Multilevel Thresholding based on Cuckoo Search Algorithm ...Keywords: Multilevel Thresholding Segmentation, CS Algorithm, Coastal Video Image, Tsallis Method. 1. INTRODUCTION Image

International Journal of Computer Engineering and Information Technology

VOL. 11, NO. 7, July 2019, 145–152

Available online at: www.ijceit.org

E-ISSN 2412-8856 (Online)

Multilevel Thresholding based on Cuckoo Search Algorithm using

Tsallis's Objective Function for Coastal Video Image Segmentation

I Gusti Ngurah Agung Pawana P1, I Made Oka Widyantara

2 and NMAED Wirastuti

3

1, 2, 3

Electrical Engineering Department, Engineering Faculty, Udayana University, Indonesia

[email protected],

[email protected],

3dewi.wirastuti @unud.ac.id

ABSTRACT Image segmentation could be a difficult surroundings is a due to

the presence of weakly correlated and ambiguous multiple

regions of interest. Many algorithms are developed to get

optimum threshold values for segmenting satellite images with

efficiency in their quality and blurred regions of image. In this

paper a novel multilevel thresholding algorithm using a Cuckoo

Search (CS) algorithm has been proposed for solving the coastal

video image segmentation problem. The optimum threshold

values are determined by the maximization of Tsaliis’s objective

function using CS algorithm. In this paper, the analysis of CS

algorithm performance is combined with Tsallis's objective

function. Based on evaluations of PSNR, FSIM and Convergence

characteristi CS, the Algorithm CS based on Tsallis objective

function evolved to be most promising and computationally

efficient for segmenting coastal video images achieve stable

global optimum thresholds. The experiments results encourages

related researches in computer vision, remote sensing and image

processing applications.

Keywords: Multilevel Thresholding Segmentation, CS

Algorithm, Coastal Video Image, Tsallis Method.

1. INTRODUCTION

Image segmentation is a basic research technology in

image processing. It can segments an image into groups is

based on several rules or models [4][9][10]. Image

segmentation is widely used in object detection, area

detection, and many other image processing applications

[26].

The coastal area is a transitional area between land and sea,

which is influenced by three influencing spells, namely

water, air, and land, so it requires a very specific

understanding. In partitioning objects in an image, the

thresholding technique uses a gray level value to define the

object boundary. The coastal area is a transitional area

between land and sea, which is influenced by three

influencing spells, namely water, air, and land, so it

requires a very specific understanding. In partitioning

objects in an image, the thresholding technique uses a gray

level value to define the object boundary.

Within the framework of coastal video image processing,

some thresholding-based segmentation techniques are

proposed in the literature. Liu et al. [19] detect coastline

change from satellite images based on onshore slope

estimation in a tidal flat. The approach [6] evaluation of

the coastline precision combines uniformity features and

the averaged image that represents a simple way of facing

textural characteristics. There are several non-monitoring

grouping methods, such as the Markov Random Fields [7]

Hierarchy and K-means [20], etc., which are exploited to

extract Coastal changes. Niedermeier et al. [23] published

approval and active contours for shoreline approvals

obtained from SAR images. Grouping interrelated pixels

between dry (dry sand) and wet (wet and air sand) using

the thresholding technique of bimodal histograms has been

supported by [29][22].

In the literature, most parametric and nonparametric bi-

level and multi-level setting procedures have been

proposed and applied mainly to gray scale images

[1][2][12][28]. Among them global threshold is considered

as the most preferred image segmentation technique

because of its simplicity, resilience, accuracy and

competence [31]. The global histogram based

segmentation technique can determine the threshold value

in multilevel thresholding. Most of them include image

thresholding technique, Otsu method that works based on

variance between classes [25] and the Kapur method

which works based on the entropy principle both prove to

be the best [16]. The Otsu and Kapur methods find the

optimal threshold that optimally divides the gray level

value of an image into several predetermined criteria. To

select the optimal threshold value, the Otsu method uses

class variants to maximize the gray histogram value, while

the Kapur method is used to maximize the histogram

entropy. However, the Otsu and Kapur methods are only

able to solve bi-level threshold problems. Both methods

will experience problems in computational time

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International Journal of Computer Engineering and Information Technology (IJCEIT), Volume 11, Issue 7, July 2019 I. G. N. A. Pawana et. al

complexity if used in multilevel thresholding problems.

