Maurer-cartan forms for fields on surfaces: application to heart fiber geometry

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Standard

Maurer-cartan forms for fields on surfaces : application to heart fiber geometry. / Piuze, Emmanuel; Sporring, Jon; Siddiqi, Kaleem.

I: IEEE Transactions on Pattern Analysis and Machine Intelligence, Bind 37, Nr. 12, 2015, s. 2492-2504.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Piuze, E, Sporring, J & Siddiqi, K 2015, 'Maurer-cartan forms for fields on surfaces: application to heart fiber geometry', IEEE Transactions on Pattern Analysis and Machine Intelligence, bind 37, nr. 12, s. 2492-2504. https://doi.org/10.1109/TPAMI.2015.2408352

APA

Piuze, E., Sporring, J., & Siddiqi, K. (2015). Maurer-cartan forms for fields on surfaces: application to heart fiber geometry. IEEE Transactions on Pattern Analysis and Machine Intelligence, 37(12), 2492-2504. https://doi.org/10.1109/TPAMI.2015.2408352

Vancouver

Piuze E, Sporring J, Siddiqi K. Maurer-cartan forms for fields on surfaces: application to heart fiber geometry. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2015;37(12):2492-2504. https://doi.org/10.1109/TPAMI.2015.2408352

Author

Piuze, Emmanuel ; Sporring, Jon ; Siddiqi, Kaleem. / Maurer-cartan forms for fields on surfaces : application to heart fiber geometry. I: IEEE Transactions on Pattern Analysis and Machine Intelligence. 2015 ; Bind 37, Nr. 12. s. 2492-2504.

Bibtex

@article{54c01ed03fea4f8e81e7bff119fa2359,
title = "Maurer-cartan forms for fields on surfaces: application to heart fiber geometry",
abstract = "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.",
author = "Emmanuel Piuze and Jon Sporring and Kaleem Siddiqi",
year = "2015",
doi = "10.1109/TPAMI.2015.2408352",
language = "English",
volume = "37",
pages = "2492--2504",
journal = "IEEE Transactions on Pattern Analysis and Machine Intelligence",
issn = "0162-8828",
publisher = "Institute of Electrical and Electronics Engineers",
number = "12",

}

RIS

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 -

ID: 130885426