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biblio.bib
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@InBook{ingemar,
author = {I. Ragnemalm and G. Borgefors},
title = {The Euclidean Distance Transform,},
chapter = {Towards a minimal shape representation using maximal discs},
publisher = {Link\"{o}ping Studies in Science and Technology. Dissertations No.
304., Link\"{o}ping University},
year = 1993,
month = apr,
pages = {245--260}
}
@InProceedings{borgerfors_min_SSAB,
author = {G. Borgefors and I. Nystr\"{o}m},
title = {Quantitative shape analysis of volume images -- reducing the set
of centres of maximal spheres},
booktitle = {Proc. SSAB Symposium on Image Analysis},
pages = {5--8},
year = 1995,
address = {Link\"{o}ping, Sweden},
month = ma,
}
@Article{Tamassia/87,
author = "R. Tamassia",
title = "On embedding a graph in the grid with the minimum
number of bends",
journal = "SIAM J. Comput.",
pages = "421--444",
year = 1987,
month = jun,
number = 3,
volume = 16,
publisher = "Society for Industrial and Applied Mathematics",
institution = "Dipartimento di Inf. e Sistemistica, Roma Univ.,
Italy",
address = "Philadelphia, PA",
cdate = "1970-01-01",
mdate = "2005-08-18",
}
@TechReport{dcoeurjo_RR_AMNP,
author = {D. Coeurjolly and J. Hulin and I. Sivignon},
title = {Finding a Minimum Medial Axis of a Discrete Shape is NP-hard},
institution = {Laboratoire LIRIS, UMR-CNRS 5205, Universit\'e Claude Bernard Lyon 1},
year = 2007,
url = {http://liris.cnrs.fr/publis/index_html?id=3158},
number = {RR-2007-026}
}
@InProceedings{lucas,
year = 2001,
title = "Multiresolution and Shape Optimization of Implicit
Skeletal Model",
author = "S. Prevost and L. Lucas and E. Bittar",
URL = "http://visinfo.zib.de/EVlib/Show?EVL-2001-86",
abstract = "Display of large volumes, progressive rendering and
selective refinements are some of the operations
supported by multiresolution technology. In this paper,
a general framework relying on the use of such
techniques applied to volume data rendering is
presented. Based on a pyramidal representation of data,
two aspects of our work are considered. First, the
decimation algorithm itself is described. The general
principle consists in gradually removing nodes of a
structural graph previously established while
respecting constraints. A second part introduces the
refinement of preliminary obtained Levels of Details
(LOD). The problem is to preserve as well as possible
the initial volume of studied objects. The goal is to
build an interactive system of visualization for the
analysis of volumetric data. The speed of treatments
associated with a good visualization should enable to
achieve a 3D survey of a natural object in a
quasi-interactive manner. The method has been
successfully applied to both synthetic and real data
(medical imaging).",
editor = "V. Skala",
keywords = "Volume data visualization, skeleton shape description,
implicit surface, multiresolution, graph
representation, shape simplification, optimization,
genetic algorithms.",
booktitle = "WSCG 2001 Conference Proceedings",
}
@Article{de_Fraysseix-Pach-Pollack/90,
author = "H. {de Fraysseix} and J. Pach and R. Pollack",
title = "How to draw a planar graph on a grid",
journal = "Combinatorica",
pages = "41--51",
year = "1990",
volume = "10",
publisher = "Akad{\'e}miai Kiad{\'o}",
address = "Budapest, North-Holland Publishing Company:
Amsterdam-New York-Oxford-Tokyo",
cdate = "1970-01-01",
mdate = "2005-08-18",
}
@Article{TCS::JansenM1995:69,
title = "The minimum broadcast time problem for several
processor networks",
author = "K. Jansen and H. M{\"u}ller",
journal = "Theoretical Computer Science",
pages = "69--85",
month = "7~" # aug,
year = "1995",
volume = "147",
number = "1--2",
}
@InProceedings{hartong,
author = {J. Hartong},
booktitle = {La mathématique non standard},
title = {Une théorie du continu},
publisher = {Editions du CNRS, Paris},
year = 1989,
series = {Fondements des Sciences}
