Image Enhancement - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 86

5.3.1 Contrast Enhancement Using the Intensification Operator

In this method, the membership values are modified using an intensifier.
Initially, the membership function is selected that finds the membership val-
ues of the pixels of an image. Then the transformation of the membership
values which are above 0.5 (default value) to much higher values and the
membership values which are lower than 0.5 to much lower values is car-
ried out in a non-linear fashion to obtain a good contrast in an image. The
contrast intensifier (INT) operation is written as

2 [ ]

2

0 05 .

⋅ μ ≤ μ ≤

mn mn

μ ʹ =

mn

121 [ ]

2

0 5 . 1

−⋅− μ ≤ μ ≤

mn mn

Once the membership values are modified, modified grey values are then
transformed to spatial domain using the inverse function. There is also an
operator called 'NINT' which uses Gaussian membership function in mem-
bership function generation [12].

5.3.2 Contrast Improvement Using Fuzzy Histogram Hyperbolization

The concept of fuzzy histogram hyperbolization was discussed by Tizhoosh
and Fochem [16]. This method modifies the membership values of the grey
levels into the logarithmic function due to non-linear human brightness per-
ception. Initially, a membership function is selected that finds the member-
ship values of the pixels of an image. A fuzzifier beta, β, which is a linguistic
hedge, is set to modify the membership function. Hedges [10,15] may be very
bright, medium bright, etc., and the selection is made on the basis of the
user's needs. The value of beta may be in the range β ∈ [0.5, 2]. Depending on
the value of β, the operation may be dilation or concentration. If the image is
a low-intensity image, then the fuzzifier β after operating on the membership
values will produce slightly bright or quiet bright images.

5.3.3 Contrast Enhancement Using IF-THEN Rules

Image quality can be improved by using human knowledge, which is highly
subjective in nature. Different observers judge the image differently. The
fuzzy rule-based approach is such a method that incorporates human intu-
itions which are non-linear in nature, and these cannot be easily characterized
by traditional modelling. As it is hard to define a precise or crisp condition
under which enhancement is applied, the fuzzy set theoretic approach is a
good approach to this solution. The rule-based approach incorporates fuzzy
rules into the conventional methods. A set of conditions on the pixel that are
related to the pixel grey level and also the pixel neighbourhood (if requires)
are defined, and these conditions will form the antecedent part of the IF-THEN
rules. Fuzzy rule-based systems make soft decisions on each condition, aggre-
gates the decision made and finally makes a decision based on the aggregation.