title: Parametric Regression on the Grassmannian.
abstract: We address the problem of fitting parametric curves on the Grassmann manifold for the purpose of intrinsic parametric regression. We start from the energy minimization formulation of linear least-squares in Euclidean space and generalize this concept to general nonflat Riemannian manifolds, following an optimal-control point of view. We then specialize this idea to the Grassmann manifold and demonstrate that it yields a simple, extensible and easy-to-implement solution to the parametric regression problem. In fact, it allows us to extend the basic geodesic model to (1) a "time-warped" variant and (2) cubic splines. We demonstrate the utility of the proposed solution on different vision problems, such as shape regression as a function of age, traffic-speed estimation and crowd-counting from surveillance video clips. Most notably, these problems can be conveniently solved within the same framework without any specifically-tailored steps along the processing pipeline.
authors.forename: Yi
authors.initials: Y
authors.lastname: Hong
authors.forename: Roland
authors.initials: R
authors.lastname: Kwitt
authors.forename: Nikhil
authors.initials: N
authors.lastname: Singh
authors.forename: Nuno
authors.initials: N
authors.lastname: Vasconcelos
authors.forename: Marc
authors.initials: M
authors.lastname: Niethammer