Two Views of P3

The reconstruction of a 3-dimensional scene from (noisy) camera images is a routine task in computer vision. This problem encompasses a number of interesting mathematical questions with deep and old roots in projective geometry, which makes them amenable to tools from algebraic geometry. In this article I will address two foundational questions that revolve around the existence of a reconstruction from two camera images. The results involve real and semialgebraic geometry, as well as classical algebraic geometry and invariant theory. This article is a written account of my talk at ISSAC 2023.