Image Processing Reference
In-Depth Information
(a)
(b)
(c)
(d)
(e )
(f)
FIGURE 1.22: Representative configuration of object points in each group.
The groups (a) to (c) have four members, each could be obtained by rotating
the configuration. The empty configuration is ignored here.
1.6 Summary
The digital topology is based on the notion of a finite neighborhood around
a point in that space. It has been found that graph theoretic modeling is con-
venient in defining different topological features in a rectangular lattice space.
They include the definition of adjacency, neighbors of a point, connected com-
ponents, connected paths, borders, interiors, skeletons, etc. This chapter sum-
marized all these important concepts and introduced some of the nontrivial
techniques of computing those features. However, in the neighborhood defini-
tion of a topological space, it is interesting to explore whether it is guided by
any algebraic form of distance function, and whether the function is a metric.
In the next chapter, we review several such metrics in the digital spaces, and
reveal their relationships with the digital topology considered in this chapter.
Exercises
1. Suppose you have a digital picture P = (G 3 ,6,26,S). What is the type
of connectivity among the foreground points? What is the type of con-
nectivity of background points? Discuss why a digital picture in the form
of (G 3 ,6,6,S) is not topologically well defined.
Search WWH ::




Custom Search