.. Edge-based-deformable-contours, 18 1.2.1 Parametric deformable models 18 1.2.1.1 Active contours: snakes, p.20

M. Geometric-deformable, 21 1.2.2.1 Curve evolution theory 21 1.2.2.2 Level set method, p.24

.. Region-based-deformable-contours, 24 1.3.1 Mumford-Shah functional model, p.25

.. Shape, 27 1.4.1 Reference shape-based models 27 1.4.2 Higher-order active contours and phase fields Higher-order active contours, p.31

E. Line, 32 1.5.1 Road network extraction, p.33

E. Hydrographic-network, 34 1.5.2.1 Geometry of river networks, p.34

A. Ghoul, I. H. Jermyn, and J. Zerubia, A Theoretical and Numerical Study of a Phase Field Higher-Order Active Contour Model of Directed Networks, ACCV, Asian Conference on Computer Vision, 2010.
DOI : 10.1007/s11263-006-6851-y

URL : https://hal.archives-ouvertes.fr/inria-00522443

A. Ghoul, I. H. Jermyn, and J. Zerubia, Segmentation of networks from VHR remote sensing images using a directed phase field HOAC model. ISPRS Technical Commission III Symposium on Photogrammetry Computer Vision and Image Analysis, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00491017

A. Ghoul, I. H. Jermyn, and J. Zerubia, A phase field higher-order active contour model of directed networks, 2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops, 2009.
DOI : 10.1109/ICCVW.2009.5457672

URL : https://hal.archives-ouvertes.fr/inria-00409910

A. Ghoul, I. H. Jermyn, and J. Zerubia, Inflection point model under phase field higher-order active contours for network extraction from VHR satellite images, European Signal Processing Conference, 2009.

A. Ghoul, I. H. Jermyn, and J. Zerubia, Phase diagram of a long bar under a higher-order active contour energy: Application to hydrographic network extraction from VHR satellite images, 2008 19th International Conference on Pattern Recognition, 2008.
DOI : 10.1109/ICPR.2008.4761894

URL : https://hal.archives-ouvertes.fr/inria-00316619

A. Ghoul, I. H. Jermyn, and J. Zerubia, Diagramme de phase d'une énergie de type contour actif d'ordre supérieur : le cas d'une barre longue. RFIA, Reconnaissance des Formes et Intelligence Artificielle, 2008.

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

L. Alvarez, F. Guichard, P. L. Lions, and J. M. , Axioms and fundamental equations in image processing. Archive for Rational Mechanics and Analysis, pp.199-257, 1993.

K. Appel and W. Haken, Every planar map is four colorable, Contemporary Math, p.98, 1996.
DOI : 10.1090/s0002-9904-1976-14122-5

URL : http://projecteuclid.org/download/pdf_1/euclid.bams/1183538218

G. Aubert, J. F. Aujol, and L. Blanc-féraud, Detecting Codimension???Two Objects in an Image with Ginzburg-Landau Models, International Journal of Computer Vision, vol.65, issue.1-2, pp.29-42, 2005.
DOI : 10.1007/s11263-005-3847-y

URL : https://hal.archives-ouvertes.fr/inria-00070744

C. Bauer, H. Bischof, and R. Beichel, Segmentation of airways based on gradient vector flow, International Workshop on Pulmonary Image Analysis, 2009.

I. B. Ayed, A. Mitiche, and Z. Belhadj, Polarimetric image segmentation via maximum-likelihood approximation and efficient multiphase level-sets, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.28, issue.9, pp.1493-1500, 2006.
DOI : 10.1109/TPAMI.2006.191

M. Bene?, V. Chalupecký, and K. Mikula, Geometrical image segmentation by the Allen???Cahn equation, Applied Numerical Mathematics, vol.51, issue.2-3, pp.187-205, 2004.
DOI : 10.1016/j.apnum.2004.05.001

J. Besag, Statistical analysis of dirty pictures*, Journal of Applied Statistics, vol.6, issue.5-6, pp.259-302, 1986.
DOI : 10.1016/0031-3203(83)90012-2

T. Blaskovics, Z. Kato, and I. H. Jermyn, Detection of circular shapes using Markov random field, Proceedings of the IEEE International Conference on Image Processing, 2009.

