Image Thresholding using Generalized Rough Sets - Rough Fuzzy Image Analysis: Foundations and Methodologies - page 59

area in the result obtained using algorithm (vi) represents a region slightly smaller than the
core region. Figure 3.9 presents an image where the sand, sea and sky regions are to be
separated. The image has a multimodal histogram and it is evident from the image that
the average gray values of the three regions do not differ by much. As can be seen from the
figure, the proposed multilevel thresholding methodology (algorithm (i)) performs better
than some of the others and as good as algorithms (ii), (iv) and (vii).
The results in Figures 3.7(c) and (d), Figures 3.8(c) and (d) and Figures 3.9(c) and (d)
demonstrate the utility of the proposed logarithmic tolerance fuzzy rough-fuzzy entropy.
Note that, as described in Section 3.4, two values g d and g b are needed to be predefined in
order to use the proposed thresholding methodology. We have considered g d = g min + 20
and g b = g max −20.

Edge Extraction

Let us consider here qualitative assessment of edge extraction results in different images in
order to evaluate the performance of various techniques. We consider the gradient mag-
nitude at every pixel in an image and determine thresholds from the associated gradient
magnitude histogram in order to perform edge extraction in that image. Gradient mag-
nitude histograms are in general unimodal and positively (right) skewed in nature. In
literature, very few techniques have been proposed to carry out bilevel thresholding in such
histograms. Among these techniques, we consider the following for comparison: (viii) uni-
modal histogram thresholding technique by Rosin (Rosin, 2001) and (ix) the thresholding
technique by Henstock et al. (Henstock and Chelberg, 1996). In addition to the aforesaid
techniques, we also consider here some of the existing thresholding techniques mentioned
previously in this section.

(a) The
Image

(b) The
Histogram

(c) Edges
by (i)

(d) Edges
by (ii)

(e) Edges
by (iii)

(f) Edges
by (v)

(g) Edges
by (viii)

(h) Edges
by (ix)

FIGURE 3.10: Performance of the various thresholding algorithms applied to mark the edges in
a gradient image

(a) The
Image

(b) The
Histogram

(c) Edges
by (i)

(d) Edges
by (ii)

(e) Edges
by (iii)

(f) Edges
by (iv)

(g) Edges
by (v)

(h) Edges
by (vi)

FIGURE 3.11: Qualitative performance of the various thresholding algorithms applied to obtain
the edge, non-edge and possible edge regions in a gradient image