Page 5 - Fister jr., Iztok, and Andrej Brodnik (eds.). StuCoSReC. Proceedings of the 2017 4th Student Computer Science Research Conference. Koper: University of Primorska Press, 2017
P. 5
ameterless Harmony Search for image
Multi-thresholding
Krishna Gopal Dhal Iztok Fister Jr. Sanjay Das
Midnapore College Faculty of Electrical University of Kalyani, Dept. of
(Autonomous),Dept. of Engineering and Computer Eng. & Technological Studies
Computer Sc. & Application Science, University of Maribor
Midnapore (West)-721101, Smetanova 17, 2000 Maribor Kalyani-741235, India
India iztok.fister1@um.si dassanjay0810@hotmail.com
krishnacse42@gmail.com
ABSTRACT developed and proved their significant performance over a
mathematical optimization field. One parameterless vari-
The Harmony Search (HS) Algorithm is one of the efficient ant of HS is reported in literature where the associated pa-
nature-inspired optimization algorithms which exhibits in- rameters initialized by constant values, including population
teresting search capability within less computational over- size [11]. In [11], an experiment with population size and
head. However, empirical studies showed that the main stopping criterion was not performed. In our research paper,
problem of this kind of algorithms is the proper setting of the these experiments have been performed, inspired by method-
associated parameters. HS associated with a few parameters ologies the same as in [4, 3]. The proposed PLHS has been
and to find out the proper combination of the parameter val- employed in a multi-thresholding based image segmentation
ues is time consuming. That’s why a parameterless variant domain, which is one of the significant pre-processing steps
has been proposed here, which does not need the tuning in computer vision application. Shannon entropy is used
over control parameters. The effect of different population here as an objective function that maximizes the entropy of
size and stopping criterion has been considered in the ex- different regions in the image. Therefore, the organization
periment. The efficiency of the proposed HS is measured in of this paper is as follows. Section 2 presents the discussion
Shannon’s entropy based image multi-thresholding field. about the HS and the associated control parameters. In sec-
tion 3, a parameterless variant of HS has been presented and
Keywords Shannon entropy based multi-thresholding is also explained.
Experimental results are discussed in section 4. The paper
Harmony Search, Control parameters, multi-thresholding, is concluded in section 5.
optimization.
2. HARMONY SEARCH (HS) ALGORITHM
1. INTRODUCTION
In the Harmony Search (HS) Algorithm [8], the individ-
Recently, several nature-inspired optimization algorithms have ual algorithms are called a ”harmony” and they are repre-
been developed which mimic the behavior of natural and bio- sented by a real vector whose dimension is n. Let Xi =
logical systems [5]. These algorithms are very powerful and {xi(1), xi(2), . . . , xi(n)} represent ith randomly generated
effective for solving the real world optimization problems harmony vector: xi(j) = l(j)+(u(j)−l(j))×rand(0, 1) f or j =
within a reasonable time [12]. In this study, the Harmony 1, 2, . . . , n and i = 1, 2.., HM S, where l(j) and u(j) denotes
Search (HS) Algorithm [8] has been taken into consideration, the upper bound and lower bound of the search space respec-
and its extension to a parameterless variant. HS proves its tively and rand(0,1) is a uniform random number between
effective performance in different optimization fields. But, 0 and 1. The HM memory is filled by the HMS harmony
the efficiency of the original HS depends on the proper tun- vector as follows:
ing of the associated three control parameters. The proper
setting of the values of these three parameters is very dif- X1
ficult for different kinds of problems. In order to overcome
that problem, one parameterless variant of HS (PLHS) is de- X2
veloped here. In literature, parameterless variants of some
algorithms, such as the Bat Algorithm (BA) [4, 3], Genetic HM = ... (1)
Algorithm [7] and Differential Evolution (DE) [6], have been
XHMS
2.1 Control Parameters in the HS Algorithm
The values of the control parameters affect the efficiency
of the algorithm under experiment significantly.To control
these parameters is the same as the controlling the explo-
ration and exploitation efficiency of the considered algo-
rithm. Therefore, the parameter tuning and control become
an essential area in the nature-inspired optimization algo-
rithms based research field. But, the setting of the control
