Mohammad Ali Abam, Mark de Berg, Peter Hachenberger, and Alireza Zarei. Streaming algorithms for line simplification. In SCG '07: Symp. on Comput. geometry, pages 175–183. ACM, 2007.

D Adalsteinsson and J.A Sethian. The fast construction of extension velocities in level set methods. Journal of Computational Physics, 148(1):2 – 22, 1999.

Pankaj K. Agarwal, Sariel Har-Peled, Nabil H. Mustafa, and Yusu Wang. Near-linear time approximation algorithms for curve simplification. Algorithmica, 42(3-4):203–219, 2005.

Eric Albin, Ronnie Knikker, Shihe Xin, Christian Oliver Paschereit, and Yves d’Angelo. Computational assessment of curvatures and principal directions of implicit surfaces from 3d scalar data. In International Conference on Mathematical Methods for Curves and Surfaces, pages 1–22. Springer, 2016.

Luigi Ambrosio and Vincenzo Maria Tortorelli. Approximation of functional depending on jumps by elliptic functional via t-convergence. Communications on Pure and Applied Mathematics, 43(8):999–1036, 1990.

A. M. Andrew. Another efficient algorithm for convex hulls in two dimensions. Information Processing Letters, 9(5):216–219, 1979.

F. Aurenhammer. Power Diagrams: Properties, Algorithms, and Applications. SIAM Journal on Computing, 16:78–96, 1987.

F. Avnaim, J.-D. Boissonnat, O. Devillers, F.P. Preparata, and M. Yvinec. Evaluating signs of determinants using single-precision arithmetic. Algorithmica, 17(2):111–132, 1997.

C. B. Barber, D. P. Dobkin, and H. Huhdanpaa. The quickhull algorithm for convex hulls. ACM Transactions on Mathematical Software (TOMS), 22(4):469–483, 1996.

Gavin Barill, Neil G Dickson, Ryan Schmidt, David IW Levin, and Alec Jacobson. Fast winding numbers for soups and clouds. ACM Transactions on Graphics (TOG), 37(4):1–12, 2018.

Mikhail Belkin and Partha Niyogi. Towards a theoretical foundation for laplacian-based manifold methods. J. Comput. Syst. Sci., 74(8):1289–1308, 2008.

Serge Belongie. Rodrigues' rotation formula. From MathWorld–A Wolfram Web Resource, created by Eric W. Weisstein.

G. Bertrand and M. Couprie. Géométrie discrète et images numériques, chapter 8. Transformations topologiques discrètes. Traité IC2. Hermès, 2007. In french.

Gilles Bertrand and Grégoire Malandain. A new characterization of three-dimensional simple points. Pattern Recognition Letters, 15(2):169–175, February 1994.

G. Borgefors. Distance transformations in digital images. Computer Vision, Graphics, and Image Processing, 34(3):344–371, jun 1986.

Alexandre Boulch and Renaud Marlet. Fast and robust normal estimation for point clouds with sharp features. Comput. Graph. Forum, 31(5):1765–1774, 2012.

H. Breu, J. Gil, D. Kirkpatrick, and M. Werman. Linear time Euclidean distance transform algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(5):529–533, 1995.

Thomas Caissard, David Coeurjolly, Jacques-Olivier Lachaud, and Tristan Roussillon. Heat kernel Laplace-Beltrami operator on digital surfaces. In 20th International Conference on Discrete Geometry for Computer Imagery, Lecture Notes in Computer Science, Vienna, Austria, September 2017. Walter G. Kropatsch, Ines Janusch and Nicole M. Artner, Springer-Verlag.

F. Cazals and M. Pouget. Estimating differential quantities using polynomial fitting of osculating jets. Computer Aided Geometric Design, 22(2):121–146, 2005.

CGal: Computational geometry algorithms library, http://www.cgal.org.

W. S. Chan and F. Chin. Approximation of polygonal curves with minimum number of line segments. In ISAAC '92: Symp. on Algorithms and Computation, pages 378–387. Springer-Verlag, 1992.