}
@article{decomp3Dstina,
AUTHOR = "Svensson, S. and {Sanniti di Baja}, G.",
TITLE = "Using distance transforms to decompose 3D discrete objects",
JOURNAL = "Image Vision \& Computing",
VOLUME = 20,
YEAR = 2002,
NUMBER = 8,
MONTH = jun,
PAGES = "529-540",
BIBSOURCE = "http://www.visionbib.com/bibliography/twod300.html#TT20209"
}
@Article{TCS::DobkinK1983,
title = "Fast Detection of Polyhedral Intersection",
author = "D.~P. Dobkin and D.~G. Kirkpatrick",
pages = "241--253",
journal = "Theoretical Computer Science",
year = "1983",
month = dec,
volume = "27",
number = "3",
preliminary = "ICALP::DobkinK1982",
}
@Article{attali_incluExclu,
title = "Inclusion-Exclusion Formulas from Independent
Complexes",
author = "D. Attali and H. Edelsbrunner",
publisher = "Springer-Verlag",
year = "2007",
abstract = "Using inclusion-exclusion, we can write the indicator
function of a union of finitely many balls as an
alternating sum of indicator functions of common
intersections of balls. We exhibit abstract simplicial
complexes that correspond to minimal
inclusion-exclusion formulas. They include the dual
complex, as defined in [3], and are characterized by
the independence of their simplices and by geometric
realizations with the same underlying space as the dual
complex.",
ISSN = "1432-0444",
journal = "Discrete \& Computational Geometry",
volume = 37,
number = 1,
pages ={59--77},
doi = "10.1007/s00454-006-1274-7",
}
@ARTICLE{borgefors:cvgip:1986,
AUTHOR = {G. Borgefors},
JOURNAL = {Computer Vision, Graphics, and Image Processing},
TITLE = {Distance Transformations in Digital Images},
YEAR = {1986},
MONTH = feb,
OPTNOTE = {},
NUMBER = {3},
PAGES = {344--371},
VOLUME = {34}
}
@inproceedings{FIORIO:2006:LIRMM-00128281:1,
title={{D}iscrete {C}ircles: an arithmetical approach with non-constant thickness},
author={Fiorio, {C}. and {T}outant, {J}.-{L}. and {J}amet, {D}.},
booktitle={{V}ision {G}eometry {X}{I}{V}, {I}{S}\&{T}/{S}{P}{I}{E} 18th {A}nnual {S}ymposium {E}lectronic {I}maging },
pages={60660{C}01-60660{C}12 },
month=01,
year=2006,
URL={http://hal-lirmm.ccsd.cnrs.fr/lirmm-00128281/en/},
}
@InProceedings{conf/dgci/FiorioT06,
title = "Arithmetic Discrete Hyperspheres and Separatingness",
author = "C. Fiorio and J.-L. Toutant",
bibdate = "2006-11-22",
bibsource = "DBLP,
http://dblp.uni-trier.de/db/conf/dgci/dgci2006.html#FiorioT06",
booktitle = "DGCI",
booktitle = "Discrete Geometry for Computer Imagery, 13th
International Conference, {DGCI} 2006, Szeged, Hungary,
October 25-27, 2006, Proceedings",
publisher = "Springer",
year = 2006,
volume = 4245,
editor = "Attila Kuba and L{\'a}szl{\'o} G. Ny{\'u}l and
K{\'a}lm{\'a}n Pal{\'a}gyi",
ISBN = "3-540-47651-2",
pages = "425--436",
series = "Lecture Notes in Computer Science",
URL = "http://dx.doi.org/10.1007/11907350_36",
}
@article{jamet_functionality,
abstract = {Naive discrete planes are well known to be functional on a coordinate plane. The aim of our paper is to extend the functionality concept to a larger family of arithmetic discrete planes, by introducing suitable projection directions ([alpha]1, [alpha]2, [alpha]3) satisfying [alpha]1v1 + [alpha]2v2 + [alpha]3v3 = w. Several applications are considered. We first study certain local configurations, that is, the (m, n)-cubes introduced in Ref. [J. Vittone, J.-M. Chassery, (n,m)-cubes and Farey Nets for Naive Planes Understanding, in: DGCI, 8th International Conference, Lecture Notes in Computer Science, vol. 1568, Springer-Verlag, 1999, pp. 76-87.]. We compute their number for a given (m, n) and study their statistical behaviour. We then apply functionality to formulate an algorithm for generating arithmetic discrete planes, inspired by Debled-Renesson [I. Debled-Renesson, Reconnaissance des Droites et Plans Discrets, These de doctorat, Universite Louis Pasteur, Strasbourg, France, 1995.]. We also prove that an arithmetic discrete plane may be endowed with a combinatorial surface structure, in the spirit of Ref. [Y. Kenmochi, A. Imiyam Combinatorial topologies for discrete planes, in: DGCI, 11th International Conference, DGCI 2003, Lecture Notes in Computer Science, vol. 2886, Springer-Verlag, 2003, pp. 144-153.].},
