? i ? |L S |), choisir un plan euclidien P i représentant de S i ,
ensemble des points entiers qui appartiennent au demi-espace négatif délimité par P i . Calculer l'objet lissé résultant O = ? i B i ,
a de sens que si elle est employée sur des objets dont le résultat attendu est un objet convexe. Par ailleurs, comme nous utilisons des morceaux plans discretsépaisdiscretsépais, il n'existe pas un unique choix possible pour le plan euclidien représentant de l'´ etape 2 ,
avoir un algorithme de bruitage plus général, nous avons programmé une extension aux objets 3D d'une méthode de bruitage d'images discrètes, développée par T. Kanungo et ses coauteurs [KHP94], dans le contexte de l'OCR. Bien que ce modèle aitétéaitété validé en 2D dans ce contexte, son emploi en 3D reste discutable. Malgré tout, l'extension 3D ayant déjàdéjàété utilisée dans ,
P (o|b, d, ? 0 , ?) d'inverser un voxel fond en un voxel objet estégalèestégalè a ? ,
A three-dimensional holes closing algorithm, Pattern Recognition Letters, vol.23, issue.5, pp.523-531, 2002. ,
DOI : 10.1016/S0167-8655(01)00152-0
URL : https://hal.archives-ouvertes.fr/hal-00621975
Le plan discret, Colloque de géométrie discrète en imagerie : fondements et applications, 1993. ,
Defining Discrete Objects for Polygonalization: The Standard Model, 10th International Conference on Discrete Geometry for Computer Imagery, volume 2301 de LNCS, pp.313-325, 2002. ,
DOI : 10.1007/3-540-45986-3_28
Numerical methods for computing interfacial mean curvature, Computational Materials Science, vol.4, issue.2, pp.103-116, 1995. ,
DOI : 10.1016/0927-0256(95)00014-H
A new characterization of three-dimensional simple points, Pattern Recognition Letters, vol.15, issue.2, pp.169-175, 1994. ,
DOI : 10.1016/0167-8655(94)90046-9
URL : https://hal.archives-ouvertes.fr/inria-00615050
Strong thinning and polyhedric approximation of the surface of a voxel object, Discrete Applied Mathematics, vol.125, issue.1, pp.93-114, 2003. ,
DOI : 10.1016/S0166-218X(02)00226-3
Modélisation géométrique et topologique des images discrètes Disponible en ligne : http://lsiit. u-strasbg.fr/Publications, Thèse, 2007. ,
Surfaces discrètes multi-´ echelle, squelettisation, polyédrisation et opérations ensemblistes sur des polyèdres, Thèse de doctorat, 2002. ,
An elementary algorithm for digital line recognition in the general case, 12th International Conference on Discrete Geometry for Computer Imagery, pp.299-310, 2005. ,
Tougne : Multigrid convergence and surface area estimation, Theoretical Foundations of Computer Vision " Geometry, Morphology, and Computational Imaging volume 2616 de LNCS, pp.101-119, 2003. ,
DOI : 10.1007/3-540-36586-9_7
Reversible discrete volume polyhedrization using marching cubes, SPIE Vision Geometry XII, pp.1-11, 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-00185160
Udupa : Surface shading in the cuberille environment, IEEE Computer Graphics and Applications, vol.5, issue.12, pp.33-43, 1985. ,
Montanvert : Géométrie discrète en analyse d'images. Traité des Nouvelles Technologies, 1991. ,
Géométrie discrète et images numérique [Coe02a] D. Coeurjolly : Visibility in discrete geometry : An application to discrete geodesic paths Algorithmique et géométrie discrète pour la caractérisation des courbes et des surfaces, 10th International Conference on Discrete Geometry for Computer Imagery, volume 2301 de LNCS Thèse, UniversitéLumì ere Lyon 2, décembre 2002. [CZ06] D. Coeurjolly et L. Zerarga : Supercover model, digital straight line recognition and curve reconstruction on the irregular isothetic grids, pp.326-33746, 2006. ,
Architecture d'un modeleur géométriquè a base topologique d'objets discrets, Journées de l'Association Française d'Informatique Graphique, IRCAD, 2005. ,
