M. Marc-a-l-e-x-a and . Wa-r-d-e-t-z-k-y, Discrete Laplacians on General Polygonal Meshes, ACM SIGGRAPH 2011 Papers. SIGGRAPH '11, vol.102, pp.62-65, 2011.

. Mikhail-b-e-l-k-i-n-et-partha-n-i-y-o-g-i, Towards a theoretical foundation for Laplacianbased manifold methods, J. Comput. Syst. Sci, vol.74, pp.1289-1308, 2008.

B. Kenneth, The surface evolver, In : Experimental Mathematics, vol.1, p.58, 1992.

A. Iwanowitsch, B. O-b-e-n-k-o, and . Boris-s-p-r-i-n-g-b-o-r-n, A Discrete LaplaceBeltrami Operator for Simplicial Surfaces, Discrete & Computational Geometry, vol.38, p.52, 2007.

B. Mikhail, S. Jian, and Y. Wa-n-g, Constructing Laplace Operator from Point Clouds in R d, Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, pp.1031-1040

B. Mikhail, S. Jian, and Y. Wa-n-g, Discrete laplace operator on meshed surfaces, Proceedings of the 24th ACM Symposium on Computational Geometry, pp.278-287, 2008.

. Thomas-c-a-i-s-s-a-r-d, C. David, J. Ly, and . Olivier-l-a-c-h-a-u-d-et-tristan-r-o-u-s--s-i-l-l-o-n, Heat kernel Laplace-Beltrami operator on digital surfaces, International Conference on Discrete Geometry for Computer Imagery, pp.241-253, 2017.

. Thomas-c-a-i-s-s-a-r-d, C. David, J. Ly, and . Olivier-l-a-c-h-a-u-d-et-tristan-r-o-u-s--s-i-l-l-o-n, Laplace-Beltrami Operator on Digital Surfaces, 2018.

C. Colin, M. Christian, . At, M. Rémy, and . A-l-g-o-u-y-r-e-s-et-chafik-s-a-m-i-r, Mesh Parameterization with Generalized Discrete Conformal Maps, Journal of mathematical imaging and vision, vol.46, p.53, 2013.

C. Fan, Spectral Graph Theory, p.51, 1997.

C. Fan and L. H-u-n-g-et-linyuan, Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics), p.51, 2006.

C. David, J. Ly, L. Jérémy, G. Va-l-l-o-i-s-;-de-rocío, M. O-n-z-Á-l-e-z--d-Í-a-z et al., Integral Based Curvature Estimators in Digital Geometry, Discrete Geometry for Computer Imagery -17th IAPR International Conference, DGCI 2013, vol.7749, p.37, 2013.

C. David, J. Ly, L. Jérémy, and . Va-l-l-o-i-s, Multigrid convergent principal curvature estimators in digital geometry, Computer Vision and Image Understanding, vol.129, p.37, 2014.

C. David, J. Ly, and . Olivier-l-a-c-h-a-u-d-et-tristan-r-o-u-s-s-i-l-l-o-n, Multigrid Convergence of Discrete Geometric Estimators, Digital Geometry Algorithms : Theoretical Foundations and Applications to Computational Imaging. Sous la dir

E. De-valentin, P. B-r-i-m-k-o-v-et-reneta, . B-a-r-n-e-va, and . Dordrecht, , vol.78, p.79, 2012.

C. David, . Ly, F. Marion, . O-a-r-e, G. Pierre et al., Piecewise smooth reconstruction of normal vector field on digital data, Computer Graphics Forum. Proc. Pacific Graphics, vol.35, 2016.

M. Robert, G. H. C-o-r-l-e-s-s, D. E. G-o-n-n-e-t, D. J. H-a-r-e, D. E. J-e-f-f-r-e-y-et et al., On the LambertW function, Adv. Comput. Math. 5, vol.1, p.95, 1996.

C. Frédéric, P. Marc, and . O-u-g-e-t, Estimating differential quantities using polynomial fitting of osculating jets, Computer Aided Geometric Design, vol.22, p.101, 2005.

C. Keenan, C. W. E-i-s-c-h-e-d-e-l-et, and M. Wa-r-d-e-t-z-k-y, Geodesics in heat : a new approach to computing distance based on heat flow, vol.32, p.106, 2013.

A. N. Mathieu-d-e-s-b-r-u-n, . H-i-r-a-n-i, L. Melvin, and J. E. M-a-r-s-d-e-n, Discrete exterior calculus, vol.52, p.30, 2005.