author = {Berthé, V. and Fiorio, C. and Jamet, D. and Philippe, F. },
booktitle = {Discrete Geometry for Computer Imagery 2005},
citeulike-article-id = 1583039,
doi = {10.1016/j.imavis.2006.06.023},
journal = {Image and Vision Computing},
keywords = {digital hyperplane},
month = {October},
number = 10,
pages = {1671--1684},
priority = 2,
title = {On some applications of generalized functionality for arithmetic discrete planes},
url = {http://www.sciencedirect.com/science/article/B6V09-4M7VB14-4/2/e10d6699aa9e6a87d3ff71cb96a32793},
volume = 25,
year = 2007
}
@article{ goldwasser95survey,
author = "M. Goldwasser",
title = "A Survey of Linear Programming in Randomized Subexponential Time",
journal = "SIGACTN: SIGACT News (ACM Special Interest Group on Automata and Computability Theory)",
volume = 26,
year = 1995,
url = "citeseer.ist.psu.edu/goldwasser95survey.html" }
@Article{ORourke:1986a,
author = "J. O'Rourke and S.~R. Kosaraju and N. Megiddo",
title = "Computing Circular Separability",
journal = "Discrete and Computational Geometry",
volume = 1,
number = 1,
pages = "105--113",
year = 1986,
ISSN = "0179-5376",
}
@InProceedings{buzer_cvxhull,
author = {L. Buzer},
title = {Computing multiple convex hulls of a simple polygonal chain in linear time},
booktitle = {23rd European Workshop on Computational Geometry},
OPTcrossref = {},
OPTkey = {},
OPTpages = {},
year = {2007},
url = {\url{http://ewcg07.tugraz.at/}},
OPTeditor = {},
OPTvolume = {},
OPTnumber = {},
OPTseries = {},
OPTaddress = {},
OPTmonth = {},
OPTorganization = {},
OPTpublisher = {},
OPTnote = {},
OPTannote = {}
}
@Article{IPL::Melkman1987,
title = "On-line construction of the convex hull of a simple
polyline",
author = "A.~A. Melkman",
pages = "11--12",
journal = "Information Processing Letters",
year = 1987,
month = apr,
volume = 25,
number = 1,
}
@Article{har-peled98,
title = "An output sensitive algorithm for discrete convex
hulls",
language = "en",
month = may,
number = 2,
pages = "125--138",
year = 1998,
URL = "http://visinfo.zib.de/EVlib/Show?EVL-1998-188",
author = "S. {Har-Peled}",
abstract = "Given a convex body C in the plane, its discrete hull
is $C^0 = ConvexHull( C {\ca}p L)$ , where $L = Z
\times Z$ is the integer lattice. We present an $O(
|C0| \log \delta(C))$-time algorithm for calculating
the discrete hull of C , where $|C^0|$ denotes the
number of vertices of $C^0$ , and $\delta(C)$ is the
diameter of $C$ . Actually, using known combinatorial
bounds, the running time of the algorithm is $O(\delta
(C)^{2/3} log \delta (C))i$ . In particular, this bound
applies when C is a disk.",
volume = 10,
copyright = "Copyright 1998, Elsevier Science, All rights
reserved.",
journal = "Computational Geometry. Theory and Applications",
}
@Article{Graham:72,
author = "R. Graham",
title = "An efficient algorithm for determining the convex hull
of a finite planar set",
journal = "Information Processing Letters",
volume = "1",
pages = "132--133",
year = "1972",
}
@Article{jarvis73,
author = "R. Jarvis",
title = "On the identification of the convex hull of a finite
set of points in the plane",
journal = "Information Processing Letters",
year = "1973",
volume = "2",
pages = "18--21",
}
@Article{journals/dcg/Chazelle93,
title = "An Optimal Convex Hull Algorithm in Any Fixed
Dimension",
author = "B. Chazelle",
journal = "Discrete \& Computational Geometry",
year = "1993",
volume = "10",
bibdate = "2002-12-09",
bibsource = "DBLP,
http://dblp.uni-trier.de/db/journals/dcg/dcg10.html#Chazelle93",
pages = "377--409",
}
@inproceedings{sphere-tree,
author = {G. Bradshaw and C. O'Sullivan},
title = {Sphere-tree construction using dynamic medial axis approximation},
