M. Abayazid, M. Kemp, and S. Misra, 3D flexible needle steering in soft-tissue phantoms using Fiber Bragg Grating sensors, 2013 IEEE International Conference on Robotics and Automation, pp.5843-5849, 2013.
DOI : 10.1109/ICRA.2013.6631418

R. L. Bishop, There is More than One Way to Frame a Curve, The American Mathematical Monthly, vol.34, issue.3, pp.246-251, 1975.
DOI : 10.1090/S0002-9939-1972-0295224-3

L. Carrat and S. Lavallee, Device and method for determining the position of an instrument in relation to medical images, p.736, 2012.

. Carl-de-boor, A Practical Guide to Splines, 1978.

T. Rida, C. Y. Farouki, and . Han, Rational approximation schemes for rotation-minimizing frames on pythagorean-hodograph curves, Computer Aided Geometric Design, vol.20, issue.7, pp.435-454, 2003.

C. Fouard, A. Deram, Y. Keraval, and E. Promayon, CamiTK: A Modular Framework Integrating Visualization, Image Processing and Biomechanical Modeling, pp.323-354, 2012.
DOI : 10.1007/8415_2012_118
URL : https://hal.archives-ouvertes.fr/hal-00806781

G. Hocking, S. Hebard, H. Christopher, and . Mitchell, A review of the benefits and pitfalls of phantoms in ultrasound-guided regional anesthesia. Regional anesthesia and pain medicine, pp.162-170, 2011.

L. Sébastien and . Digabel, Algorithm 909: Nomad: Nonlinear optimization with the mads algorithm, ACM Trans. Math. Softw, vol.3744, issue.4, pp.1-4415, 2011.

A. Leroy, M. Baumann, P. Mozer, J. Troccaz, and V. Daanen, System and method for imaging and locating punctures under prostatic echography, US Patent, vol.8369, p.592, 2013.

Y. Park, S. Elayaperumal, B. Daniel, S. Chang-ryu, M. Shin et al., Realtime estimation of 3-d needle shape and deflection for mri-guided interventions, Mechatronics, IEEE/ASME Transactions on, issue.6, pp.15906-915, 2010.
DOI : 10.1109/tmech.2010.2080360
URL : http://europepmc.org/articles/pmc4577522?pdf=render

T. K. Podder, D. P. Clark, and J. Sherman, Effects of tip geometry of surgical needle an assessment of force and deflection, 2005.

H. Christian and . Reinsch, Smoothing by spline functions, Numerische Mathematik, 1967.

L. G. Adeline, G. Robert, I. Chagnon, P. Bricault, A. Cinquin et al., A generic three-dimensional static force distribution basis for a medical needle inserted into soft tissue, Journal of the Mechanical Behavior of Biomedical Materials, vol.28, pp.156-170, 2013.

R. J. Roesthuis, M. Kemp, J. J. Van-den-dobbelsteen, and S. Misra, Three-Dimensional Needle Shape Reconstruction Using an Array of Fiber Bragg Grating Sensors, IEEE/ASME Transactions on Mechatronics, vol.19, issue.4, pp.1115-1126, 2014.
DOI : 10.1109/TMECH.2013.2269836

G. Wan, Z. Wei, L. Gardi, D. B. Downey, and A. Fenster, Brachytherapy needle deflection evaluation and correction, Medical Physics, vol.21, issue.4, pp.902-909, 2005.
DOI : 10.1016/0301-5629(95)00044-5

W. Wang, B. Jüttler, D. Zheng, and Y. Liu, Computation of rotation minimizing frames, ACM Transactions on Graphics, vol.27, issue.1, 2008.
DOI : 10.1145/1330511.1330513
URL : http://i.cs.hku.hk/~gfxgroup/publications/RMF_rev.pdf

W. Yang, Conception et intgration de microsystmes sur un cylindre pour la mesure de ses dformations : application un outil du domaine de la sant, EEATS, 2011.

W. Yang, A. Bonvilain, T. Alonso, A. Moreau-gaudry, and S. Basrour, Modelling and characterization of an instrumented medical needle in sight of new microsensor design for its insertion guidance, 2010 Annual International Conference of the IEEE, pp.6465-6468, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00560545

J. Yi, X. Zhu, H. Zhang, L. Shen, and X. Qiao, Spatial shape reconstruction using orthogonal fiber Bragg grating sensor array, Mechatronics, vol.22, issue.6, pp.679-687, 2010.
DOI : 10.1016/j.mechatronics.2011.10.005