D. Adalsteinsson and J. A. Sethian, The Fast Construction of Extension Velocities in Level Set Methods, Journal of Computational Physics, vol.148, issue.1, pp.2-22, 1999.
DOI : 10.1006/jcph.1998.6090

M. Barzohar and D. Cooper, Automatic finding of main roads in aerial images by using geometric-stochastic models and estimation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.18, issue.7, pp.707-721, 1996.
DOI : 10.1109/34.506793

A. Bossavit, Applied differential geometry: A compendium, 2002.

V. Caselles, F. Catte, T. Coll, and F. Dibos, Geometric models for active contours, Proceedings., International Conference on Image Processing, pp.1-31, 1993.
DOI : 10.1109/ICIP.1995.537567

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. F. Chan and L. A. Vese, Active contours without edges, IEEE Transactions on Image Processing, vol.10, issue.2, pp.10-2266, 2001.
DOI : 10.1109/83.902291

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1828

Y. Chen, S. Thiruvenkadam, H. D. Tagare, F. Huang, D. Wilson et al., On the incorporation of shape priors into geometric active contours, Proc. IEEE Workshop VLSM, pp.145-152, 2001.

L. D. Cohen, On active contour models and balloons, CVGIP: Image Understanding, vol.53, issue.2, pp.211-218, 1991.
DOI : 10.1016/1049-9660(91)90028-N

D. Cremers, C. Schnorr, and J. Weickert, Diffusion-snakes: combining statistical shape knowledge and image information in a variational framework, Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision, pp.137-144, 2001.
DOI : 10.1109/VLSM.2001.938892

M. A. Fischler, J. M. Tenenbaum, and H. C. Wolf, Detection of roads and linear structures in low-resolution aerial imagery using a multisource knowledge integration technique, Computer Graphics and Image Processing, vol.15, issue.3, pp.201-223, 1981.
DOI : 10.1016/0146-664X(81)90056-3

A. Foulonneau, P. Charbonnier, and F. Heitz, Geometric shape priors for region-based active contours, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429), pp.413-416, 2003.
DOI : 10.1109/ICIP.2003.1247269

P. Fua and Y. G. Leclerc, Model driven edge detection, Machine Vision and Applications, vol.8, issue.1, pp.45-56, 1990.
DOI : 10.1007/BF01211451

D. Geman and B. Jedynak, An active testing model for tracking roads in satellite images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.18, issue.1, pp.1-14, 1996.
DOI : 10.1109/34.476006

URL : https://hal.archives-ouvertes.fr/inria-00073935

S. Jehan-besson, M. Barlaud, and G. Aubert, DREAM2S: Deformable Regions Driven by an Eulerian Accurate Minimization Method for Image and Video Segmentation, Int'l J. Comp. Vis, vol.53, pp.45-70, 2003.
DOI : 10.1007/3-540-47977-5_24

URL : https://hal.archives-ouvertes.fr/hal-00664596

I. H. Jermyn, Invariant Bayesian estimation on manifolds, The Annals of Statistics, vol.33, issue.2, pp.583-605, 2005.
DOI : 10.1214/009053604000001273

URL : http://arxiv.org/abs/math/0506296

I. H. Jermyn and H. Ishikawa, Globally optimal regions and boundaries as minimum ratio weight cycles, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.23, issue.10, pp.1075-1088, 2001.
DOI : 10.1109/34.954599

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.100.7360

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

S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum, and A. Yezzi, Gradient flows and geometric active contour models, Proceedings of IEEE International Conference on Computer Vision, pp.810-815, 1995.
DOI : 10.1109/ICCV.1995.466855

URL : https://hal.archives-ouvertes.fr/hal-00002665

R. Kimmel and A. M. Bruckstein, On regularized laplacian zero crossings and other optimal edge integrators, International Journal of Computer Vision, vol.53, issue.3, pp.225-243, 2003.
DOI : 10.1023/A:1023030907417

C. Lacoste, X. Descombes, and J. Zerubia, A comparative study of point processes for line network extraction in remote sensing, Research Report, vol.4516, 2002.
URL : https://hal.archives-ouvertes.fr/inria-00072072

I. Laptev, T. Lindeberg, W. Eckstein, C. Steger, and A. Baumgartner, Automatic extraction of roads from aerial images based on scale space and snakes, Machine Vision and Applications, vol.12, issue.1, pp.23-31, 2000.
DOI : 10.1007/s001380050121

M. E. Leventon, W. E. Grimson, and O. Faugeras, Statistical shape influence in geodesic active contours, Proc. IEEE CVPR, pp.316-322, 2000.

