectangle shape for splitting. It is required to adapt the method to Czech conditions as well. The first part focuses on the analysis of scientific publications, which describes the development and current situation of procedural modeling issues. Then the methodology of suggested algorithm is described that tests a change of the envelope to the trapezium shape, respectively to the quadrangle shape. In conclusion, the proposed algorithms are tested on the real data in CityEngine, which offered the possibility of using procedural approach to automatically generate 3D parcels. The whole process is controlled by the limitations of development plans of the selected urban areas. Powered by TCPDF (www.tcpdf.org)
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Clifford algebras in colour theory and image analysis
Tichý, Radek ; Vašík, Petr (referee) ; Hrdina, Jaroslav (advisor)
This thesis deals with conformal geometric algebra CGA for colour image processing, particularly with colour segmentation. For this reason it is not sufficient to work in RGB colour space. It is more convenient to use a colour space called CIELAB. CIELAB is endowed by Euclidean metric corresponding with human perception of colours. Afterwards an algorithm for an object detection via CGA based on colour differences is included. The final part of the thesis deals with least squares fitting of sphere to points using CGA. The sphere fitting is then used to adjust colour differences in an image to improve the algorithm for an object detection.
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The process of city block modeling using a procedural programming language
Koucká, Lucie ; Štych, Přemysl (advisor) ; Brůha, Lukáš (referee)
The master thesis deals with a block subdivision into parcels using procedural modeling. The main goal focuses on improving of the existing method called OBB-based Subdivision that uses auxiliary envelopes of rectangle shape for splitting. It is required to adapt the method to Czech conditions as well. The first part focuses on the analysis of scientific publications, which describes the development and current situation of procedural modeling issues. Then the methodology of suggested algorithm is described that tests a change of the envelope to the trapezium shape, respectively to the quadrangle shape. In conclusion, the proposed algorithms are tested on the real data in CityEngine, which offered the possibility of using procedural approach to automatically generate 3D parcels. The whole process is controlled by the limitations of development plans of the selected urban areas. Powered by TCPDF (www.tcpdf.org)
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