A. Aggarwal, H. Booth, J. O'rourke, S. Suri, and C. Yap, Finding minimal convex nested polygons, Information and Computation, vol.83, issue.1, pp.98-110, 1989.

E. Andres, R. Acharya, and C. Sibata, Discrete analytical hyperplanes, CVGIP: Graphical Model and Image Processing, vol.59, issue.5, pp.302-309, 1997.

E. Andres and M. Jacob, The discrete analytical hyperspheres, IEEE Trans. Vis. Comput. Graph, vol.3, issue.1, pp.75-86, 1997.

T. Asano, V. E. Brimkov, and R. P. Barneva, Some theoretical challenges in digital geometry: A perspective, Discrete Appl. Math, vol.157, issue.16, pp.3362-3371, 2009.

I. Bárány, R. Howe, and L. Lovász, On integer points in polyhedra: A lower bound, Combinatorica, vol.12, issue.2, pp.135-142, 1992.

A. I. Barvinok, Lattice points and lattice polytopes, Handbook of Discrete and Computational Geometry, pp.153-176, 2004.

M. Beck and S. Robins, Computing the Continuous Discretely, Undergraduate Texts in Mathematics, 2007.

V. E. Brimkov, E. Andres, and R. P. Barneva, Object discretizations in higher dimensions, Pattern Recognition Letters, vol.23, issue.6, pp.623-636, 2002.

V. E. Brimkov, D. Coeurjolly, and R. Klette, Digital planarity-A review, vol.155, pp.468-495, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00185059

L. Buzer, A linear incremental algorithm for naive and standard digital lines and planes recognition, Graphical Models, vol.65, pp.61-76, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00622020

L. Buzer, A simple algorithm for digital line recognition in the general case, Pattern Recognition, vol.40, issue.6, pp.1675-1684, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00622016

K. L. Clarkson, Algorithms for polytope covering and approximation, Algorithms and Data Structures, Third Workshop, WADS '93, pp.246-252, 1993.

D. Coeurjolly, Y. Gérard, J. Reveilì-es, and L. Tougne, An elementary algorithm for digital arc segmentation, Discrete Applied Mathematics, vol.139, issue.1-3, pp.31-50, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00185216

W. Cook, M. Hartmann, R. Kannan, and C. Mcdiarmid, On integer points in polyhedra, Combinatorica, vol.12, issue.1, pp.27-37, 1992.

G. Das and D. Joseph, The complexity of minimum convex nested polyhedra, Proceedings of the 2nd Canadian Conference of Computational Geometry, pp.296-301, 1990.

I. Debled-rennesson and J. P. Reveilles, A linear algorithm for incremental digital display of circular arcs, International Journal of Pattern Recognition and Artificial Intelligence, vol.9, pp.635-662, 1995.

L. Dorst and A. W. Smeulders, Discrete representation of straight lines, IEEE Trans. Pattern Anal. Mach. Intell, vol.6, issue.4, pp.450-463, 1984.

H. Edelsbrunner and F. Preparata, Minimum polygonal separation, Information and Computation, vol.77, issue.3, pp.218-232, 1988.

E. Ehrhart, Sur les polyèdres rationnels homothétiques homothétiquesà n dimensions, Comptes Rendus de l'Académie des Sciences, vol.254, pp.616-618, 1962.

F. Feschet and L. Tougne, On the min DSS problem of closed discrete curves, Discrete Applied Mathematics, vol.151, issue.1-3, pp.138-153, 2005.
URL : https://hal.archives-ouvertes.fr/hal-01517146

C. Fiorio and J. Toutant, Arithmetic discrete hyperspheres and separatingness, Discrete Geometry for Computer Imagery, 13th International Conference, pp.425-436, 2006.
URL : https://hal.archives-ouvertes.fr/lirmm-00128277

S. Forchhammer and C. Kim, Digital squares, vol.2, pp.672-674, 1988.

Y. Gérard, Recognition of digital polyhedra with a fixed number of faces, Discrete Geometry for Computer Imagery-19th IAPR International Conference, DGCI 2016, pp.415-426, 2016.

Y. Gérard, D. Coeurjolly, and F. Feschet, Giftwrapping based preimage computation algorithm, Pattern Recognition, vol.42, issue.10, pp.2255-2264, 2009.

