L. Alvarez, F. Guichard, P. Lions, and J. Morel, Axioms and fundamental equations of image processing, Archive for Rational Mechanics and Analysis, vol.11, issue.3, pp.199-257, 1993.
DOI : 10.1117/12.7974127

L. Alvarez and J. Morel, Formalization and computational aspects of image analysis, Acta Numerica, vol.1, pp.1-59, 1994.
DOI : 10.1137/0729052

H. Asada and M. Brady, The Curvature Primal Sketch, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.8, issue.1, pp.2-14, 1986.
DOI : 10.1109/TPAMI.1986.4767747

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

F. Attneave, Some informational aspects of visual perception., Psychological Review, vol.61, issue.3, pp.61-183, 1954.
DOI : 10.1037/h0054663

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

C. Ballester, V. Caselles, and P. Monasse, The tree of shapes of an image, ESAIM: Control, Optimisation and Calculus of Variations, pp.1-18, 2003.

F. Cao and L. Moisan, Geometric Computation of Curvature Driven Plane Curve Evolutions, SIAM Journal on Numerical Analysis, vol.39, issue.2, pp.624-646, 2002.
DOI : 10.1137/S0036142999363863

URL : https://hal.archives-ouvertes.fr/hal-00171303

V. Caselles, B. Coll, and J. Morel, A Kanizsa programme, in Variational Methods for Discontinuous Structures, pp.35-55, 1994.

V. Caselles, E. Meinhardt, and P. Monasse, Constructing the Tree of Shapes of an Image by Fusion of the Trees of Connected Components of Upper and Lower Level Sets, Positivity, vol.12, issue.1, pp.12-55, 2008.
DOI : 10.1007/s11117-007-2150-2

V. Caselles and P. Monasse, Geometric Description of Images as Topographic Maps ISBN: 978-3-642-04610-0, pp.978-981, 2010.
DOI : 10.1007/978-3-642-04611-7

Y. G. Chen, Y. Giga, and S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, Journal of Differential Geometry, vol.33, issue.3, pp.749-786, 1991.
DOI : 10.4310/jdg/1214446564

A. Ciomaga, P. Monasse, and J. Morel, Level lines shortening yields an image curvature microscope, 2010 IEEE International Conference on Image Processing, pp.4129-4132, 2010.
DOI : 10.1109/ICIP.2010.5649850

URL : https://hal.archives-ouvertes.fr/hal-00654440

A. Ciomaga and J. Morel, A Proof of Equivalence between Level Lines Shortening and Curvature Motion in Image Processing, SIAM Journal on Mathematical Analysis, vol.45, issue.3, pp.1047-1067, 2013.
DOI : 10.1137/11082347X

URL : https://hal.archives-ouvertes.fr/hal-00564416

M. G. Crandall and P. Lions, Convergent difference schemes for nonlinear parabolic equations and mean curvature motion, Numerische Mathematik, vol.75, issue.1, pp.17-41, 1996.
DOI : 10.1007/s002110050228

L. C. Evans and J. Spruck, Motion of level sets by mean curvature. I, Journal of Differential Geometry, vol.33, issue.3, pp.635-681, 1991.
DOI : 10.4310/jdg/1214446559

M. Gage and R. S. Hamilton, The heat equation shrinking convex plane curves, Journal of Differential Geometry, vol.23, issue.1, pp.69-96, 1986.
DOI : 10.4310/jdg/1214439902

M. A. Grayson, The heat equation shrinks embedded plane curves to round points, Journal of Differential Geometry, vol.26, issue.2, pp.285-314, 1987.
DOI : 10.4310/jdg/1214441371

F. Guichard, J. Morel, and R. Ryan, Contrast invariant image analysis and PDEs, preprint, 2001.

B. Julesz, Textons, the elements of texture perception and their interactions, Nature, vol.32, issue.5802, pp.290-91, 1981.
DOI : 10.1098/rstb.1980.0091

D. Marr, The low-level symbolic representation of intensity changes in an image, tech. report, Massachusetts Institute of Technology, 1974.

K. Mikula and D. Sev?ovi?, Evolution of plane curves driven by a nonlinear function of curvature and anisotropy, SIAM Journal on Applied Mathematics, pp.61-1473, 2001.

F. Mockhtarian and A. Mackworth, A theory of multiscale, curvature-based shape representation for planar curves, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.8, pp.789-805, 1992.
DOI : 10.1109/34.149591

L. Moisan, Affine plane curve evolution: a fully consistent scheme, IEEE Transactions on Image Processing, vol.7, issue.3, pp.411-420, 1998.
DOI : 10.1109/83.661191

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

P. Monasse and F. Guichard, Fast computation of a contrast-invariant image representation, IEEE Transactions on Image Processing, vol.9, issue.5, pp.860-872, 2000.
DOI : 10.1109/83.841532

M. Mondelli and A. Ciomaga, Finite Difference Schemes for MCM and AMSS, Image Processing On Line, vol.1, 2011.
DOI : 10.5201/ipol.2011.cm_fds

URL : http://doi.org/10.5201/ipol.2011.cm_fds

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.12-490021, 1988.
DOI : 10.1016/0021-9991(88)90002-2

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

G. Sapiro and A. Tannenbaum, Affine invariant scale-space, International Journal of Computer Vision, vol.8, issue.1, pp.25-44, 1993.
DOI : 10.1017/CBO9780511753138

A. Witkin, Scale-space filtering: A new approach to multi-scale description, ICASSP '84. IEEE International Conference on Acoustics, Speech, and Signal Processing, pp.1019-1021, 1984.
DOI : 10.1109/ICASSP.1984.1172729