Educational

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

Getting started

We propose below a selection of books to start in discrete geometry and mathematical morphology.
More advanced books are listed in the Materials section.

  • 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 (eds.), Géométrie Discrète en analyse d'images, Hermès, 1991 (in French)
  • David Coeurjolly, Annick Montanvert and Jean-Marc Chassery (eds.), Géométrie Discrète et images numériques, Traité IC2, Hermès, 2007(in French)
  • Laurent Najman, Hugues Talbot Morphologie mathématique : Tome 1, Approches déterministes Hermes Science Publications (26 août 2008) (in French)
  • Laurent Najman, Hugues Talbot Mathematical Morphology: From Theory to Applications, Wil ey-ISTE; 1 edition (August 23, 2010)
  • Laurent Najman, Hugues Talbot Morphologie mathématique : Tome 2, Estimation, choix et mise en oeuvre Hermes Science Publications (3 septembre 2010) (in French)
  • Valentin E. Brimkov and Reneta P. Barneva,Digital Geometry Algorithms: Theoretical Foundations and Applications to Computational Imaging, Springer Lecture Notes in Computational Vision and Biomechanics, 2012
  • Ullrich Köthe, Annick Montanvert and Pierre Soille, Applications of Discrete Geometry and Mathematical Morphology, Springer LNCS 7346, 2012
  • Punam Saha, Gunilla Borgefors, Gabriella Sanniti di Baja, Skeletonization, Theory, Methods and Applications, Academic Press, June 2017
Web resources:

  • 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

Discrete geometry can be structured into several subfields. Of course this kind of classification is not unique... we proposed below a structure as logical as possible in the following. For each subfield, we expect to propose (as soon as possible...) some main references, lectures or slides provided by members and links to data sets and codes.

  • nD objects and recognition
    • digitization frameworks and models, discrete analytical objects (lines, planes, circles, ...), recognition algorithms
  • Discrete Tomography image reconstruction, and uniqueness from X-rays
Do not hesitate to help us to complete these subfields. Thanks in advance!

Tutorials on Discrete Geometry and Mathematical Morphology

Different tutorial were proposed in link to different majors events like ACCV and ICPR:
  • ACPR 2019 Tutorial on Digital Geometry in Pattern Recognition: The purpose of this tutorial presented by Jacques-Olivier Lachaud and Bertrand Kerautret was to present new efficient and easy to reproduce algorithms dedicated to the robust extraction of geometric features on digital objects.
  • ACCV 2016 Tutorial on Digital Geometry Processing: The aim of this tutorial proposed by Bertrand Kerautret was to present the new robust geometric estimators (like normals, tangents, curvature and local noise estimators). Starting from their theoretical description up to their concrete implementation in the emerging DGtal Library framework.
  • ACCV 2016 Tutorial Content-Adaptive Morphological Filters.
    • This tutorial presented byu Hugues Talbot1 and Michael H.F. Wilkinson was is intended for PhD students and other researchers who have limited or no familiarity with advanced morphological filters. (slide are avaible here).
  • ICPR 2016 Tutorial on Graph-based Mathematical Morphology
    • This tutorial was proposed by Laurent Najman and Hugues Talbot and it aims at disseminating graph-based ideas stemming from the mathematical morphology community to the interested public of ICPR attendees.

Materials

Books

  • V. Kovalevsky Geometry of Locally Finite Spaces. Publishing House Dr. Baerbel Kovalevski, Berlin. ISBN 978-3-9812252-0-4, 2008
  • 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.
  • G. Herman and A. Kuba, Discrete Tomography: Foundations, Algorithms, and Applications, Birkhauser, 1999
  • G. Herman and A. Kuba, Advances in Discrete Tomography and its Applications, Birkhauser, 2007.

Journals

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



Since 2013, we collect every year the references of DG papers published in these journals:

Conferences

  • Discrete Geometry and Mathematical Morphology (DGMM)
    Main TC18 conference, held every 18 months. For more information, see DGMM.
  • Discrete Geometry for Computer Imagery (DGCI)
    Previously held every 18 months, discontinued in favor of DGMM. For more information, see DGCI.
  • International Symposium on Mathematical Morphology (ISMM)
    Previously held every 2 years, discontinued in favor of DGMM. For more information, see ISMM.
  • International Conference on Pattern Recognition (ICPR)
    Main IAPR conference, held every 2nd year.
  • Vision Geometry
    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)
    Conference held every 18 months.
  • International Conference on Computer Analysis of Images and Patterns (CAIP)
    Conference held every 2nd year.
  • 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.
  • International Workshop on Computational Topology in Image Context (CTIC)
    Workshop held every 18 months.
  • 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.