DocumentCode :
3601478
Title :
Maurer-Cartan Forms for Fields on Surfaces: Application to Heart Fiber Geometry
Author :
Piuze, Emmanuel ; Sporring, Jon ; Siddiqi, Kaleem
Author_Institution :
Sch. of Comput. Sci. & the Centre for Intell. Machines, McGill Univ., Montreal, QC, Canada
Volume :
37
Issue :
12
fYear :
2015
Firstpage :
2492
Lastpage :
2504
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.
Keywords :
biomedical MRI; geometry; matrix algebra; medical image processing; statistical analysis; Maurer-Cartan matrix; diffusion magnetic resonance imaging; direct local measurements; heart fiber geometry; local neighborhoods; muscle fiber orientation; statistical analysis; Approximation methods; Differential geometry; Geometry; Numerical models; Transmission line matrix methods; Differential Geometry; Differential geometry; Diffusion MRI; Heart Wall Myofibers; Maurer-Cartan Form; Maurer-Cartan form; Moving Frames; diffusion MRI; heart wall myofibers; moving frames;
fLanguage :
English
Journal_Title :
Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publisher :
ieee
ISSN :
0162-8828
Type :
jour
DOI :
10.1109/TPAMI.2015.2408352
Filename :
7053934
Link To Document :
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