Abstract
In this approach, it is possible to show that some particular properties of a digital concept are the same as the corresponding properties of its continuous original. The considerations in Chapter 1 demonstrate that it is necessary to introduce a special graph structure into a discrete representation in order to ensure the required properties of a digital analog of a continuous concept. Thus, while defining a digital analog, one must specify at the same time in whichgraph structure this analog is defined. For example, if one defines a digital analog of a simple closed curve as a subgraph of the digital plane Z 2 in which each point is 4-adacent to exactly two other points, then the Jordan curve theorem holds for this curve in a graph with changeable 4/8-adjacency or in a well-composed graph. However, as demonstrated in Chapter 1, the Jordan curve theorem does not hold for the simple closed 4-curve in a graph with only one 4-adjacency relation. If we use the changeable ad- acenc 4/ 8 , we have 4-connectedness for the foreground and 8-connectedness for the j Y background. Consequently, connected components are not intrinsic features of the digital representation and the neighborhoods of points are not homogeneous as it is the case for ℝ2 with the usual topology.
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© 1998 Springer Science+Business Media Dordrecht
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Latecki, L.J. (1998). Graph-based Approach. In: Discrete Representation of Spatial Objects in Computer Vision. Computational Imaging and Vision, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9002-0_3
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DOI: https://doi.org/10.1007/978-94-015-9002-0_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4982-7
Online ISBN: 978-94-015-9002-0
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