Image Processing Reference
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sidered for qualitative and quantitative performance comparison with that obtained using
the two aforementioned techniques.
Throughout this section, we consider the grayness ambiguity measure given in (3.30),
which signifies measuring the ambiguity using the proposed logarithmic class of entropy
functions. The quantities in (3.29) which are used in (3.30) are calculated considering that
the pairs of lower and upper approximations of the sets Υ T and Υ T represent a tolerance
fuzzy rough-fuzzy set. The aforesaid statement, according to the terminology given in
Section 3.2.3, signifies that logarithmic tolerance fuzzy rough-fuzzy entropy is used in this
section to get the grayness ambiguity measure. We consider the values of the parameters
∆ and ω respectively as 8 and 6 gray levels, and the base β as e, without loss of generality.
Note that, the logarithmic tolerance fuzzy rough-fuzzy entropy is a representative of the
proposed entropies which can be used to capture grayness ambiguity due to both fuzzy
boundaries and rough resemblance.
(a) The Image
(b) Graylevel Histogram
(c) Segmentation by (i)
(d) Segmentation by (ii)
(e) Segmentation by (iii)
(f) Segmentation by (iv)
(g) Segmentation by (v)
(h) Segmentation by (vi)
(i) Segmentation by (vii)
FIGURE 3.7: Segmentation obtained using the various thresholding algorithms applied to sepa-
rate dark and bright regions in an image
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