Bhandari et al. Presented an evolutionary algorithm based

color image segmentation technique using Tsallis entropy,

where the researchers suggested the q parameter as a

tuning factor to determine the threshold value for

segmentation [3]. The qualitative and quantitative

experimental results show that the proposed method

selects the threshold value effectively and correctly. A

global nonparametric approach, the Otsu, Kapur, Tsai, and

Kittler methods are simpler and successful for bi-level

thresholding [28]. When the number of threshold levels

increases, the complexity of thresholding problems also

increases and traditional methods require more

computational time. In overcoming the computational

complexity of most global methods, bi-level procedures

and heuristic based multilevels have been proposed by

researchers for gray scale [1][2], RGB [32], multi-spectral

and hyperspectral images [13][14].

Optimization algorithms are developed with the aim of

solving complex problems in terms of time and resources.

Meta-heuristic algorithms such as cuckoo search

[1][33][37], bee colony [1], and firefly [31] Genetic

algorithms (GA) [17], ant colony optimization [38], honey

bee optimization [15], particle swam optimization (PSO)

[21], and bacterial foraging algorithm (BF) [30] used to

solve the m-level image thresholding problem. Most of the

methods discussed above are applied and validated in gray

scale image classes. Genetic algorithms are inspired by the

idea of evolution of natural selection which effectively

finds optimal thresholds. Research [8] has shown that

genetic algorithms have a tendency to meet optima locally

rather than global values that cause misclassification of

objects in segmented images. Whereas the PSO shows

some unsatisfactory problems such as the inability to find

global optimization values, low speed of convergence, and

so on. BF algorithm provides good performance based on

the quality of the solution and the speed of convergence

compared to other multilevel threshold methods. However,

the robustness and efficiency of the BF algorithm depends

on the size of the chemo taxi step, ie a large step size helps

bacteria to find optimal positions faster but does not ensure

global optimality. On the other hand, the small step size of

the chemo taxis guarantees that bacteria will find a global

optimum but require a large processing time.

In general, the parametric thresholding approach that is

computationally expensive, time consuming, and several

times its performance decreases depending on image

quality [18] [27]. Therefore, several studies have proposed

several methods for increasing the convergence rate of

optimization algorithms by keeping computing time low.

The multi thresholding harmony search algorithm (HSMA)

has been proposed by [24] as an effort to reduce

computational overhead in optimization algorithms for

image segmentation. Research [35] presents a new

approach to automatic shoreline detection based on video

images. Combine the original harmony search algorithm

(HSA) and the Cretaceous algorithm as an objective

function to get the optimal threshold value to improve

segmentation quality. HSMA takes a random sample in the

search space in the image histogram. These samples build

every harmony (candidate solution) in the context of the

HSA, while the quality is evaluated by considering the

objective function used by the Otsu or Cretaceous method.

Another approach is to implement multilevel segmentation

based on the Cuckoo Search (CS) algorithm proposed by

[33]. The CS algorithm requires fewer search parameters

compared to other optimization algorithms. Theoretical

analysis has shown that the update equation of the cuckoo

search algorithm satisfies the nature of global convergence.

So the convergence of CS algorithms to global optimal

solutions is guaranteed, while other algorithms converge

rapidly, but not to the best globally.

