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Local and Global Energies for Shape Analysis in Medical Imaging

Varano, Valerio; Piras, Paolo; Gabriele, Stefano; Teresi, Luciano; Nardinocchi, Paola; Dryden, Ian L.; Torromeo, Concetta; Schiariti, Michele; Puddu, Paolo E.


Valerio Varano

Paolo Piras

Stefano Gabriele

Luciano Teresi

Paola Nardinocchi

Ian L. Dryden

Concetta Torromeo

Michele Schiariti

Paolo E. Puddu


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 Rie-mannian 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 threefold decomposition in spherical, deviatoric and non affine components. Such a Parallel Transport also conserves the-energy, strictly related to the total elastic strain energy stored by the body in the original deformation. New machinery is here presented in order to calculate the bending energy on the body only (body bending energy) in order 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 conserve 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 developed in order to better represent the relationship between the-energy, the strain energy and the so called bending-energy densities.

Journal Article Type Article
Journal International Journal for Numerical Methods in Biomedical Engineering
Print ISSN 2040-7939
Electronic ISSN 2040-7947
Publisher Wiley
Peer Reviewed Peer Reviewed
Institution Citation Varano, V., Piras, P., Gabriele, S., Teresi, L., Nardinocchi, P., Dryden, I. L., …Puddu, P. E. (in press). Local and Global Energies for Shape Analysis in Medical Imaging. International Journal for Numerical Methods in Biomedical Engineering,
Keywords Shape analysis; bending energy; strain energy; parallel transport
Publisher URL
Additional Information This is the peer reviewed version of the following article: Varano, V, Piras, P, Gabriele, S, et al. Local and Global Energies for Shape Analysis in Medical Imaging. Int J Numer Meth Biomed Engng. 2019;e3252, which has been published in final form at This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.

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