Abstract
In Chapter 1 we have provided a heuristic introduction to homology using graphs that are made up of vertices (zero-dimensional cubes) and edges (one-dimensional cubes). Before that we motivated the need for a computational theory of homology using examples from image processing where it was natural to think of the images as being presented in terms of pixels (two-dimensional cubes), voxels (three-dimensional cubes), and even tetrapus (four-dimensional cubes). In Section 2.1 we formalize and generalize these examples to cubical complexes.
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© 2004 Springer-Verlag New York, Inc.
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Kaczynski, T., Mischaikow, K., Mrozek, M. (2004). Cubical Homology. In: Computational Homology. Applied Mathematical Sciences, vol 157. Springer, New York, NY. https://doi.org/10.1007/0-387-21597-2_2
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DOI: https://doi.org/10.1007/0-387-21597-2_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2354-7
Online ISBN: 978-0-387-21597-6
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