A generalized preimage for the digital analytical hyperplane recognition, Second International Symposium on Visual Computing, pp.476-489, 2000. ,
DOI : 10.1016/j.dam.2008.05.030
URL : https://hal.archives-ouvertes.fr/hal-00354684
Architecture d'un modeleur géométriquè a base topologique d'objets discrets et méthodes de reconstruction en dimensions 2 et 3, Thèse, 2006. ,
Eléments de géométrie discrète ? Vers uné etude des structures discrètes bruitées HabilitationàHabilitationà diriger des recherches ,
Debled-Rennesson : A linear algorithm for polygonal representations of digital sets, 11th International Workshop on Combinatorial Image Analysis, pp.307-319, 2006. ,
Optimal Blurred Segments Decomposition in Linear Time, 12th International Conference on Discrete Geometry for Computer Imagery, pp.371-382, 2005. ,
DOI : 10.1007/978-3-540-31965-8_34
URL : https://hal.archives-ouvertes.fr/inria-00000112
Optimal blurred segments decomposition of noisy shapes in linear time [DRR95] I. Debled-Rennesson et J.-P.Reveilì es : A linear algorithm for segmentation of digital curves, Computers & Graphics International Journal of Pattern Recognition and Artificial Intelligence, vol.30, issue.96, pp.30-36635, 1995. ,
Segmentation of discrete curves into fuzzy segments Smeulders : Discrete representation of straight lines, 9th International Workshop on Combinatorial Image Analysis, volume 12 de Electronic Notes in Discrete MathematicsFBF09] A. Faure, L. Buzer et F. Feschet : Tangential cover for thick digital curves. Pattern Recognition, pp.450-463, 1984. ,
Tangential cover for thick digital curves Fourier : Solution d'une questionparticulì ere du calcul des inégalités : Polyhedrization of the boundary of a voxel object, 14th International Conference on Discrete Geometry for Computer Imagery 8th International Conference on Discrete Geometry for Computer Imagery, volume 1568 de Lecture Notes in Computer Science, pp.358-369, 1999. ,
Recognizing arithmetic straight lines and planes [FT99] F. Feschet et L. Tougne : Optimal time computation of the tangent of a discrete curve : application to the curvature Marne-la-Vallee, France, mars 1999. [FT06] C. Fiorio et J.-L. Toutant : Arithmetic discrete hyperspheres and separatingness, Discrete combinatorial surfaces. Graphical Models and Image Processing 6th International Workshop on Discrete Geometry for Computer Imagery, volume 1176 de LNCS 8th International Conference on Discrete Geometry for Computer Imagery, volume 1568 de LNCS 13th International Conference on Discrete Geometry for Computer Imagery, pp.20-26, 1992. ,
An elementary digital plane recognition algorithm Gérard : A fast and elementary algorithm for digital plane recognition Computing the width of a point set in 3-space An efficient algorithm for determining the convex hull of a finite planar set, 9th International Workshop on Combinatorial Image Analysis, pp.169-183, 1972. ,
Herman : Discrete multidimensional jordan surfaces CVGIP : Graphical Model and Image Processing Geometry of Digital Spaces Multigrid analysis of curvature estimators Disponible en ligne : http://perception.inrialpes.fr/ Publications, Thèse, Université d'Auvergne Proceedings of Image and Vision Computing New ZealandHM95] R. Horaud et O. Monga : Vision par ordinateur : outils fondamentaux, 2 e ´ edition. ´ Editions Hermès Houle et G.T. Toussaint : Computing the width of a set. IEEE Transactions on Pattern Analysis and Machine Intelligence, pp.507-515, 1988. ,
Generic digital Image library Disponible en ligne : http://gforge.liris.cnrs. fr/projects/imagene. [Kar84] N. Karmarkar : A new polynomial-time algorithm for linear programming Haralick et I. Phillips : Nonlinear local and global document degradation models, Combinatorica International Journal of Imaging Systems and Technology, vol.4, issue.53, pp.373-395220, 1984. ,
