Procrustes methods for projective shape
Seminar Room 2, Newton Institute Gatehouse
Projective shape is important in computer vision to represent the information in a scene that is invariant under different camera views. The simplest example is the cross ratio, which represents the projective shape of four collinear points. One way to study projective shape is through projective invariants. However, a disadvantage is that there seems to be no natural metric structure on these invariants, making it difficult to quantify differences between different projective shapes. The purpose of this talk is to describe a metric structure for projective shapes. Then, using Procrustes methods, the beginnings of a statistical theory will be developed to construct averages and describe variability for a collection of projective shapes.