L. De and G. Spi71, soit S, une vari et e dii erentiable de dimension n. Soit p un point de S, S p l'espace tangent t a S en p. Soit ~ v un vecteur tangent t a S en p

. A. Fig, 1 { Deux cliques d'ordre 2 e t une clique d'ordre 1

A. J. Askne, P. Dammert, L. Ulander, and G. Smith, C-band repeat-pass interferometric SAR observations of the forest, IEEE Transactions on Geoscience and Remote Sensing, vol.35, issue.1, 1997.
DOI : 10.1109/36.551931

A. , M. Artigue, and V. Gautheron, Syst emes dii erentiels -etude graphique, CE- DIC, 1983.

A. R. Abraham, J. E. Marsden, and T. S. Ratiu, Manifolds, tensor analysis and applications, 1988.

]. R. Bam93 and . Bamler, Phase statics and decorrelation in SAR interferograms, Proceedings of IGARSS'93, 1993.

]. J. Bar91 and . Baranger, Analyse Num erique, 1991.

B. F. Barbaresco, S. Bonney, J. , and B. Monnier, Contours actifs g eodesiques et a mod eles contraints pourle suivi des orages dans un contexte multisenseur : radar, interferometre VHF, satellite IR, GRETSI'97, p.1997

B. , J. P. Berroir, I. Herlin, and I. Cohen, A numerical model for large deformation on meteorological images, International Conference o n Analysis and Optimisation of Systems, Images, Wavelets and PDE's, 1996.
URL : https://hal.archives-ouvertes.fr/inria-00532686

B. , P. J. Besl, and R. C. Jain, Three-dimensional object recognition, Surveys, vol.17, issue.1, pp.75-145, 1985.

]. D. Bibliographie-bon91 and . Bone, Fourier fringe analysis: the two dimensional phase unwrapping problem, Applied Optics, vol.30, pp.3227-3632, 1991.

B. , S. T. Barnard, and W. B. Thompson, Disparity analysis of images, Univ. of Minnesota, 1979.

]. J. Can86 and . Canny, A computational approach to edge detection. Pattern Analysis and Machine Intelligence, p.1986

C. I. Cohen, N. Ayache, and P. Sulger, Tracking points on deformable objects using curvature information, Proceedings of the Second European Conference on Computer Vision 1992, pp.458-466, 1992.
DOI : 10.1007/3-540-55426-2_51
URL : https://hal.archives-ouvertes.fr/inria-00074965

C. , C. H. Chou, and Y. C. Chen, Moment-preserving pattern matching, Pattern Recognition, vol.23, pp.461-474, 1990.

C. , R. T. Chin, and C. R. Dyer, Model-based recognition in robot vision, Surveys, vol.18, issue.1, pp.67-108, 1986.

C. R. Courant, K. O. Friedrichs, and H. Lewy, On the Partial Difference Equations of Mathematical Physics, IBM Journal of Research and Development, vol.11, issue.2, pp.215-235, 1967.
DOI : 10.1147/rd.112.0215

C. , J. K. Cheng, and T. S. Huang, A subgraph isomorphism algorithm using resolution, Pattern Recognition, vol.13, pp.371-379, 1981.

]. I. Ch97a, I. Cohen, and . Herlin, Curves matching using geodesic path, SCIA'97, 1997.

]. I. Ch97b, I. Cohen, and . Herlin, Tracking meteorological structures through curves matching us ing geodesic paths, 1997.

B. Cohen and I. Herlin, Curves matching using geodesic paths, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231), 1998.
DOI : 10.1109/CVPR.1998.698686
URL : https://hal.archives-ouvertes.fr/inria-00532724

C. , L. D. Cohen, and R. Kimmel, Global minimum for active contour models: A minimal path appro ach, Proceedings of the conference on Computer Vision and Pattern Recognition, pp.666-673, 1996.