E. Charrier and L. Buzer. An efficient and quasi-linear worst-case time algorithm for digital plane recognition. In Proc. Int. Conf. Discrete Geometry for Computer Imagery (DGCI'2008), Lyon, France, volume 4992 of LNCS, pages 346–357. Springer, 2008.

Emilie Charrier and Lilian Buzer. Approximating a real number by a rational number with a limited denominator: A geometric approach. Discrete Applied Mathematics, 157(16):3473 – 3484, 2009.

John Chaussard and Michel Couprie. Surface thinning in 3d cubical complexes. In Petra Wiederhold and Reneta P. Barneva, editors, IWCIA, volume 5852 of Lecture Notes in Computer Science, page 135–148. Springer, 2009.

Frédéric Chazal, David Cohen-Steiner, André Lieutier, and Boris Thibert. Stability of curvature measures. In Computer Graphics Forum, volume 28, pages 1485–1496. Wiley Online Library, 2009.

David Coeurjolly and Jacques-Olivier Lachaud. A simple discrete calculus for digital surfaces. In International Conference on Discrete Geometry and Mathematical Morphology, pages 341–353. Springer, 2022.

D. Coeurjolly and A. Montanvert. Optimal separable algorithms to compute the reverse euclidean distance transformation and discrete medial axis in arbitrary dimension. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(3):437–448, mar 2007.

David Coeurjolly, Jacques-Olivier Lachaud, and Jérémy Levallois. Integral based Curvature Estimators in Digital Geometry. In B. Medrano R. Gonzalez-Diaz, M.J. Jimenez, editor, 17th International Conference on Discrete Geometry for Computer Imagery (DGCI 2013), Lecture Notes in Computer Science, pages 215–227. Springer Verlag, March 2013.

David Coeurjolly, Jacques-Olivier Lachaud, and Jérémy Levallois. Multigrid Convergent Principal Curvature Estimators in Digital Geometry. Computer Vision and Image Understanding, June 2014.

D. Coeurjolly, M. Foare, P. Gueth, and J.-O. Lachaud. Piecewise smooth reconstruction of normal vector field on digital data. Comput. Graph. Forum, 35(7):157–167, 2016. Proc. of Pacific Graphics 2016.

David Coeurjolly, Pierre Gueth, and Jacques-Olivier Lachaud. Digital surface regularization by normal vector field alignment. In 20th International Conference on Discrete Geometry for Computer Imagery, volume LNCS of 20th International Conference on Discrete Geometry for Computer Imagery, page 197–209, Vienna, Austria, 2017.

David Coeurjolly, Pierre Gueth, and Jacques-Olivier Lachaud. Regularization of voxel art. In ACM SIGGRAPH Talk, 2018.

D Coeurjolly. Algorithmique et géométrie discrète pour la caractérisation des courbes et des surfaces. Thèse, Université Lumière Lyon 2, Laboratoire ERIC, 2002.

David Coeurjolly. Distance Transformation, Reverse Distance Transformation and Discrete Medial Axis on Toric Spaces. In International Conference on Pattern Recognition, page 3541, Tampa, United States, December 2008.

David Coeurjolly. Fast and Accurate Approximation of Digital Shape Thickness Distribution in Arbitrary Dimension . Computer Vision and Image Understanding, 116(12):1159–1167, December 2012.

David Coeurjolly. 2D Subquadratic Separable Distance Transformation for Path-Based Norms. In 18th International Conference on Discrete Geometry for Computer Imagery, LNCS. Springer, September 2014.

David Cohen-Steiner and Jean-Marie Morvan. Restricted delaunay triangulations and normal cycle. In Proceedings of the nineteenth annual symposium on Computational geometry, pages 312–321, 2003.

David Cohen-Steiner and Jean-Marie Morvan. Second fundamental measure of geometric sets and local approximation of curvatures. Journal of Differential Geometry, 74(3):363–394, 2006.

Michel Couprie and Gilles Bertrand. Asymmetric parallel 3d thinning scheme and algorithms based on isthmuses. Pattern Recognition Letters, 76:22 – 31, 2016. Special Issue on Skeletonization and its Application.

