Felix Rydell: Grassmannians and Chow Varieties - Moduli Spaces in Computer Vision

Structure-from-Motion in Computer Vision creates 3D models of objects based on 2D images. The first step in this pipeline is to identify key features in each image, and match these across the different views. These key features are typically points, although lines and curves can also be identified. After having estimated the camera parameters, we obtain world features by triangulation, which refers to finding the world features that best correspond to the matched image features. To do this systematically, we need to be able to parametrize the set of all lines and curves in 3D efficiently. This is done with the help of Grassmannians and Chow Varieties. These are classical moduli spaces in Algebraic Geometry whose points represent linear subspaces and varieties of general fixed dimension and degree. In this talk, we describe and explain these moduli spaces and their applications to Structure-from-Motion in Computer Vision.