
Afreen et al.
Otsu in the year 1979 [
13
] presented a method for selecting threshold from grey-level histograms. But, inadequate
articulation of between-class variance raises the cost of computation of the algorithm, specifically in the selection of
multi-level threshold. Otsu’s thresholding aims at automatic threshold selection and region-based segmentation and is
one of the most accurate techniques for image thresholding because of its simple calculation. Differential Evolution is a
reasonably recent population-based evolutionary model which depends on the mutation operation as its prominent step.
It efficiently explores large search spaces and exhibits superior results in the following criteria: (1) shorter convergence
speed than other evolutionary algorithms, (2) fewer number of parameter adjustments, making it particularly easy to
implement.
Tsai (1985)[
14
] uses the moment-preserving principle to determine thresholds of grey-level input images - the Tsallis
entropy technique, a prominent function used for image thresholding. Kittler et al.(1986) work with the assumption that
the grey levels of every entity within an image are usually distributed. Kapur et al. (1985) further introduced a robust
method for grey-level image thresholding by utilizing the histogram entropy (Kapur et al., 1985)[15].
Entropy-based approaches have earned popularity among all the distinctive image thresholding methods. PCO,
influenced by the social behaviours like flocking of birds or schooling of fishes (Akay et al., 2013[
16
]; Maitra et al.
2008[
17
]; Yin, et al. 2007[
18
]), ant colony optimization (ACO) influenced by the pasturing conduct of ant colonies
(Ye et al., 2005[
20
]; Tao et al., 2007[
19
]) Artificial Bee Colony (ABC) inspired by the pasturing conduct of honey bee
swarm (Cuevaset al., 2012 [21], Akay et al., 2013;).
Another recent area of research inspired by the coordinated intelligence in a swarm of insects or animals has also
emerged called Swarm intelligence. One of the widespread and recently developed Swarm Intelligence-based techniques
is the ABC algorithm, presented by Karaboga D. (2005)[
22
], that simulates the foraging behavior of honey bee colonies.
Numerous studies have demonstrated that the performance of Artificial Bee Colony (ABC) method is competitive and
comparable with other population-based techniques.
The MABC method given by Bhandari et al.(2014) introduces an advanced solution search formula (Gao et al., 2012)
in charge for its more promising search solution. Within this search equation, the bee explores only closer to the best
solution of the iteration before to improve exploitation. The results demonstrate that MABC is best suited for multilevel
thresholding of images to attain optimal thresholds for satellite images in comparison to Artificial Bee Colony based
algorithms and Particle Swarm Optimization based techniques. Evaluating the advantages, such algorithms are the
preferred choice for finding the optimum thresholds in simple images. For example, the Genetic Algorithm (GA) and
the improved Genetic Algorithm (Zhang et al., 2014 [23]) are frequently in use to multilevel thresholding scenarios.
The Swarm Intelligence based computing methods can find efficient and optimal solutions for any objective function
and have been widely used with an ability to generate highly accurate results in case of complex problems as well. It
has also been found by statistical analysis that the Swarm Intelligence based algorithms perform well in multi-level
thresholding scenarios (Kurban et al., 2014 [24]).
2 BRIEF EXPLANATION OF THE ALGORITHMS USED IN THIS STUDY
2.1 Otsu’s thresholding
2.1.1 Bi-level thresholding
In Bi-level thresholding, the aim is to find a threshold to minimize the variance between classes in the segmented image.
Otsu’s algorithm tends to achieve better results when two different peaks are present in the histogram of the original
image, one corresponding to the background and the other to the foreground. The entire range of pixels are iterated and
the Otsu’s threshold is determined when the between-class variances are minimum. Hence, the Otsu’s threshold tends to
be decided by the class with greater variance.Hence, Otsu’s method tends to produce sub-optimal results when there is
an occurrence of two or more peaks within the histogram of the image or if one of the classes has a significant variance.
The total mean and variance are calculated based on the following formulas: The entire set of pixels are distributed into
2 classes,
C1←pixels having grey levels [1, t]
C2←pixels having grey levels [t+ 1, ..., L].
where tcorresponds to Otsu’s threshold
The probability distribution of the two classes is denoted by:
C1:p1
w1(t), ..., pr
w1(t)(1)