CS has been designed to solve continuous problems, so

that CS adjustments are needed in the construction of

coastline detection research. In this study focuses on new

approaches to image segmentation. Combining the CS

algorithm method is based on its performance to produce a

stable random value and optimize Tsallis's objective

function by finding the threshold value in the multilevel

segmentation of coastal video images. This research is

organized as follows: Part 2 briefly describes various

thresholding techniques for image segmentation. Section 3

provides an overview of nature-inspired algorithms, which

were used in this study. Section 4 evaluates the results of

the performance measurements of the Cuckoo Search

algorithm which are validated by a series of numbers and

tables. Finally Section 5 presents the conclusions of this

study.

2. THRESHOLDING TECHNIQUES FOR

IMAGE SEGMENTATION

The optimization problem is to find variable values that

optimize objective / fitness functions. This paper, the

objective function for the CS algorithm at the multilevel

threshold is designed based on Tsallis entropy.

2.1 Multilevel Thresholding

Graylevel contained in the image is very thin, the simple

thresholding method is not able to handle this type of

image. So that a method such as multilevel thresholding is

needed to divide the gray level levels into the appropriate

sub-regions. Multilevel thresholding is a process that cuts

graylevel in an image into several clear regions. This type

of thresholding technique requires more than one threshold

for input image and cutting image into certain regions. It

can be mathematically formulated as:

𝑇0 = 𝐼 𝑥,𝑦 ∈ 𝑋|0 ≤ 𝐼 𝑥, 𝑦 ≤ 𝑡1 − 1 ;

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𝑇0 = 𝐼 𝑥,𝑦 ∈ 𝑋|0 ≤ 𝐼 𝑥, 𝑦 ≤ 𝑡1 − 1 ; 𝑇1 = 𝐼 𝑥,𝑦 ∈ 𝑋|𝑡1 ≤ 𝐼 𝑥,𝑦 ≤ 𝑡2 − 1 ; 𝑇𝑖 = 𝐼 𝑥,𝑦 ∈ 𝑋|𝑡𝑖 ≤ 𝐼 𝑥,𝑦 ≤ 𝑡𝑖+1 − 1 ; 𝑇𝑚 = 𝐼 𝑥,𝑦 ∈ 𝑋|𝑡𝑚 ≤ 𝐼 𝑥,𝑦 ≤ 𝑁 − 1 ; (1)

where X is the image used for processing, I(x, y) shows the

value of pixel intensity referred by the coordinate values

specified by x and y and ti = 1, 2 . . . m where m is the

total number of distinct threshold values.

2.2 Tsallis entropy

In image processing, the Tsallis entropy method can be

used for threshold search. This threshold search is

generally used to separate the background and foreground

parts of an image. The commonly used way is to change

the image first into a grayscale image and then compile a

histogram by calculating how many pixels of that image

have graylevel x. Each gray level x will then be tested to

determine the most optimal threshold. for each class, the

tsallis entropy equation can be formula given en Eq. (2) as

follows:

𝑠𝑞 =1− 𝑝𝑖

𝑞𝑘𝑖=1

𝑞 − 1 (2)

where pi ranges from 0 to 1 which denotes the probability

of the modeled system to be in state i. The parameter q

which gives the measure of non-extensivity of the system

under consideration is called as Tsallis parameter. So to

get tsallis entropy from the whole image, it can be written

as follows:

𝑆𝑞 𝑓𝑔𝑐 + 𝑏𝑔

𝑐 = 𝑆𝑞 𝑓𝑔𝑐 + 𝑆𝑞 𝑏𝑔

𝑐 + 1− 𝑞 . 𝑆𝑞 𝑓𝑔𝑐 .𝑆𝑞 𝑏𝑔

𝑐 where 𝑐 = 1, for gray− scale images (3)

where fg and bg shows the foreground and background of

an image. This method can be used for segmenting gray

scale and color images. Multilevel (m-level) image

thresholding by Tsallis entropy method [17][16] thus can

be formulated as:

