M. Silcowitz-hansen, S. Niebe, and K. Erleben, A nonsmooth nonlinear conjugate gradient method for??interactive contact force problems, The Visual Computer, vol.26, issue.6-8, pp.893-901, 2010.
DOI : 10.1007/s00371-010-0502-6

S. Nicolau, L. Soler, D. Mutter, and J. Marescaux, Augmented reality in laparoscopic surgical oncology, Surgical Oncology, vol.20, issue.3, pp.189-201, 2011.
DOI : 10.1016/j.suronc.2011.07.002

H. Kenngott, M. Wagner, M. Gondan, F. Nickel, M. Nolden et al., Real-time image guidance in laparoscopic liver surgery: first clinical experience with a guidance system based on intraoperative CT imaging, Surgical Endoscopy, vol.83, issue.1, pp.933-940, 2014.
DOI : 10.1007/s00464-013-3249-0

N. Haouchine, J. Dequidt, I. Peterlik, E. Kerrien, M. Berger et al., Image-guided simulation of heterogeneous tissue deformation for augmented reality during hepatic surgery, 2013 IEEE International Symposium on Mixed and Augmented Reality (ISMAR), pp.199-208, 2013.
DOI : 10.1109/ISMAR.2013.6671780
URL : https://hal.archives-ouvertes.fr/hal-00842855

P. Pratt, D. Stoyanov, M. Visentini-scarzanella, and G. Yang, Dynamic Guidance for Robotic Surgery Using Image-Constrained Biomechanical Models, Medical Image Computing and Computer-Assisted Intervention, pp.77-85, 2010.
DOI : 10.1007/978-3-642-15705-9_10

S. Suwelack, S. Röhl, S. Bodenstedt, D. Reichard, R. Dillmann et al., Physics-based shape matching for intraoperative image guidance, Medical Physics, vol.27, issue.4, p.111901, 2014.
DOI : 10.1118/1.4896021.1

N. Haouchine, S. Cotin, I. Peterlik, J. Dequidt, M. Lopez et al., Impact of Soft Tissue Heterogeneity on Augmented Reality for Liver Surgery, IEEE Transactions on Visualization and Computer Graphics, vol.21, issue.5, pp.584-597, 2015.
DOI : 10.1109/TVCG.2014.2377772
URL : https://hal.archives-ouvertes.fr/hal-01136728

M. Sermesant, C. Forest, X. Pennec, H. Delingette, and N. Ayache, Deformable biomechanical models: Application to 4D cardiac image analysis, Medical Image Analysis, vol.7, issue.4, pp.475-488, 2003.
DOI : 10.1016/S1361-8415(03)00068-9
URL : https://hal.archives-ouvertes.fr/inria-00615637

M. Baumann, P. Mozer, V. Daanen, and J. Troccaz, Prostate Biopsy Assistance System with Gland Deformation Estimation for Enhanced Precision, Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part I, ser. MIC- CAI '09, pp.67-74, 2009.
DOI : 10.1007/978-3-642-04268-3_9
URL : https://hal.archives-ouvertes.fr/hal-00420370

H. Courtecuisse, J. Allard, P. Kerfriden, S. P. Bordas, S. Cotin et al., Real-time simulation of contact and cutting of heterogeneous soft-tissues, Medical Image Analysis, vol.18, issue.2, pp.394-410, 2014.
DOI : 10.1016/j.media.2013.11.001
URL : https://hal.archives-ouvertes.fr/hal-01097108

M. Kass, A. Witkin, and D. Terzopoulos, Snakes: Active contour models, International Journal of Computer Vision, vol.5, issue.6035, pp.321-331, 1988.
DOI : 10.1007/BF00133570
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.124.5318

T. Shen, H. Li, and X. Huang, Active Volume Models for Medical Image Segmentation, IEEE Transactions on Medical Imaging, vol.30, issue.3, pp.774-791, 2011.
DOI : 10.1109/TMI.2010.2094623

J. Schaerer, C. Casta, J. Pousin, and P. Clarysse, A dynamic elastic model for segmentation and tracking of the heart in MR image sequences, Medical Image Analysis, vol.14, issue.6, pp.738-749, 2010.
DOI : 10.1016/j.media.2010.05.009
URL : https://hal.archives-ouvertes.fr/hal-00877519

S. Speidel, S. Roehl, S. Suwelack, R. Dillmann, H. Kenngott et al., Intraoperative surface reconstruction and biomechanical modeling for soft tissue registration, Proc. Joint Workshop on New Technologies for Computer Robot Assisted Surgery, 2011.

