Numerical Methods for Geometric Vision: From Minimal to Large Scale Problems

Abstract

This thesis presents a number of results and algorithms for the numerical solution of problems in geometric computer vision. Estimation of scene structure and camera motion using only image data has been one of the central themes of research in photogrammetry, geodesy and computer vision. It has important applications for robotics, autonomous vehicles, cartography, architecture, the movie industry, photography etc. Images inherently provide ambiguous and uncertain data about the world. Hence, geometric computer vision turns out to be as much about statistics as about geometry. Basically we consider two types of problems: Minimal problems where the number of constraints exactly matches the number of unknowns and large scale problems which need to be addressed using e cient optimization algorithms. Solvers for minimal problems are used heavily during preprocessing to eliminate outliers in uncertain data. Such problems are usually solved by nding the zeros of a system of polynomial equations.