Abstract
In order to guarantee consistent descriptions of image structure, it is desirable to base such descriptions on topological principles. Thus, we want to be able to derive topological representations from segmented images. This paper discusses two methods to achieve this goal by means of the recently introduced XPMaps. First, it improves an existing algorithm that derives topological representations from region images and crack edges, and second, it presents a new algorithm that can be applied to standard 8-connected edge images.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R. Adams, L. Bischof: “Seeded Region Growing”, IEEE Trans. Pattern Analysis and Machine Intelligence, 16(6), pp. 641–647, 1994
J.-P. Braquelaire, J.-P. Domenger: “Representation of Segmented Images with Discrete Geometric Maps”, Image and Vision Computing, 17(10),715–735, 1999
C. Brice, C. Fennema: “Scene Analysis Using Regions”, Artificial Intelligence, 1(3), pp. 205–226, 1970
J. Canny: “A Computational Approach to Edge Detection”, IEEE Trans. Pattern Analysis and Machine Intelligence, 8(6), pp. 679–698, 1986
M. Couprie, G. Bertrand: “Topological Grayscale Watershed Transformation”, in: Proc. of SPIE Vision Geometry V, SPIE vol. 3168, pp. 136–146, 1997
J.-F. Dufourd, F. Puitg: “Functional specification and prototyping with oriented combinatorial maps”, Computational Geometry 16 (2000) 129–156
E. Khalimsky, R. Kopperman, P. Meyer: “Computer Graphics and Connected Topologies on Finite Ordered Sets”, J. Topology and its Applications, vol. 36, pp. 1–27, 1990
U. Köthe: “Generische Programmierung für die Bildverarbeitung”, PhD thesis, Computer Science Department, University of Hamburg, 2000
U. Köthe: “XPMaps and Topological Segmentation-a Unified Approach to Finite Topologies in the Plane”, in: A. Braquelaire, J.-O. Lachaud, A. Vialard (eds.): Proc. of 10th Intl. Conf. Discrete Geometry for Computer Imagery (DGCI 2002), Lecture Notes in Computer Science 2310, pp. 22–33, Berlin: Springer, 2002; longer version appeared as: Univ. Hamburg, Dept. of Informatics Technical Report FBI-HH-M-308/0, 2001
V. Kovalevsky: “Finite Topology as Applied to Image Analysis”, Computer Vision, Graphics, and Image Processing, 46(2), pp. 141–161, 1989
T. Pavlidis: “Structural Pattern Recognition”, New York: Springer, 1977
Rosenfeld: “Adjacency in Digital Pictures”, Information and Control vol. 26, pp. 24–33, 1974
Rothwell, J. Mundy, W. Hoffman, V.-D. Nguyen: “Driving Vision By Topology”, in: IEEE Intl. Symposium on Computer Vision, pp. 395–400, 1995
M. Sonka, V. Hlavac, R. Boyle: “Image processing, Analysis, and Machine Vision”, Brooks/Cole Publishing Comp., 1998
L. Vincent, P. Soille: “Watersheds in digital spaces: an efficient algorithm based on immersion simulations”, IEEE Trans. Pattern Analysis and Machine Intelligence, 13(6), pp. 583–598, 1991
S. Winter: “Topological Relations between Discrete Regions”, in: M. Egenhofer, J. Herring (eds.): Advances in Spatial Databases, pp. 310–327, Lecture Notes in Computer Science vol. 951, Berlin: Springer, 1995
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Köthe, U. (2003). Deriving Topological Representations from Edge Images. In: Asano, T., Klette, R., Ronse, C. (eds) Geometry, Morphology, and Computational Imaging. Lecture Notes in Computer Science, vol 2616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36586-9_20
Download citation
DOI: https://doi.org/10.1007/3-540-36586-9_20
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00916-0
Online ISBN: 978-3-540-36586-0
eBook Packages: Springer Book Archive