Michel Couprie, David Coeurjolly, and Rita Zrour. Discrete bisector function and euclidean skeleton in 2d and 3d. Image and Vision Computing, 25(10):1543–1556, 2007.

K. Crane, C. Weischedel, and M. Wardetzky. Geodesics in heat: a new approach to computing distance based on heat flow. ACM Transactions on Graphics (TOG), 32(5):152, 2013.

L. Cuel, J.-O. Lachaud, and B. Thibert. Voronoi-based geometry estimator for 3d digital surfaces. In Proc. Int. Conf. Discrete Geometry for Computer Imagery (DGCI'2014), Sienna, Italy, Lecture Notes in Computer Science, 2014. Submitted.

P.E. Danielsson. Euclidean distance mapping. Computer Graphics and image processing, 14(3):227–248, 1980.

Fernando de Goes, Keenan Crane, Mathieu Desbrun, Peter Schröder, and others. Digital geometry processing with discrete exterior calculus. In ACM SIGGRAPH 2013 Courses, page 7. ACM, 2013.

Fernando De Goes, Andrew Butts, and Mathieu Desbrun. Discrete differential operators on polygonal meshes. ACM Transactions on Graphics (TOG), 39(4):110–1, 2020.

I. Debled-Renesson and J.-P. Reveillès. A linear algorithm for segmentation of discrete curves. International Journal of Pattern Recognition and Artificial Intelligence, 9:635–662, 1995.

I. Debled-Rennesson, F. Feschet, and J. Rouyer-Degli. Blurred segments decomposition in linear time. In E. Andres, G. Damiand, and P. Lienhardt, editors, Proceedings of the 12th International Conference on Discrete Geometry for Computer Imagery, volume 3429 of LNCS, pages 371–382, Poitiers, France, April 2005. Springer-Verlag.

I. Debled-Rennesson, J-L. Rémy, and J. Rouyer-Degli. Linear Segmentation of Discrete Curves into Fuzzy Segments. Discrete Applied Mathematics, 151(1-3):122–137, October 2005.

Mathieu Desbrun, Anil N Hirani, Melvin Leok, and Jerrold E Marsden. Discrete exterior calculus. arXiv preprint math/0508341, 2005.

H. Edelsbrunner, D. Kirkpatrick, and R. Seidel. On the shape of a set of points in the plane. IEEE Transactions on Information Theory, 29(4):551–559, July 1983.

Alexandre Faure and Fabien Feschet. Tangential cover for thick digital curves. In DGCI 2008, volume 4992 of LNCS, pages 368–369. Springer-Verlag, 2008.

Herbert Federer. Curvature measures. Transactions of the American Mathematical Society, 93(3):418–491, 1959.

Fabien Feschet and Jacques-Olivier Lachaud. Full convexity for polyhedral models in digital spaces. In Étienne Baudrier, Benoît Naegel, Adrien Krähenbühl, and Mohamed Tajine, editors, Discrete Geometry and Mathematical Morphology, volume 13493 of Lecture Notes in Computer Science, pages 98–109, Cham, 2022. Springer International Publishing.

Fabien Feschet and Jacques-Olivier Lachaud. An envelope operator for full convexity to define polyhedral models in digital spaces. J. Math. Imaging Vis., 65(5):754–769, 2023.

Fabien Feschet and Jacques-Olivier Lachaud. New characterizations of full convexity. In Sara Brunetti, Andrea Frosini, and Simone Rinaldi, editors, Discrete Geometry and Mathematical Morphology (DGMM'2024), April 15-18, Firenze, pages 41–53, Cham, 2024. Springer Nature Switzerland.

Fabien Feschet and Laure Tougne. Optimal time computation of the tangent of a discrete curve: Application to the curvature. In Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery, DCGI '99, pages 31–40, London, UK, UK, 1999. Springer-Verlag.

M. Foare, J.-O. Lachaud, and H. Talbot. Numerical implementation of the ambrosio-tortorelli functional using discrete calculus and application to image resoration and inpainting. In Proc. 1st Workshop on Reproducible Research in Pattern Recognition (RRPR2016), pages 91–103, Cancun, Mexico, 2016.

