Doctoral Theses in Mathematical Sciences 2015:2

is thesis presents contributions to structure-and-motion estimation. In par-ticular, the problem of view planning is considered, and continuous and discrete optimization-based algorithms are given for how to plan the path of a sensor to its destination, while balancing the competing goals of path length and reconstruction accuracy. e same concepts are then applied to the problem of sequential 3D reconstruction from unordered image sequences. Using co-variance propagation and image order selection for view planning, significant gains in robustness and computational efficiency are achieved. A second topic is refractive structure-and-motion, specifically the problem of absolute pose estimation when the camera and structure are separated by an optically refract-ing plane. Using methods from algebraic geometry for solving multivariate polynomial systems, efficient minimal and near-minimal solvers are constructed. Finally, a practical method for calibrating a set of cameras under refraction is given, including an algorithm for efficient refractive bundle adjustment