Abstract
By viewing the grey scale values of 2-dimensional (2-D) images as elevation values above the image definition domain, geomorphological terms such as crest lines, watersheds, catchment basins, valleys, and plateaus have long been used in digital image processing for referring to image features useful for image analysis tasks. Because mathematical morphology relies on a topographic representation of 2-D images allowing for grey scale images to be viewed as 3-D sets, it naturally offers a wide variety of transformations for extracting topographic features. This paper presents some advances related to the imposition of minima, the lower complete transformation, the hit-or-miss transform, and the extraction of crest lines by a skeletonisation procedure.
This work was supported by the EC-JRC EuroLandscape Project.
Chapter PDF
Similar content being viewed by others
Keywords
References
G. Bertrand, J.-C. Everat, and M. Couprie. Image segmentation through operators based upon topology. Journal of Electronic Imaging, 6(4):395–405, 1997.
S. Beucher. Segmentation d’images et morphologie mathématique. PhD thesis, Ecole des Mines de Paris, June 1990.
S. Beucher and F. Meyer. The morphological approach to segmentation: The watershed transformation. In E. Dougherty, editor, Mathematical morphology in image processing, pages 433–481. Marcel Dekker, New York, 1993.
E. Breen and R. Jones. Attribute openings, thinnings, and granulometries. Computer Vision and Image Understanding, 64(3):377–389, 1996.
S. Collins. Terrain parameters directly from a digital elevation model. The Canadian Surveyor, 29(5):507–518, December 1975.
M. Couprie and G. Bertrand. Tesselations by connection in orders. In Proc. of Discrete Geometry for Computer Imagery’2000, Uppsala, volume 1953 of Lecture Notes in Computer Science, pages 15–26. Springer-Verlag, 2000.
M. Couprie, F. Nivando Bezerra, and G. Bertrand. Grayscale image processing using topological operators. In L. Latecki, R. Melter, D. Mount, and A. Wu, editors, Vision Geometry VIII, volume SPIE-3811, pages 261–272, 1999.
H. Digabel and C. Lantuéjoul. Iterative algorithms. In J.-L. Chermant, editor, Quantitative analysis of microstructures in materials sciences, biology and medicine, pages 85–99, Stuttgart, 1978. Dr. Riederer-Verlag GmbH.
J. Garbrecht and L. Martz. The assignment of drainage direction over flat surfaces in raster digital elevation models. Journal of Hydrology, 193:204–213, 1997.
V. Goetcherian. From binary to grey tone image processing using fuzzy logic concepts. Pattern Recognition, 12:7–15, 1980.
R. Haralick. Ridges and valleys on digital images. Computer Vision, Graphics, and Image Processing, 22:28–38, 1983.
D. Mark. Automated detection of drainage networks from digital elevation models. Cartographica, 21:168–178, 1984.
F. Meyer. Skeletons and perceptual graphs. Signal Processing, 16:335–363, 1989.
F. Meyer and S. Beucher. Morphological segmentation. Journal of Visual Communication and Image Representation, 1(1):21–46, September 1990.
C. Pudney. Distance-ordered homotopic thinning: A skeletonization algorithm for 3D digital images. Computer Vision and Image Understanding, 72(3):404–413, December 1998.
V. Ranwez and P. Soille. Order Independent Homotopic Thinning. In G. Bertrand, M. Couprie, and L. Perroton, editors, Proc. of Discrete Geometry for Computer Imagery’99, volume 1568 of Lecture Notes in Computer Science, pages 337–346. Springer-Verlag, 1999.
V. Ranwez and P. Soille. Order independent homotopic thinning for binary and grey tone anchored skeletons. Pattern Recognition Letters, 2002, Publication pending.
C. Ronse. A topological characterization of thinning. Theoretical Computer Science, 43:31–41, 1986.
P. Salembier and J. Serra. Flat zones filtering, connected operators, and filters by reconstruction. IEEE Transactions on Image Processing, 4(8):1153–1160, August 1995.
J. Serra. Image analysis and mathematical morphology. Academic Press, London, 1982.
J. Serra and P. Salembier, editors. Mathematical morphology and its applications to signal processing, 1993. Universitat Politècnica de Catalunya, Barcelona.
P. Soille. Spatial distributions from contour lines: An efficient methodology based on distance transformations. Journal of Visual Communication and Image Representation, 2(2):138–150, June 1991.
P. Soille. Morphologie mathématique: du relief à la dimensionalité —Algorithmes et méthodes-. PhD thesis, Université catholique de Louvain; en collaboration avec l’Ecole des Mines de Paris, February 1992.
P. Soille. Generalized geodesic distances applied to interpolation and shape description. In J. Serra and P. Soille, editors, Mathematical Morphology and its Applications to Image Processing, pages 193–200. Kluwer Academic Publishers, 1994
P. Soille. Generalized geodesy via geodesic time. Pattern Recognition Letters, 1235–1240, December 1994
P. Soille. Morphological image analysis: Principles and Applications. Springer-Verlag, Berlin, New York, 1999. Second extended edition to appear in 2002, see also http://ams.egeo.sai.jrc.it/soille
P. Soille. On morphological operators based on rank filters. Pattern Recognition, 2002.
P. Soille. Carving and adpative drainage enforcement of grid digital elevation models. Water Resources Research, Submitted.
P. Soille and M. Ansoult. Automated basin delineation from digital elevation models using mathematical morphology. Signal Processing, 20: 171–182, June 1990.
P. Soille and C. Gratin. An efficient algorithm for drainage networks extraction on DEMs. Journal of Visual Communication and Image Representation, 5(2): 181–189, June 1994.
S. Svensson, G. Borgefors, and I. Nyström. On reversible skeletonization using anchor-points from distance transforms. Journal of Visual Communication and Image Representation, 10:379–397, 1999.
H. Talbot and L. Vincent. Euclidean skeletons and conditional bisectors. In P. Maragos, editor, Visual Communications and Image Processing, volume SPIE-1818, pages 862–876, 1992.
B. Verwer, P. Verbeek, and S. Dekker. An efficient cost algorithm applied to distance transforms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(4):425–429, April 1989.
L. Vincent and P. Soille. Watersheds in digital spaces: An efficient algorithm based on immersion simulations. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(6):583–598, June 1991.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Soille, P. (2002). Advances in the Analysis of Topographic Features on Discrete Images. In: Braquelaire, A., Lachaud, JO., Vialard, A. (eds) Discrete Geometry for Computer Imagery. DGCI 2002. Lecture Notes in Computer Science, vol 2301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45986-3_16
Download citation
DOI: https://doi.org/10.1007/3-540-45986-3_16
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43380-4
Online ISBN: 978-3-540-45986-6
eBook Packages: Springer Book Archive