booktitle = {SCA '02: Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation},
year = 2002,
isbn = {1-58113-573-4},
pages = {33--40},
location = {San Antonio, Texas},
doi = {http://doi.acm.org/10.1145/545261.545267},
publisher = {ACM Press},
address = {New York, NY, USA},
}
@MastersThesis{jospin_transmission,
author = {L. Jospin},
title = {Transmission progressive d'images 3D à partir du calcul de l'axe médian},
school = {Ecole Normale Supérieure de Lyon},
year = 2006,
type = {Rapport Master Recherche},
address = {Laboratoire LIRIS},
note = {\url{http://liris.cnrs.fr/publis?id=2983}},
url= {http://liris.cnrs.fr/publis?id=2983}
}
@inproceedings{lossless,
author = "F. Dupont and B. Gilles and A. Baskurt",
booktitle = "PCS'O3 (Picture Coding Symposium)",
title = "Lossless and Scalable 3D obbject coding method based on medial axis transformation",
year = 2003
}
@article{minset_log,
author = {U. Feige},
title = {A threshold of ln n for approximating set cover},
journal = {J. ACM},
volume = 45,
number = 4,
year = 1998,
issn = {0004-5411},
pages = {634--652},
doi = {http://doi.acm.org/10.1145/285055.285059},
publisher = {ACM Press},
address = {New York, NY, USA},
}
@article{lieutier_MA,
abstract = {Medial axis Transform is sometimes used as an intermediate representation in algorithms for meshing or recognition of shapes from digitized data. This raises the question whether the Medial Axis captures fundamental topological invariants of the object. The (positive) answer has been known already in the case of smooth objects. The main result presented here is the homotopy equivalence of any bounded open subset of with its medial axis.},
author = {Lieutier, A. },
booktitle = {Solid Modeling Theory and Applications},
citeulike-article-id = {1460869},
journal = {Computer-Aided Design},
keywords = {axis medial},
month = {September},
number = {11},
pages = {1029--1046},
priority = {2},
title = {Any open bounded subset of has the same homotopy type as its medial axis},
url = {http://www.sciencedirect.com/science/article/B6TYR-4BMY0HG-1/2/de886b1f20753fc8c42e28c271fdcb56},
volume = {36},
year = {2004}
}
@Article{BarBen96,
author = "R. Bar-Yehuda and E. Ben-Hanoch",
title = "A linear time algorithm for covering simple polygons
with similar rectangles",
journal = "Intern. J. of Computational Geometry and
Applications",
year = "1996",
volume = "6",
number = "1",
pages = "79--102",
}
@Book{dcg-handbook,
title = "Handbook of Discrete and Computational Geometry",
booktitle = "Handbook of Discrete and Computational Geometry",
publisher = "CRC Press",
year = "1997",
editor = "J.~E. Goodman and J. O'Rourke",
}
@InCollection{m-etps-88,
author = "G. Matheron",
title = "Examples of topological properties of skeletons",
booktitle = "Image Analysis and Mathematical Morphology, Volume
2: Theoretical Advances",
publisher = "Academic Press",
year = 1988,
editor = "J. Serra",
pages = "217--238",
address = "Londres",
annote = "Theoritical results on skeletons"
}
@incollection{flux,
abstract = {Geometric shapes are identified with their features. For computational purposes a concrete mathematical definition of features is required. In this paper we use a topological approach, namely dynamical systems, to define features of shapes. To exploit this definition algorithmically we assume that a point sample of the shape is given as input from which features of the shape have to be approximated. We translate our definition of features to the discrete domain while mimicking the set-up developed for the continuous shapes. Experimental results show that our algorithms segment shapes in two and three dimensions into so-called features quite effectively. Further, we develop a shape matching algorithm that takes advantage of our robust feature segmentation step.},
author = {Dey, T. and Giesen, J. and Goswami, S. },
citeulike-article-id = {1454362},
journal = {Algorithms and Data Structures},
keywords = {no-tag},
pages = {25--36},
