43
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Parallel transport of local strains

ORCID Icon, ORCID Icon, , , ORCID Icon &
Pages 520-528 | Received 16 Jan 2018, Accepted 17 May 2018, Published online: 07 Jun 2018

References

  • Adams DC, Collyer ML. 2009. A general framework for the analysis of phenotypic trajectories in evolutionary studies. Evolution. 63(5):1143–1154.
  • Armon S, Efrati E, Kupferman R, Sharon E. 2011. Geometry and mechanics in the opening of chiral seed pods. Science. 333(6050):1726–1730.
  • Bookstein FL. 1989. Principal warps: thin-plate splines and the decomposition of deformations. IEEE Trans Pattern Anal Mach Intell. 11(6):567–585.
  • Buckley PF, Dean D, Bookstein FL, et al. 1999. Three dimensional magnetic resonance-based morphometrics and ventricular dysmorphology in schizophrenia. Biol Psychiatry. 45:62–67.
  • Ciarlet PG. 2005. An introduction to differential geometry with applications to elasticity. Dordrecht, The Netherlands: Springer.
  • Collyer ML, Adams DC. 2013. Phenotypic trajectory analysis: comparison of shape change patterns in evolution and ecology. Hystrix. 24(1):75–83.
  • DiCarlo A, Milicchio F, Paoluzzi A, Shapiro V. 2009. Discrete physics using metrized chains. In: 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling. San Francisco (CA): ACM; p. 135–145.
  • do Carmo Valero MP. 1992. Riemannian geometry. Boston: Birkhäuser. (Mathematics: Theory & Applications).
  • Evangelista A, Gabriele S, Nardinocchi P, Piras P, Puddu P, Teresi L, Torromeo C, Varano V. 2015. Non-invasive assessment of functional strain lines in the real human left ventricle via speckle tracking echocardiography. J Biomech. 48(3):465–471.
  • Gabriele S, Nardinocchi P, Varano V. 2015. Evaluation of the strain-line patterns in a human left ventricle: a simulation study. Comput Methods Biomech Biomed Eng. 18(7):790–798.
  • Huckemann S, Hotz T, Munk A. 2010. Intrinsic manova for Riemannian manifolds with an application to kendall’s space of planar shapes. IEEE Trans Pattern Anal Mach Intell. 32(4):593–603.
  • Logg A, Mardal KA, Wells G. 2012. Automated solution of differential equations by the finite element method: the fenics book. Vol. 84. Springer-Verlag Berlin Heidelberg: Springer Science & Business Media.
  • Madeo A, Piras P, Re F, Gabriele S, Nardinocchi P, Teresi L, Torromeo C, Chialastri C, Schiariti M, Giura G, et al. 2015. A new 4d trajectory-based approach unveils abnormal lv revolution dynamics in hypertrophic cardiomyopathy. PloS One. 10(4):e0122376.
  • Miller MI, Qiu A. 2009. The emerging discipline of computational functional anatomy. Neuroimage. 45(1):S16–S39.
  • Miller MI, Younes L, Trouvé A. 2014. Diffeomorphometry and geodesic positioning systems for human anatomy. Technology. 2(01):36–43.
  • Minozzi M, Nardinocchi P, Teresi L, Varano V. 2017. Growth-induced compatible strains. Math Mech Solids. 22(1):62–71.
  • Nardinocchi P, Teresi L, Varano V. 2012. Strain induced shape formation in fibred cylindrical tubes. J Mech Phys Solids. 60(8):1420–1431.
  • Nardinocchi P, Teresi L, Varano V. 2013. The elastic metric: a review of elasticity with large distortions. Int J Non-Linear Mech. 56:34–42.
  • Piras P, Evangelista A, Gabriele S, Nardinocchi P, Teresi L, Torromeo C, Schiariti M, Varano V, Puddu PE. 2014. 4d-analysis of left ventricular heart cycle using procrustes motion analysis. PloS One. 9(1):e86896.
  • Piras P, Teresi L, Gabriele S, Evangelista A, Esposito G, Varano V, Torromeo C, Nardinocchi P, Puddu PE. 2015. Systo-diastolic lv shape analysis by geometric morphometrics and parallel transport highly discriminates myocardial infarction. In: International Workshop on Statistical Atlases and Computational Models of the Heart. Switzerland: Springer International Publishing; p. 119–129.
  • Piras P, Torromeo C, Evangelista A, Gabriele S, Esposito G, Nardinocchi P, Teresi L, Madeo A, Schiariti M, Varano V, et al. 2017. Homeostatic left heart integration and disintegration links atrio-ventricular covariation’s dyshomeostasis in hypertrophic cardiomyopathy. Sci Rep. 7(1):1–12. Article ID 6257.
  • Trouvé A, Younes L. 2005. Metamorphoses through lie group action. Found Comput Math. 5(2):173–198.
  • Twining C, Marsland S, Taylor C. 2011. Metrics, connections, and correspondence: the setting for groupwise shape analysis. In: Boykov Y, Kahl S, Lempitsky V, Schmidt FR, editors. International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition. Berlin, Heidelberg: Springer; p. 399–412.
  • Varano V, Gabriele S, Teresi L, Dryden I, Puddu P, Torromeo C, Piras P. 2015. Comparing shape trajectories of biological soft tissues in the size-and-shape space. In: BIOMAT 2014 International Symposium on Mathematical and Computational Biology. Singapore: World Scientific Publishing. p. 351–365.
  • Varano V, Gabriele S, Teresi L, Dryden I, Puddu P, Torromeo C, Piras P. 2017. The TPS direct transport: a new method for transporting deformations in the size-and-shape space. Int J Comput Vision. 124(3):384–408.
  • Xie Q, Kurtek S, Le H, Srivastava A. 2013. Parallel transport of deformations in shape space of elastic surfaces. In: Proceedings of the IEEE International Conference on Computer Vision. p. 865–872.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.