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

F. Attneave, Some informational aspects of visual perception., Psychological Review, vol.61, issue.3, pp.183-193, 1954.
DOI : 10.1037/h0054663

C. Ballester, V. Caselles, and P. Monasse, The tree of shapes of an image, ESAIM: Control, Optimisation and Calculus of Variations, vol.9, pp.1-18, 2003.
DOI : 10.1051/cocv:2002069

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.55-73, 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.

Y. 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. 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, H. , and R. S. , 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, R. , and R. , 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.91-97, 1981.
DOI : 10.1098/rstb.1980.0091

D. Marr, The low-level symbolic representation of intensity changes in an image, 1974.

K. Mikula and D. , Evolution of plane curves driven by a nonlinear function of curvature and anisotropy, SIAM Journal on Applied Mathematics, vol.61, issue.5, pp.1473-1501, 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=10.1.1.27.4081

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=10.1.1.413.5254

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