TY - JOUR
T1 - Maurer-cartan forms for fields on surfaces
T2 - application to heart fiber geometry
AU - Piuze, Emmanuel
AU - Sporring, Jon
AU - Siddiqi, Kaleem
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
U2 - 10.1109/TPAMI.2015.2408352
DO - 10.1109/TPAMI.2015.2408352
M3 - Journal article
C2 - 26539853
VL - 37
SP - 2492
EP - 2504
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
SN - 0162-8828
IS - 12
ER -