Y. Gérard, I. Debled-rennesson, and P. Zimmermann, An elementary digital plane recognition algorithm, Discrete Applied Mathematics, vol.151, issue.1-3, pp.169-183, 2005.

Y. Gérard, L. Provot, and F. Feschet, Introduction to digital level layers, Discrete Geometry for Computer Imagery-16th IAPR International Conference, pp.83-94, 2011.

C. Haase and G. M. Ziegler, On the maximal width of empty lattice simplices, Eur. J. Comb, vol.21, issue.1, pp.111-119, 2000.

R. Klette and A. Rosenfeld, Digital geometry : geometric methods for digital picture analysis. The Morgan Kaufmann series in computer graphics and geometric modeling, 2004.

R. Krishnaswamy and C. E. Kim, Digital parallelism, perpendicularity, and rectangles, IEEE Trans. Pattern Anal. Mach. Intell, vol.9, issue.2, pp.316-321, 1987.

H. Lenstra, Integer programming with a fixed number of variables, Mathematics of Operations Research, vol.8, pp.538-548, 1983.

M. Lindenbaum and A. M. Bruckstein, On recursive, O(N) partitioning of a digitized curve into digital straight segments, IEEE Trans. Pattern Anal. Mach. Intell, vol.15, issue.9, pp.949-953, 1993.

N. Megiddo, Linear-time algorithms for linear programming in r 3 and related problems, SIAM J. Comput, vol.12, issue.4, pp.759-776, 1983.

N. Megiddo, On the complexity of polyhedral separability, Discrete and Computational Geometry, vol.3, issue.4, pp.325-337, 1988.

A. Nakamura and K. Aizawa, Digital squares. Computer Vision, Graphics, and Image Processing, vol.49, pp.357-368, 1990.

T. P. Nguyen and I. Debled-rennesson, Arc segmentation in linear time, Computer Analysis of Images and Patterns-14th International Conference, pp.84-92, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00594835

B. Nill and G. M. Ziegler, Projecting lattice polytopes without interior lattice points, Math. Oper. Res, vol.36, issue.3, pp.462-467, 2011.

J. O'rourke, Computational geometry column 4, SIGACT News, vol.19, issue.2, pp.22-24, 1988.

G. Pick, Geometrisches zur zahlenlehre, Sitzungsberichte des deutschen naturwissenschaftlichmedicinischen Vereines für Böhmen, vol.19, pp.311-319, 1965.

L. Provot and Y. Gérard, Recognition of digital hyperplanes and level layers with forbidden points, Combinatorial Image Analysis-14th International Workshop, IWCIA 2011, pp.144-156, 2011.
URL : https://hal.archives-ouvertes.fr/hal-02092767

L. Provot, Y. Gérard, and F. Feschet, Digital level layers for digital curve decomposition and vectorization, IPOL Journal, vol.4, pp.169-186, 2014.
URL : https://hal.archives-ouvertes.fr/hal-02092762

S. Rabinowitz, A census of convex lattice polygons with at most one interior lattice point, Ars Combinatorica, vol.28, pp.83-96, 1989.

A. Rosenfeld and R. Klette, Digital straightness, Electr. Notes Theor. Comput. Sci, vol.46, pp.1-32, 2001.

A. Schrijver, Theory of Linear and Integer Programming, 1986.

A. Sebö, An introduction to empty lattice simplices, Integer Programming and Combinatorial Optimization, 7th International IPCO Conference, pp.400-414, 1999.

I. Stojmenovi´cstojmenovi´c and R. Tosi´ctosi´c, Digitization schemes and the recognition of digital straight lines, hyperplanes and flats in arbitrary dimensions, Vision Geometry, vol.119, pp.197-212, 1991.

J. Toutant, E. Andres, G. Largeteau-skapin, and R. Zrour, Implicit digital surfaces in arbitrary dimensions, Discrete Geometry for Computer Imagery-18th IAPR International Conference, pp.332-343, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01019467

J. Toutant, E. Andres, and T. Roussillon, Digital circles, spheres and hyperspheres: From morphological models to analytical characterizations and topological properties, Discrete Applied Mathematics, vol.161, pp.2662-2677, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00857691