C. 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

]. C. Cmka, D. Carnec, C. Massonet, and . King, Measurement of land subsidence by means of diierential SAR interferometry

]. C. Cmkb, D. Carnec, C. Massonet, and . King, Potentiel d'application de l'interf erom etrie SAR dii erentielle a l a d etection de mouvements de terrain

C. Carnec, D. Massonet, J. Villain, and C. King, Potential application of diierential SAR interferometry for monitoring the impact of underground mining, The First Workshop on SAR Interferometry, T okyo, Japan Earth Environment Observation Committe, National Space Agency of Japan, 1994.

]. T. Cri86 and . Crimmins, Geometric lter for reducing speckle, Optical engineering, vol.25, pp.651-654, 1986.

]. E. Dan80 and . Danielsson, Euclidean distance mapping, Computer Vision, Graphics, and Image Processing, vol.14, pp.227-248, 1980.

D. , S. Dupont, and M. Berthod, Interf erom etrie radar et d eroulement de phase Rapport de recherche, R R No 2344, Carmo. Diierential Geometry of Curves and Surfaces, 1976.

]. Y. Del93 and . Delignon, Etude statistique d'images radar de la surface de la mer, 1993.

]. R. Bibliographie-der87 and . Deriche, Optimal edge detection using recursive ltering, International Journal of Computer Vision, pp.167-187, 1987.

]. S. Dup93 and . Dupont, D eroulement de phase en interf erom etrie radar rapport de stage, Ecole Sup erieure en Sciences Informatiques, 1993.

]. S. Dup97 and . Dupont, G en eration de mod eles num eriques de terrain par interf erom etrie ROS, 1997.

E. , C. L. Epstein, and M. Gage, The curve shortening ow, Wave motion: Theory, modeling and Computation, 1987.

F. Fruneau and J. Achache, D etection du glissement de terrain de Saint- Etienne de Tin ee par interf erom etrie SAR et mod elisation, C.R. Acad. Sci, pp.809-816, 1995.

F. , O. D. Faugeras, and M. Berthod, Improving consistency and reducing ambiguity in stochastic labeling: An optimization approach, PAMI, vol.3, issue.4, pp.412-424, 1981.

F. G. Fornaro, G. Franchetti, and R. Lanari, Interferometric SAR phase unwrapping using Green's formulation, IEEE Transactions on Geoscience and Remote Sensing, vol.34, issue.3, pp.720-727, 1996.
DOI : 10.1109/36.499751

F. K. Feigl, A. Sergent, and D. Jacq, Estimation of an earthquake focal mechanism from a satellite radar interferogram: Application to the December 4, 1992 Landers aftershock, Geophysical Research Letters, vol.99, issue.9, pp.1037-1040, 1995.
DOI : 10.1029/94GL03212

F. V. Frost, J. Stiles, K. Shanmugan, and J. Holtzman, A model for radar images and its application to adaptative digital ltering of multiplicative noise, IEEE Trans. on Pattern Analysis and Machine Intelligence, vol.4, pp.157-166, 1982.

G. A. Gu-eziec and N. Ayache, Smoothing and matching of 3-d space curves, International Journal of Computer Vision, vol.79, issue.3, pp.79-104, 1994.
DOI : 10.1007/BF01420985

G. J. Gomes, D. Darsa, B. Costa, and L. Velho, Warping and Morphing og Graphical Objects, 1999.

G. , R. M. Goldstein, H. Engelhardt, B. Kamb, and R. M. Frolich, Satellite radar interferometry for monitoring ice sheet motion: Application to an antartic ice stream, Science, vol.262, pp.1525-1529, 1993.

G. , S. Geman, and D. Geman, Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE Trans. Pattern Anal. Machine Intell, vol.6, issue.6, pp.721-741, 1984.

G. A. Goshtasby, S. H. Gage, and J. F. Bartholic, A t wo-stage cross correlation approach to template matching, PAMI, vol.7, issue.2, pp.374-378, 1984.

G. A. Gabriel, R. Goldstein, and H. Zebker, Mapping small elevation changes over large areas: Differential radar interferometry, Journal of Geophysical Research, vol.91, issue.B5, pp.9183-9191, 1989.
DOI : 10.1029/JB094iB07p09183

]. F. Gir92 and . Girault, Auscultation par imagerie num erique de quelques versants instables, 1992.

