View Planning and Refractive Modeling for Structure and Motion

Abstract: This thesis presents contributions to structure-and-motion estimation, a central topic in the field of geometric computer vision. In particular, 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. The same concepts are then applied to the problem of sequential 3D reconstruction from unordered image sequences. By propagating reconstruction uncertainties and actively selecting the order in which images are used via view planning, significant gains in robustness and computational efficiency are achieved. The second topic of the thesis is refractive structure-and-motion, specifically the problem of absolute pose estimation when the camera and structure are separated by an optically refracting 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.