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The Introduction and Application of General Regression Model
Hrabec, Pavel ; Štarha, Pavel (referee) ; Bednář, Josef (advisor)
This thesis sumarizes in detail general linear regression model, including testing statistics for coefficients, submodels, predictions and mostly tests of outliers and large leverage points. It describes how to include categorial variables into regression model. This model was applied to describe saturation of photographs of bread, where input variables were, type of flour, type of addition and concntration of flour. After identification of outliers it was possible to create mathematical model with high coefficient of determination, which will be usefull for experts in food industry for preliminar identification of possible composition of bread.
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Modelling of NURBS curves and surfaces in the projective space
Ondroušková, Jana ; Štarha, Pavel (referee) ; Martišek, Dalibor (advisor)
In the first part I discuss ancestors of NURBS curves and surfaces, rather Ferguson, Beziere, Coons and B-spline curves and surfaces and furthermore B-spline functions. In the second part I devote to NURBS curves and surfaces, their description as a linear combination of B-spline functions in the projective space. I specify conical arcs more detailed, their submit in the projective space and NURBS surfasec given as tensor product of NURBS curves. Last part is devote to describtion programs for modeling conicals and NURBS surface.
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Integral transforms and their applications
Béreš, Lukáš ; Štarha, Pavel (referee) ; Franců, Jan (advisor)
This bachelor's thesis deals with integral transforms and their applications. Its aim is to get together basic properties of Laplace and Fourier transforms and then illustrate their application in solving partial dierential equations, by calculating specic tasks with numerical experiments in MATLAB software.
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Numerical Methods of Image Analysis for Optimal Lens Focusing
Mikuláček, Pavel ; Loučka, Pavel (referee) ; Štarha, Pavel (advisor)
The bachelor thesis deals with determining the optimal focus of the lens. It includes part of the mathematical theory associated with this problem. It explains the mathematical procedure that can be used to decide on the optimal focus of the lens. The result of the work is a single-purpose application that processes images of the Sun and can determine the optimal position of the focusing ring.
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Software Design of Single Purpose Machine for Visual Inspection
Horák, Daniel ; Krejsa, Jiří (referee) ; Štarha, Pavel (advisor)
This master’s thesis deals with the fundamentals of machine vision application and its practical implementation. The research part is focused on the basic possibilities of image acquisition and image processing in different dimensions. The practical part describes the design of the dimension control algorithm using a 3D camera. This algorithm is then implemented in a single-purpose machine for optical dimension control.
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Object tracking in high-speed camera images
Myška, Michal ; Druckmüller, Miloslav (referee) ; Štarha, Pavel (advisor)
This master thesis is dealing with object tracking in high-speed camera images, within what we are trying to find their trajectory and orientation. The mathematical theory associated with this problem as well as the methods used fo image processing are described here. The main outcome is an application with a user interface through which we can calculate the desired parameters of the individual objects.
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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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Extruded fibers ovality measurement
Loučka, Pavel ; Procházková, Jana (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. This paper deals with analytical description of fibre ovality measurement using two different approaches based on the principles of linear algebra and projective geometry. As a result, a considerable part of the work is devoted to these branches of mathematics with particular regard to analytical conics theory. Additionally, the work contains a brief mention of technical realization of ovality measurement and its possible difficulties.
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Computer-aided method of analytic surfaces modelling
Stodola, Jakub ; Štarha, Pavel (referee) ; Martišek, Dalibor (advisor)
The first part of the thesis deals with projections of points from an Euclidean space into a plane and displaying of the resulted planar points on a computer. The second part focuses on a discretization of analytically specified surfaces. This is an approximation with network points. Due to the previous part, we are able to display them on a computer. The third part is dedicated to various types of coating fillings. Finally, the software solution is added.
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