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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.
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Movement Identification in the Space
Šolony, Marek ; Beran, Vítězslav (referee) ; Potúček, Igor (advisor)
The aim of this paper is to suggest optical system capable of movement identification in space and its reconstruction. The motion capture system uses markers attached to parts of human body, and a camera pair to capture the movement. This paper describes step-by-step parts of this system. Epipolar geometry is used to deal with problem of object correspondence between two views.
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Structure From Motion From Multiple Views
Mrkvička, Daniel ; Štarha, Pavel (referee) ; Procházková, Jana (advisor)
This thesis deals with the reconstruction of the scene using two or more images. It describes the whole reconstruction process consisting of detecting points in images, finding the appropriate geometry between images and resulting projection of these points into the space of scene. The thesis also includes a description of the application, which demonstrates the described methods.
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The methods of texture mapping on point cloud
Květný, Michal ; Štarha, Pavel (referee) ; Procházková, Jana (advisor)
This diploma thesis deals with a mapping of textures obtained from ordinary photographs onto the three-dimensional point clouds created by a 3D scanner device. The thesis proposes a mapping method that consists of reconstruction of a sparse point cloud from input photos and registration of the point cloud with an input dense point cloud using FPFH (Fast Point Feature Histogram) descriptors. The thesis also contains an implementation of the proposed method in C++ programming language which is tested on a real world data.
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Projective geometry codes
Požárková, Zuzana ; Drápal, Aleš (advisor) ; Holub, Štěpán (referee)
In the presented work we define a class of error-correcting codes based on incidence vectors of projective geometries, including the necessary basis of coding theory and projective geometries. A detailed calculation is performed to show the dimension of these codes. In conclusion we concern ourselves with majority decoding. This work is a summary of the results of some known authors engaged in this field. We continue on some of these results and we present evidence of some of the statements, which have been proven differently by other authors.
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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.
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Photogrammetric Image Analysis
Velebová, Jana ; Španěl, Michal (referee) ; Zemčík, Pavel (advisor)
This thesis is dedicated photogrammetric image analysis that makes it possible from your photos with the help selected methods to determine the location and dimensions of objects recorded on them. There are explained the basics of photogrammetry and its current application. Chapters focused on digital imaging describing its characteristics, treatment options and key points findability for the scene calibration. For a comprehensive view are in this thesis introduced examples of existing software, its possibilities and use in practice.
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Ovality measurement of extruded fiber using three cameras
Loučka, Pavel ; Martišek, Dalibor (referee) ; Štarha, Pavel (advisor)
One of the important parameters observed during extruded fibre fabrication is its diameter. The diameter can be measured with a single scanning camera assuming that the fibre section has a circular shape. As proved in practice, another important parameter is ovality, that is the rate of fibre flattening. This paper assumes that the fibre section shape is elliptical. In such a case, at least three different views on examined fibre are needed. Mathematical part of this paper is concerned with analytical description of fibre ovality measurement using two different approaches based on the knowledge of linear algebra, projective geometry and conic sections theory. Main goal of this paper is thus to use both mathematical theory and image analysis methods for ovality and diameter determination. Precise calcluation of such quantities is, however, conditioned on precise camera system calibration, which is described in the paper as well. Additionally, the work contains a brief mention of technical realization of ovality measurement and its possible difficulties.
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Structure From Motion From Multiple Views
Mrkvička, Daniel ; Štarha, Pavel (referee) ; Procházková, Jana (advisor)
This thesis deals with the reconstruction of the scene using two or more images. It describes the whole reconstruction process consisting of detecting points in images, finding the appropriate geometry between images and resulting projection of these points into the space of scene. The thesis also includes a description of the application, which demonstrates the described methods.
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