Abstract
The goal of this paper is to construct an algebraic-topological representation of a 80–adjacent doxel-based 4–dimensional digital object. Such that representation consists on associating a cell complex homologically equivalent to the digital object. To determine the pieces of this cell complex, algorithms based on weighted complete graphs and integral operators are shown. We work with integer coefficients, in order to compute the integer homology of the digital object.
Chapter PDF
Similar content being viewed by others
References
Diestel, R.: Graph Theory. Springer, Heidelberg (2005)
Fristch, R., Piccinini, R.A.: Cellular structure in topology. Cambridge University Press, Cambridge (1990)
Gonzalez-Diaz, R., Jimenez, M.J., Medrano, B., Molina-Abril, H., Real, P.: Integral Operators for Computing Homology Generators at Any Dimension. In: Ruiz-Shulcloper, J., Kropatsch, W.G. (eds.) CIARP 2008. LNCS, vol. 5197, pp. 356–363. Springer, Heidelberg (2008)
Herman, G.T.: Discrete multidimensional Jordan surfaces. CVGIP: Graphical Models and Image Processing 54, 507–515 (1992)
Kenmochi, Y., Imiya, A., Ichikawa, A.: Boundary Extraction of Discrete Objects. Computer Vision and Image Understanding 71, 281–293 (1998)
Kalvin, A.D., Cutting, C.B., Haddad, B., Noz, M.E.: Constructing topologically connected surfaces for the comprehensive analysis of 3D medical structures. In: Proc. of SPIE, vol. 1445, pp. 247–258 (1991)
Lorensen, W.E., Cline, H.E.: Marching cubes: A high-resolution 3D surface construction algorithm. Computer Graphics 21, 163–169 (1988)
Pacheco, A., Real, P.: Getting topological information for a 80-adjacency doxel-based 4D volume through a polytopal cell complex. In: Bayro-Corrochano, E., Eklundh, J.-O. (eds.) CIARP 2009. LNCS, vol. 5856, pp. 279–286. Springer, Heidelberg (2009)
Pacheco, A., Real, P.: Polyhedrization, homology and orientation. Progress in Combinatorial Image Analysis, 151–164 (2009)
Udupa, J.K.: Multidimensional digital boundaries. CVGIP: Graphical Models and Image Processing 56, 311–323 (1994)
Voss, K.: Discrete Images, Objects, and Functions in Zn. Algorithms and Combinatorics (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pacheco, A., Real, P. (2011). Associating Cell Complexes to Four Dimensional Digital Objects. In: Debled-Rennesson, I., Domenjoud, E., Kerautret, B., Even, P. (eds) Discrete Geometry for Computer Imagery. DGCI 2011. Lecture Notes in Computer Science, vol 6607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19867-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-19867-0_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19866-3
Online ISBN: 978-3-642-19867-0
eBook Packages: Computer ScienceComputer Science (R0)