L. Ambrosio, V. Caselles, S. Masnou, and J. M. Morel, Connected components of sets of finite perimeter and applications to image processing, Journal of the European Mathematical Society, vol.3, issue.1, pp.39-92, 2001.
DOI : 10.1007/PL00011302

K. Astrom, Fundamental limitations on projective invariants of planar curves. Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.17, issue.1, pp.77-81, 1995.

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

J. Canny, A Computational Approach to Edge Detection . Pattern Analysis and Machine Intelligence, IEEE Transactions on PAMI, vol.8, issue.6, pp.679-698, 1986.

F. Cao, J. L. Lisani, J. M. Morel, P. Musé, and F. Sur, A Theory of Shape Identification, Lecture Notes in Mathematics, vol.1948, 2008.
DOI : 10.1007/978-3-540-68481-7

URL : https://hal.archives-ouvertes.fr/inria-00319719

F. Cao, P. Musé, and F. Sur, Extracting Meaningful Curves from Images, Journal of Mathematical Imaging and Vision, vol.21, issue.11, pp.159-181, 2005.
DOI : 10.1007/s10851-005-4888-0

URL : https://hal.archives-ouvertes.fr/inria-00104264

V. Caselles and P. Monasse, Computation of the Tree of Bilinear Level Lines, Lecture Notes in Mathematics, pp.141-153978, 2010.
DOI : 10.1007/978-3-642-04611-7_7

V. Caselles and P. Monasse, Geometric Description of Images as Topographic Maps, Lecture Notes in Mathematics, vol.1984, 2010.
DOI : 10.1007/978-3-642-04611-7

URL : https://hal.archives-ouvertes.fr/hal-00654314

V. Caselles and J. M. Morel, Topographic Maps and Local Contrast Changes in Natural Images, International Journal of Computer Vision, vol.33, issue.1, pp.5-27, 1999.
DOI : 10.1023/A:1008144113494

P. Cavanagh, The artist as neuroscientist, Nature, vol.6, issue.7031, pp.301-307, 2005.
DOI : 10.1073/pnas.96.4.1680

A. Desolneux, L. Moisan, and J. M. Morel, Edge Detection by Helmholtz Principle, Journal of Mathematical Imaging and Vision, vol.14, issue.3, pp.271-284, 2001.
DOI : 10.1023/A:1011290230196

URL : https://hal.archives-ouvertes.fr/hal-00170793

R. Grompone-von-gioi, J. Jakubowicz, J. M. Morel, and G. Randall, LSD: A Fast Line Segment Detector with a False Detection Control, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.32, issue.4, pp.722-732, 2010.
DOI : 10.1109/TPAMI.2008.300

F. Guichard, J. M. Morel, and R. Ryan, Contrast invariant image analysis and PDE's. http://www.cmla.enscachan .fr/Membres/morel.html 16. Kanizsa, G.: Organization in Vision: Essays on Gestalt Perception, 1979.

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

H. Krim and A. Yezzi, Statistics and Analysis of Shapes. Modeling and Simulation in Science, Engineering and Technology, 2006.

J. L. Lisani, L. Moisan, J. M. Morel, and P. Monasse, On the Theory of Planar Shape, Multiscale Modeling & Simulation, vol.1, issue.1, pp.1-24, 2003.
DOI : 10.1137/S1540345902410846

URL : https://hal.archives-ouvertes.fr/hal-00171327

J. Matas, O. Chum, U. Martin, and T. Pajdla, Robust wide baseline stereo from maximally stable extremal regions, Proceedings of the British Machine Vision Conference, pp.384-393, 2002.

G. Matheron, Random Sets and Integral Geometry, 1975.

E. Meinhardt, E. Zacur, A. Frangi, and V. Caselles, 3D Edge Detection by Selection of Level Surface Patches, Journal of Mathematical Imaging and Vision, vol.13, issue.6, 2008.
DOI : 10.1007/s10851-008-0118-x

E. Meinhardt-llopis, Edge detection by selection of pieces of level lines, 2008 15th IEEE International Conference on Image Processing, pp.613-616, 2008.
DOI : 10.1109/ICIP.2008.4711829

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

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

J. M. Morel and G. Yu, ASIFT: A New Framework for Fully Affine Invariant Image Comparison, SIAM Journal on Imaging Sciences, vol.2, issue.2, pp.438-469, 2009.
DOI : 10.1137/080732730

P. Musé, On the definition and recognition of planar shapes in digital images, 2004.

J. Rabin, J. Delon, and Y. Gousseau, A Statistical Approach to the Matching of Local Features, SIAM Journal on Imaging Sciences, vol.2, issue.3, pp.931-958, 2009.
DOI : 10.1137/090751359

URL : https://hal.archives-ouvertes.fr/hal-00168285

J. Serra, Image Analysis and Mathematical Morphology, 1983.

M. Tepper, Detecting clusters and boundaries: a twofold study on shape representation, 2011.

M. Tepper, D. Acevedo, N. Goussies, J. Jacobo, and M. Mejail, A decision step for Shape Context matching, 2009 16th IEEE International Conference on Image Processing (ICIP), 2009.
DOI : 10.1109/ICIP.2009.5414443

M. Tepper, F. Gómez, P. Musé, A. Almansa, and M. Mejail, Morphological Shape Context: Semi-locality and Robust Matching in Shape Recognition, Progress in Pattern Recognition, pp.15-129, 2009.
DOI : 10.1007/978-3-642-10268-4_15

M. Tepper, P. Musé, A. Almansa, and M. Mejail, Finding Edges by a Contrario Detection of Periodic Subsequences, Image Analysis, Computer Vision, and Applications Lecture Notes in Computer Science, vol.7441, pp.773-780978, 2012.
DOI : 10.1007/978-3-642-33275-3_95

M. Wertheimer, Laws of organization in perceptual forms A source book of Gestalt psychology, pp.71-88, 1938.