𝑆𝑞𝑐0 𝑡 =

1− 𝑝𝑖𝑐

𝑝𝑖𝑐𝑡1−1

𝑖=0

𝑡1−1𝑖=0

𝑞 − 1; 𝑆𝑞

𝑐1 (𝑡) =

1− 𝑝𝑖𝑐

𝑝𝑖𝑐𝑡2−1

𝑖=𝑡1

𝑡2−1𝑖=𝑡1

𝑞 − 1

𝑆𝑞𝑐𝑗 𝑡 =

1− 𝑝𝑖𝑐

𝑝𝑖𝑐𝑡𝑗+1−1

𝑖=𝑡𝑗

𝑡1−1𝑖=𝑡𝑗

𝑞 − 1; 𝑆𝑞

𝑐𝑚 (𝑡) =

1− 𝑝𝑖𝑐

𝑝𝑖𝑐𝑡−1

𝑖=𝑡𝑚

𝑁−1𝑖=𝑡𝑚

𝑞 − 1 (4)

yielding the optimum threshold values as:

𝑡0 , 𝑡1 ,… . 𝑡𝑚 = arg𝑚𝑎𝑥 𝑆𝑞𝑐0 𝑡 + 𝑆𝑞

𝑐1 𝑡 … . 𝑆𝑞𝑐𝑚 𝑡

+1 1− 𝑞 . 𝑆𝑞𝑐0 𝑡 . 𝑆𝑞

𝑐1 𝑡 .𝑆𝑞𝑐𝑚 (𝑡)

subject to 𝑃𝑐0 + 𝑃𝑐1 − 1 < 𝑆𝑐0 < 1− 𝑃𝑐0 + 𝑃𝑐1 ;

𝑃𝑐1 + 𝑃𝑐2 − 1 < 𝑆𝑐1 < 1− 𝑃𝑐1 + 𝑃𝑐2 ; 𝑃𝑐(𝑚−1) + 𝑃𝑐𝑚 − 1 < 𝑆𝑐(𝑚−1) < 1− 𝑃𝑐(𝑚−1) + 𝑃𝑐𝑚 (5)

𝑃𝑐0 ,𝑃𝑐1 ,…𝑃𝑐𝑚 can be formed from the probability

distribution of pixel values corresponding to the threshold

levels 𝑡0 ∗, 𝑡1 ∗, . . . 𝑡𝑚 ∗ given by:

𝑃𝑐0 = 𝑝𝑖𝑐

𝑡1−1

𝑖=0

; 𝑃𝑐1 = 𝑝𝑖𝑐

𝑡2−1

𝑖=𝑡1

; …𝑃𝑐𝑚 = 𝑝𝑖𝑐

𝐿−1

𝑖=𝑡𝑚

; (6)

2.3 Cuckoo Search (CS) algorithm

Cuckoo Search found by [28] is a meta-heuristic algorithm

adopted from the behavior of cuckoo birds in breeding.

Cuckoo Search is categorized as a natural-inspired strategy

whose concept is inspired by natural events. The

philosophy and process contained in Cuckoo Search are

inspired by the cuckoo habit in its breeding process. Due

to the good individual selection to be brought to the next

generation, Cuckoo Search can also be categorized as

Evolutionary Computation (EC). In the optimization

process, for simplification use several lines:

1. One egg will be laid at a time by each cuckoo in any

nest chosen randomly.

2. Nest which have the best quality eggs are carried

over to the forthcoming generation.

3. The probability of host species discovering cuckoo’s

egg lies within the probability range pa [0,1] and

the total number if nests if fixed.

min max min

,0,1

i j j j jx x rand x x (7)

When the generation of new solutions x(t+1)

for a cuckoo i,

L´evy flight is shown as follows:

𝑥𝑖 𝑡 + 1 = 𝑥𝑖 𝑡 + 𝛼 ⊕ 𝐿𝑒𝑣𝑦(𝜆) (8)

where 𝛼 > 0 is the length of steps related to the scale of

the problem (can be used 𝛼 = 1 ) and ⊕ is the entrywise

multiplication. In this problem a long step is used,

mengikuti which follows the CS algorithm:

𝑠𝑡𝑒𝑝 =𝑢

|𝑣|1/𝛽, 0 < 𝛽 ≤ 2

𝑢~𝑁 0,𝜎𝑢 ,𝑣~𝑁 0,𝜎𝑣

𝜎𝑢 = 𝑟 1 + 𝛽 sin 𝜋𝛽/2

𝑟 1 + 𝛽 /2 𝛽2 𝛽/2 /2

1/𝛽

𝜎𝑣 = 1

(9)

where 𝛼 step size. Lévy Flights simulates randomly

following Lévy distribution as follows:

𝐿é𝑣𝑦 𝜆 = 𝑡−𝜆 ; 1 < 𝜆 ≤ 3 (10)

Nonlinear relationships of variance in retribution rates as

given in Equation (11) help in exploring search spaces that

are not known to be more efficient than models with linear

relationships.

𝜎2 𝑡 ~𝑡2−𝛽 ; 1 ≤ 𝛽 ≤ 2 (11)

The repetitive process continues until it reaches the global

optimum. The CS algorithm flow is given in Figure 1.

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3. IMAGE SEGMENTATION USING

CUCKOO SEARCH

In segmenting coastal video images, video images are

partitioned into different classes and each class has

different segmentation quality and unclear images on the

object. To overcome variations in image quality and

blurred image areas, a multilevel threshold technique with

an optimization algorithm is used, so as to select the

optimal threshold value in image segmentation. Selecting

the optimal threshold until the threshold does not have a

change is important in segmentation. The purpose of this

work is to improve the quality and accuracy of image

segmentation using multilevel thresholding techniques

based on the CS algorithm. The developed segmentation

system consists of three main modules (Fig. 2): set

objective function, segmentation used CS, threshold

selection, image segmentation. The data parameters used

are as follows:

Table 1: Parameters used for CS

Parameters Value

Number of nest 25

Alien egg discovery rate pa 0.5

Bound of value for egg 6

Max generation 100

The CS algorithm optimizes the threshold value using an

optimization algorithm with the objective function of

Tsallis. Figure 1 shows the CS algorithm flow chart used

in the research for coastal image segmentation.

Using input as in Table 1 as a parameter which will then

be segmented by the CS algorithm to produce a stable

random value and optimize Tsallis's objective function by

finding the best threshold value. In a nest host there can be

two eggs, in other words the nest can store more than one

solution except to simplify the problem, a nest will only

store one solution (egg). Based on the three rules of the

basic CS steps above, the CS algorithm flowchart can be

summarized as the following pseudo code (Algorithm 1)

Start

Objektif function (t)*

Generate new population (n)

End

No

t <Generasi Maks)

or (stop the criteria)

Cuckoo search ramdomly

with Levy Flights

(Fi>Fj)

Release (pa) from the worst nest and make a new

place; Save the best solution (nest with the best

solution); Sort and find the best solution

Change j with a

new solution

Yes

No

Fig. 1. Flowchart of CS Algorithm.

Image segmentation based on threshold

Threshold selection

Set Objective function(Tsallis)

Cuckoo Search

Fig. 2. Blok diagram of CS based image segmentation.

149


Algorithm 1: CS Algorithm

1: Population Initialization: , ; 1, 2.... , 1, 2,....i jx i N j n (7);

2: Fitness value computation for a defined objective function

1 2; , ....T

nf x x x x x ;

3: if (ITER < MAXITER) then

4: Generate new solution space by retaining the current

best; 5: Fitness value computation; Memorize best nest;

6: if ak p then

7: Step size generation;

8: Replace worst nest by Lévy flight (11);

9: Fitness value computation; Memorize best nest;

10: Update the Counter;

11: Find best fitness value so far;

12: else

13: Retain those nests;

14: end

15: end

16: Find the optimum solutions;

4. PERFORMANCE MEASUREMENT

The performance of the Cuckoo Search algorithm in

optimizing image segmentation was measured using

several quantitative measurements. Measurement methods

used are Peak to Signal Noise Ratio (PSNR), Standard

Deviation (STD) and Feature Similarity Index (FSIM).

