Image Processing Reference
In-Depth Information
with τ. So, the isothetic error frequency (IEF) (or, simply error frequency),
given by
1
N
f(τ,d
⊥
) =
|{p∈I : dev
⊥
(p →
p) = d
⊥
}|,
(4.15)
versus τ and d
⊥
, acts as the second measure that provides the error distribu-
tion for the polygonal approximation of I.
4.4 Approximation on Gray-Scale Images
Edges carry meaningful gray-level discontinuities and hence define the
boundary of an object present in a real-world image. A geometric economy of
representation of these edges is furthered to a great extent if straight edges
can be derived directly from a gray-scale image. A sequence of straight edges
results in an e
cient polygonal representation of a digital object, which, in
turn, can be used for subsequent applications, such as volume rendering and
multi-resolution modeling [137, 194], image/video retrieval [144], shape coding
[159, 112, 191], etc.
Conventional polygonal (or poly-chain) approximation of a (thinned) dig-
ital curve [13, 183, 205, 225] of an object in a gray-scale image requires the
following steps:
1. Find the edge map (usually multi-pixel thick).
2. Thin the edge map by a suitable algorithm.
3. Find the polygonal form by edge tracking.
The entire procedure based on the above steps is, therefore, not only sus-
ceptible to pitfalls of the adopted edge extraction algorithm and subsequent
thinning, but also affected by inter-stage dependence and high runtime. In-
stead of this, we can extract the (apparently) straight edges present in a
gray-scale image without resorting to a conventional edge-detection algorithm
(which usually produces thick and rough edges) and without using any thin-
ning. The salient features of the algorithm, as explained in [168], are as follows:
i) Exponential averaging of Prewitt response [92]. An edge is always one-
pixel thick, after being detected.
ii) Checking the straightness. An edge is detected as a sequence of piecewise
linear components.
iii) Speedy execution. Simple integer operations are required while checking
the straightness of (a part of) an edge.