T. Brox and D. Cremers, On Local Region Models and a Statistical Interpretation of??the??Piecewise Smooth Mumford-Shah Functional, International Journal of Computer Vision, vol.18, issue.9, pp.184-193, 2009.
DOI : 10.1007/s11263-008-0153-5

V. Caselles, F. Catte, T. Coll, and F. Dibos, A geometric model for active contours in image processing, Numerische Mathematik, vol.36, issue.4, pp.1-31, 1993.
DOI : 10.1007/BF01385685

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.266-277, 2001.
DOI : 10.1109/83.902291

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

T. F. Chan and L. A. Vese, A level set algorithm for minimizing the Mumford-Shah functional in image processing, Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision, 2001.
DOI : 10.1109/VLSM.2001.938895

L. Chen, Phase-Field Models for Microstructure Evolution, Annual Review of Materials Research, vol.32, issue.1, pp.113-140, 2002.
DOI : 10.1146/annurev.matsci.32.112001.132041

Y. Chen, S. Thiruvenkadam, H. D. Tagare, F. Huang, D. Wilson et al., On the incorporation of shape priors into geometric active contours, Proceedings of the IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision, 2001.

Y. M. Chen, H. D. Tagare, S. R. Thiruvenkadam, F. Huang, D. Wilson et al., Using prior shapes in geometric active contours in a variational framework, International Journal of Computer Vision, vol.12, issue.3, pp.50315-328, 2002.

J. Cheng and S. W. Foo, Dynamic directional gradient vector flow for snakes, IEEE Transactions on Image Processing, vol.15, issue.6, pp.1563-1571, 2006.
DOI : 10.1109/TIP.2006.871140

M. Cieplak, A. Giacometti, A. Maritan, A. Rinaldo, I. Rodríguez-iturbe et al., Models of fractal river basins, Journal of Statistical Physics, p.91, 1998.

I. Cohen and L. D. Cohen, A Hybrid Hyperquadric Model for 2-D and 3-D Data Fitting, Computer Vision and Image Understanding, vol.63, issue.3, pp.527-541, 1996.
DOI : 10.1006/cviu.1996.0039

URL : https://hal.archives-ouvertes.fr/inria-00074483

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

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.158.8722

L. D. Cohen and I. Cohen, Finite-element methods for active contour models and balloons for 2-D and 3-D images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.15, issue.11, pp.1131-1147, 1993.
DOI : 10.1109/34.244675

T. F. Cootes and C. J. Taylor, Active shape models -smart snakes, British Machine Vision Conference, pp.266-275, 1992.

E. Coppola, B. Tomassetti, L. Mariotti, M. Verdecchia, and G. Visconti, Cellular automata algorithms for drainage network extraction and rainfall data assimilation. Hydrological sciences-journal-des sciences hydrologiques, pp.579-592, 2007.

D. Cremers, Dynamical statistical shape priors for level set-based tracking, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.28, issue.8, pp.1262-1273, 2006.
DOI : 10.1109/TPAMI.2006.161

D. Cremers, Nonlinear dynamical shape priors for level set segmentation, Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition, 2007.

D. Cremers, Nonlinear Dynamical Shape Priors for??Level Set Segmentation, Journal of Scientific Computing, vol.18, issue.9, pp.132-143, 2008.
DOI : 10.1007/s10915-008-9220-x

D. Cremers and S. Soatto, A pseudo-distance for shape priors in level set segmentation, Proceedings of the IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision, 2003.

D. Cremers, C. Schnörr, 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, 2001.
DOI : 10.1109/VLSM.2001.938892

D. Cremers, F. Tischhauser, J. Weickert, and C. Schnörr, Diffusion snakes: Introducing statistical shape knowledge into the mumford-shah functional, International Journal of Computer Vision, vol.50, issue.3, pp.295-313, 2002.
DOI : 10.1023/A:1020826424915

D. Cremers, T. Kohlberger, and C. Schnörr, Shape statistics in kernel space for variational image segmentation, Pattern Recognition, vol.36, issue.9, pp.1929-1943, 2003.
DOI : 10.1016/S0031-3203(03)00056-6

D. Cremers, S. J. Osher, and S. Soatto, Kernel Density Estimation and Intrinsic Alignment for Shape Priors in Level Set Segmentation, International Journal of Computer Vision, vol.127, issue.2, pp.335-351, 2006.
DOI : 10.1007/s11263-006-7533-5

D. Cremers, M. Rousson, and R. Deriche, A Review of Statistical Approaches to Level Set Segmentation: Integrating Color, Texture, Motion and Shape, International Journal of Computer Vision, vol.18, issue.9, pp.195-215, 2007.
DOI : 10.1007/s11263-006-8711-1

A. P. Dempster, N. M. Laird, and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society. Series B (Methodological ), vol.39, issue.1, pp.1-38, 1977.

