Local and global energies for shape analysis in medical imaging.
bending energy
parallel transport
shape analysis
strain energy
Journal
International journal for numerical methods in biomedical engineering
ISSN: 2040-7947
Titre abrégé: Int J Numer Method Biomed Eng
Pays: England
ID NLM: 101530293
Informations de publication
Date de publication:
02 2020
02 2020
Historique:
received:
21
12
2018
revised:
25
06
2019
accepted:
08
08
2019
pubmed:
25
8
2019
medline:
5
2
2021
entrez:
25
8
2019
Statut:
ppublish
Résumé
In a previous contribution, a new Riemannian shape space, named TPS space, was introduced to perform statistics on shape data. This space was endowed with a Riemannian metric and a flat connection, with torsion, compatible with the given metric. This connection allows the definition of a Parallel Transport of the deformation compatible with the three-fold decomposition in spherical, deviatoric, and non-affine components. Such a parallel transport also conserves the Γ-energy, strictly related to the total elastic strain energy stored by the body in the original deformation. A new approach is here presented in order to calculate the bending energy on the body alone (body bending energy) and to restrict it exclusively within physical boundaries of objects involved in the deformation analysis. The novelty of this new procedure resides in the fact that we propose a new metric to be preserved during the TPS direct transport. This allows transporting the shape change more coherently with the mechanical meaning of the deformation. The geometry of the TPS space is then further discussed in order to better represent the relationship between the Γ-energy, the strain energy, and the so-called bending energy densities.
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Langues
eng
Sous-ensembles de citation
IM
Pagination
e3252Informations de copyright
© 2019 John Wiley & Sons, Ltd.
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