Computer graphics and connected topologies on finite ordered sets, Topology and its Applications, vol.36, issue.1, pp.1-17, 1990. ,
Multi-scale analysis of discrete contours fo unsupervised noise detection, 13th International Workshop on Combinatorial Image Analysis, pp.187-200, 2009. ,
Finite topology as applied to image analysis. Computer Vision, Graphics and Image Processing, pp.141-161, 1989. ,
Algorithms and data structures for computer topology, Digital and Image Geometry, pp.38-58, 2001. ,
Geometry of Locally Finite Spaces. Dr, Baerbel Kovalevski, 2008. ,
Digital Geometry : Geometric Methods For Digital Picture Analysis, 2004. ,
Superfaces: polygonal mesh simplification with bounded error, IEEE Computer Graphics and Applications, vol.16, issue.3, pp.64-77, 1996. ,
DOI : 10.1109/38.491187
Topologically defined iso-surfaces, 6th International Workshop on Discrete Geometry for Computer Imagery, pp.245-256, 1996. ,
DOI : 10.1007/3-540-62005-2_21
URL : http://dept-info.labri.u-bordeaux.fr/~lachaud/./RR-LIP/rr2.ps.gz
Coding cells of digital spaces : a framework to write generic digital topology algorithms, Electronic Notes in Discrete Mathematics, vol.12, pp.337-348, 2003. ,
Marching cubes: A high resolution 3D surface construction algorithm, ACM SIGGRAPH Computer Graphics, vol.21, issue.4, pp.163-169, 1987. ,
DOI : 10.1145/37402.37422
Fast estimation of mean curvature on the surface of a 3d discrete object, 7th International Workshop on Discrete Geometry for Computer Imagery, volume 1347 de LNCS, pp.175-186, 1997. ,
Des outils pour les surfaces discrètes : estimation d'invariants géométriques , préservation de la topologie, tracé géodésiques Disponible en ligne : http://www.greyc.ensicaen.fr/EquipeImage/ publications/Pub/PostScript/tlenoir.ps.gz. [Lev44] K. Levenberg : A method for the solution of certain non-linear problems in least squares, Thèse, pp.164-168, 1944. ,
Topological models for boundary representation : a comparison with ndimensional generalized maps, Computer-Aided Design, vol.23, issue.1, pp.59-82, 1991. ,
N-dimensional generalized combinatorial maps and cellular quasi-manifolds, International Journal on Computational Geometry and Applications, vol.4, issue.3, pp.275-324, 1994. ,
Montanvert : Continuous analogs of digital boundaries : a topological approach to iso-surfaces, Graphical Models and Image Processing, vol.63, pp.129-164, 2000. ,
Fast computation of the normal vector field of the surface of a 3-D discrete object, 6th International Workshop on Discrete Geometry for Computer Imagery, volume 1176 de LNCS, pp.101-112, 1996. ,
DOI : 10.1007/3-540-62005-2_9
URL : https://hal.archives-ouvertes.fr/hal-00965759
Analysis and comparative evaluation of discrete tangent estimators, 12th International Conference on Discrete Geometry for Computer Imagery, pp.240-251, 2005. ,
Vialard et F. de Vieilleville : Fast, accurate and convergent tangent estimation on digital contours, Image and Vision Computing, issue.10, pp.251572-1587, 2007. ,
A definition of surfaces of Z 3 : A new 3D discrete Jordan theorem, Theoretical Computer Science, vol.186, issue.12, pp.1-41, 1997. ,
An algorithm for least-squares estimation of nonlinear parameters, SIAM Journal on Applied Mathematics, vol.11, issue.2, pp.431-441, 1963. ,
Topological segmentation of discrete surfaces, International Journal of Computer Vision, vol.17, issue.6, pp.183-197, 1993. ,
DOI : 10.1007/BF01420736
URL : https://hal.archives-ouvertes.fr/inria-00615557
A note on discrete representation of lines, pp.481-490, 1985. ,
