Maurer-Cartan Forms for Fields on Surfaces : Application to Heart Fiber Geometry
We study the space of first order models of smooth frame fields using the method of moving frames. By exploiting the Maurer-Cartan matrix of connection forms we develop geometrical embeddings for frame fields which lie on spherical, ellipsoidal and generalized helicoid surfaces. We design methods fo...
| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 37(2015), 12 vom: 21. Dez., Seite 2492-504 |
|---|---|
| 1. Verfasser: | |
| Weitere Verfasser: | , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2015
|
| Zugriff auf das übergeordnete Werk: | IEEE transactions on pattern analysis and machine intelligence |
| Schlagworte: | Journal Article Research Support, Non-U.S. Gov't |
| Zusammenfassung: | We study the space of first order models of smooth frame fields using the method of moving frames. By exploiting the Maurer-Cartan matrix of connection forms we develop geometrical embeddings for frame fields which lie on spherical, ellipsoidal and generalized helicoid surfaces. We design methods for optimizing connection forms in local neighborhoods and apply these to a statistical analysis of heart fiber geometry, using diffusion magnetic resonance imaging. This application of moving frames corroborates and extends recent characterizations of muscle fiber orientation in the heart wall, but also provides for a rich geometrical interpretation. In particular, we can now obtain direct local measurements of the variation of the helix and transverse angles, of fiber fanning and twisting, and of the curvatures of the heart wall in which these fibers lie |
|---|---|
| Beschreibung: | Date Completed 15.08.2016 Date Revised 06.11.2015 published: Print Citation Status MEDLINE |
| ISSN: | 1939-3539 |
| DOI: | 10.1109/TPAMI.2015.2408352 |