Abstract
This paper proposes 2D, 3D and 4D discrete sampling grids with optimal topological and spectral properties. It is shown here that those grids have advantages with respect to the classically used ℤn grid. The proposed 3D grids are used to achieve surface extraction from volume data. Results are shown for a medical imaging application.
Chapter PDF
Similar content being viewed by others
References
A. Rosenfeld, A. Kak Digital picture processing Academic Press Inc. 1982.
J.K. Udupa, G.T. Herman 3-D Imaging in Medicine CRC Press, 1989.
C. Kittel Introduction to solid-state physics John Wiley & Sons Inc. 1971.
D. Schwarzenbach Cristalographie Presses polytechniques et universitaires romandes, 1993.
J.H. Conway, N.J.A. Sloane Sphere packing lattice and groups Second edition, Springer-Verlag, A series of comprehensive studies in mathematics. 1993.
H.S.M. Coxeter Introduction to Geometry second edition John Wiley & Sons Inc. 1969.
K. Miyazaki An adventure in multidimensional space A Wile Inter-science publication, John Wiley & Sons Inc. 1983
E. Viterbo, E. Biglieri Computing the voronoi cell of a lattice: the diamond-cutting algorithm IEEE transactions on information theory; Vol 42, No. 1, January 1996.
L.C. Kinsey Topology of surfaces Undergraduate Texts in Mathematics, Spriger-Verlag, New York, 1993.
V. Kovalevsky Shape in picture, a mathematical desciption of shape in gray levels images. Springer-Verlag; NATO ASI series, Series F: Computer and systems science Vol 126. 1992.
D.E. Dudgeon, R.M. Mersereau Multidimensional digital signal processing Prentice-Hall, Englwood Cliffs; NJ; 1984.
D. Nogly, M. Schladt. Digital Topology on Graphs Computer Vision and Image Understanding, Vol. 63, No. 2; March; pp 394–396, 1996.
W.E. Lorensen, H.E. Cline. Marching Cubes: A high resolution 3D surface construction algorith Computer Graphics, Vol. 21, No. 4, Jul 1987. pp 163–169.
E.R. Dougherty Mathematical Morphology in image processing. Marcel Dekker, New York 1991.
J. Serra Image Analysis and Mathematical Morphology. Academic Press Inc. 1982
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ibáñez, L., Hamitouche, C., Roux, C. (1996). Determination of discrete sampling grids with optimal topological and spectral properties. In: Miguet, S., Montanvert, A., Ubéda, S. (eds) Discrete Geometry for Computer Imagery. DGCI 1996. Lecture Notes in Computer Science, vol 1176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62005-2_15
Download citation
DOI: https://doi.org/10.1007/3-540-62005-2_15
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62005-1
Online ISBN: 978-3-540-49595-6
eBook Packages: Springer Book Archive