Name
Abstract | ||
|---|---|---|
Statistical shape analysis can be done in a Riemannian framework by endowing the set of shapes with a Riemannian metric. Sobolev metrics of order two and higher on shape spaces of parametrized or unparametrized curves have several desirable properties not present in lower order metrics, but their discretization is still largely missing. In this paper, we present algorithms to numerically solve the geodesic initial and boundary value problems for these metrics. The combination of these algorithms enables one to compute Karcher means in a Riemannian gradient-based optimization scheme and perform principal component analysis and clustering. Our framework is sufficiently general to be applicable to a wide class of metrics. We demonstrate the effectiveness of our approach by analyzing a collection of shapes representing HeLa cell nuclei. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1137/16M1066282 | SIAM JOURNAL ON IMAGING SCIENCES |
Keywords | Field | DocType |
shape analysis,shape registration,Sobolev metric,geodesics,Karcher mean,B-splines | Equivalence of metrics,Topology,Boundary value problem,Discretization,Statistical shape analysis,Mathematical analysis,Sobolev space,Cluster analysis,Mathematics,Geodesic,Principal component analysis | Journal |
Volume | Issue | ISSN |
10 | 1 | 1936-4954 |
Citations | PageRank | References |
2 | 0.41 | 11 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Martin Bauer | 1 | 52 | 10.45 |
| M. Bruveris | 2 | 58 | 4.53 |
| Philipp Harms | 3 | 4 | 1.80 |
| Jakob Møller-Andersen | 4 | 2 | 0.41 |