Image Processing Reference
In-Depth Information
inside the figure and nearest to the contour of the figure form the OBQ
image. Since a CSLS is not a closed figure, its OBQ is obtained after
closing it by drawing a vertical or horizontal line from the DSLS to either
the X or Y axis. It can be immediately understood that there is a main
grid direction such that there exists only one digitization point in every
column in the direction, if the equation of the line is y = mx + c where
0 ≤ m ≤ 1 and 0 ≤ c < 1. That direction turns out to be the direction
of the X - axis. In this case, the OBQ image of the CSLS may be given
by (i,⌊mi + c⌋), where i is an integer that ranges from x
1
to x
2
. For an
illustration, consider the CSLS in Fig. 3.1. The CSLS is AB and the
shaded part is considered to be its interior.
We may note that the inner digitization is the same as the Object Bound-
ary Quantization (OBQ) in one direction of traversal of the straight line
l.
A DSLS is represented by a chain code (refer to Section 1.3.3.2), which is
denoted by the arrowhead line in Fig. 3.1. It is always assumed that the DSLS
starts at the point (0,⌊c⌋) when the equation of the straight line is y = mx+c.
The chain code in this case is 1011101110. A block of continuous 0s or 1s in
chain code is called its run and the number of symbols in a run is called its
run length.
FIGURE 3.1: The OBQ of a continuous straight line and its digitization.
A set of digital points D is called straight if it is the digitization of a
CSLS. Since the concept of digital straightness was introduced in the mid-
1970s, many characterizations of digital straight lines have been formulated,
and many algorithms for determining whether a digital arc is straight have