G. S. Miller, The motion dynamics of snakes and worms, Proceedings of ACM SIGGRAPH 1988, pp.169-173, 1988.

L. Ibai, A. Hugo, A. Iker, and B. Diego, Real-time deformation, registration and tracking of solids based on physical simulation, Mixed and Augmented Reality (ISMAR), 2014 IEEE International Symposium on, 2014.

T. F. Cootes, C. J. Taylor, D. H. Cooper, and J. Graham, Active Shape Models-Their Training and Application, Computer Vision and Image Understanding, vol.61, issue.1, pp.38-59, 1995.
DOI : 10.1006/cviu.1995.1004
URL : https://www.escholar.manchester.ac.uk/api/datastream?publicationPid=uk-ac-man-scw:1d1862&datastreamId=POST-PEER-REVIEW-PUBLISHERS.PDF

I. Matthews and S. Baker, Active Appearance Models Revisited, International Journal of Computer Vision, vol.60, issue.2, pp.135-164, 2004.
DOI : 10.1023/B:VISI.0000029666.37597.d3

M. Salzmann, J. Pilet, S. Ilic, and P. Fua, Surface Deformation Models for Nonrigid 3D Shape Recovery, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.29, issue.8, pp.1481-1487, 2007.
DOI : 10.1109/TPAMI.2007.1080

F. L. Bookstein, Principal warps: thin-plate splines and the decomposition of deformations, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.11, issue.6, pp.567-585, 1989.
DOI : 10.1109/34.24792

T. W. Sederberg and S. R. Parry, Free-form deformation of solid geometric models, ACM SIGGRAPH Computer Graphics, vol.20, issue.4, pp.151-160, 1986.
DOI : 10.1145/15886.15903

A. Bartoli, Maximizing the Predictivity of Smooth Deformable Image Warps through Cross-Validation, Journal of Mathematical Imaging and Vision, vol.4, issue.1, pp.133-145, 2008.
DOI : 10.1007/s10851-007-0062-1
URL : https://hal.archives-ouvertes.fr/hal-00344556

J. Lim and M. Yang, A direct method for modeling non-rigid motion with thin plate spline, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR'05), 12005, pp.1196-1202

R. Richa, A. P. Bó, and P. Poignet, Robust 3D Visual Tracking for Robotic-Assisted Cardiac Interventions, Proceedings of the 13th international conference on Medical image computing and computerassisted intervention, pp.267-274, 2010.
DOI : 10.1007/978-3-642-15705-9_33
URL : https://hal.archives-ouvertes.fr/lirmm-00812544

D. Rueckert, L. Sonoda, C. Hayes, D. Hill, M. Leach et al., Nonrigid registration using free-form deformations: application to breast MR images, IEEE Transactions on Medical Imaging, vol.18, issue.8, pp.712-721, 1999.
DOI : 10.1109/42.796284
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.126.4732

A. Bartoli and A. Zisserman, Direct Estimation of Non-Rigid Registration, Procedings of the British Machine Vision Conference 2004, pp.899-908, 2004.
DOI : 10.5244/C.18.92

D. Pizarro and A. Bartoli, Feature-Based Deformable Surface Detection with Self-Occlusion Reasoning, International Journal of Computer Vision, vol.18, issue.8, pp.54-70, 2012.
DOI : 10.1007/s11263-011-0452-0

J. Pilet, V. Lepetit, and P. Fua, Fast Non-Rigid Surface Detection, Registration and Realistic Augmentation, International Journal of Computer Vision, vol.20, issue.2, pp.109-122, 2008.
DOI : 10.1007/s11263-006-0017-9

J. Zhu and M. R. Lyu, Progressive Finite Newton Approach To Real-time Nonrigid Surface Detection, 2007 IEEE Conference on Computer Vision and Pattern Recognition, pp.1-8, 2007.
DOI : 10.1109/CVPR.2007.383200

V. Gay-bellile, A. Bartoli, and P. Sayd, Direct Estimation of Nonrigid Registrations with Image-Based Self-Occlusion Reasoning, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.32, issue.1, pp.87-104, 2010.
DOI : 10.1109/TPAMI.2008.265
URL : https://hal.archives-ouvertes.fr/hal-00344663

A. Hilsmann, D. C. Schneider, and P. Eisert, Realistic cloth augmentation in single view video under occlusions, Computers & Graphics, vol.34, issue.5, pp.567-574, 2010.
DOI : 10.1016/j.cag.2010.05.015

