National Repository of Grey Literature 10 records found  Search took 0.01 seconds. 
Geometric algebras and neural networks
Zapletal, Jakub ; Procházková, Jana (referee) ; Vašík, Petr (advisor)
This thesis deals with the use of geometric algebras in the field of neural networks. First, Conformal Geometric Algebra (CGA) and Geometric Algebra for Conics (GAC) and their Python implementations are introduced. The functioning of neural networks is then described, including an explanatory example. Finally, both topics are connected by using the appropriate library in the Python language, and the possibilities of geometric algebras for different models of neural networks are demonstrated on several examples.
Application of Geometric Algebras in Quantum Computing
Michálek, Jan ; Eryganov, Ivan (referee) ; Vašík, Petr (advisor)
Tato práce se zabývá využitím geometrických algeber v oblasti kvantového počítání. Nejprve je definována obecná Cliffordova algebra a následně je odvozena specifická komplexní geometrická algebra, která je vhodná pro reprezentaci kvantových výpočtů. Tento přístup je porovnán s tradiční metodou použití klasické maticové reprezentace. Cílem práce je poskytnout poznatky o potenciálních výhodách použití geometrických algeber pro kvantové výpočty.
Inverse Kinematics of a Serial Robot Arm with a Given Effector Trajectory in Geometric Algebra
Procházka, Ludvík ; Návrat, Aleš (referee) ; Vašík, Petr (advisor)
In this thesis we find not only solution of inverse kinematics problem, but also an introduction to the theory of geometric algebras. The focus of the thesis is the description of conformal geometric algebra CGA, which we use to solve the planar inverse kinematics of the serial robotic arm. Part of the work is an attachment containing algorithms for solving inverse kinematics of the serial robotic arm when specific trajectory is required.
Geometric algebra applications
Machálek, Lukáš ; Návrat, Aleš (referee) ; Vašík, Petr (advisor)
Tato diplomová práce se zabývá využitím geometrické algebry pro kuželosečky (GAC) v autonomní navigaci, prezentované na pohybu robota v trubici. Nejprve jsou zavedeny teoretické pojmy z geometrických algeber. Následně jsou prezentovány kuželosečky v GAC. Dále je provedena implementace enginu, který je schopný provádět základní operace v GAC, včetně zobrazování kuželoseček zadaných v kontextu GAC. Nakonec je ukázán algoritmus, který odhadne osu trubice pomocí bodů, které umístí do prostoru pomocí středů elips, umístěných v obrazu, získaných obrazovým filtrem a fitovacím algoritmem.
Geometric algebra computations
Tomešová, Tereza ; Vechetová, Jana (referee) ; Vašík, Petr (advisor)
This thesis deals with computing in geometric algebra and its illustration in software CLUCalc. Firstly, it introduces fundamental terms and properties of vector space, scalar product and Clifford algebra. Consequently, the term geometric algebra, its products and operations are defined. These terms are illustrated on a specific exampel, i.e. translation and rotation of a sphere along fixed curve in software CLUCalc.
Image corrections by CGA
Machálek, Lukáš ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
This thesis deals with conformal geometric algebra (CGA) in image processing. We focus on correct definitions of notions in geometric algebra, which we use for correcting image defects. First, the concepts of vector space are mentioned, then, the properties of geometric algebra are observed. Consequently, the 3D point is conformaly embedded into CGA, thereafter, another geometric objects are described with their representations in null spaces. In the end, the thesis deals with object transformation and with image defects correction.
Applications of quaternions and Clifford algebras in robotics
Hujňák, Jaroslav ; Hrdina, Jaroslav (referee) ; Návrat, Aleš (advisor)
This bachelor thesis focuses on Clifford algebras and their subalgebras, quaternions and geometric algebra G(3, 1). The thesis describes teoretical basis of Clifford algebras, which is used in chapter dedicated to geometric algebra G(3, 1). Examples of applications geometric algebra G(3, 1) in robotic systems are shown by using transformations and objects of that algebra.
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.
3D scene reconstruction using Clifford algebras
Hrubý, Jan ; Návrat, Aleš (referee) ; Hrdina, Jaroslav (advisor)
Tato diplomová práce má za cíl seznámit čtenáře se stále ještě relativně novou a neznámou oblastí matematiky, s geometrickou algebrou. Nejdříve jsou uvedeny základní definice a poté jsou studovány vlastnosti obecné geometrické algebry. Další velká část textu se věnuje Konformní geometrické algebře, která je v současnosti jedna z nejvíce zkoumaných a aplikovaných geometrických algeber. Jsou popsány její algebraické a geometrické vlastnosti, konkrétně schopnost reprezentovat určité geometrické objekty jako vektory. Taktéž umožňuje počítat jejich průniky a konformní transformace. Další část textu je zaměřena na aplikace Konformní geometrické algebry, nejdříve k popisu kinematiky robotické ruky a poté v binokulárním viděni.
Three-dimensional kinematics of eye movements
Stodola, Marek ; Velan, Petr (referee) ; Hrdina, Jaroslav (advisor)
The goal of this thesis is to describe eye movements and general eye position using apparatus of geometric algebra. The introduction covers the theory about the appropriate geometric algebra, followed by the classifications of the eye movements and the terms used to describe these movements. Following this, the calculations that describe eye position derived from a single observed point are listed, for distant and close points. In addition, the possible eye movements in respect to the axis in which an eye can rotate is described, for any general position. All the calculations are based on Donders' law and Listing's law.