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Analytic representation of affine transformations in the plane
Horáčková, Blanka ; Beran, Filip (advisor) ; Zamboj, Michal (referee)
The thesis deals with three main topics - isometric, similar, and affine transformations of the plane from the point of view of analytic geometry. In the first chapter, the most basic concepts are recalled, which will be subsequently dealt with throughout the thesis. The second chapter focuses on identical transformations. Here, we find an analytic representation of this transformation in matrix and complex forms. The third chapter focuses on similar transformations. The central point is then the decomposition of similarity into identity and identicalness, where knowledge of both similarities and identities are combined. The last chapter focuses on affinities. This chapter is not so theoretical anymore but focuses mainly on the characteristic elements of affine transformations and examples. This work's important and beneficial factor is the solved examples, supplemented by several figures. The work is intended primarily for mathematics students as a study material. However, it may also be used by secondary school teachers to supplement the secondary school curriculum.
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Stitching of Full Sphere Panoramic Image
Vénos, Michal ; Beneš, Radek (referee) ; Říha, Kamil (advisor)
Bachelor's thesis deals with stitching panoramic image, from its beginning given by setting properties of camera and 303SPH Manfrotto panoramic head, to assembly of images captured in different kinds of scenery. This work describes the transformation used with stitching images, for calculating the matrix homograph from specific points of correspondence and transfer from plane to cylindrical or spherical coordinates. It also includes a description of the functions using the OpenCV library used in the assembly.
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Advanced registration of image sequences from video-ophthalmoscope
Dufková, Barbora ; Chmelík, Jiří (referee) ; Kolář, Radim (advisor)
This master's thesis deals with the issue of registration of ophthalmic video sequences. It describes basic geometric transformations that can be used for registration. The basic methods of image registration are also presented, from which the most suitable variant for this application is selected. This is then implemented using a script created in the MATLAB environment. The proposed method is further evaluated objectively using the brightness profile method, using mutual information and correlation, and using retinal vessel skeleton. The effect of polynomial transformation on registration and possible optimizations of the algorithm are discussed.
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Stitching of Full Sphere Panoramic Image
Vénos, Michal ; Beneš, Radek (referee) ; Říha, Kamil (advisor)
Bachelor's thesis deals with stitching panoramic image, from its beginning given by setting properties of camera and 303SPH Manfrotto panoramic head, to assembly of images captured in different kinds of scenery. This work describes the transformation used with stitching images, for calculating the matrix homograph from specific points of correspondence and transfer from plane to cylindrical or spherical coordinates. It also includes a description of the functions using the OpenCV library used in the assembly.
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Numerical Method of Image Registration Using Nonlinear Geometric Transform
Stodola, Jakub ; Druckmüller, Miloslav (referee) ; Štarha, Pavel (advisor)
The goal of the thesis is to find general nonlinear geometric transformation, which compensates irregular deformation of images, so that they could be registered. In the introductory part, necessary mathematical tools are stated, especially convolution, correlation and Fourier transform. In the next part, method of phase correlation is stated, followed by algorithms used for finding the geometric transformation. Those algorithms are implemented in computer program, that is included.
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