G. , D. Ghiglia, and M. Pritt, Two-Dimensional Phase Unwrapping. Theory, Algorithms and Software, 1998.

G. , D. Ghiglia, and L. Romero, Direct phase estimation from phase diierence using fast elliptic partial diierential equation solvers. Optic letters, pp.1107-1109, 1989.

G. , D. Ghiglia, and L. Romero, Robust two dimensional weighted and unweighted phase unwrapping that use fast transforms and iterative methods, Journal of the Optical Society of America, vol.11, pp.107-1117

G. , R. M. Goldstein, H. A. Zebker, and C. L. Werner, Satellite radar interferometry: Two-dimensional phase unwrapping, Radio Science, vol.23, issue.4, pp.713-720, 1988.

H. L. Herlin, D. Er-eziat, G. Giraudon, C. Nguyen, and C. Graagne, Segmentation of echocardiographic images with markov random elds, Third european Conference on Computer Vision, 1994.

H. E. Huot, I. Cohen, and I. Herlin, An unwrapping method for interferometric SAR images, International Conference on Acoustics, Speech, and Signal Processing, pp.2853-2858, 1997.

]. Her94 and . Herland, Surveillance op erationnelle des glaces au moyen du SAR d'ERS-1. Observation de la terre { Bulletin trimestriel, pp.6-8, 1994.

H. , E. Huot, and I. Herlin, D etection d'eeets phasim etriques SAR li es a des changements d' etat de surface, ORASIS'97, 1997.

]. E. Hh98a, I. Huot, and . Herlin, Cropland detection with SAR interferometry: A segmentation model, International Conference on Acoustics, Speech, and Signal Processing, pp.2853-2858, 1998.

]. E. Hh98b, I. Huot, and . Herlin, A model for detecting phasimetric SAR eeects coming from rainy e v ents, Proceedings of International Conference o n I m a g e Processing, ICIP'98, 1998.

H. E. Huot, I. Herlin, and D. , Segmentation of temporal eeects on phasimetric SAR images, Proceedings of International Conference on Pattern Recognition, ICPR'98, pp.1390-1392, 1998.

H. E. Huot, I. Herlin, and I. Cohen, Segmentation d'image d'interf erom etrie radar, Journ ees ORASIS'96, 1996.

H. , G. Henebry, and D. Rieck, Applying principal components analysis to image time series: eeects on scene segmentation and spatial structures, Proceedings of IGARSS'96, pp.448-450, 1996.

H. Huot, J. R-u-d-a-n-t, N. Classeau, B. Flasque, P. Guillope et al., Image processing for multitemporal SAR images, Proceedings of European Symposium on Remote Sensing , volume SAR Image Analysis, Modelling, and Techniques
URL : https://hal.archives-ouvertes.fr/inria-00532723

B. K. Horn and B. G. Schunk, Determining optical flow, Artificial Intelligence, vol.17, issue.1-3, pp.185-203, 1981.
DOI : 10.1016/0004-3702(81)90024-2

H. Ph, K. Hartl, X. Thiel, J. Wu, and . Sievers, Application de l'interf erom etrie du SAR d'ERS-1 dans l'Antartique, pp.1-4, 1994.

]. B. Hun79 and . Hunt, Matrix formulation of the reconstruction phases values from phases diierences, Journal of the Optical Society of America, vol.69, pp.393-399, 1979.

H. E. Huot, H. Yahia, I. Herlin, and I. Cohen, Mise en correspondance de surfaces par chemins g eod esiques

H. , R. Hummel, and S. Zucker, On the foundation of relaxation labeling process, IEEE Trans. Pattern Anal. Machine Intell, vol.6, issue.6, pp.267-280, 1983.

K. R. Kimmel, A. Amir, and A. F. Bruckstein, Finding shortest paths on surfaces using level sets propagation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.17, issue.6, pp.635-640, 1995.
DOI : 10.1109/34.387512

K. , R. Kimmel, and A. M. Bruckstein, Tracking level sets by l e v el sets: A method for solving the shape from shading problem, CVIU, vol.62, issue.1, pp.47-58, 1995.