Marion Foare, Jacques-Olivier Lachaud, and Hugues Talbot. Image restoration and segmentation using the Ambrosio-Tortorelli functional and discrete calculus. In Pattern Recognition (ICPR), 2016 23rd International Conference on, pages 1418–1423, Cancun, Mexico, 2016. IEEE.

Matteo Focardi. On the variational approximation of free-discontinuity problems in the vectorial case. Mathematical Models and Methods in Applied Sciences, 11(4):663–684, 2001.

Joseph HG Fu. Curvature measures of subanalytic sets. American Journal of Mathematics, pages 819–880, 1994.

Y. Gerard, I. Debled-Rennesson, and P. Zimmermann. An elementary digital plane recognition algorithm. Discrete Applied Mathematics, 151(1–3):169–183, 2005.

Leo J Grady and Jonathan R Polimeni. Discrete calculus: Applied analysis on graphs for computational science. Springer Science & Business Media, 2010.

R.L. Graham. An efficient algorithm for determining the convex hull of a finite planar set. Information Processing Letters, 1:132–133, 1972.

T. Hirata. A unified linear-time algorithm for computing distance maps. Information Processing Letters, 58:129, 1996.

Imagene, Generic digital Image library.

B. Kerautret and J.-O. Lachaud. Curvature Estimation along Noisy Digital Contours by Approximate Global Optimization. Pattern Recognition, 42(10):2265–2278, October 2009.

Bertrand Kerautret and Jacques-Olivier Lachaud. Meaningful Scales Detection along Digital Contours for Unsupervised Local Noise Estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 34(12):2379–2392, December 2012.

Reinhard Klette and Azriel Rosenfeld. Digital geometry - geometric methods for digital picture analysis. Morgan Kaufmann, 2004.

J. O. Lachaud and A. Montanvert. Digital surfaces as a basis for building isosurfaces. In Proceedings 1998 International Conference on Image Processing. ICIP98, volume 2, pages 977–981 vol.2, October 1998.

Jacques-Olivier Lachaud and Annick Montanvert. Continuous Analogs of Digital Boundaries: A Topological Approach to Iso-Surfaces. Graphical Models, 62(3):129–164, May 2000.

J.-O. Lachaud and M. Said. Two efficient algorithms for computing the characteristics of a subsegment of a digital straight line. Discrete Applied Mathematics, 161:2293–2315, oct 2013.

J.-O. Lachaud and A. Vialard. Geometric measures on arbitrary dimensional digital surfaces. In G. Sanniti di Baja, S. Svensson, and I. Nyström, editors, Proc. Int. Conf. Discrete Geometry for Computer Imagery (DGCI'2003), Napoli, Italy, volume 2886 of LNCS, pages 434–443. Springer, 2003.

Jacques-Olivier Lachaud, X. Provençal, and Tristan Roussillon. Two plane-probing algorithms for the computation of the normal vector to a digital plane. J. Math. Imaging Vis., (1):23–39.

Jacques-Olivier Lachaud, Anne Vialard, and François de Vieilleville. Fast, accurate and convergent tangent estimation on digital contours. Image Vision Comput., 25(10):1572–1587, October 2007.

Jacques-Olivier Lachaud, Pascal Romon, and Boris Thibert. Corrected curvature measures. working paper or preprint, July 2019.

J-O Lachaud, Pascal Romon, Boris Thibert, and David Coeurjolly. Interpolated corrected curvature measures for polygonal surfaces. In Computer Graphics Forum, volume 39, pages 41–54. Wiley Online Library, 2020.

Jacques-Olivier Lachaud, Jocelyn Meyron, and Tristan Roussillon. An optimized framework for plane-probing algorithms. Journal of Mathematical Imaging and Vision, 2020.

J.-O. Lachaud. Coding cells of digital spaces: a framework to write generic digital topology algorithms. In A. Del Lungo, V. Di Gesù, and A. Kuba, editors, Proc. Int. Work. Combinatorial Image Analysis (IWCIA'2003), Palermo, Italy, volume 12 of ENDM. Elsevier, 2003.