C. R. Dillabaugh, K. O. Niemann, and D. Richardson, Semi-automated extraction of rivers from digital imagery, GeoInformatica, vol.6, issue.3, pp.263-284, 2002.
DOI : 10.1023/A:1019718019825

P. S. Dodds and D. H. Rothman, Geometry of river networks.???I.???Scaling, fluctuations, and deviations, Physical Review E, vol.63, issue.1, 2000.
DOI : 10.1103/PhysRevE.63.016115

P. S. Dodds and D. H. Rothman, Geometry of river networks. II. Distributions of component size and number, Physical Review E, vol.63, issue.1, 2000.
DOI : 10.1103/PhysRevE.63.016116

P. S. Dodds and D. H. Rothman, Geometry of river networks. III. Characterization of component connectivity, Physical Review E, vol.63, issue.1, 2000.
DOI : 10.1103/PhysRevE.63.016117

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

M. F. Fortier, D. Ziou, C. Armenakis, and S. Wang, Survey of work on road extraction in aerial and satellite images, 1999.

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), 2003.
DOI : 10.1109/ICIP.2003.1247269

M. Gastaud, M. Barlaud, and G. Aubert, Combining shape prior and statistical features for active contour segmentation. IEEE TCSVT special session on Audio and Video Analysis forInteractive Multimedia Services, pp.726-734, 2004.

S. Geman and D. Geman, Stochastic relaxation, gibbs distributions, and the bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.6, issue.9, pp.721-741, 1984.

R. Gonzalez-cinca, R. Folch, L. Benitez, J. Ramirez-piscina, A. Casademunt et al., Phase-field models in interfacial pattern formation out of equilibrium, 2003.

M. A. Grayson, Shortening Embedded Curves, The Annals of Mathematics, vol.129, issue.1, pp.71-111, 1989.
DOI : 10.2307/1971486

U. Grenander, Y. Chow, and D. M. Keenan, Hands: a pattern theoretic study of biological shapes, p.27, 1991.
DOI : 10.1007/978-1-4612-3046-5

H. Grossauer and O. Scherzer, Using the Complex Ginzburg-Landau Equation for Digital Inpainting in 2D and 3D, Proceedings of Scale-Space, pp.225-236, 2003.
DOI : 10.1007/3-540-44935-3_16

R. E. Horton, Drainage-basin characteristics, Transactions, American Geophysical Union, vol.13, issue.1, pp.350-361, 1932.
DOI : 10.1029/TR013i001p00350

R. E. Horton, EROSIONAL DEVELOPMENT OF STREAMS AND THEIR DRAINAGE BASINS; HYDROPHYSICAL APPROACH TO QUANTITATIVE MORPHOLOGY, Geological Society of America Bulletin, vol.56, issue.3, pp.275-370, 1945.
DOI : 10.1130/0016-7606(1945)56[275:EDOSAT]2.0.CO;2

P. Horvath, A Multispectral Data Model for Higher-Order Active Contours and Its Application to Tree Crown Extraction, Advanced Concepts for Intelligent Vision Systems, 2007.
DOI : 10.1007/978-3-540-74607-2_18

URL : https://hal.archives-ouvertes.fr/inria-00152357

P. Horvath, I. H. Jermyn, Z. Kato, and J. Zerubia, A higher-order active contour model of a ???gas of circles??? and its application to tree crown extraction, Pattern Recognition, vol.42, issue.5, 2006.
DOI : 10.1016/j.patcog.2008.09.008

URL : https://hal.archives-ouvertes.fr/inria-00115631

P. Horvath, I. H. Jermyn, Z. Kato, and J. Zerubia, A Higher-Order Active Contour Model for Tree Detection, 18th International Conference on Pattern Recognition (ICPR'06), 2006.
DOI : 10.1109/ICPR.2006.79

