Classical Invariant Theory in Computer Vision 

Title: Classical Invariant Theory in Computer Vision  Abstract: Given two sets of n points in space, typically one expects their images in two different (projective) cameras to be distinct. However, it can be that the images are the same up to a projective transformation, which is an instance of ill-posedness in computer vision. In this talk we will see that generically, this can happen only for point sets with at most seven elements, and that it is possible to determine the Zariski-closure of the locus of camera centers under which images coincide. The techniques rely on moduli spaces of n ordered points in the projective plane, classical invariant theory, and extensive computations in Macaulay2.  Joint work with Giorgio Ottaviani at the University of Florence.