priority = {2},
title = {Shape Segmentation and Matching with Flow Discretization},
url = {http://www.springerlink.com/content/6qwfh2adqmm60n30
},
year = {2003}
}
@INPROCEEDINGS{laurefab,
author = {Feschet, F. and Tougne, L.},
title = {Optimal Time Computation of the Tangent of a Discrete Curve : Application to the Curvature},
booktitle = {8th International Workshop in Discrete Geometry for Computer Imagery},
year = {1999},
pages = {31--40},
publisher = {Springer-Verlag, LNCS, 1568}
}
@PhdThesis{deVieilleville_these,
author = {F. de Vieilleville},
title = {Analyse des parties linéaires des objets discrets pour l'extraction de caractéristiques géométriques},
school = {Université de Bordeaux 1},
year = 2007,
type = {Thèse de Doctorat}
}
@PHDTHESIS{Thiel_hdr,
AUTHOR = {E. Thiel},
TITLE = {G\'eom\'etrie des distances de chanfrein},
TYPE = {{H}abilitation \`a {D}iriger des {R}echerches},
SCHOOL = {universit\'e de la M\'editerran\'ee},
ADDRESS = {Aix-Marseille 2},
YEAR = {2001},
MONTH = dec,
NOTE = {{\tt http\string://www.\linebreak[0]lif-sud.univ-mrs.fr/\string~thiel/hdr}},
}
@Article{Lachaud00a,
author = {J.-O. Lachaud and A. Montanvert},
title = {{C}ontinuous analogs of digital boundaries: A topological
approach to iso-surfaces},
journal = "Graphical Models and Image Processing",
publisher = {Academic Press},
year = 2000,
volume = 62,
pages = {129--164}
}
@PhdThesis{havran,
author = {V. Havran},
title = {Heuristic Ray Shooting Algorithms},
school = {Czech Technical University, Faculty of Electrical Engineering, Department of Computer Science and Engineering},
year = 2001,
url = {http://www.cgg.cvut.cz/~havran/DISSVH/phdthesis.html}
}
@TechReport{antoine_RR,
title = {{A framework for dynamic implicit curve approximation by
an irregular discrete approach}},
author = {A. {Vacavant} and D. {Coeurjolly} and L.
{Tougne}},
year = {2007},
institution = {LIRIS UMR 5205 CNRS/INSA de Lyon/Université Claude Bernard
Lyon 1/Université Lumière Lyon 2/Ecole Centrale de Lyon},
number = {RR-LIRIS-2007-020},
language = {en},
url = {http://liris.cnrs.fr/publis/?id=2962}
}
@PhdThesis{dexet_these,
author = {M. Dexet},
title = {Architecture d'un modeleur géométrique à base topologique d'objets discrets et méthodes de reconstruction en dimensions 2 et 3},
school = {Université de Poitiers},
year = 2006,
type = {Thèse de Doctorat}
}
@Article{bb20013,
author = "L. J. Latecki and C. Conrad and A. Gross",
title = "Preserving Topology by a Digitization Process",
journal = "Journal of Mathematical Imaging and Vision",
volume = "8",
year = "1998",
number = "2",
month = mar,
pages = "131--159",
URL = "http://dx.doi.org/10.1023/A:1008273227913",
bibsource = "http://www.visionbib.com/bibliography/twod289.html#TT19121",
}
@InProceedings{Cook:1971,
author = "S.~A. Cook",
year = "1971",
title = "The complexity of theorem-proving procedures",
booktitle = "Proceedings of the 3rd Annual ACM Symposium on Theory
of Computing",
address = "New York",
pages = "151--158",
}
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author = "T. Cormen and C. Leiserson and R. Rivest",
title = "Introduction {\`a} l'algorithmique",
publisher = "Dunod",
ISBN= "2 10 003128 7",
year=1990
}
@Article{journals/rc/RueherS97,
title = "Concurrent Cooperating Solvers over Reals",
author = "M. Rueher and C. Solnon",
journal = "Reliable Computing",
year = "1997",
number = "3",
volume = "3",
bibdate = "2004-07-29",
bibsource = "DBLP,
http://dblp.uni-trier.de/db/journals/rc/rc3.html#RueherS97",
pages = "325--333",
URL = "http://dx.doi.org/10.1023/A:1009939327927",
}
@inproceedings{bruynooghe1994cir,
title={{CLP(intervals) Revisited}},
author={Benhamou, F. and Mc Allester, D. and Van Hentenryck, P.},
booktitle={Proceedings of the 1994 International Symposium on Logic Programming},
pages={124--138},
year=1994,
publisher={MIT Press}
}
@Article{snyder-92,
author = "J.~M. Snyder",
journal = "Computer Graphics",
month = jul,