PSNR are used to measure noise levels from segmented

images. FSIM is a measurement method used to determine

the similarity of original image features with segmented

images [27] [38]. The values of PSNR, and FSIM can be

defined by equations:

2

10

25510logPSNR

MSE

(12)

𝑆𝑇𝐷 = 𝜎 =1

𝑁𝑁𝑖=1𝑋𝑖 − 𝜇

2 (13)

( ) ( )

( )

x X L m

x X m

S x PC xFSIM

PC x

(14)

Table 2: Quality Evaluation of segmentation after applying CS algorithm using Tsallis method

Segmentation image Histogram k Threshold PSNR STD FSIM

2 46 93 6.9032 33.2340 0.8554

4 46 93 140 187 15.3374 60.6767 0.9229

6 37 74 110 143

176 210

19.8714 64.7418 0.9431

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5. Results and discussions

In order to find an optimal value for the parameter k an

threshold ranging from 2, 4 to 6 was defined based on

previous results obtained in the pilot study (visual

evaluation). This section describes the results of

experiments on coastal video image segmentation. CS

performance based on Tsallis as an objective function is

shown in Table 2. These values provide segmentation

results for three different threshold levels. The value of the

CS algorithm performance metric is evaluated. This

optimization algorithm is tested for the objective function

that Tsallis has. Experiments were conducted on

MATLAB R2018a which runs on Intel® Core TM i5 PCs

with 1.80 GHz CPU and 8 GB RAM. The test results show

that adding a threshold value can increase the PSNR and

FSIM values. The higher the PSNR shows

(a) (b) (c)

Fig. 3. Convergence of CS using Tsallis entropy method, (a) k = 2, (b) k = 4, (c) k = 6

Table 3: CS detection results using the Tsallis method

t Original image Segmentation Detection Result

M

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n

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n

g

N

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n

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A

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the lower noise in segmented images. FSIM is used to

measure the similarity of features of original images with

segmented images. A higher FSIM value indicates the

original image features and segmented images have high

similarities.

Visually, segmented images at each threshold value are

associated with histogram values and evolution of

conformity values during the implementation of the CS

method. Therefore, to result a good regional classification,

this study uses the same threshold value (th), with 6 level

thresholds for the entire coastline detection system

segmentation process. Figure 3 shows the convergence

characteristics of coastal video image segmentation by

mapping the suitability of the number of iterations in each

threshold value. Segmentation with level threshold 2

displays the characteristics of stable convergence at the

9th iteration. While for the level threshold 4 is stable at

the 21st iteration and for the level threshold 6 is stable at

the 78th iteration. Figure 4 shows the results of CS

detection using the Tsallis entropy method showing

original images with segmented images and line detection

results. The CS algorithm combined with the objective

function of Tsallis using a test of increasing the threshold

number can affect the renewal of fitness values in fewer

iterations.

6. CONCLUSIONS

The multilevel thresholding method based on the CS

algorithm was proposed in this study. Combining

intelligent search capabilities of the CS algorithm and the

use of the objective function of Tsallis. Performance

measurement from this study uses two main parameters,

namely PSNR and FSIM.

PSNR is used to assess the quality of segmentation taking

into account between segmented images and original

images, while FSIM is used to measure the similarity of

features from original images with segmented images. A

higher FSIM value indicates the original image features

and segmented images have high similarities. This study

analyzes the performance of CS algorithms when

combined with Tsallis's objective function. The results

showed that the combination of CS algorithms and Tsallis

functions gave better results than conventional

segmentation methods.

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Documents

Multilevel Thresholding based on Cuckoo Search Algorithm ...Keywords: Multilevel Thresholding Segmentation, CS Algorithm, Coastal Video Image, Tsallis Method. 1. INTRODUCTION Image