Name
Abstract | ||
|---|---|---|
Hodge theory is a beautiful synthesis of geometry, topology, and analysis which has been developed in the setting of Riemannian manifolds. However, spaces of images, which are important in the mathematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We believe that this constitutes a step toward understanding the geometry of vision. Appendix B by Anthony Baker discusses a separable, compact metric space with infinite-dimensional α-scale homology. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/s10208-011-9107-3 | Foundations of Computational Mathematics |
Keywords | Field | DocType |
Hodge theory,L,2,cohomology,Metric spaces,Harmonic forms,Medium-scale geometry,58A14,54E05,55P55,57M50 | Fisher information metric,Mathematical analysis,Convex metric space,Intrinsic metric,Metric space,Hodge dual,Mathematics,Injective metric space,Geometry and topology,Hodge theory | Journal |
Volume | Issue | ISSN |
12 | 1 | Foundations of Computational Mathematics 12:1 (2012) 1-48 |
Citations | PageRank | References |
5 | 0.70 | 12 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Laurent Bartholdi | 1 | 27 | 8.74 |
| Thomas Schick | 2 | 5 | 0.70 |
| Nat Smale | 3 | 5 | 0.70 |
| Steve Smale | 4 | 694 | 105.28 |