S. Shen, W. Shi, and Y. Liu, Monocular 3-D Tracking of Inextensible Deformable Surfaces Under <formula formulatype="inline"><tex Notation="TeX">$L_2$</tex> </formula>-Norm, IEEE Transactions on Image Processing, vol.19, issue.2, pp.512-521, 2010.
DOI : 10.1109/TIP.2009.2038115

M. Perriollat, R. Hartley, and A. Bartoli, Monocular Template-based Reconstruction of Inextensible Surfaces, International Journal of Computer Vision, vol.67, issue.2, pp.124-137, 2011.
DOI : 10.1007/s11263-010-0352-8
URL : https://hal.archives-ouvertes.fr/hal-00344576

M. Salzmann and P. Fua, Linear local models for monocular reconstruction of deformable surfaces Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.33, issue.5, pp.931-944, 2011.

M. Salzmann, R. Hartley, and P. Fua, Convex Optimization for Deformable Surface 3-D Tracking, 2007 IEEE 11th International Conference on Computer Vision, pp.1-8, 2007.
DOI : 10.1109/ICCV.2007.4409031
URL : http://hdl.handle.net/1885/30700

F. Moreno-noguer, M. Salzmann, V. Lepetit, and P. Fua, Capturing 3D stretchable surfaces from single images in closed form, 2009 IEEE Conference on Computer Vision and Pattern Recognition, pp.1842-1849, 2009.
DOI : 10.1109/CVPR.2009.5206758
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.231.7277

]. A. Agudo, B. Calvo, and J. M. , Finite Element based sequential Bayesian Non-Rigid Structure from Motion, 2012 IEEE Conference on Computer Vision and Pattern Recognition, pp.1418-1425, 2012.
DOI : 10.1109/CVPR.2012.6247829
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.347.6961

S. Wuhrer, J. Lang, and C. Shu, Tracking Complete Deformable Objects with Finite Elements, 2012 Second International Conference on 3D Imaging, Modeling, Processing, Visualization & Transmission, pp.1-8, 2012.
DOI : 10.1109/3DIMPVT.2012.16

A. Malti, R. Hartley, A. Bartoli, and J. Kim, Monocular templatebased 3d reconstruction of extensible surfaces with local linear elasticity, Computer Vision and Pattern Recognition (CVPR), 2013 IEEE Conference on, pp.1522-1529, 2013.

N. Haouchine, J. Dequidt, M. Berger, and S. Cotin, Single view augmentation of 3D elastic objects, 2014 IEEE International Symposium on Mixed and Augmented Reality (ISMAR), pp.199-208, 2014.
DOI : 10.1109/ISMAR.2014.6948432
URL : https://hal.archives-ouvertes.fr/hal-01056323

S. F. Gibson and B. Mirtich, A survey of deformable modeling in computer graphics, Tech. Rep, 1997.

A. Nealen, M. Müller, R. Keiser, E. Boxerman, and M. Carlson, Physically Based Deformable Models in Computer Graphics, Computer Graphics Forum, vol.25, issue.1, pp.809-836, 2006.
DOI : 10.1145/1015706.1015733

E. Sifakis and J. Barbic, FEM simulation of 3D deformable solids, ACM SIGGRAPH 2012 Posters on, SIGGRAPH '12, pp.1-2050, 2012.
DOI : 10.1145/2343483.2343501

J. Barbic and D. L. James, Real-Time subspace integration for St. Venant-Kirchhoff deformable models, ACM Transactions on Graphics, vol.24, issue.3, pp.982-990, 2005.
DOI : 10.1145/1073204.1073300

H. Zhong, M. P. Wachowiak, and T. M. Peters, A real time finite element based tissue simulation method incorporating nonlinear elastic behavior, Computer Methods in Biomechanics and Biomedical Engineering, vol.5744, issue.3, pp.177-189, 2005.
DOI : 10.1002/vis.4340010208

R. Kikuuwe, H. Tabuchi, and M. Yamamoto, An edge-based computationally efficient formulation of Saint Venant-Kirchhoff tetrahedral finite elements, ACM Transactions on Graphics, vol.28, issue.1, p.8, 2009.
DOI : 10.1145/1477926.1477934

C. Guébert, C. Duriez, and L. Grisoni, Unified processing of constraints for interactive simulation, Workshop in Virtual Reality Interactions and Physical Simulation VRIPHYS' 2008

