Abstract
The goal of the following analysis is to estimate the computational complexity of the Voronoi tessellation of an image performed with an algorithm based on mathematical morphology. The morphological dilation operation is used to implement a set of distance functions (distance transformations) with a variety of structuring elements that approximate distance metrics, such as the Euclidean, city block and chessboard distances. The analysis has been performed for 2-D morphological Voronoi tessellation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
F.P. Preparata and M.I. Shamos, Computational Geometry, New York: Springer-Verlag, 1985.
N. Ahujia and B.J. Schachter, Pattern Models. New York: J. Wiley, 1983.
I. Pitas and A.N. Venetsanopoulos, Nonlinear Digital Filters: Principles and Applications. Boston: Kluwer Academic, 1990.
R.C. Gonzalez and R.E. Wintz, Digital Image Processing: An Introduction. Addison Wesley, 1992.
G. Borgefors, “Distance Transformations in Digital Images,” Comput. Vision, Graphics, Image Proc., vol. 34, pp. 344–371, 1986.
J.E. Mazille, “Mathematical Morphology and Convolutions,” Journal of Microscopy, vol. 156, pp. 3–13, 1989.
Q.Z. Ye, “The Signed Euclidean Distance Transform and Its Applications,” Proc. 9th Intern. Conf. on Pattern Recognition, pp. 495–499, Rome, Italy 1988.
C. Kotropoulos I. Pitas and A. Maglara, “Voronoi Tessellation and Delaunay Triangulation Using Euclidean Disk Growing in Ζ 2,” Int. Conf. on Acoust. Speech and Signal Processing, Mineapolis, 1993.
I. Pitas and C. Kotropoulos, “Texture Analysis and Segmentation of Seismic Images,” IEEE Proc. Int. Conf. on Acoust. Speech and Signal Processing, Glasgow, 1989.
F. Y. 0 Shin and O. R. Mitchell, “A Mathematical Morphology Approach to Euclidean Distance Transformation,” IEEE Trans. on Image Processing, vol. 1, no. 2, pp. 197–204, April 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Kalaitzis, E.G., Pitas, I. (1994). Performance Analysis of a Morphological Voronoi Tessellation Algorithm. In: Serra, J., Soille, P. (eds) Mathematical Morphology and Its Applications to Image Processing. Computational Imaging and Vision, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1040-2_26
Download citation
DOI: https://doi.org/10.1007/978-94-011-1040-2_26
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4453-0
Online ISBN: 978-94-011-1040-2
eBook Packages: Springer Book Archive