Abstract
The shape-tree semilattice is a new framework for quasi-self-dual morphological processing, where eroded images have all shapes shrunk in a contrast-invariant way. This approach was recently introduced, and is further investigated here. Apart of reviewing their original definition, different algorithms for computing the shape-tree morphological operators are presented.
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. Keshet, “Shape-Tree Semilattice,” Journal of Mathematical Imaging and Vision, special issue of mathematical morphology after 40 years, scheduled to March 2005.
J. Serra, Image Analysis and Mathematical Morphology, Vol. 1, London: Academic Press, 1982.
H.J.A.M. Heijmans, “Connected Morphological Operators for Binary Images,” Computer Vision and Image Understanding, Vol. 73, No. 1, pp. 99–120, 1999.
P. Soille, Morphological Image Analysis: Principles and Applications, NY: Springer, 2nd edition, 2003.
R. Keshet (Kresch), “Mathematical Morphology on Complete Semilattices and its Applications to Image Processing,” Fundamenta Informaticae, Vol. 41, Nos. 1–2, pp. 33–56, January 2000.
H.J.A.M. Heijmans and R. Keshet, “Inf-semilattice approach to self-dual morphology,” Journal of Mathematical Imaging Vision, Vol. 17, No. 1, pp. 55–80, July 2002.
P. Monasse and F. Guichard, “Fast computation of a contrast-invariant image representation,” IEEE Trans. on Image Processing, No. 9, Vol. 5, pp. 860–872, May 2000.
P. Monasse and F. Guichard, “Scale-space from a level lines tree,” Journal of Visual Communication and Image Representation, Vol. 11, pp. 224–236, 2000.
V. Caselles and P. Monasse, “Grain filters,” Journal of Mathematical Imaging and Vision, Vol. 17, No. 3, pp. 249–270, November 2002.
C. Ballester, V. Caselles and P. Monasse, “The Tree of Shapes of an Image,” ESAIM: Control, Optimisation and Calculus of Variations, Vol. 9, pp. 1–18, 2003.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer
About this paper
Cite this paper
Keshet, R. (2005). Shape-Tree Semilattices. In: Ronse, C., Najman, L., Decencière, E. (eds) Mathematical Morphology: 40 Years On. Computational Imaging and Vision, vol 30. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3443-1_14
Download citation
DOI: https://doi.org/10.1007/1-4020-3443-1_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3442-8
Online ISBN: 978-1-4020-3443-5
eBook Packages: Computer ScienceComputer Science (R0)