Chirality in Multiview Geometry

Abstract

This thesis studies mathematical problems associated with reconstructing a three dimensional scene from images. Using the traditional pinhole camera model and tools from multiview geometry, we pose these problems from an algebraic perspective. We then build on this model to respect the physical constraint that cameras can only see points in front of them. We explore this constraint, known as chirality, using techniques from topology, real algebraic geometry, and optimization. Our results provide a complete semialgebraic description of the set of world points in front of an arrangement of cameras. We use this to classify when a set of point pairs is the image of a scene in front of two cameras.