计算机视觉中多项式方程组求解方法分析及应用-analysis and application of solving polynomial equations in computer vision.docxVIP

AbstractWith the rapid improvement of computer performance, computer vision is more and more widely applied to many situations, such as remote sensing image analysis, text recognition, medical image processing, multimedia technologies and image databases aspects. Many problems in computer vision, such as 3D reconstruction, three-point panorama stitching, are optimized based on polynomial expressions of reprojection error, and eventually are converted to polynomial equations solving.The problems of polynomial equations which are involved in computer vision are usually solved by Grobner basis algorithm. The nature of Grobner basis theory is that it begins from any ideal generator of the multivariate polynomial ring, engraves and then calculates a set of “good” nature of generator, while this generator with “good” nature will help us study structure of the ideal and do some operations.We use Grobner basis to solve the polynomial equations which are generated by 3D reconstruction. But in the calculation processing, elimination of the first term of polynomial equations led to a lot of errors, thus it restricts its application. This thesis uses redundant linear bases to avoid the problem, and in order to improve the stability of the algorithm, we use QR and SVD decomposition to select basis from redundant linear bases.In order to improve computational efficiency and stability of triangulation and three-point panorama stitching, we develop a new method to improve the performance of polynomial equations solving based on action matrix, and this generic method has very broad application prospect.Key words：Computer Vision, Grobner Basis Algorithm, 3D Reconstruction, Action Matrix.目录摘要........................................................................................................................................ IAbstract ..................................................................................................................................... II目录............