note = "Proceedings SIGGRAPH'92.",
number = "2",
title = "Interval Analysis For Computer Graphics",
volume = "26",
year = "1992",
tag = "I74",
}
@Book{mo:RatschekRokne:84,
author = "H. Ratschek and J. Rokne",
title = "Computer Methods for the Range of Functions",
publisher = "Ellis Horwood Ltd.",
year = "1984",
address = "Chichester",
pages = "168",
}
@book{citeulike:748022,
abstract = {{This book treats an important set of techniques that provide a mathematically rigorous and complete error analysis for computational results. It shows that interval analysis provides a powerful set of tools with direct applicability to important problems in scientific computing. }},
author = {Moore, R.~E. and Bierbaum, F. },
citeulike-article-id = 748022,
howpublished = {Paperback},
isbn = 0898711614,
keywords = {arithmetic interval},
priority = 2,
year = 1979,
publisher = {{Soc for Industrial \& Applied Math}},
title = {Methods and Applications of Interval Analysis},
url = {http://www.amazon.ca/exec/obidos/redirect?tag=citeulike04-20{\&}path=ASIN/0898711614}
}
@Book{Moor66a,
author = "R.~E. Moore",
title = "Interval Analysis",
publisher = "Prentice-Hall",
year = "1966",
address = "Englewood Cliffs, N.J.",
referred = "[Garl85a] \# 967, 969; [Bart70a]; [Chan74a];
[Corl82a]; [Corl87a]; [Corl88a]; [Corl91a]; [Gray67a];
[Gray74a]; [Hali83a]; [Iri84a]; [Kuba72a]; [Moor79a];
[Rall80a]; [Rall81a]; [Yohe79a].",
comment = "German translation: {\sl Intervallanalyse,\/}
translated by D. Pfaffenzeller, R. Oldenburg,
M{\"u}nchen, 1968.",
keywords = "boundary value problems; wrapping effect; coordinate
transformation; Taylor coefficients.",
abstract = "Chapter ten of this book discusses the machine
generation of Taylor coefficients. Basic recursion
relations are presented.",
}
@Book{Moore79a,
author = "R.~E. Moore",
year = "1979",
title = "Methods and Applications of Interval Arithmetic",
series = "Studies in Applied Mathematics",
publisher = "SIAM",
address = "Philadelphia",
}
@PhdThesis{pion,
author = {S. Pion},
title = {De la géométrie algorithmique au calcul géométrique},
school = {Université Nice Sophia-Antipolis},
year = {1999},
type = {Thése de doctorat},
OPTkey = {},
OPTtype = {},
OPTaddress = {},
OPTmonth = {},
OPTnote = {},
OPTannote = {}
}
@Article{bb33412,
author = "D. Cohen Or and A. Kaufman",
title = "Fundamentals of Surface Voxelization",
journal = "Graphical Models and Image Processing",
volume = "57",
year = "1995",
number = "6",
month = nov,
pages = "453--461",
bibsource = "http://www.visionbib.com/bibliography/describe478.html#TT31590",
}
@Article{journals/pami/HilaireT06,
title = "Robust and Accurate Vectorization of Line Drawings",
author = "X. Hilaire and K. Tombre",
journal = "IEEE Trans. Pattern Anal. Mach. Intell",
year = "2006",
number = "6",
volume = "28",
bibdate = "2006-08-23",
bibsource = "DBLP,
http://dblp.uni-trier.de/db/journals/pami/pami28.html#HilaireT06",
pages = "890--904",
URL = "http://doi.ieeecomputersociety.org/10.1109/TPAMI.2006.127",
}
@InProceedings{Vee02,
author = {Veelaert, P.},
title = {Concurrency of Line Segments in Uncertain Geometry},
booktitle = DGCI,
pages = {289--300},
year = {2002},
editor = {Braquelaire, A. and Lachaud, J.-O. and Vialard, A.},
volume = {2301},
address = {Bordeaux, France},
series = LNCS,
publisher = {Springer-Verlag}
}
@Article{Vee99,
author = {Veelaert, P.},
title = {Geometric Constructions in the Digital Plane},
journal = {Journal of Mathematical Imaging and Vision},
year = {1999},
volume = {11},
pages = {99--118}
}
@Book{Herman98b,
author = {Herman, G. T.},
title = {Geometry of digital spaces},
publisher = {Birkh\"{a}user, Boston},
year = {1998}
}
@Book{samet90,
author = {H. Samet},
title = {The Design and Analysis of Spatial Data Structures},
publisher = {Addison-Wesley Reading MA},
year = 1990
}
@Article{citeulike_1259280,
abstract = "A variation of the Hough Transform that is aimed at
detecting digital lines has been recently suggested.
