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, 1993.
DOI : 10.1007/BF00375127

L. Ambrosio, N. Gigli, and G. Savaré, Calculus and heat ow on metric measure spaces and applications to spaces with Ricci curvature bounded below, Inventiones mathematicae, vol.195, issue.2, p.289391, 2014.

L. Ambrosio and S. D. Marino, Equivalent denitions of BV space and total variation in metric measure spaces, Journal of Functional Analysis, vol.266, issue.7, p.41504188, 2014.

A. B. Arehart, L. Vincent, and B. B. Kimia, Mathematical morphology: The Hamilton-Jacobi connection, 1993 (4th) International Conference on Computer Vision, p.215219, 1993.
DOI : 10.1109/ICCV.1993.378217

Z. M. Balogh, A. Engulatov, L. Hunziker, and O. E. Maasalo, Functional Inequalities and HamiltonJacobi Equations in Geodesic Spaces, Potential Analysis, vol.36, issue.2, p.317337, 2012.

M. Bardi and L. C. Evans, On Hopf's formulas for solutions of Hamilton-Jacobi equations, Nonlinear Analysis: Theory, Methods & Applications, vol.8, issue.11, p.13731381, 1984.
DOI : 10.1016/0362-546X(84)90020-8

S. G. Bobkov, I. Gentil, and M. Ledoux, Hypercontractivity of HamiltonJacobi equations, J. Math. Pures Appl, vol.80, issue.7, p.669696, 2001.

R. Van-den-boomgaard and L. Dorst, The morphological equivalent of Gaussian scalespace, Proc. of Gaussian Scale-Space Theory, 1997.

M. Breuÿ and J. Weickert, Highly accurate PDE-based morphology for general structuring elements, Proc. of Scale Space and Variational Methods in Computer Vision, 2009.

M. R. Bridson and A. Haeiger, Metric spaces of non-positive curvature, Grundlehren der mathematischen Wissenschaften, vol.319, 1999.
DOI : 10.1007/978-3-662-12494-9

R. W. Brockett and P. Maragos, Evolution equations for continuous-scale morphology, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing
DOI : 10.1109/ICASSP.1992.226260

F. Camillia, A. Festab, and D. Schiebornc, An approximation scheme for a Hamilton Jacobi equation dened on a network, Applied Numerical Mathematics, vol.73, p.3347, 2013.

M. G. Crandall, H. Ishii, and P. Lions, User's guide to viscosity solutions of second order partial dierential equations, Bulletin of the American Mathematical Society, vol.27, issue.1, p.167, 1992.

E. H. Diop and J. Angulo, MULTISCALE IMAGE ANALYSIS BASED ON ROBUST AND ADAPTIVE MORPHOLOGICAL SCALE-SPACES, Image Analysis & Stereology, vol.33, issue.2, p.975728, 2014.
DOI : 10.5566/ias.993

URL : https://hal.archives-ouvertes.fr/hal-00975728

F. Dragoni, Metric HopfLax formula with semicontinuous data. Discrete Contin, Dyn. Syst, vol.17, issue.4, p.713729, 2007.

D. Burago, Y. Burago, and S. Ivanov, A course in metric geometry, Graduate Studies in Mathematics, vol.33, 2001.
DOI : 10.1090/gsm/033

A. Elmoataz, X. Desquesnes, O. Lézoray, and O. , Non-Local Morphological PDEs and <formula formulatype="inline"> <tex Notation="TeX">$p$</tex></formula>-Laplacian Equation on Graphs With Applications in Image Processing and Machine Learning, IEEE Journal of Selected Topics in Signal Processing, vol.6, issue.7, pp.764-779, 2012.
DOI : 10.1109/JSTSP.2012.2216504

A. Fathi, Weak KAM Theorem in Lagrangian Dynamics. Series: Cambridge Studies in Advanced Mathematics, 2014.

N. Gozlan, C. Roberto, and P. Samson, Hamilton Jacobi equations on metric spaces and transport entropy inequalities, Revista Matem??tica Iberoamericana, vol.30, issue.1, pp.133-163, 2014.
DOI : 10.4171/RMI/772

URL : https://hal.archives-ouvertes.fr/hal-00795829

M. Herty, U. Ziegler, and S. Göttlich, Numerical discretization of Hamilton-Jacobi equations on networks. Networks and Heterogeneous Media, p.685705, 2013.

P. T. Jackway and M. Deriche, Scale-space properties of the multiscale morphological dilation-erosion, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.18, issue.1, p.3851, 1996.
DOI : 10.1109/34.476009

J. Lott and C. Villani, HamiltonJacobi semigroup on length spaces and applications

P. Maragos, Slope transforms: theory and application to nonlinear signal processing, IEEE Transactions on Signal Processing, vol.43, issue.4, p.864877, 1995.
DOI : 10.1109/78.376839

P. Maragos, Dierential morphology and image processing, IEEE Trans. on Image Processing, vol.5, issue.1, p.922937, 1996.

F. Meyer and P. Maragos, Multiscale Morphological Segmentations Based on Watershed, Flooding, and Eikonal PDE, Proc. of Scale-Space'99, p.351362, 1999.
DOI : 10.1007/3-540-48236-9_31

V. Ta, A. Elmoataz, and O. Lezoray, Nonlocal PDEs-Based Morphology on Weighted Graphs for Image and Data Processing, IEEE Trans. on Image Processing, vol.20, issue.6, p.15041516, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00708975

C. Villani, Optimal transport. Old and new
URL : https://hal.archives-ouvertes.fr/hal-00974787