P. Horvath, I. H. Jermyn, Z. Kato, and J. Zerubia, A higher-order active contour model of a ???gas of circles??? and its application to tree crown extraction, Pattern Recognition, vol.42, issue.5, pp.699-709, 2009.
DOI : 10.1016/j.patcog.2008.09.008

URL : https://hal.archives-ouvertes.fr/inria-00115631

S. Ingrassia and R. Rocci, Constrained monotone EM algorithms for finite mixture of multivariate Gaussians, Computational Statistics & Data Analysis, vol.51, issue.11, pp.5339-5351, 2007.
DOI : 10.1016/j.csda.2006.10.011

E. Ising, Beitrag zur theorie des ferromagnetismus Zeitschrift für Physik, pp.253-258, 1925.
DOI : 10.1007/bf02980577

M. Jehan-besson, G. Barlaud, and . Aubert, DREAM 2 S: Deformable regions driven by an Eulerian accurate minimization method for image and video segmentation Bibliography 173, International Journal of Computer Vision, vol.53, issue.1, pp.45-70, 2003.
DOI : 10.1023/A:1023031708305

H. Jermyn, On the Use of Functionals on Boundaries in Hierarchical Models of Object Recognition, 2000.

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, 1995.
DOI : 10.1109/ICCV.1995.466855

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

S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum, and A. Yezzi, Conformal curvature flows: From phase transitions to active vision. Archive for Rational Mechanics and Analysis, pp.275-301, 1996.
DOI : 10.1007/bf00379537

URL : https://hal.archives-ouvertes.fr/hal-00002650

E. Klassen, A. Srivastava, W. Mio, and S. Joshi, Analysis of planar shapes using geodesic paths on shape spaces, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.26, issue.3, pp.372-383, 2004.
DOI : 10.1109/TPAMI.2004.1262333

M. S. Kulikova, I. H. Jermyn, X. Descombes, E. Zhizhina, and J. Zerubia, A marked point process model with strong prior shape information for extraction of multiple, arbitrarilyshaped objects, International Journal of Computer Vision and Image Processing, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00503183

C. Lacoste, X. Descombes, J. Zerubia, and N. Baghdadi, Unsupervised line network extraction from remotely sensed images by polyline process, Proc. European Signal Processing Conference (EUSIPCO), 2004.

C. Lacoste, X. Descombes, J. Zerubia, and N. Baghdadi, Extraction of hydrographic networks from satellite images using a hierarchical model within a stochastic geometry framework, Proc. European Signal Processing Conference (EUSIPCO), 2005.

C. Lacoste, X. Descombes, and J. Zerubia, Unsupervised line network extraction in remote sensing using a polyline process, Pattern Recognition, vol.43, issue.4, pp.1631-1641, 2010.
DOI : 10.1016/j.patcog.2009.11.003

I. Laptev, H. Mayer, T. Lindeberg, W. Eckstein, C. Steger et al., 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

Y. G. Leclerc, Constructing simple stable descriptions for image partitioning, International Journal of Computer Vision, vol.1, issue.2, pp.73-102, 1989.
DOI : 10.1007/BF00054839

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.2727

W. Lenz, Beitrag zum verstndnis der magnetischen erscheinungen in festen krpern, Physikalische Zeitschrift, vol.21, pp.613-615, 1920.

M. E. Leventon, W. E. Grimson, and O. Faugeras, Statistical shape influence in geodesic active contours, Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition, 2000.

B. Li and S. T. Acton, Automatic active model initialization via poisson inverse gradient, IEEE Transactions on Image Processing, vol.17, issue.8, pp.1406-1420, 2008.

B. Lohani, D. C. Mason, T. R. Scott, and B. Sreenivas, Extraction of tidal channel networks from aerial photographs alone and combined with laser altimetry, International Journal of Remote Sensing, vol.3871, issue.1, pp.5-25, 2006.
DOI : 10.1145/357994.358023

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

R. Mantilla and V. K. Gupta, A GIS Numerical Framework to Study the Process Basis of Scaling Statistics in River Networks, IEEE Geoscience and Remote Sensing Letters, vol.2, issue.4, pp.404-408, 2005.
DOI : 10.1109/LGRS.2005.853571