Other Hough algorithms are intended to detect straight
lines in the analog pre-image. These approaches are
analyzed and compared in terms of the relation between
the achievable resolution and the required number of
accumulators, using a definition of resolution that is
based on the Geometric Probability measure of straight
lines. It is shown that the `analog' approach is
greatly superior in high resolution applications, where
a `digital' Hough Transform would generally require an
infeasibly large number of accumulators.",
author = "N. Kiryati and M. Lindenbaum and A. M. Bruckstein",
citeulike-article-id = "1259280",
journal = "Pattern Recognition Letters",
keywords = "aht",
month = may,
number = "5",
pages = "291--297",
priority = "0",
title = "Digital or analog Hough transform?",
URL = "http://www.sciencedirect.com/science/article/B6V15-4F5V7W4-5/2/0865c5a772b30bc3ebd5bd0759b57ab5",
volume = "12",
year = "1991",
}
@InProceedings{citeulike_1259277,
abstract = "Not Available",
author = "D. Cyganski and W. F. Noel and J. A. Orr",
booktitle = "Proc. SPIE Vol. 1260, p. 148-159, Sensing and
Reconstruction of Three-Dimensional Objects and Scenes,
Bernd Girod; Ed.",
citeulike-article-id = "1259277",
editor = "B. Girod",
keywords = "aht",
month = jan,
pages = "148--159",
priority = "2",
series = "Presented at the Society of Photo-Optical
Instrumentation Engineers (SPIE) Conference",
title = "Analytic Hough transform",
URL = "http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1990SPIE.1260..148C",
volume = "1260",
year = "1990",
}
@InProceedings{citeulike_1259274,
abstract = "In this paper an implementation of the analytic Hough
transform (AHT) for exact digital line detection is
developed that employs a new, efficient data structure.
This new structure eliminates the need to represent
each digital line parameter region that is developed
during the analysis of the image by empolying a region
divider representation. A relative storage scheme is
employed thast permits reconstruction of region
occupancy information during the search for digital
line support. Furthermore, it is shown that all values
in the AHT data structure may be stored as rational
numbers with fixed and finite numerator and denominator
ranges defined by the image resolution. As a result,
all floating point computations are replaced by faster,
fixed word-size, integer operations.",
author = "Y. Liu and D. Cyganski and R. F. Vaz",
booktitle = "Proc. SPIE Vol. 1607, p. 298-309, Intelligent Robots
and Computer Vision X: Algorithms and Techniques, David
P. Casasent; Ed.",
citeulike-article-id = "1259274",
editor = "D. P. Casasent",
keywords = "aht",
month = feb,
pages = "298--309",
priority = "0",
series = "Presented at the Society of Photo-Optical
Instrumentation Engineers (SPIE) Conference",
title = "Efficient implementation of the analytic Hough
transform for exact linear feature extraction",
URL = "http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1992SPIE.1607..298L",
volume = "1607",
year = "1992",
}
@Book{citeulike_1210872,
author = "J.-M. Chassery and D. Coeurjolly and I.
Sivignon",
citeulike-article-id = "1210872",
doi = "10.1007/11907350_1",
journal = ": Discrete Geometry for Computer Imagery",
keywords = "perso preimage",
pages = "1--16",
priority = "2",
title = "Duality and Geometry Straightness, Characterization
and Envelope",
URL = "http://dx.doi.org/10.1007/11907350_1",
year = "2006",
}
@InProceedings{citeulike_1210870,
author = "D. Coeurjolly and F. Dupont and L. Jospin
and Isabelle Sivignon",
citeulike-article-id = "1210870",
doi = "10.1007/11907350_35",
journal = ": Discrete Geometry for Computer Imagery",
keywords = "perso reversible",
pages = "413--424",
priority = "0",
title = "Optimization Schemes for the Reversible Discrete
Volume Polyhedrization Using Marching Cubes
Simplification",
URL = "http://dx.doi.org/10.1007/11907350_35",
year = "2006",
}
@Book{citeulike_1210869,
author = "Isabelle Sivignon and David Coeurjolly",
citeulike-article-id = "1210869",
doi = "10.1007/11907350_57",
journal = ": Discrete Geometry for Computer Imagery",
keywords = "digital np perso plane",
pages = "674--685",
priority = "0",
title = "Minimal Decomposition of a Digital Surface into
Digital Plane Segments Is {NP}-Hard",
URL = "http://dx.doi.org/10.1007/11907350_57",
year = "2006",
}
@Book{bernoulli,
author = "J. Bernoulli",
chapter = "Sur une nouvelle espece de calcul",
citeulike-article-id = "1203808",
keywords = "digital line",
pages = "255--284",
priority = "0",
title = "Recueil pour les astronomes",
year = "1771",
}
@Article{citeulike_1191383,
address = "Piscataway, NJ, USA",
author = "E. Andres and M.-A Jacob",
citeulike-article-id = "1191383",
doi = "10.1109/2945.582354",
ISSN = "1077-2626",
journal = "IEEE Transactions on Visualization and Computer
Graphics",
keywords = "circle sphere",
month = jan,
number = "1",
pages = "75--86",
priority = "2",
publisher = "IEEE Educational Activities Department",
title = "The Discrete Analytical Hyperspheres",
URL = "http://dx.doi.org/10.1109/2945.582354",
volume = "3",
year = "1997",
}
@Article{citeulike_1191382,
abstract = "This paper presents a new approach to discrete
circles, rings, and an immediate extension to spheres.
