Gradually Varied Extensions

  • Li M. Chen


In this chapter, we generalize the concept of gradually varied functions to gradually varied mappings. In  Chap. 3, we mainly discussed the function from a discrete space to {1, 2, ⋯ , n} or {A 1, A 2, ⋯ , A n }. This chapter focuses on gradually varied functions from a discrete space to another discrete space. For instance, a digital surface is defined as a mapping f from an n-dimensional digital manifold D to an m-dimensional grid space Σ m . A discrete surface is said to be gradually varied if two points in D, p and q, are adjacent, implying that f(p) and f(q) are adjacent in Σ m . In this Chapter, a basic extension theorem will be proven and some counter examples will be presented.


Varied Mapping Polynomial Time Algorithm Discrete Space Varied Surface Varied Extension 
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© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  • Li M. Chen
    • 1
  1. 1.University of the District of ColumbiaWashingtonUSA

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