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.

Abstract

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.

Citation

Varano, V., Piras, P., Gabriele, S., Teresi, L., Nardinocchi, P., Dryden, I. L., Torromeo, C., Schiariti, M., & Puddu, P. E. (2020). Local and Global Energies for Shape Analysis in Medical Imaging. International Journal for Numerical Methods in Biomedical Engineering, 36(2), Article e3252. https://doi.org/10.1002/cnm.3252

• Journal Article Type: Article
• Acceptance Date: Aug 8, 2019
• Online Publication Date: Aug 23, 2019
• Publication Date: 2020-02
• Deposit Date: Aug 16, 2019
• Publicly Available Date: Aug 24, 2020
• Journal: International Journal for Numerical Methods in Biomedical Engineering
• Print ISSN: 2040-7939
• Electronic ISSN: 2040-7947
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 36
• Issue: 2
• Article Number: e3252
• DOI: https://doi.org/10.1002/cnm.3252
• Keywords: Shape analysis; bending energy; strain energy; parallel transport
• Public URL: https://nottingham-repository.worktribe.com/output/2440998
• Publisher URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/cnm.3252
• 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 https://doi.org/10.1002/cnm.3252. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
• Contract Date: Aug 16, 2019