D. C. Mason, T. R. Scott, and H. J. Wang, Extraction of tidal channel networks from airborne scanning laser altimetry, ISPRS Journal of Photogrammetry and Remote Sensing, vol.61, issue.2, pp.6167-83, 2006.
DOI : 10.1016/j.isprsjprs.2006.08.003

H. Mayer, I. Laptev, and A. Baumgartner, Multi-scale and snakes for automatic road extraction, Proceedings of the European Conference on Computer Vision, pp.720-733, 1998.
DOI : 10.1007/BFb0055700

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.8408

S. K. Mcfeeters, The use of the Normalized Difference Water Index (NDWI) in the delineation of open water features, International Journal of Remote Sensing, vol.42, issue.7, pp.1425-1432, 1996.
DOI : 10.1080/01431168608948944

T. Mcinerney and D. Terzopoulos, Topologically adaptable snakes, Proceedings of IEEE International Conference on Computer Vision, 1995.
DOI : 10.1109/ICCV.1995.466850

T. Mcinerney and D. Terzopoulos, T-snakes: Topology adaptive snakes, Medical Image Analysis, vol.4, issue.2, pp.73-91, 2000.
DOI : 10.1016/S1361-8415(00)00008-6

J. B. Mena, State of the art on automatic road extraction for GIS update: a novel classification, Pattern Recognition Letters, vol.24, issue.16, pp.3037-3058, 2003.
DOI : 10.1016/S0167-8655(03)00164-8

T. K. Moon, The expectation-maximization algorithm, IEEE Signal Processing Magazine, vol.13, issue.6, pp.47-60, 1996.
DOI : 10.1109/79.543975

D. Mumford and J. Shah, Boundary detection by minimizing functionals, Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition, 1985.

D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Communications on Pure and Applied Mathematics, vol.3, issue.5, pp.577-685, 1989.
DOI : 10.1002/cpa.3160420503

URL : http://nrs.harvard.edu/urn-3:HUL.InstRepos:3637121

J. F. O-'callaghan and D. M. Mark, The extraction of drainage networks from digital elevation data, Computer Vision, Graphics, and Image Processing, pp.323-344, 1984.

M. Ortner, X. Descombes, and J. Zerubia, Building Outline Extraction from Digital Elevation Models Using Marked Point Processes, International Journal of Computer Vision, vol.24, issue.5, pp.107-132, 2007.
DOI : 10.1007/s11263-005-5033-7

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 R. Deriche, Geodesic active regions and level set methods for supervised texture segmentation, International Journal of Computer Vision, vol.46, issue.3, pp.223-247, 2002.
DOI : 10.1023/A:1014080923068

N. Paragios, O. Mellina-gottardo, and V. Ramesh, Gradient vector flow fast geometric active contours, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.26, issue.3, pp.402-407, 2004.
DOI : 10.1109/TPAMI.2004.1262337

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.64.1640

T. Peng, I. H. Jermyn, V. Prinet, and J. Zerubia, Incorporating generic and specific prior knowledge in a multi-scale phase field model for road extraction from VHR images, IEEE Transactions on Geoscience and Remote Sensing, vol.1, issue.2, pp.139-146, 2008.

T. Peng, I. H. Jermyn, V. Prinet, and J. Zerubia, An Extended Phase Field Higher-Order Active Contour Model for Networks and Its Application to Road Network Extraction from VHR Satellite Images, Proceedings of the European Conference on Computer Vision, 2008.
DOI : 10.1007/978-3-540-88690-7_38

T. Peng, I. H. Jermyn, V. Prinet, and J. Zerubia, Extended Phase Field Higher-Order Active Contour Models for??Networks, International Journal of Computer Vision, vol.27, issue.4, pp.111-128, 2010.
DOI : 10.1007/s11263-009-0304-3

URL : https://hal.archives-ouvertes.fr/inria-00503900

G. Perrin, X. Descombes, and J. Zerubia, A marked point process model for tree crown extraction in plantations, IEEE International Conference on Image Processing 2005, 2005.
DOI : 10.1109/ICIP.2005.1529837

R. Peteri, J. Celle, and T. Ranchin, Detection and extraction of road networks from high resolution satellite mages, Proceedings of the IEEE International Conference on Image Processing, 2003.

