V. V. Appia and A. J. Yezzi, Active geodesics: Region-based active contour segmentation with a global edge-based constraint, 2011 International Conference on Computer Vision, pp.1975-1980, 2011.
DOI : 10.1109/ICCV.2011.6126468

V. I. Arnold, Plane curves, their invariants, perestroikas and classification, Advances in Soviet Mathematics, vol.21, pp.33-91, 1994.
DOI : 10.1090/ulect/005

F. Benmansour and L. Cohen, Fast Object Segmentation by Growing Minimal Paths from??a??Single Point on 2D or 3D Images, Journal of Mathematical Imaging and Vision, vol.16, issue.1, pp.209-221, 2009.
DOI : 10.1007/s10851-008-0131-0
URL : https://hal.archives-ouvertes.fr/hal-00691876

V. Caselles, R. Kimmel, and G. Sapiro, Geodesic active contours, Proceedings of IEEE International Conference on Computer Vision, pp.61-79, 1997.
DOI : 10.1109/ICCV.1995.466871
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.2196

T. Chan and L. Vese, Active contours without edges, IEEE Transactions on Image Processing, vol.10, issue.2, pp.266-277, 2001.
DOI : 10.1109/83.902291
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1828

L. Cohen and R. Kimmel, Global minimum for active contour models: a minimal path approach, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.57-78, 1997.
DOI : 10.1109/CVPR.1996.517144

T. Deschamps and L. Cohen, Fast extraction of minimal paths in 3D images and applications to virtual endoscopy11A preliminary version of this work was presented at the ECCV???2000 Conference., Medical Image Analysis, vol.5, issue.4, pp.281-299, 2001.
DOI : 10.1016/S1361-8415(01)00046-9

D. Eppstein, Finding the k Shortest Paths, SIAM Journal on Computing, vol.28, issue.2, pp.652-673, 1998.
DOI : 10.1137/S0097539795290477

A. Falcão, J. Stolfi, and R. Lotufo, The image foresting transform: theory, algorithms, and applications, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.26, issue.1, pp.19-29, 2004.
DOI : 10.1109/TPAMI.2004.1261076

A. Falcão, J. Udupa, and F. Miyazawa, An ultra-fast user-steered image segmentation paradigm: live wire on the fly, IEEE Transactions on Medical Imaging, vol.19, issue.1, pp.55-62, 2000.
DOI : 10.1109/42.832960

O. Gérard, T. Deschamps, M. Greff, and L. D. Cohen, Real-Time Interactive Path Extraction with On-the-Fly Adaptation of the External Forces, European Conference on Computer Vision (ECCV), pp.807-821, 2002.
DOI : 10.1007/3-540-47977-5_53

V. Kaul, A. Yezzi, and Y. Tsai, Detecting Curves with Unknown Endpoints and Arbitrary Topology Using Minimal Paths, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.34, issue.10, pp.1952-1965, 2012.
DOI : 10.1109/TPAMI.2011.267

O. Michailovich, Y. Rathi, and A. Tannenbaum, Image Segmentation Using Active Contours Driven by the Bhattacharyya Gradient Flow, IEEE Transactions on Image Processing, vol.16, issue.11, pp.2787-2801, 2007.
DOI : 10.1109/TIP.2007.908073

J. Mille, S. Bougleux, and L. Cohen, Minimally overlapping paths sets for closed contour extraction, International Conference on Computer Vision Theory and Applications (VISAPP), 2012.
URL : https://hal.archives-ouvertes.fr/hal-00707333

J. Mille and L. Cohen, Geodesically Linked Active Contours: Evolution Strategy Based on Minimal Paths, 2 nd International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), pp.163-174, 2009.
DOI : 10.1016/0167-8396(90)90023-K
URL : https://hal.archives-ouvertes.fr/hal-00691910

P. Miranda, A. Falcão, and T. Spina, Riverbed: A Novel User-Steered Image Segmentation Method Based on Optimum Boundary Tracking, IEEE Transactions on Image Processing, vol.21, issue.6, pp.3042-3052, 2012.
DOI : 10.1109/TIP.2012.2188034

E. Mortensen and W. Barrett, Interactive Segmentation with Intelligent Scissors, Graphical Models and Image Processing, vol.60, issue.5, pp.349-384, 1998.
DOI : 10.1006/gmip.1998.0480
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.89.2987

C. Rother, V. Kolmogorov, and A. Blake, "GrabCut", ACM Transactions on Graphics, vol.23, issue.3, pp.309-314, 2004.
DOI : 10.1145/1015706.1015720

J. A. Sethian, A fast marching level set method for monotonically advancing fronts., Proceedings of the National Academy of Science, pp.1591-1595, 1996.
DOI : 10.1073/pnas.93.4.1591

J. N. Tsitsiklis, Efficient algorithms for globally optimal trajectories, IEEE Transactions on Automatic Control, vol.40, issue.9, pp.1528-1538, 1995.
DOI : 10.1109/9.412624
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.15.8514

D. J. Williams and M. Shah, A Fast algorithm for active contours and curvature estimation, Computer Vision, Graphics, and Image Processing: Image Understanding, pp.14-26, 1992.
DOI : 10.1016/1049-9660(92)90003-L

J. Y. Yen, Shortest Loopless Paths in a Network, Management Science, vol.17, issue.11, pp.712-716, 1971.
DOI : 10.1287/mnsc.17.11.712