T. M. Alcorn and C. W. Hoggar, Preprocessing of data for character recognition, Marconi Review, pp.61-81, 1969.

A. D. Alexandrov and Y. G. Reshetnyak, General Theory of Irregular Curves Mathematics and its Applications, 1989.

S. Arlot and P. Massart, Data-driven calibration of penalties for least-squares regression, Journal of Machine Learning Research, vol.10, pp.245-279, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00287631

J. D. Banfield and A. E. Raftery, Ice Floe Identification in Satellite Images Using Mathematical Morphology and Clustering about Principal Curves, Journal of the American Statistical Association, vol.26, issue.417, pp.7-16, 1992.
DOI : 10.1080/01621459.1963.10500845
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.475.4614

A. Barron, L. Birgé, and P. Massart, Risk bounds for model selection via penalization. Probability Theory and Related Fields, pp.301-413, 1999.
DOI : 10.1007/s004400050210

P. L. Bartlett, S. Boucheron, and G. Lugosi, Model Selection and Error Estimation, Machine Learning, pp.85-113, 2001.
DOI : 10.2139/ssrn.248567
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.141.4491

J. Baudry, C. Maugis, and B. Michel, Slope heuristics: overview and implementation, Statistics and Computing, vol.6, issue.2, 2011.
DOI : 10.1007/s11222-011-9236-1
URL : https://hal.archives-ouvertes.fr/hal-00461639

L. Birgé, P. Massart-for-lucien-le, and C. , From Model Selection to Adaptive Estimation, Festschrift Research Papers in Probability and Statistics, pp.55-87, 1997.
DOI : 10.1007/978-1-4612-1880-7_4

L. Birgé and P. Massart, Minimal penalties for Gaussian model selection. Probability Theory and Related Fields, pp.33-73, 2007.

C. Brunsdon, Path estimation from GPS tracks, Proceedings of the 9th International Conference on GeoComputation, National Centre for Geocomputation, 2007.

B. S. Caffo, C. M. Crainiceanu, L. Deng, and C. W. Hendrix, A Case Study in Pharmacologic Colon Imaging Using Principal Curves in Single-Photon Emission Computed Tomography, Journal of the American Statistical Association, vol.103, issue.484, pp.1470-1480, 2008.
DOI : 10.1198/016214508000000832

K. Chang and J. Ghosh, Principal curves for nonlinear feature extraction and classification, SPIE Applications of Artificial Neural Networks in Image Processing III, pp.120-129, 1998.

P. J. Corkeron, P. Anthony, and R. Martin, Ranging and diving behaviour of two offshore bottlenose dolphins, Tursiops sp., off eastern Australia, Journal of the Marine Biological Association of the UK, vol.84, issue.2, pp.465-468, 2004.
DOI : 10.1017/S0025315404009464h

G. De, Principal curves: a new technique for indirect and direct gradient analysis, Ecology, vol.80, pp.2237-2253, 1999.

P. Delicado, Another Look at Principal Curves and Surfaces, Journal of Multivariate Analysis, vol.77, issue.1, pp.84-116, 2001.
DOI : 10.1006/jmva.2000.1917
URL : http://doi.org/10.1006/jmva.2000.1917

E. S. Deutsch, Preprocessing for character recognition, Proceedings of the IEE?NPL Conference on Pattern Recognition, pp.179-190, 1968.

T. Duchamp and W. Stuetzle, Extremal properties of principal curves in the plane, The Annals of Statistics, vol.24, issue.4, pp.1511-1520, 1996.
DOI : 10.1214/aos/1032298280

R. M. Dudley, The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, Journal of Functional Analysis, vol.1, issue.3, pp.290-330, 1967.
DOI : 10.1016/0022-1236(67)90017-1

R. M. Dudley, Uniform Central Limit Theorems. Cambridge Studies in Advanced Mathematics, 1999.

J. Einbeck, G. Tutz, and L. Evers, Exploring Multivariate Data Structures with Local Principal Curves, Proceedings of the 28th Annual Conference of the Gesellschaft für Klassifikation Studies in Classification , Data Analysis, and Knowledge Organization, pp.256-263, 2005.
DOI : 10.1007/3-540-28084-7_28
URL : http://dro.dur.ac.uk/5290/1/5290.pdf?DDD21+dma0je

J. Einbeck, G. Tutz, and L. Evers, Local principal curves, Statistics and Computing, vol.88, issue.4, pp.301-313, 2005.
DOI : 10.1007/s11222-005-4073-8

E. R. Engdahl and A. Villaseñor, 41 Global seismicity: 1900???1999, International Handbook of Earthquake and Engineering Seismology, pp.665-690, 2002.
DOI : 10.1016/S0074-6142(02)80244-3

H. Friedsam and W. A. Oren, The application of the principal curve analysis technique to smooth beamlines, Proceedings of the 1st International Workshop on Accelerator Alignment, 1989.