N. Pinto, D. D. Cox, and J. J. Dicarlo, Why is Real-World Visual Object Recognition Hard?, PLoS Computational Biology, vol.58, issue.1, pp.27-34, 2008.
DOI : 10.1371/journal.pcbi.0040027.sg004

URL : http://doi.org/10.1371/journal.pcbi.0040027

R. Potts, Some generalized order-disorder transformations, Proceedings of the Cambridge Philosophical Society, p.106109, 1952.
DOI : 10.1103/PhysRev.60.252

L. J. Quackenbush, A review of techniques for extracting linear features from imagery Photogrammetric engineering and remote sensing, pp.1383-1392, 2004.

C. Reinbacher, T. Pock, C. Bauer, and H. Bischof, Variational segmentation of elongated volumetric structures, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2010.
DOI : 10.1109/CVPR.2010.5539771

T. R. Raviv, N. Kiryati, and N. A. Sochen, Unlevel-sets: Geometry and prior-based segmentation, Proceedings of the European Conference on Computer Vision, 2004.

T. R. Raviv, N. Kiryati, and N. A. Sochen, Prior-based Segmentation and Shape Registration in the Presence of Perspective Distortion, International Journal of Computer Vision, vol.50, issue.3, pp.309-328, 2007.
DOI : 10.1007/s11263-006-9042-y

M. Rochery, I. H. Jermyn, and J. Zerubia, Phase field models and higher-order active contours, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1, pp.61-75, 2005.
DOI : 10.1109/ICCV.2005.189

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.5983

M. Rochery, I. H. Jermyn, and J. Zerubia, Higher Order Active Contours, International Journal of Computer Vision, vol.24, issue.12, pp.27-42, 2006.
DOI : 10.1007/s11263-006-6851-y

URL : https://hal.archives-ouvertes.fr/inria-00070352

J. W. Rouse, R. H. Haas, J. A. Schell, and D. W. Deering, Monitoring vegetation systems in the great plains with ERTS, Earth Resources Technology Satellite Symposium, NASA SP-351, pp.309-317, 1973.

M. Rousson, Cue integration and front evolution in image segmentation, 2004.
URL : https://hal.archives-ouvertes.fr/tel-00327560

M. Rousson and N. Paragios, Shape Priors for Level Set Representations, Proceedings of the European Conference on Computer Vision, 2002.
DOI : 10.1007/3-540-47967-8_6

M. Rousson and N. Paragios, Prior Knowledge, Level Set Representations & Visual Grouping, International Journal of Computer Vision, vol.18, issue.3, pp.231-243, 2007.
DOI : 10.1007/s11263-007-0054-z

URL : https://hal.archives-ouvertes.fr/hal-00918700

C. Samson, L. Blanc-féraud, G. Aubert, and J. Zerubia, A variational model for image classification and restoration, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.22, issue.5, pp.460-472, 2000.
DOI : 10.1109/34.857003

G. Sapiro, Geometric partial differential equations and image analysis, 2001.
DOI : 10.1017/CBO9780511626319

G. Sapiro and A. Tannenbaum, Affine invariant scale-space, International Journal of Computer Vision, vol.8, issue.1, pp.25-44, 1993.
DOI : 10.1007/BF01420591

J. A. Sethian, Level Set Methods Evolving Interfaces in Geometry Fluid Mechanics, Computer Vision and Materials Science, 1996.

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

K. Siddiqi, Y. B. Lauziére, A. Tannenbaum, and S. W. Zucker, Area and length minimizing flows for shape segmentation, IEEE Transactions on Image Processing, vol.7, issue.3, pp.433-443, 1998.
DOI : 10.1109/83.661193

A. Srivastava, S. Joshi, W. Mio, and X. Liu, Statistical shape analysis: clustering, learning, and testing, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.27, issue.4, pp.590-602, 2003.
DOI : 10.1109/TPAMI.2005.86

L. H. Staib and J. S. Duncan, Boundary finding with parametrically deformable models, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.11, pp.1061-1075, 1992.
DOI : 10.1109/34.166621

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

G. Székely, A. Kelemen, C. Brechbühler, and G. Gerig, Segmentation of 2-D and 3-D objects from MRI volume data using constrained elastic deformations of flexible Fourier contour and surface models, Medical Image Analysis, vol.1, issue.1, pp.19-34, 1996.
DOI : 10.1016/S1361-8415(01)80003-7

H. D. Tagare, Deformable 2-D template matching using orthogonal curves, IEEE Transactions on Medical Imaging, vol.16, issue.1, pp.108-117, 1997.
DOI : 10.1109/42.552060

J. Tang, S. Millington, S. T. Acton, J. Crandall, and S. Harwitz, Ankle cartilage surface segmentation using directional gradient vector flow snakes, Proceedings of the IEEE International Conference on Image Processing, 2004.