Jacques-Olivier Lachaud. An alternative definition for digital convexity. In Joakim Lindblad, Filip Malmberg, and Natasa Sladoje, editors, Discrete Geometry and Mathematical Morphology (Proc. DGMM2021), volume 12708 of Lecture Notes in Computer Science, pages 269–282, Cham, 2021. Springer International Publishing.

Jacques-Olivier Lachaud. An Alternative Definition for Digital Convexity. Journal of Mathematical Imaging and Vision, 64:718–735, 2022.

Samuli Laine. A topological approach to voxelization. Comput. Graph. Forum, 32(4):77–86, 2013.

Longin Jan Latecki, Ulrich Eckhardt, and Azriel Rosenfeld. Well-Composed Sets. Computer Vision and Image Understanding, 61(1):70–83, 1995.

A. Lenoir, R. Malgouyres, and M. Revenu. Fast computation of the normal vector field of the surface of a 3D discrete object. 6th Discrete Geometry for Computer Imagery, pages 101–112, 1996.

Alexandre Lenoir, Rémy Malgouyres, and Marinette Revenu. Fast computation of the normal vector field of the surface of a 3-d discrete object. In International Conference on Discrete Geometry for Computer Imagery, pages 101–112. Springer, 1996.

T. Lewiner, V. Mello, A. Peixoto, S. Pesco, and H. Lopes. Fast generation of pointerless octree duals. Computer Graphics, (5):1–9.

Buzer Lilian. Computing multiple convex hulls of a simple polygonal chain in linear time. In 23rd European Workshop on Computational Geometry, pages 114–117, 2007.

Jui-Ting Lu, Tristan Roussillon, and David Coeurjolly. A new lattice-based plane-probing algorithm. In Étienne Baudrier, Benoît Naegel, Adrien Krähenbühl, and Mohamed Tajine, editors, Discrete Geometry and Mathematical Morphology, pages 366–381, Cham, 2022. Springer International Publishing.

C. Maurer, R. Qi, and V. Raghavan. A Linear Time Algorithm for Computing Exact Euclidean Distance Transforms of Binary Images in Arbitrary Dimensions. IEEE Trans. Pattern Analysis and Machine Intelligence, 25:265–270, 2003.

Nelson Max. Weights for computing vertex normals from facet normals. Journal of graphics tools, 4(2):1–6, 1999.

Avraham A. Melkman. On-line construction of the convex hull of a simple polyline. Inf. Process. Lett., 25(1):11–12, April 1987.

Avraham A. Melkman. On-line Construction of the Convex Hull of a Simple Polyline. Inf. Process. Lett., 25(1):11–12, April 1987.

Nicolas Mellado, Gaël Guennebaud, Pascal Barla, Patrick Reuter, and Christophe Schlick. Growing least squares for the analysis of manifolds in scale-space. In Computer Graphics Forum, volume 31, pages 1691–1701. Wiley Online Library, 2012.

Q. Mérigot, M. Ovsjanikov, and L. Guibas. Voronoi-based curvature and feature estimation from point clouds. IEEE Transactions on Visualization and Computer Graphics, 17(6):743–756, 2011.

S A Molchanov. Diffusion processes and riemannian geometry. Russian Mathematical Surveys, 30(1):1, 1975.

Gregory M Nielson, Gary Graf, Ryan Holmes, Adam Huang, and Mariano Phielipp. Shrouds: optimal separating surfaces for enumerated volumes. In VisSym, volume 3, pages 75–84, 2003.

Stanley Osher and Ronald Fedkiw. Level Set Methods and Dynamic Implicit Surfaces. Springer, 2003 edition, November 2003.

L. Papier and J. Françon. Evalutation de la normale au bord d'un objet discret 3D. Revue de CFAO et d'informatique graphique, 13:205–226, 1998.

Min Ki Park, Seung Joo Lee, and Kwan H. Lee. Multi-scale tensor voting for feature extraction from unstructured point clouds. Graphical Models, 74(4):197–208, 2012.

H Pottmann, J Wallner, Y Yang, Y Lai, and S Hu. Principal curvatures from the integral invariant viewpoint. Computer Aided Geometric Design, 24(8-9):428–442, 2007.