. Mathieu-d-e-s-b-r-u-n, M. Mark, S. Peter, H. C-h-r-Ö-d-e-r-et-alan, N. B-a-r-r.-;-de-warren et al., Implicit Fairing of Irregular Meshes Using Diffusion and Curvature Flow, Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1999, vol.57, p.52, 1999.

, DGtal : Digital Geometry tools and algorithms library, p.102

D. Jesse and . O-u-g-l-a-s, A Method of Numerical Solution of the Problem of Plateau, Annals of Mathematics, vol.29, issue.4, p.57, 1927.

D. Jesse and . O-u-g-l-a-s, Solution of the Problem of Plateau, Transactions of AMS, p.57, 1931.

D. Tamal, R. Pawas, and Y. Wa-n-g, Convergence, Stability, and Discrete Approximation of Laplace Spectra, vol.114, p.94, 2010.

J. Richard and . D-u-f-f-i-n, Distributed and Lumped Networks, In : Journal of Mathematics and Mechanics, vol.8, p.52, 1959.

H. Gerhard-d-z-i-u-k-;-de-stefan, L. I-l-d-e-b-r-a-n-d-t-et-rolf, and . Berlin, Finite Elements for the Beltrami operator on arbitrary surfaces, Partial Differential Equations and Calculus of Variations. Sous la dir, p.52, 1988.

D. Gerhard, An algorithm for evolutionary surfaces, Numerische Mathematik 58.1 (déc. 1990), vol.58, p.52

H. Rémy, M. A-l-g-o-u-y-r-e-s-et-colin, and C. , Convergence of binomial-based derivative estimation for 2 noisy discretized curves, Theoretical Computer Science, vol.412, p.71, 2011.

C. E. Lawrence and . Va-n-s, Partial differential equations. Providence, R.I, p.21, 2010.

G. Fa-b-e-r and . Beweis, daß unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt. T. 1923,8. Sitzungsbericht der Bayerischen Akademie der Wissenschaften. München, p.24, 1923.

. Herbert-f-e-d-e-r-e-r, Curvature measures, Transactions of the American Mathematical Society, vol.93, p.35, 1959.

. Herbert-f-e-d-e-r-e-r, Geometric measure theory. Grundlehren der mathematischen Wissenschaften, vol.35, p.32, 1969.

S. Michael, H. F-l-o-at-e-r-et-kai, A. O-r-m-a-n-n-;-de-neil, M. S. D-o-d-g-s-o-n, A. F-l-o-at-e-r-et-malcolm et al., Surface Parameterization : a Tutorial and Survey, Advances in Multiresolution for Geometric Modelling, p.65, 2005.

F. Frédéric, J. Bernard, and L. E-s-a-f-f-r-e, An adaptive filtering method to evaluate normal vectors and surface areas of 3D objects. Application to snow images from X-ray tomography, IEEE Transactions on Image Processing, vol.14, p.32, 2005.

. Koji-f-u-j-i-w-a-r-a, Eigenvalues of Laplacians on a Closed Riemannian Manifold and Its Nets, Proceedings of the American Mathematical Society, vol.123, p.52, 1995.

J. Leo, P. G-r-a-d-y-et-jonathan, and . O-l-i-m-e-n-i, Discrete calculus : Applied analysis on graphs for computational science, p.53, 2010.

G. Carolyn, L. O-r-d-o-n-et-david, and . W-e-b-b, You Can't Hear the Shape of a Drum, American Scientist, vol.84, p.23, 1996.

R. Paul and . H-a-l-m-o-s, Finite Dimensional Vector Spaces. Annals of mathematics studies, p.54, 1948.

H. Jenny and . A-r-r-i-s-o-n, Stokes' theorem for nonsmooth chains, Bulletin of the American Mathematical Society, vol.29, p.53, 1993.

H. Jenny and . A-r-r-i-s-o-n, Flux across nonsmooth boundaries and fractal Gauss/Green/Stokes' theorems, Journal of Physics A : Mathematical and General, vol.32, p.53, 1999.

T. Gabor and . H-e-r-m-a-n, Geometry of Digital Spaces. Applied and Numerical Harmonic Analysis. Birkhäuser Boston, p.31, 2012.

H. Tor, . I-l-d-e-b-r-a-n-d, L. Andres, M. Ralph, J. D. Ü-l-l-e-r et al., Direct three-dimensional morphometric analysis of human cancellous bone : microstructural data from spine, femur, iliac crest, and calcaneus, In : Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research, vol.14, issue.7, p.32, 1999.