StuCoSReC Proceedings of the 2017 4th Student Computer Science Research Conference DOI: https://doi.org/10.26493/978-961-7023-40-4.5-12 5
Maribor, Slovenia, 11 October
Multi-thresholding
Krishna Gopal Dhal Iztok Fister Jr. Sanjay Das
Midnapore College Faculty of Electrical University of Kalyani, Dept. of
(Autonomous),Dept. of Engineering and Computer Eng. & Technological Studies
Computer Sc. & Application Science, University of Maribor
Midnapore (West)-721101, Smetanova 17, 2000 Maribor Kalyani-741235, India
India iztok.fister1@um.si dassanjay0810@hotmail.com
krishnacse42@gmail.com
ABSTRACT developed and proved their significant performance over a
mathematical optimization field. One parameterless vari-
The Harmony Search (HS) Algorithm is one of the efficient ant of HS is reported in literature where the associated pa-
nature-inspired optimization algorithms which exhibits in- rameters initialized by constant values, including population
teresting search capability within less computational over- size [11]. In [11], an experiment with population size and
head. However, empirical studies showed that the main stopping criterion was not performed. In our research paper,
problem of this kind of algorithms is the proper setting of the these experiments have been performed, inspired by method-
associated parameters. HS associated with a few parameters ologies the same as in [4, 3]. The proposed PLHS has been
and to find out the proper combination of the parameter val- employed in a multi-thresholding based image segmentation
ues is time consuming. That’s why a parameterless variant domain, which is one of the significant pre-processing steps
has been proposed here, which does not need the tuning in computer vision application. Shannon entropy is used
over control parameters. The effect of different population here as an objective function that maximizes the entropy of
size and stopping criterion has been considered in the ex- different regions in the image. Therefore, the organization
periment. The efficiency of the proposed HS is measured in of this paper is as follows. Section 2 presents the discussion
Shannon’s entropy based image multi-thresholding field. about the HS and the associated control parameters. In sec-
tion 3, a parameterless variant of HS has been presented and
Keywords Shannon entropy based multi-thresholding is also explained.
Experimental results are discussed in section 4. The paper
Harmony Search, Control parameters, multi-thresholding, is concluded in section 5.
optimization.
2. HARMONY SEARCH (HS) ALGORITHM
1. INTRODUCTION
In the Harmony Search (HS) Algorithm [8], the individ-
Recently, several nature-inspired optimization algorithms have ual algorithms are called a ”harmony” and they are repre-
been developed which mimic the behavior of natural and bio- sented by a real vector whose dimension is n. Let Xi =
logical systems [5]. These algorithms are very powerful and {xi(1), xi(2), . . . , xi(n)} represent ith randomly generated
effective for solving the real world optimization problems harmony vector: xi(j) = l(j)+(u(j)−l(j))×rand(0, 1) f or j =
within a reasonable time [12]. In this study, the Harmony 1, 2, . . . , n and i = 1, 2.., HM S, where l(j) and u(j) denotes
Search (HS) Algorithm [8] has been taken into consideration, the upper bound and lower bound of the search space respec-
and its extension to a parameterless variant. HS proves its tively and rand(0,1) is a uniform random number between
effective performance in different optimization fields. But, 0 and 1. The HM memory is filled by the HMS harmony
the efficiency of the original HS depends on the proper tun- vector as follows:
ing of the associated three control parameters. The proper
setting of the values of these three parameters is very dif- X1
ficult for different kinds of problems. In order to overcome
that problem, one parameterless variant of HS (PLHS) is de- X2
veloped here. In literature, parameterless variants of some
algorithms, such as the Bat Algorithm (BA) [4, 3], Genetic HM = ... (1)
Algorithm [7] and Differential Evolution (DE) [6], have been
XHMS
2.1 Control Parameters in the HS Algorithm
The values of the control parameters affect the efficiency
of the algorithm under experiment significantly.To control
these parameters is the same as the controlling the explo-
ration and exploitation efficiency of the considered algo-
rithm. Therefore, the parameter tuning and control become
an essential area in the nature-inspired optimization algo-
rithms based research field. But, the setting of the control
StuCoSReC Proceedings of the 2017 4th Student Computer Science Research Conference DOI: https://doi.org/10.26493/978-961-7023-40-4.5-12 5
Maribor, Slovenia, 11 October
