Parametric Regression on the Grassmannian
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, followin...
| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 38(2016), 11 vom: 18. Nov., Seite 2284-2297 |
|---|---|
| 1. Verfasser: | |
| Weitere Verfasser: | , , , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2016
|
| Zugriff auf das übergeordnete Werk: | IEEE transactions on pattern analysis and machine intelligence |
| Schlagworte: | Journal Article |
| Zusammenfassung: | 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 |
|---|---|
| Beschreibung: | Date Completed 06.06.2017 Date Revised 06.06.2017 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
| ISSN: | 1939-3539 |