The circle, called arithmetical circle is defined by
diophantine equations. The integer radius circles with
the same centre pave the plane. It is easy to determine
if a point is on, inside, or outside a circle. This was
not easy to do with previous definitions of circles,
like Bresenham's. We show that the arithmetical circle
extends Bresenham's circle. We give an efficient
incremental generation algorithm. The arithmetical
circle has many extensions. We present briefly
half-integer centered circles with a generation
algorithm, 4-connected circles, and a general ring
definition. We finish with the arithmetical sphere, an
immediate 3D extension of arithmetical circle. We give
elements to build a algorithm for generating the
sphere.",
author = "Eric Andres",
citeulike-article-id = "1191382",
doi = "10.1016/0097-8493(94)90164-3",
journal = "Computers \& Graphics",
keywords = "circle",
month = "",
number = "5",
pages = "695--706",
priority = "0",
title = "Discrete circles, rings and spheres",
URL = "http://www.sciencedirect.com/science/article/B6TYG-48TKKK6-B/2/aeeefd3348fdac950085ea0ddf8c57a6",
volume = "18",
year = "1994",
}
@Book{citeulike_1191380,
abstract = "{Digital geometry is about deriving geometric
information from digital pictures. The field emerged
from its mathematical roots some forty-years ago
through work in computer-based imaging, and it is used
today in many fields, such as digital image processing
and analysis (with applications in medical imaging,
pattern recognition, and robotics) and of course
computer graphics. <B>Digital Geometry</B> is the first
book to detail the concepts, algorithms, and practices
of the discipline. This comphrehensive text and
reference provides an introduction to the mathematical
foundations of digital geometry, some of which date
back to ancient times, and also discusses the key
processes involved, such as geometric algorithms as
well as operations on pictures.<br><br>*A comprehensive
text and reference written by pioneers in digital
geometry, image processing and analysis, and computer
vision<BR>*Provides a collection of state-of-the-art
algorithms for a wide variety of geometrical picture
analysis tasks, including extracting data from digital
images and making geometric measurements on the
data<BR>*Includes exercises, examples, and references
to related or more advanced work} {Computer graphics is
about taking mathematical representations of objects
and transforming them into visual displays. Digital
geometry concerns the reverse process; it is about
deriving geometric information from digital pictures.
There have been over one thousand papers published in
the forty-year history of digital geometry, but until
now, never a book that defines and covers the field.
Digital Geometry: Geometric Methods for Digital Picture
Analysis details the concepts, algorithms, and
practices of the field. It is a discipline studied by a
huge number of researchers in fields such as digital
image processing, medical imaging, robotics, and of
course computer graphics. However, digital geometry is
relatively new and still emerging as a unique field and
the lack of books has made it difficult for researchers
in many areas (including applied mathematics) to
benefit from this work.}",
author = "R. Klette and A. Rosenfeld",
citeulike-article-id = "1191380",
howpublished = "Hardcover",
ISBN = "1-55860-861-3",
keywords = "no-tag",
month = aug,
priority = "0",
publisher = "{Morgan Kaufmann}",
title = "Digital Geometry: Geometric Methods for Digital Image
Analysis (The Morgan Kaufmann Series in Computer
Graphics)",
URL = "http://www.amazon.fr/exec/obidos/ASIN/1558608613/citeulike04-21",