D. G. Tarboton, Fractal river networks, Horton's laws and Tokunaga cyclicity, Journal of Hydrology, vol.187, issue.1-2, pp.105-117, 1996.
DOI : 10.1016/S0022-1694(96)03089-2

M. Taron, N. Paragios, and M. Jolly, Registration with Uncertainties and Statistical Modeling of Shapes with Variable Metric Kernels, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.31, issue.1, pp.99-113, 2009.
DOI : 10.1109/TPAMI.2008.36

URL : https://hal.archives-ouvertes.fr/hal-00712244

K. Thornton, J. Agren, and P. W. Voorhees, Modelling the evolution of phase boundaries in solids at the meso- and nano-scales, Acta Materialia, vol.51, issue.19, pp.5675-5710, 2003.
DOI : 10.1016/j.actamat.2003.08.008

A. Tsai, A. J. Yezzi, and A. S. Willsky, Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification, IEEE Transactions on Image Processing, vol.10, issue.8, pp.1169-1186, 2001.
DOI : 10.1109/83.935033

C. J. Tucker, Red and photographic infrared linear combinations for monitoring vegetation, Remote Sensing of Environment, vol.8, issue.2, pp.127-150, 1979.
DOI : 10.1016/0034-4257(79)90013-0

A. M. Turing, The Chemical Basis of Morphogenesis, Philosophical Transactions of the Royal Society B: Biological Sciences, vol.237, issue.641, pp.37-72, 1952.
DOI : 10.1098/rstb.1952.0012

M. Vaillant, M. I. Miller, A. L. Younes, and A. Trouvé, Statistics on diffeomorphisms via tangent space representations, NeuroImage, vol.23, pp.161-169, 2004.
DOI : 10.1016/j.neuroimage.2004.07.023

L. A. Vese and T. F. Chan, A multiphase level set framework for image segmentation using the Mumford and Shah model, International Journal of Computer Vision, vol.50, issue.3, pp.271-293, 2002.
DOI : 10.1023/A:1020874308076

S. Vinson, L. D. Cohen, and F. Perlant, Extraction of rectangular buildings using DEM and orthoimage, Scandinavian Conference on Image Analysis (SCIA'01), 2001.

M. Wei, Y. Zhou, and M. Wan, A fast snake model based on non-linear diffusion for medical image segmentation, Computerized Medical Imaging and Graphics, vol.28, issue.3, pp.109-117, 2004.
DOI : 10.1016/j.compmedimag.2003.12.002

C. Xu and J. L. Prince, Gradient Vector Flow, Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition, 1997.
DOI : 10.1007/978-0-387-31439-6_712

C. Xu and J. L. Prince, Generalized gradient vector flow external forces for active contours, Signal Processing, vol.71, issue.2, pp.131-139, 1998.
DOI : 10.1016/S0165-1684(98)00140-6

A. Yezzi, S. Kichenassamy, A. Kumar, P. Olver, and A. Tannenbaum, A geometric snake model for segmentation of medical imagery, IEEE Transactions on Medical Imaging, vol.16, issue.2, pp.199-209, 1997.
DOI : 10.1109/42.563665

URL : https://hal.archives-ouvertes.fr/hal-00002725

J. Youn and J. S. Bethel, Adaptive snakes for urban road extraction, International Archives of Photogrammetry and Remote Sensing, pp.465-470, 2004.

A. L. Yuille, P. W. Hallinan, and D. S. Cohen, Feature extraction from faces using deformable templates, International Journal of Computer Vision, vol.26, issue.6, pp.99-111, 1992.
DOI : 10.1007/BF00127169

S. C. Zhu and A. Yuille, Region competition: unifying snakes, region growing, energy/Bayes/MDL for multi-band image segmentation, Proceedings of IEEE International Conference on Computer Vision, pp.884-900, 1996.
DOI : 10.1109/ICCV.1995.466909