In these lectures, I will discuss algebraic problems that arise in computer vision. In that domain, reconstruction is a central task, that is, building good 3D models from datasets of multiple noisy 2D images. It is known that parts of this inverse problem amount to solving structured systems of polynomial equations.
In the first lecture, I will give an overview of the application, and sketch popular algorithmic pipelines for 3D reconstruction. In the second lecture, I will focus on the role played by polynomial equation solvers. We will cover one of the first solvers for camera orientation estimation, still widely used today, and then proceed to state-of-the-art methodology for solver design based on Groebner bases. The third lecture will present ongoing developments. These include an alternative approach to solvers based on numerical path-tracking, and fascinatingly similar problems that have emerged in the biomedical imaging sciences.
No familiarity with algebraic geometry or computer vision will be assumed at any point.