Beitrage zur Theorie der Linearen Ungleichungen, Thèse de doctorat, 1936. ,
Surfaces in three-dimensional digital images, Information and Control, vol.51, issue.3, pp.227-247, 1981. ,
DOI : 10.1016/S0019-9958(81)90290-4
Morphologie mathématique 1 : approches déterministes. Traité IC2 ? série Signal et Image, Hermès ? Lavoisier, 2008. ,
Maintenance of configurations in the plane, Journal of Computer and System Sciences, vol.23, issue.2, pp.166-204, 1981. ,
Polyédrisation et visualisation d'objets discrets tridimensionnels, Thèse, 1999. ,
Buzer et I. Debled-Rennesson : Recognition of blurred pieces of discrete planes, 13th International Conference on Discrete Geometry for Computer Imagery, pp.65-76, 2006. ,
Provot et I. Debled-Rennesson : Geometric feature estimators for noisy discrete surfaces, 14th International Conference on Discrete Geometry for Computer Imagery, pp.275-286, 2008. ,
Provot et I. Debled-Rennesson : Segmentation of noisy discrete surfaces, 12th International Workshop on Combinatorial Image Analysis, pp.160-171, 2008. ,
Disponible en ligne : ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/ PhD/PhD1994/PhD1994-09.ps.Z. [PF98] L. Papier et J. Françon : ´ Evaluation de la normale au bord d'un objet discret 3d, Pro05] Laurent Provot : Reconnaissance de morceaux de plans discrets bruités Disponible en ligne, pp.205-226, 1994. ,
Reveilì es : Géométrie discrète, calculs en nombre entiers et algorithmique, Thèse d'´ etat, 1991. ,
Editing 3d binary images using distance transforms, International Conference on Pattern Recognition, p.6030, 2000. ,
Chassery : Decomposition of a 3d discrete object surface into discrete plane pieces, Algorithmica, vol.38, issue.1, pp.25-43, 2004. ,
Chassery : Discrete surface segmentation into discrete planes, 10th International Workshop on Combinatorial Image Analysis, pp.458-473, 2004. ,
Reversible Polygonalization of a 3D Planar Discrete Curve: Application on Discrete Surfaces, 12th International Conference on Discrete Geometry for Computer Imagery, pp.347-358, 2005. ,
DOI : 10.1007/978-3-540-31965-8_32
URL : https://hal.archives-ouvertes.fr/hal-00185147
De la caractérisation des primitivesàprimitivesà la reconstruction polyédrique de surfaces en géométrie discrète. Thèse, Institut National Polytechnique de Grenoble Disponible en ligne, 2004. ,
A Comprehensive Introduction to Differential Geometry, 1999. ,
Chamfer masks : discrete distance functions, geometrical properties and optimization The Hague, The Netherlands, 11th ICPR, pp.244-247, 1992. ,
Solving geometric problems with the rotating calipers, Proceedings of IEEE MELECON'83, 1983. ,
Normal Computation for Discrete Surfaces in 3D Space, Computer Graphics Forum, vol.16, issue.3, pp.15-26, 1997. ,
DOI : 10.1111/1467-8659.16.3conferenceissue.3
Varying neighborhood parameters for the computation of normals on surfaces in discrete space, Computer Graphics International, pp.616-625, 1998. ,
Udupa : Multidimensional digital boundaries. CVGIP : Graphical Model and Image Processing, pp.311-323, 1994. ,
Boundary Detection in Multidimensions, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.4, issue.1, pp.41-50, 1982. ,
DOI : 10.1109/TPAMI.1982.4767193
Chassery : Recognition of digital naive planes and polyhedrization, 9th International Conference on Discrete Geometry for Computer Imagery, 1953. ,
Disponible en ligne : http: //www.lis.inpg.fr/fileadmin/stages_dea_theses/theses Dekker : An efficient uniform cost algorithm applied to distance transforms, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.11, issue.4, pp.425-429, 1989. ,
Primal-Dual interior-moint methods, SIAM, 1997. ,
Normal estimation in 3d discrete space. The Visual Computer, pp.278-291, 1992. ,