F. Grenoble, Eurographics association, pp.21-29, 2008.

A. Shaji, A. Varol, P. Fua, A. Yashoteja, S. Jain et al., Resolving occlusion in multiframe reconstruction of deformable surfaces, CVPR 2011 WORKSHOPS, pp.31-36, 2011.
DOI : 10.1109/CVPRW.2011.5981724

H. Bay, A. Ess, T. Tuytelaars, and L. Van-gool, Speeded-Up Robust Features (SURF), Computer Vision and Image Understanding, vol.110, issue.3, pp.346-359, 2008.
DOI : 10.1016/j.cviu.2007.09.014

M. C. Yip, D. G. Lowe, S. E. Salcudean, R. N. Rohling, and C. Y. Nguan, Tissue Tracking and Registration for Image-Guided Surgery, IEEE Transactions on Medical Imaging, vol.31, issue.11, pp.2169-2182, 2012.
DOI : 10.1109/TMI.2012.2212718

F. Faure, C. Duriez, H. Delingette, J. Allard, B. Gilles et al., SOFA: A Multi-Model Framework for Interactive Physical Simulation, 2012.
DOI : 10.1007/8415_2012_125
URL : https://hal.archives-ouvertes.fr/hal-00681539

J. Bosman, N. Haouchine, J. Dequidt, I. Peterlik, S. Cotin et al., The Role of Ligaments: Patient-Specific or Scenario-Specific?, Lecture Notes in Computer, vol.8789, pp.228-232, 2014.
DOI : 10.1007/978-3-319-12057-7_26
URL : https://hal.archives-ouvertes.fr/hal-01068077

K. Miller and J. Lu, On the prospect of patient-specific biomechanics without patient-specific properties of tissues, Journal of the Mechanical Behavior of Biomedical Materials, vol.27, issue.0, pp.154-166, 2013.
DOI : 10.1016/j.jmbbm.2013.01.013

N. Snavely, S. M. Seitz, and R. Szeliski, Photo tourism: Exploring photo collections in 3d, ACM SIGGRAPH 2006, pp.835-846, 2006.

A. Bartoli, Y. Gerard, F. Chadebecq, and T. Collins, On template-based reconstruction from a single view: Analytical solutions and proofs of well-posedness for developable, isometric and conformal surfaces, 2012 IEEE Conference on Computer Vision and Pattern Recognition, pp.2026-2033, 2012.
DOI : 10.1109/CVPR.2012.6247906

S. Cotin, H. Delingette, and N. Ayache, Real-time elastic deformations of soft tissues for surgery simulation Visualization and Computer Graphics, IEEE Transactions on, vol.5, issue.1, pp.62-73, 1999.

B. D. Lucas and T. Kanade, An iterative image registration technique with an application to stereo vision, Proceedings of the 7th international joint conference on Artificial intelligence -Volume 2, ser. IJCAI'81, pp.674-679, 1981.

P. A. Yushkevich, J. Piven, H. C. Hazlett, R. Smith, J. C. Ho et al., User-guided 3D active contour segmentation of anatomical structures: Significantly improved efficiency and reliability, NeuroImage, vol.31, issue.3, pp.1116-1128, 2006.
DOI : 10.1016/j.neuroimage.2006.01.015

I. Peterlík, C. Duriez, and S. Cotin, Modeling and Real-Time Simulation of a Vascularized Liver Tissue, Medical Image Computing and Computer-Assisted Intervention, pp.50-57, 2012.
DOI : 10.1007/978-3-642-33415-3_7

L. Maier-hein, P. Mountney, A. Bartoli, H. Elhawary, D. Elson et al., Optical techniques for 3D surface reconstruction in computer-assisted laparoscopic surgery, Medical Image Analysis, vol.17, issue.8, pp.974-996, 2013.
DOI : 10.1016/j.media.2013.04.003

R. Plantefeve, I. Peterlik, H. Courtecuisse, R. Trivisonne, J. Radoux et al., Atlas-Based Transfer of Boundary Conditions for Biomechanical Simulation, International Conference on Medical Image Computing and Computer-Assisted Intervention, ser. MICCAI'14, pp.33-40, 2014.
DOI : 10.1007/978-3-319-10470-6_5
URL : https://hal.archives-ouvertes.fr/hal-01070339

C. J. Paulus, L. Untereiner, H. Courtecuisse, S. Cotin, and D. Cazier, Virtual cutting of deformable objects based on efficient topological operations, The Visual Computer, vol.199, issue.5, pp.6-8, 2015.
DOI : 10.1007/s00371-015-1123-x
URL : https://hal.archives-ouvertes.fr/hal-01208546