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

Emmanuel Piuze; Jon Sporring; Kaleem Siddiqi

doi:10.1109/TPAMI.2015.2408352

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

Emmanuel Piuze, Jon Sporring, Kaleem Siddiqi

Department of Computer Science

9 Citations (Scopus)

2 Downloads (Pure)

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.

Original language	English
Journal	IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume	37
Issue number	12
Pages (from-to)	2492-2504
Number of pages	13
ISSN	0162-8828
DOIs	https://doi.org/10.1109/TPAMI.2015.2408352
Publication status	Published - 1 Dec 2015

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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.",

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AU - Piuze, Emmanuel

AU - Sporring, Jon

AU - Siddiqi, Kaleem

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Y1 - 2015/12/1

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.

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JO - IEEE Transactions on Pattern Analysis and Machine Intelligence

JF - IEEE Transactions on Pattern Analysis and Machine Intelligence

IS - 12

ER -

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

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