R. Malladi, J. A. Sethian, and B. C. Vemuri, Shape modeling with front propagation: a level set approach, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.17, issue.2, pp.158-175, 1995.
DOI : 10.1109/34.368173

N. Merlet and J. Zerubia, New prospects in line detection by dynamic programming, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.18, issue.4, pp.426-431, 1996.
DOI : 10.1109/34.491623

W. M. Neuenschwander, P. Fua, L. Iverson, G. Székely, and O. Kubler, Ziplock snakes, International Journal of Computer Vision, vol.25, issue.3, pp.191-201, 1997.
DOI : 10.1023/A:1007924018415

S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988.
DOI : 10.1016/0021-9991(88)90002-2

N. Paragios and R. Deriche, Geodesic Active Regions: A New Framework to Deal with Frame Partition Problems in Computer Vision, Journal of Visual Communication and Image Representation, vol.13, issue.1-2, pp.249-268, 2002.
DOI : 10.1006/jvci.2001.0475

N. Paragios and M. Rousson, Shape priors for level set representations, Proc. ECCV, pp.78-92, 2002.

T. Pavlidis, Algorithms for Graphics and Image Processing, chapter 7, 1982.

M. Rochery, I. H. Jermyn, and J. Zerubia, Étude d'une nouvelle classe de contours actifs pour la détection de routes dans des images de télédétection, Proc. GRETSI, 2003.

M. Rochery, I. H. Jermyn, and J. Zerubia, Higher order active contours and their application to the detection of line networks in satellite imagery, Proc. IEEE Workshop VLSM, at ICCV, 2003.

M. Rochery, I. H. Jermyn, and J. Zerubia, Gap closure in (road) networks using higher-order active contours, 2004 International Conference on Image Processing, 2004. ICIP '04., 2004.
DOI : 10.1109/ICIP.2004.1421444

M. Rochery, I. H. Jermyn, and J. Zerubia, New higher-order active contour energies for network extraction, IEEE International Conference on Image Processing 2005, 2005.
DOI : 10.1109/ICIP.2005.1530182

J. A. Sethian, Level Set Methods and Fast Marching Methods: Evolving Interfaces in Geometry Fluid Mechanics, Computer Vision and Materials Science, 1999.

J. A. Sethian, Fast marching methods. SIAM Rev, pp.41-2199, 1996.
DOI : 10.1007/978-3-540-70529-1_379

K. Siddiqi, B. B. Kimia, and C. Shu, Geometric Shock-Capturing ENO Schemes for Subpixel Interpolation, Computation and Curve Evolution, Graphical Models and Image Processing, vol.59, issue.5, pp.278-301, 1997.
DOI : 10.1006/gmip.1997.0438

A. Steiner, R. Kimmel, and A. M. Bruckstein, Shape enhancement and exaggeration, Graphical Models and Image Processing, vol.60, issue.2, pp.1112-1124, 1998.

R. Stoica, X. Descombes, and J. Zerubia, A Gibbs Point Process for Road Extraction from Remotely Sensed Images, International Journal of Computer Vision, vol.57, issue.2, pp.121-136, 2004.
DOI : 10.1023/B:VISI.0000013086.45688.5d

M. Sussman and E. Fatemi, An Efficient, Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow, SIAM Journal on Scientific Computing, vol.20, issue.4, pp.1165-1191, 1997.
DOI : 10.1137/S1064827596298245

M. Sussman, P. Smereka, and S. Osher, A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow, Journal of Computational Physics, vol.114, issue.1, pp.146-159, 1994.
DOI : 10.1006/jcph.1994.1155

F. Tupin, H. Maitre, J. Mangin, J. Nicolas, and E. Pechersky, Detection of linear features in SAR images: application to road network extraction, IEEE Transactions on Geoscience and Remote Sensing, vol.36, issue.2, pp.434-453, 1998.
DOI : 10.1109/36.662728

A. Vasilevskiy and K. Siddiqi, Flux maximizing geometric flows, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, issue.12, pp.1565-1578, 2002.
DOI : 10.1109/TPAMI.2002.1114849

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.20.99

. Unité-de-recherche-inria-sophia and . Antipolis, route des Lucioles -BP 93 -06902 Sophia Antipolis Cedex (France) Unité de recherche INRIA Futurs : Parc Club Orsay Université -ZAC des Vignes 4, 2004.

I. Unité-de-recherche and . Lorraine, Technopôle de Nancy-Brabois -Campus scientifique 615, rue du Jardin Botanique -BP 101 -54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu -35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l'Europe -38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Rocquencourt, Domaine de Voluceau -Rocquencourt -BP 105 -78153 Le Chesnay Cedex

I. De-voluceau-rocquencourt, BP 105 -78153 Le Chesnay Cedex (France) http://www.inria.fr ISSN, pp.249-6399