K. Z. Kato, M. Berthod, and J. Zerubia, A hierarchical Markov random eld model and multi-temperature annealing for parallel image classiication, pp.1993-94, 1938.

K. G. Kattenborn, H. Klaedtke, S. Guumlth, and M. Reich, Potential of ERS- 1 SAR for agricultural statics, 1996.

K. D. Kuan, A. Sawchunk, and P. Chavel, Adaptative restauration of images with speckle, IEEE Trans. on Acoustics, Speech and Signal Processing, pp.373-383, 1987.

]. R. Kskb95a, D. Kimmel, N. Shaked, A. M. Kiryati, and . Bruckstein, Skeletonization via distance maps and level sets, CVIU, vol.62, issue.3, pp.382-391

]. R. Kskb95b, K. Kimmel, B. B. Siddiqi, A. M. Kimia, and . Bruckstein, Shape from shading: Level set propagation and viscosity solutions, IJCV, vol.16, issue.2, pp.107-133, 1995.

K. M. Kass, A. Witkin, and D. Terzopoulos, Snakes: Active contour models, International Journal of Computer Vision, vol.5, issue.6035, pp.312-313, 1988.
DOI : 10.1007/BF00133570

L. , O. Looeld, and C. Arndt, Etimating the derivative of modulo-mapped phases, Proceedings of International Conference on Acoustics, Speech, and Signal Processing, 1997.

]. D. Lab96 and . Labrousse, Mod elisation markovienne pour le d eroulement de phases interf erom etriques SAR, 1996.

L. D. Labrousse, S. Dupont, and M. Berthod, SAR interferometry: a markovian approach to phase unwrapping with a discontinuity model, IGARSS'96, 1996.

L. Lee, Speckle analysis and smoothing of synthetic aperture radar images, Computer Graphics and Image Processing, vol.17, issue.1, pp.24-32, 1981.
DOI : 10.1016/S0146-664X(81)80005-6

L. Legoupil, F. Fawal, M. Desvignes, M. Revenu, P. Allain et al., Matching of Curvilinear Structures: Application to the Identification of Cortical Sulci on 3D magnetic resonance brain image, Proccedings of Pattern Recognition in Practice, 1994.
DOI : 10.1016/B978-0-444-81892-8.50021-3
URL : https://hal.archives-ouvertes.fr/hal-00981832

L. A. Lerios, C. D. Garrnkle, and M. Levoy, Feature-based volume metamorphosis, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques , SIGGRAPH '95, pp.449-464, 1995.
DOI : 10.1145/218380.218502

]. G. Lkvl97, R. Lemoine, H. Kidd, and . Van-leeuwen, Methodological advancements in using ERS SAR data for crop area estimation, Proceedings of the 3rd ERS Symposium on Spaceborne Radar Imagery, 1997.

L. , I. Lyuboshenko, and H. Ma^-tre, Phase unwrapping for interferometric SAR using helmholtz equation eigenfunctions and the rst green's identity, Journal of the Optical Society of America

B. Lyuboshenko and H. Ma^-tre, Implementing a stable integral method for interferometric phase unwrapping, Proceedings of EUSAR'98, pp.253-256, 1998.

L. H. Laur, T. L. Toan, and A. Lopes, Textural segmentation of SAR images using rst order statistical parameters, IGARSS'87 Symposium, pp.1463-1468, 1987.

L. Q. Lin, J. Vesecky, and H. A. Zebker, New approaches in interferometric SAR data processing, IEEE Transactions on Geoscience and Remote Sensing, vol.30, issue.3, 1992.
DOI : 10.1109/36.142934

L. H. Lim, W. Xu, and X. Huang, Two new practical methods for phase unwrapping, International Geoscience and Remote Sensing Symposium, 1995.

]. I. Lyu96 and . Lyuboshenko, Une m ethode stable de d eveloppement de la phase en interf erom etrie ROS, 1996.

