Šiame magistro darbe aptarsime keletą projekcijos metodų: tai pagrindinių komponenčių analizė (Principal Component Analysis (PCA)), daugiamačių skalių (Multidimensional Scaling (MDS)) ir santykinės perspektyvos (relational perspective map (RPM)). Tirsime, kuris iš trijų pradinių projekcijos taškų parinkimo būdų - atsitiktinis, pagrindinių komponenčių ar didžiausių dispersijų garantuoja mažesnę paklaidą RPM algoritme. Atliksime paprasto RPM algoritmo, pasiūlyto autoriaus James Xinzhi Li modifikaciją. Taip pat tirsime parametrus r,a (mokymo greičiai), nustatysime, kaip jie įtakoja RPM algoritmo konvergavimą. Integruosime MDS ir RPM algoritmus į internetinę terpę. Vizualiai vaizduosime daugiamačių duomenų projekcijas. / This paper deals with a methods, called the relational perspective map and multidimentional scaling. Relational perspective map that visualizes multidimensional data onto two-dimensional closed plane. It tries to preserve the distances between the multidimensional data in the lowerdimensional space. But the most important feature of the relational perspective map is the ability to visualize data in a non-overlapping manner so that it reveals small distances better than other known visualization methods. In the methods are In this paper, the features of relational perspective map are explored experimentally and some disadvantages are noticed. We have proposed a modification of this method, which enables us to avoid them. Also we have stored RPM and MDS algorithms in php language and included them in web site for testing these methods online. But allow testing only small data, because algorithms in php language works longer that stored in c++ language.

In this work, a triangulation method, a classic algorithm for Sammon’s projection and the combination of Sammon’s algorithm and the triangulation method for mapping of new points are examined in details. The combination of Sammon’s algorithm and triangulation method is created. The algorithms of triangulation method, Sammon’s algorithm and their combination are realized in Microsoft Visual Basic 5.0. These algorithms are developed and examined on the view on the following stand points: * Visual evaluation of data projection; * Evaluation of time of data mapping; * Evaluation of projection error. The triangulation method is quite fast, however only (2m-3) distances among examined data points are exactly preserved. Sammon’s algorithm tries to preserve all m(m-1)/2 distances among data points, but it is quite slow: whenever a new point must be mapped, all visualization procedure must be repeated over. This question is solved using the combination of the triangulation method and Sammon’s projection. On purpose to get the more exact data projection onto a plane, we must to map more initial points using Sammon’s projection and less new points using the triangulation method. The combination of these methods is used, whenever new points of the data must be quickly mapped. This method performs quite fast and quite a little precision is lost. The discovered new ways for fast mapping of points in a high-dimensional space onto a plane and it makes a background for the further research... [to full text]

A variety of techniques exist for three-dimensional reconstruction when multiple views are available, but less attention has been given to reconstruction when only a single view is available. Such a situation is normal in astronomy, when a galaxy (for example) is so distant that it is impossible to obtain views from significantly different angles. In this thesis I examine the problem of reconstructing the three-dimensional structure of a galaxy from this single viewpoint. I accomplish this by taking advantage of the image formation process, symmetry relationships, and other structural assumptions that may be made about galaxies. Most galaxies are approximately symmetric in some way. Frequently, this symmetry corresponds to symmetry about an axis of rotation, which allows strong statements to be made about the relationships between luminosity at each point in the galaxy. It is through these relationships that the number of unknown values needed to describe the structure of the galaxy can be reduced to the number of constraints provided by the image so the optimal reconstruction is well-defined. Other structural properties can also be described under this framework. I provide a mathematical framework and analyses that prove the uniqueness of solutions under certain conditions and to show how uncertainty may be precisely and explicitly expressed. Empirical results are shown using real and synthetic data. I also show a comparison to a state-of-the-art two-dimensional modelling technique to demonstrate the contrasts between the two frameworks and show the important advantages of the three-dimensional approach. In combination, the theoretical and experimental aspects of this thesis demonstrate that the proposed framework is versatile, practical, and novel---a contribution to both computer science and astronomy.

Three-dimensional reconstruction of small objects has been one of the most challenging problems over the last decade. Computer graphics researchers and photography professionals have been working on improving 3D reconstruction algorithms to fit the high demands of various real life applications. In this thesis, we implemented a 3D scanner system based on fringe projection method. Two different methods have been implemented and used as the unwrapping solution in fringe projection method. A parameterization tool has been created in order to generate different fringe patterns for distinctive needs in the fringe projection method. Considering our first practical implementation (based on phase shifting and multi wavelength techniques) the number of pictures used in phase shifting method has been decreased and the effects of reducing the fringe patterns on the level of precision of the 3D model have been investigated. Optical arrangement and calibration of the system (fringe projection method) have been studied, and numerous suggestions have been proposed to improve the precision of the system. Also, an evaluation method has been implemented based on calibration techniques. The error rate on both surface and height of the 3D model compare with the object has been calculated.

Thesis (M. Ed.(Opvoedkundige sielkunde))-University of Pretoria, 2006. / Includes bibliographical references. Available on the Internet via the World Wide Web.

Thesis (Ph.D.)--University of Melbourne, the Australian Centre, 2004. / Typescript (photocopy). Includes bibliographical references (leaves 294-320 (v. 1)).

Thesis (M. Sc.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

Thèses (Ph.D.)--Université de Sherbrooke (Canada), 2004. / Titre de l'écran-titre (visionné le 20 juin 2006). Publié aussi en version papier.

Thèses (M.Sc.A.)--Université de Sherbrooke (Canada), 2001. / Titre de l'écran-titre (visionné le 20 juin 2006). Publié aussi en version papier.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1993. / Vita. Abstract. Includes bibliographical references (leaves 95-100). Also available via the Internet.