
Surface approximation using Bspline and Tspline
Pálková, Tereza ; Loučka, Pavel (referee) ; Procházková, Jana (advisor)
The bachelor thesis focuses on Bspline representation of surfaces and its generalization Tspline. The work is divided into three main parts. The introduction lays down the theoretical foundations of both surfaces and presents their mathematical properties. The second part deals with the implementation of algorithms in Matlab software. The final part contains the application of the algorithms on real data obtained by 3D scanning and a comparison of both surfaces in terms of utilization.


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 singlepurpose application that processes images of the Sun and can determine the optimal position of the focusing ring.


The comparison of edge detectors
Dula, Marek ; Loučka, Pavel (referee) ; Procházková, Jana (advisor)
In this bachelor thesis we focus on the comparison of different methods for finding edges and filtering noise in the image. In the introduction, we focus on basic concepts related to the issue. Subsequently, we describe the individual methods of edge detection and noise filtering in the picture. The next part contains software processing of individual methods in Matlab software. Finally, we compare the individual noise filters and edge detectors.


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.


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.