]. G. Mal92 and . Malandain, Filtrage, Topologie et mise en correspondance d'images m edicales multidimensionnelles, 1992.

]. D. Mas and . Massonnet, Coseismic deformation eld of the M=6.7 Northridge, California earthquake of january 17, 1994 recorded by two radar satellites using interferometry, Geophysical Research Letters

M. D. Massonnet, P. Briole, and A. Arnaud, D e a t i o n o f m o u n t Etna monitored by spaceborne radar interferometry, Nature { International Weekly Journal of Science, vol.375, pp.567-570, 1995.

]. D. Mf95a, K. Massonnet, and . Feigl, Discrimination of geophysical phenomena in satellite radar interferograms, Geophysical Research Letters, vol.22, issue.12, pp.1537-1540, 1995.

]. D. Mf95b, K. Massonnet, and . Feigl, Satellite radar interfeometric map of the coseismic deformation eld of the M=6.1 Eureka Valley, California earthquake of may 17, Geophysical Research Letters, issue.12, pp.221541-1544, 1993.

M. D. Massonnet, K. Feigl, M. Rossi, and F. Adragna, Radar interferometric mapping of deformation in the year after the Landers earthquake, Nature, vol.369, issue.6477, pp.227-230, 1994.
DOI : 10.1038/369227a0

]. K. Mog58 and . Mogi, Relation between the eruption of various volcanoes and the deformation of the ground surface around them. Bulletin of the earthquake research institute, pp.99-134, 1958.

M. , D. Massonnet, and T. Rabaute, Radar interfometry: limits and potential, IEEE Transactions on Geoscience and Remote Sensing, pp.31-455, 1993.

]. D. Mrc93a, B. Massonnet, C. Rogron, and . Carmona, From Optics to Radar, Spot and ERS Applications, chapter Evaluation des changements de phase de surface sur de grandes zones, 1993.

M. Massonnet, M. Rossi, C. Carmona, F. Adragna, G. Peltzer et al., The displacement eld of the Landers earthquake mapped by radar interferometry, Nature { International Weekly Journal of Science, vol.364, pp.138-142, 1993.

O. , S. Osher, and J. A. Sethian, Fronts propagating with curvature dependent speed: Algorithms based on Hamilton{Jacobi formulations, J. of Comput. Physics, vol.79, pp.12-49, 1988.

P. , N. Paragios, and R. Deriche, Geodesic active regions for motion estimation and tracking, ICCV99, p.688, 1999.
URL : https://hal.archives-ouvertes.fr/inria-00073043

P. , F. Perlant, and D. Massonnet, Diierent spot dem applications for studies in SAR interferometry, XVII ISPRS Congress, Commission IV, v ol. XXIX:87{ 93, 1991.

P. Prati, F. Rocca, A. M. Guarineri, and E. Damonti, Seismic vibration for SAR focusing: Interferometrical applications, Geoscience R emote Sensing, 1990.

]. M. Bibliographie-pri96 and . Pritt, Phase unwrapping by means of multigrid techniques for interferometric sar, IEEE Trans. on Geoscience and Remote Sensing, vol.34, issue.3, pp.728-738, 1996.

R. Rudant, A. Bedidi, R. Calonne, D. Massonnet, G. Nesti et al., Laboratory experiments for the interpretation of phase shift in SAR interferograms, Proceedings of Fringe'96, 1996.

R. Rudant, A. Edidi, D. Massonnet, G. Nesti, and R. Calonne, Analyse d'une s equence d'interf erogrammes dii erentiels obtenus a partir de donn ees ERS-1 sur le site de Naizin en Bretagne, Symposium International de Toulouse, 1995.

]. J. Ric94 and . Richards, Remote Sensing Digital Image Analysis. springer-verlag, 1994.

S. Serra and M. Berthod, Optimal subpixel matching of contour chains and segments, Proceedings of IEEE International Conference on Computer Vision, pp.402-407, 1995.
DOI : 10.1109/ICCV.1995.466911

]. J. Set96 and . Sethian, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Materials Sciences, 1996.

