Image Processing Reference
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3. 010100010 is not a DSS, since F3 fails (singular element 1 is not uni-
formly spaced).
4. 010010010 is a DSS, since F1-F3 are true.
It may be noted that, for a chain code sequence 010100100, the question
of uniform spacing (as stated in F3) of the singular element 1 remains unan-
swered, because there is one 0 between the first two consecutive 1s, and there
are two 0s between the next two consecutive 1s. The first formal characteri-
zation of DSS, which also brought in a further specification of Property F3,
was however provided a few years later in [176], as stated in the following
properties of DSS.
Theorem 4.3 (Rosenfeld [176]). Necessary conditions for a DSS (DSL) are
as follows.
The runs have at most two directions, differing by 45 0 , and for one of
these directions, the run length must be 1.
R1:
R2:
The runs can have only two lengths, which are consecutive integers.
R3:
One of the run lengths can occur only once at a time.
R4:
For the run length that occurs in runs, these runs can themselves have
only two lengths, which are consecutive integers; and so on.
It may be noted that the above four properties, R1-R4, still do not allow a
formulation of su cient conditions for the characterization of a DSS, but they
specify F3 by a recursive argument on run lengths. Thus, 010100100 qualifies
as a DSS by R1-R4, since the intermediate run-lengths (i.e., 1 and 2) of 0s
are consecutive.
4.2 Approximate Straightness
In a digital image containing one or more objects with fairly straight edges,
the set of (approximate) digital straight line segments carries strong geometric
information of the underlying objects. Hence, the concept of approximate
digital straight segments (ADSS) has been proposed in [13]. In the ADSS,
some of the most fundamental properties of DSS are preserved and some are
relaxed (see Fig. 4.4). The number of ADSS extracted from a set of digital
curve segments S in a real-world scenario is usually fewer than that of DSS
cover, since many visually straight segments may fail to satisfy all stringent
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