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Educational

Educational

The following lists are not complete. Please contact us if you have any suggestion on modifications.

Getting started

• A. Rosenfeld and A.C. Kak, Digital Image Processing, Academic Press, 1982.
• K.Voss, Discrete Images, Objects, and Functions in Zⁿ, Springer 1993.
• T.Y. Kong and A. Rosenfeld, Topological Algorithms for Digital Image Processing, North Holland, 1996.
• L. S. Davis (ed.), Foundations of Image Understanding; Kluwer, Amsterdam (2001).
• Jean-Marc Chassery and Annick Montanvert, Géométrie Discrète en analyse d'images, Hermès, 1991 (in French)

• I. Bloch, Digital Representations (in the "Grids, cells, structure and topology" subfield):
  Tessellation and grids, Digital topology, Representations of some geometrical entities and Distance Transform.

Subfields and related lectures

• Grids, cells, structures and topology
digital topology, border/frontier tracking, graph theory and combinatorics

• nD objects and recognition
digitization frameworks and models, discrete analytical objects (lines, planes, circles, ...), recognition algorithms

• Discrete distances and skeletons
square and diamond distances, chamfer distances, euclidean distance, skeletons, medial axis and medial lines/surfaces

• Discrete geometrical transforms
rotations, magnification

• Various shape representation
hulls, multiscale shapes, Fourier moments, fractals, ...

• Features extraction and similarity measures
convexity, lengths and areas, curvature, normals, ...

• Examples of applications
image rendering, compression, ...

Materials

Books

• L. Chen Discrete Surfaces and Manifolds: A Theory of Digital-Discrete Geometry and Topology, Scientific & Practical Computing,2004.
• R. Klette, A. Rosenfeld Digital Geometry, geometric methods for digital picture analysis, Morgan Kaufman, 2004.
• R. Klette, A. Rosenfeld, F. Slodoba, Advances in Digital and Computational Geometry, Springer Verlag, 1998.
• G. T. Herman, Geometry of Digital Spaces, Birkhauser 1998.
• L. J. Latecki, Discrete Representation of Spatial Objects in Computer Vision, Series on Computational Imaging and Vision, ed. M. Viergever, Kluwer Academic Publishers, Dordrecht, 1998.
• S. Marchand-Maillet and Y.M. Sharaiha, Binary Digital Image Processing, Academic Press, 2000.
• G. Bertrand, A. Imiya, R. Klette (eds.), Digital and Image Geometry, Lecture Notes in Computer Science, LNCS 2243, Springer, 2001.

Journals

Works and results related to discrete geometry are usually published in the following journals:

Computational Geometry

Computer Vision, and Image Understanding

Discrete and Computational Geometry

Discrete Applied Mathematics (a special issue of the 10th IWCIA, 2001, is avaliable Volume 139, Issues 1-3, April 2004)

Graphical Models (previously Graphical Models and Image Processing)

IEEE Computer Graphics and Applications

IEEE Transactions on Image Processing

IEEE Transactions on Pattern Analysis and Machine Intelligence

IEEE Transactions on Visualization and Computer Graphics

Image and Vision Computing

International Journal on Pattern Recognition and Artificial Intelligence

Journal of Mathematical Imaging and Vision

Journal of Topology and its Applications

Journal of Visual Communication and Image Representation

Pattern Recognition

Pattern Recognition Letters

Theoretical Computer Science

Conferences

• Discrete Geometry for Computer Imagery (DGCI)
  Main conference for TC18, held every 18 months.
Next edition in Montréal (QC) Canada, September 30 - October 2, 2009.
For more information, see next Events on discrete geometry.


• International Conference on Pattern Recognition (ICPR)
  Main IAPR conference, held every 2nd year.
• Vision Geomtery
  as part of the IS&T/SPIE Annual Symposium on Electronic Imaging.
• Dagstuhl Seminars
  Seminars on various topic organized at Schloss Dagstuhl international conference and research center for computer science.
• Workshop on Discrete Tomography and its Applications
  
• International Workshop on Combinatorial Image Analysis (IWCIA)
  Workshop on parallel and combinatorial image analysis.
• International Conference on Computer Analysis of Images and Patterns (CAIP)
  Conference held every 2nd year.
• International Symposium on Mathematical Morphology (ISMM)
  
• Scandinavian Conference on Image Analysis (SCIA)
  Conference held every 2nd year in one of the Scandinavian countries.
• International Conference on Image Analysis and Processing (ICIAP)
  Conference held every 2nd year in Italy.
• Reconnaissance des Formes et Intelligence Artificielle (RFIA)
  Conference held in France.
• Workshop on Digital Topology
  
• International Workshop on Visual Form (IWVF)
  Workshop held approximately every 3rd year.

Open problems

During the winterschool "Digital and Image Geometry" held in Dagstuhl, Germany, December 2000, it was suggested to create a web site on open problems in digital and image geometry. Following that suggestion, Prof. Reinhard Klette, Auckland, New Zeeland keeps updated:

IAPR-TC18 webpage