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With the ever increasing modernization of computers, image processing and analysis is becoming more and more necessary in various sectors. In computer vision and model-based vision for example, algebraic methods are gaining momentum in performing adjustments that play essential roles in obtaining accurate structure and motion estimates, while in photogrammetry they are used to perform bundle adjustment to obtain dense 3-dimensional (3D) surface models from images taken from photographs. Most recently, there is a close link between CV and photogrammetry, as unordered image blocks from close range and UAVs have to be processed. Indeed, in recent years, the demand for realistic reconstruction and modeling of objects and human bodies is increasing both for animation and medical applications. In radiostereometric analysis (RSA), for example, algebraic methods play the significant role of constructing the projection geometries and reconstructing the 3D-coordinates of the patient markers. Radiostereometric analysis has been widely used in orthopaedics for studying, e.g., prosthetic implant migration and wear, joint stability and kinematics, bone growth, and fracture healing. These applications of algebraic methods, just to list but a few, underscores the need for further improvements and refinements of the existing techniques, and also testing others that could offer more flexibility and optimum results. This book presents modern and efficient algebraic methods that are capable of meeting the challenges posed by the need for efficient algorithms to process and analyze images. The book will be useful to computer scientists, geographers, Earth scientists, mathematicians and environmentalists to list a few.
List of contents
Basics of Algebraic Groebner Basis technique.- Basics of Algebraic Resultant techniques.- EIV Model and its Solutions.- Orthogonal Procrustes Analysis.- Generalized Isotropic Procrustes Analysis.- Photogrammetric Positioning - Basics of three-dimensional resection and intersection.- Closed form solution of P4P or the three-dimensional resection problem in terms of M obius barycentric coordinates.- Closed form solution of the twin P4P or the combined three-dimensional resection-intersection problem in terms of M obius barycentric coordinates.- Estimable quantities in projective networks.- The Inverse Problem of algebroprojective Photogrammetry.- Fundamentals of Photogrammetry.- Fundamentals of Remote Sensing.- Basic relations in Photogrammetry and Remote Sensing.- Algebraic Formulation of Photogrammetric Spatial Resection.- Application of Groebner Basis techniques.- Application of numeric-symbolic computations via CAS.- Application of Pareto optimality to the Resection Problem.- Robot vision based on an exact solution of the three-dimensional resection-intersection.- Advanced Digital Camera Calibration with Additional Parameters.- Bayesian Bundle Block Adjustment.- Merging Laser Scanning and Photogrammetry in Bundle Block Adjustment.- High Density/Semi Global Matching for Point Cloud Generation.- 3D Models Global Registration by Generalized Procrustes Methods.- Image External orientation by Anisotropic Procrustes problems.