N. Anil and . H-i-r-a-n-i, Discrete exterior calculus, vol.30, p.31, 2003.

K. John, . H-u-n-t-e-r, and . Bruno-n-a-c-h-t-e-r-g-a-e-l-e, Applied Analysis. World Scientific, vol.44, p.41, 2001.

V. D. William and . H-o-d-g-e, The Theory and Applications of Harmonic Integrals. Cambridge mathematical library, p.21, 1989.

. Bibliographie,

H. Klaus, P. I-l-d-e-b-r-a-n-d-t-et-konrad, and . Lt-h-i-e-r, On approximation of the Laplace-Beltrami operator and the Willmore energy of surfaces, Computer Graphics Forum, vol.30, p.70, 2011.

H. Klaus, . I-l-d-e-b-r-a-n-d-t, P. Konrad, M. Lt-h-i-e-r, and . Wa-r-d-e-t-z-k-y, On the convergence of metric and geometric properties of polyhedral surfaces, English. In : Geometriae Dedicata, vol.123, issue.1, p.53, 2006.

R. Martin and H. A-r-a-l-i-c-k-et-linda-s-h-a-p-i-r-o, Computer and Robot Vision. 1st, 1992.

J. Jürgen, Riemannian Geometry and Geometric Analysis. Springer Universitat texts, p.22, 2005.

K. Mark, Can One Hear the Shape of a Drum ?, In : The American Mathematical Monthly, vol.73, p.24, 1966.

P. Hermann-k-a-r-c-h-e-r-et-konrad and . Lt-h-i-e-r, Construction of triply periodic minimal surfaces, Philosophical Transactions of the Royal Society of London A : Mathematical, Physical and Engineering Sciences, vol.354, p.52, 1996.

. Reinhard-k-l-e-t-t-e-et-azriel-r-o-s-e-n-f-e-l-d, Digital geometry : geometric methods for digital picture analysis. The Morgan Kaufmann series in computer graphics and geometric modeling, vol.33, p.31, 2004.

. Edgar-k-r-a-h-n, Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises, Mathematische Annalen 94.1 (déc. 1925), p.24

. Jacques-olivier-l-a-c-h-a-u-d, Non-Euclidean spaces and image analysis : Riemannian and discrete deformable models, discrete topology and geometry, Université Sciences et Technologies, p.34, 2006.

D. Peter, Linear algebra and its applications v. 10, p.54, 2007.

W. E. L-o-r-e-n-s-e-n-et and H. E. C-l-i-n-e, Marching Cubes : A High Resolution 3D Surface Construction Algorithm, Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques. SIGGRAPH '87, pp.163-169, 1987.

L. Jérémy, . Va-l-l-o-i-s, C. David, . Ly, and . Jacques-olivier-l-a-c-h-a-u-d, ParameterFree and Multigrid Convergent Digital Curvature Estimators, Discrete Geometry for Computer Imagery -18th IAPR International Conference, vol.84, p.83, 2014.

J. David, C. Ly, L. Jérémy, and . Va-l-l-o-i-s, Robust and Convergent Curvature and Normal Estimators with Digital Integral Invariants, Modern Approaches to Discrete Curvature. Sous la dir, p.39, 2017.

M. John and . L-e-e, Introduction to Smooth Manifolds, Graduate Texts in Mathematics, vol.14, p.16, 2003.

L. László and . Vá-s-z, Random Walks on Graphs : A Survey, Combinatorics, Paul Erd? os is Eighty. T. 2. Budapest : János Bolyai Mathematical Society, pp.353-398, 1996.

D. Peter, D. Robert, and . R-i-c-h-t-m-y-e-r, Survey of the stability of linear finite difference equations, Communications on Pure and Applied Mathematics, vol.9, p.43, 1956.

. Jacques-olivier-l-a-c-h-a-u-d and . Boris-t-h-i-b-e-r-t, Properties of Gauss Digitized Shapes and Digital Surface Integration, Journal of Mathematical Imaging and Vision, vol.54, p.83, 2016.

L. Bruno and . Hao-(richard)-z-h-a-n-g, Spectral Mesh Processing, ACM SIG-GRAPH 2010 Courses. SIGGRAPH '10, vol.8, p.52, 2010.