H Pottmann, J Wallner, Q Huang, and Y Yang. Integral invariants for robust geometry processing. Computer Aided Geometric Design, 26(1):37–60, 2009.

I. Ragnemalm. The Euclidean Distance Transform. PhD thesis, 1993.

J.-P. Reveillès. Géométrie discrète, calcul en nombres entiers et algorithmique. Thèse d'etat, Université Louis Pasteur, Strasbourg, France, 1991. In french.

Steven Rosenberg. The Laplacian on a Riemannian Manifold. Cambridge University Press, 1997. Cambridge Books Online.

A. Rosenfeld and J.-L. Pfaltz. Sequential operations in digital picture processing. Journal of the ACM (JACM), vol:13pp471–494, 1966.

A. Rosenfeld and J. Pfaltz. Distance functions on digital pictures. Pattern Recognition, 1:33–61, 1968.

Tristan Roussillon and Jacques-Olivier Lachaud. Digital Plane Recognition with Fewer Probes. In 21st IAPR International Conference on Discrete Geometry for Computer Imagery, volume 11414 of Lecture Notes in Computer Science, pages 380–393, Marne-la-Vallée, France, March 2019. Couprie M. and Cousty J. and Kenmochi Y. and Mustafa N., Springer, Cham.

Tristan Roussillon and Isabelle Sivignon. Faithful polygonal representation of the convex and concave parts of a digital curve. Pattern Recognition, 44(10-11):2693–2700, October 2011.

Tristan Roussillon. An arithmetical characterization of the convex hull of digital straight segments. In Elena Barcucci, Andrea Frosini, and Simone Rinaldi, editors, Discrete Geometry for Computer Imagery, volume 8668 of Lecture Notes in Computer Science, pages 150–161. Springer International Publishing, 2014.

M. Said and J.-O. Lachaud. Computing the characteristics of a subsegment of a digital straight line in logarithmic time. In Proc. International Conference on Discrete Geometry for Computer Imagery (DGCI2011), volume 6607 of Lecture Notes in Computer Science, pages 320–332, Nancy, France, apr 2011. Springer.

M. Said, J.-O. Lachaud, and F. Feschet. Multiscale Discrete Geometry. In Proc. International Conference on Discrete Geometry for Computer Imagery (DGCI2009), volume 5810 of Lecture Notes in Computer Science, pages 118–131, Montréal, Québec Canada, 2009. Springer.

T. Saito and J.-I. Toriwaki. New algorithms for Euclidean distance transformations of an $n$-dimensional digitized picture with applications. Pattern Recognition, 27:1551–1565, 1994.

J. A. Sethian. Fast marching methods. SIAM Review, 41:199–235, 1998.

Michael Ian Shamos. Computational geometry. 1978.

Nicholas Sharp, Yousuf Soliman, and Keenan Crane. The vector heat method. ACM Trans. Graph., 38(3), 2019.

Isabelle Sivignon. A near-linear time guaranteed algorithm for digital curve simplification under the fréchet distance. In Discrete Geometry for Computer Imagery, volume 6607 of Lecture Notes in Computer Science, pages 333–345. Springer Berlin Heidelberg, 2011.

Isabelle Sivignon. Walking in the farey fan to compute the characteristics of a discrete straight line subsegment. In Discrete Geometry for Computer Imagery, volume 7749 of Lecture Notes in Computer Science, pages 23–34. Springer-Verlag, 2013.

Isabelle Sivignon. Algorithms for fast digital straight segments union. In Elena Barcucci, Andrea Frosini, and Simone Rinaldi, editors, Discrete Geometry for Computer Imagery, volume 8668 of Lecture Notes in Computer Science, pages 344–357. Springer International Publishing, 2014.

Godfried T. Toussaint and David Avis. On a convex hull algorithm for polygons and its application to triangulation problems. Pattern Recognition, 15(1):23 – 29, 1982.

S. R S Varadhan. On the behavior of the fundamental solution of the heat equation with variable coefficients. Communications on Pure and Applied Mathematics, 20(2):431–455, 1967.

Peter Wintgen. Normal cycle and integral curvature for polyhedra in riemannian manifolds. Differential geometry, 21, 1982.