S. , T. W. Sederberg, and E. Greenwood, A physically based approach to 2D shape blending, Computer Graphics, Siggraph'92 Conference proceedings, pp.25-34, 1992.

S. , L. G. Shapiro, and R. M. Haralick, Structural descriptions and inexact matching, PAMI, vol.3, issue.5, pp.504-519, 1981.

S. Sapiro, R. Kimmel, D. Shacked, B. Kimia, and A. Bruckstein, Implementing continuous-scale morphology via curve evolution, Pattern Recognition, vol.26, issue.9, pp.1363-1372, 1993.
DOI : 10.1016/0031-3203(93)90142-J

S. , F. Stein, and G. G. Medioni, Structural indexing: EEcient two dimensional object recognition1198{1204, December1992. BIBLIOGRAPHIE Spa95] U. Spagnolini. 2-D phase unwrapping and instantaneous frequency estimation, PAMI IEEE Trans. on Geoscience and Remote Sensing, vol.14, issue.333, pp.579-589, 1995.

]. M. Spi71 and . Spivak, A comprehensive introduction to diierential geometry, 1971.

S. , J. A. Sethian, and J. Strain, Crystal growth and dendritic solidiication, Journal of Computational Physics, vol.98, pp.231-253, 1992.

]. R. Sze89 and . Szeliski, Fast parallel surface interpolation with applications to digital cartography, 1989.

]. D. Ter84 and . Terzopoulos, Multiresolution algorithms in computational vision, IU84, pp.225-262, 1984.

T. , T. Paj, and L. Van-gool, Matching of 3D curves using semi diierential invariants, IEEE Proceedings of the International Conference on Computer Visio n, pp.390-395, 1995.

]. J. Thi94 and . Thirion, Extremal points: deenition and application to 3D image registration, IEEE Proceedings of Computer Vision and Pattern Recognition, pp.587-592, 1994.

]. J. Tho79 and . Thorpe, Elementary Topics In Diierential Geometry, 1979.

]. E. Tro96 and . Trouv-e, Imagerie interf erentielle en radar a ouverture synth etique, 1996.

T. , H. Takajo, and T. Takahashi, Least-squares phase estimation from the phase diierence, Journal of the Optical Society of America, vol.5, issue.3, pp.416-425, 1988.

]. F. Tup97 and . Tupin, Reconnaissances des formes et analyse de sc ene en imagerie radar a ouverture synth etique, 1997.

]. A. Bibliographie-vdk84, J. J. Van-doorn, and . Koenderink, Spatiotemporal integration in the detection of coherent motion, Vision Research, vol.24, issue.1, pp.47-53, 1984.

]. G. Win95 and . Winkler, Image Analysis, Random Fields and Dynamic Monte Carlo Methods, 1995.

W. , U. Wegm-uller, and C. L. Werner, Farmland monitoring with SAR interferometry, IGARSS'95, 1995.

W. , U. Wegm-uller, C. L. Werner, D. , and M. Borgeaud, Land-surface analysis using ERS-1 SAR interferometry, ESA bulletin, vol.81, pp.30-37, 1995.

X. , G. Xu, and Z. Zhang, Epipolar Geometry in Stereo, Motion, and Object Recognition: A Uniied Approach, 1996.

]. Z. Zf92a, O. D. Zhang, and . Faugeras, Estimation of displacements from two 3-D frames obtained from stereo, PAMI, issue.12, pp.141141-1156, 1992.

]. Z. Zf92b, O. D. Zhang, and . Faugeras, Estimation of displacements from two 3D frames obtained from stereo, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.12, pp.1141-1156, 1992.

Z. Zebker, P. Rosen, R. Goldstein, A. Gabriel, and C. Werner, On the derivation of coseismic displacement elds using diierential radar interferometry: the Landers earthquake, Journal of Geophysical Research, vol.99, issue.B10, pp.19-617, 1994.

Z. , H. Zebker, and J. Villasenor, Decorrelation in interferometric radar echoes, IEEE Trans. on Geoscience and Remote Sensing, vol.3, issue.0, 1992.