M. Uwe, Numerical solutions for the surface diffusion flow in three space dimensions, p.52, 2001.

M. Christian and . At, Discrete Riemann surfaces and the Ising model, Communications in Mathematical Physics, vol.218, p.53, 2001.

M. Christian and . At, Discrete Complex Structure on Surfel Surfaces". English. In : Discrete Geometry for Computer Imagery. T. 4992. Lecture Notes in Computer Science

H. Springer-berlin, , p.53, 2008.

M. Mark, D. Mathieu, . E-s-b-r-u-n, S. Peter, H. C-h-r-Ö-d-e-r-et-alan et al., Discrete Differential-Geometry Operators for Triangulated 2-Manifolds, Visualization and Mathematics III. Sous la dir, vol.57, p.52, 2003.

M. Subbaramiah and . I-n-a-k-s-h-i-s-u-n-d-a-r-a-m, Eigenfunctions on Riemannian manifolds, J. Indian Math. Soc, vol.17, p.24, 1953.

A. M. Stanislav and . O-l-c-h-a-n-o-v, Diffusion Processes and Riemannian Geometry, Russian Mathematical Surveys, vol.30, p.67, 1975.

J. Va-n, Generalized Curvatures. 1 re éd, p.37, 2008.

M. Subbaramiah and P. I-n-a-k-s-h-i-s-u-n-d-a-r-a-m-et-agneta, Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds, Can. J. Math, vol.1, p.24, 1949.

P. Henry, . M-c-k-e-a-n-jr, M. Et-isadore, and . S-i-n-g-e-r, Curvature and the eigenvalues of the Laplacian, J. Differential Geom, vol.1, issue.1-2, p.24, 1967.

R. James and . M-u-n-k-r-e-s, Elements of Algebraic Topology, vol.117, p.30, 1984.

O. Maks, C. Etienne, . O-r-m-a-n, B. Michael, and . R-o-n-s-t-e-i-n, Computing and Processing Correspondences with Functional Maps, ACM SIGGRAPH, 2017.

, Courses. SIGGRAPH '17, vol.5, p.23, 2017.

P. Theodosios, Algorithms for Graphics and Image Processing, p.34, 1982.

P. Hélène, . E-r-r-i-e-r, L. Jérémy, . Va-l-l-o-i-s, C. David et al., Interactive Curvature Tensor Visualization on Digital Surfaces, Lecture Notes in Computer Sciences. International Conference on Discrete Geometry for Computer Imagery, p.39, 2016.

P. Konrad and . Lt-h-i-e-r, Computational Aspects of Discrete Minimal Surfaces, p.52, 2002.

. Bibliographie,

P. Konrad and . Lt-h-i-e-r, Unstable Periodic Discrete Minimal Surfaces, p.52, 2002.

P. Helmut, J. Wa-l-l-n-e-r, Y. Yu-kun-l-a-i-et-shimin, and H. , Principal curvatures from the integral invariant viewpoint, Computer Aided Geometric Design, vol.24, p.37, 2007.

P. Helmut, J. Wa-l-l-n-e-r, H. Qi-xing, and Y. A. Yong-liang, Integral invariants for robust geometry processing, Computer Aided Geometric Design, vol.26, p.37, 2009.

P. Konrad and . Lt-h-i-e-r-et-eike-p-r-e-u-s-s, Identifying vector field singularities using a discrete Hodge decomposition, Visualization and Mathematics, vol.3, p.52, 2003.

P. Ulrich-p-i-n-k-a-l-l-et-konrad and . Lt-h-i-e-r, Computing discrete minimal surfaces and their conjugates, vol.57, p.52

P. Konrad and . Lt-h-i-e-r-et-wayne-r-o-s-s-m-a-n, Discrete constant mean curvature surfaces and their index, p.52, 2002.

Q. Hongxing, C. Yi, and Y. Wa-n-g, Laplace-Beltrami Operator on Point Clouds Based on Anisotropic Voronoi Diagram, Computer Graphics Forum, p.53

R. Tibor, Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, p.57, 1933.

X. Guoliang, Convergence of discrete Laplace-Beltrami operators over surfaces, Computers and Mathematics with Applications, vol.48, p.99, 2004.

X. Guoliang, Discrete Laplace-Beltrami operators and their convergence, Computer Aided Geometric Design, vol.21, p.99, 2004.

. Hao-z-h-a-n-g, Discrete combinatorial Laplacian operators for digital geometry processing, SIAM Conference on Geometric Design, vol.57, p.56, 2004.