C. R. Genovese, M. Perone-pacifico, I. Verdinelli, and L. Wasserman, The Geometry of Nonparametric Filament Estimation, Journal of the American Statistical Association, vol.2, issue.498, 2010.
DOI : 10.1080/01621459.2012.682527

D. J. Harding and G. S. Berghoff, Fault scarp detection beneath dense vegetation cover: airborne lidar mapping of the Seattle fault zone, Proceedings of the American Society of Photogrammetry and Remote Sensing Annual Conference, 2000.

T. Hastie and W. Stuetzle, Principal Curves, Journal of the American Statistical Association, vol.26, issue.406, pp.502-516, 1989.
DOI : 10.1080/03610927508827223

H. Hotelling, Analysis of a complex of statistical variables into principal components., Journal of Educational Psychology, vol.24, issue.6, pp.417-441, 1933.
DOI : 10.1037/h0071325

B. Kégl and A. Krzy?ak, Piecewise linear skeletonization using principal curves, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, issue.1, pp.59-74, 2002.
DOI : 10.1109/34.982884

B. Kégl, A. Krzy?ak, T. Linder, and K. Zeger, Learning and design of principal curves, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.22, issue.3, pp.281-297, 2000.
DOI : 10.1109/34.841759

A. N. Kolmogorov and S. V. Fomin, Introductory Real Analysis, 1975.

V. Koltchinskii, Rademacher penalties and structural risk minimization, IEEE Transactions on Information Theory, vol.47, issue.5, pp.1902-1914, 2001.
DOI : 10.1109/18.930926
URL : http://bayes.stat.washington.edu/jaw/COURSES/STOP/593.sp.00/PAPERS/radpen1.pdf

E. Lebarbier, Detecting multiple change-points in the mean of Gaussian process by model selection, Signal Processing, vol.85, issue.4, pp.717-736, 2005.
DOI : 10.1016/j.sigpro.2004.11.012
URL : https://hal.archives-ouvertes.fr/inria-00071847

M. Lerasle, Optimal model selection in density estimation. Annales de l'Institut Henri Poincaré
URL : https://hal.archives-ouvertes.fr/hal-00422655

K. V. Mardia, J. T. Kent, and J. M. Bibby, Multivariate Analysis, 1979.

P. Massart, Concentration Inequalities and Model Selection Ecole d'Eté de Probabilités de Saint-Flour XXXIII ?, Lecture Notes in Mathematics, 2003.

C. Mcdiarmid, On the method of bounded differences, Surveys in Combinatorics, pp.148-188, 1989.
DOI : 10.1017/CBO9781107359949.008

K. Reinhard and M. Niranjan, Parametric subspace modeling of speech transitions, Speech Communication, vol.27, issue.1, pp.19-42, 1999.
DOI : 10.1016/S0167-6393(98)00067-3

S. Sandilya and S. R. Kulkarni, Principal curves with bounded turn, IEEE Transactions on Information Theory, vol.48, issue.10, pp.2789-2793, 2002.
DOI : 10.1109/TIT.2002.802614

A. Saumard, The slope heuristics in heteroscedastic regression Available at http://hal.archives-ouvertes.fr, 2010.

C. Spearman, "General Intelligence," Objectively Determined and Measured, The American Journal of Psychology, vol.15, issue.2, pp.201-293, 1904.
DOI : 10.2307/1412107

D. C. Stanford and A. E. Raftery, Finding curvilinear features in spatial point patterns: principal curve clustering with noise, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.22, issue.6, pp.2237-2253, 2000.
DOI : 10.1109/34.862198

R. Tibshirani, Principal curves revisited, Statistics and Computing, vol.11, issue.4, pp.183-190, 1992.
DOI : 10.1007/BF01889678

J. J. Verbeek, N. Vlassis, and B. Kröse, A Soft k-Segments Algorithm for Principal Curves, Proceedings of International Conference on Artificial Neural Networks, pp.450-456, 2001.
DOI : 10.1007/3-540-44668-0_63
URL : https://hal.archives-ouvertes.fr/inria-00321506

W. C. Wong and A. C. Chung, Principal curves to extract vessels in 3D angiograms, 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, pp.1-8, 2008.
DOI : 10.1109/CVPRW.2008.4563015