Principles And Methods Of Space Resection Based On Geometric Algebra

With the flying development and popularization of new sensors and position systems,besides with the large scale spreading and applications of Digital Photogrammetry Workstation,the high technology and digital photogrammetry have brought us with great convenience. But atthe same time, the development of photogrammetry's basic theories is ignored slowly.Geometric Algebra and Conformal Geometric Algebra can describe the space transformationsstraightforward and compute with the high dimension entities in a simple and direct manner. Atthis point, compared to the traditional photogrammetry base on"point", Geometric Algebra andConformal Geometric Algebra may have great advantages and worth on researching. Thisdissertation use Geometric Algebra as a tool, makes a comprehensive study on the subjectsrelated to the most basic content of photogrammetric positioning—Space Resection based onGeometric Algebra. The followings are what we have done in the dissertation:1. The purpose and significance of the research are introduced, the origin and developmentof Geometric Algebra, the current status of domestic and foreign about the research ofGeometric Algebra and Conformal Geometric Algebra.2. Induce the basic principles of Geometric Algebra in detail, mainly include EuclideanGeometric Algebra, Projective Geometric Algebra, Conformal Geometric Algebra besides withthe embranchment such as Dual Quaternions and Motor Algebra. Summarize the expressionsand transformations about kinds of entities such as points, lines and planes. This is a storage ofbasic principles, in practical terms, it will be used when changing from the 3-Dimension spaceto a higher dimension space.3. Based on the foundation of the theory of rotation matrix described by the CGA, weprogram the classical rotation matrix on Maple, and through the comparision, validate thecorrectness of Geometric Algebra when it describing the rotation in a non-matrix formcompared with the classic rotation matrix.4. Set up the stratification theory of space resection based on Geometric Algebra, discussthe transformation-relationships between different Geometric Algebra space systems. On thebase of the classical collinearity equation in photogrammetry, deduce the conformal constraintequations and explain the stratification of equations detailed in the frame of ConformalGeometric Algebra.5. Based on the theory and arithmetic of Geometric Algebra described about SpaceResection, we have done experiments at large include of kinds of image data, then, analysed and compared with the classical arithmetic. Via the experiments, summarize the advantages anddisadvantages of Geometric Algebra, draw up the impersonal conclusions. At last, analyse theforegroud of the use of Geometric Algebra in photogrammetry and the main problems whichare need to solve as soon as possible.