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The exploitation capability of the Harris Hawks optimization (HHO) is limited. This problem is solved here by incorporating features of Cuckoo search (CS). This paper proposes a new algorithm called Harris hawkscuckoo search (HHOCS) algorithm. The algorithm is validated using 23 Benchmark functions. A statistical analysis is carried out. Convergence of the proposed algorithm is studied. Nonetheless, converting color breast thermogram images into grayscale for segmentation is not effective. To overcome the problem, we suggest an RGB colour component based multilevel thresholding method for breast cancer thermogram image analysis. Here, 8 different images from the Database for Research Mastology with Infrared images are considered for the experiments. Both 1D Otsu’s betweenclass variance and Kapur's entropy are considered for a fair comparison. Our proposal is evaluated using the performance metrics – Peak Signal to Noise Ratio (PSNR), Feature Similarity Index (FSIM), Structure Similarity Index (SSIM). The suggested method outperforms the grayscale based multilevel thresholding method proposed earlier. Moreover, our method using 1D Otsu’s fitness functions performs better than Kapur’s entropy based approach. The proposal would be useful for analysis of infrared images. Finally, the proposed HHOCS algorithm may be useful for function optimization to solve real world engineering problems.
optimizer, Harris Hawks optimization, cuckoo search, multilevel thresholding, thermogram image analysis
Breast cancer is most common among women. Over 2.1 million women get affected each year, and the death rates are highly related to the breast cancer [1]. It is the second most common cancer in women after lungs cancer. Breast Cancer mostly begins in the ducts or lobules after uncontrolled growth of the cells. Breast cancer can spread to distant organs, so an early treatment is required. Cancer is a disease with multiple factors, so advanced screening of the breasts is required for analysis of the tumor formation. Breast cancer can be classified in several stages, the initial stage, which is known as DCIS (ductal carcinoma in situ), the growth of cells is limited in ducts. In the next stage, the formation of tumor occurs, and also has a small group of cancer cells. When the size of the tumor grows, it spreads to lymph nodes and distant organs such as bones, liver, brain or lungs.
Advanced screening of breasts is required for analysis of tumor formation as an extra aid to a radiophysicist. There are various Medical imaging techniques used for early analysis of breast cancer, Such as Breast Ultrasound (Sonogram), Magnetic Resonance (MRI), Thermography, Mammography, Positron Emission Tomography (PET), Computed Tomography (CT), Integrated PET/CT, MRI and PET, Ultrasound and MRI.
Mammography is one of the popular diagnostic techniques used for the detection of breast cancer. Mammography involves exposure to Xray radiation on the human body. Due to the exposure to radiation, there is a possibility of further cancer cell growth. Sometimes Mammography, Breast MRI and Breast Ultrasound show “falsepositive” results, in which the person needs an additional test or even more. This could lead to another mammogram or a different test.
On the other hand, thermography is a clinical procedure where a thermal camera captures the infrared radiation of the human body at controlled room temperature and produces the digital thermal images. A body emits infrared radiation above absolute zero temperature. A thermal image shows the temperature variations of the body. The infrared radiation emitted by the surface of the body has wavelength ranges from 0.8µm to 10 µm. Thermography is a noninvasive process, no exposure to radiations and does not involve in compression of breast tissues [2]. Thermography provides information on the growth of cancer cells before the formation of a tumour. No radiation is involved as the temperature variation of the body provides vascular activity information.
Image Segmentation Partitions images into regions into homogeneous classes. For image segmentation, several techniques have been studied throughout the years. Multilevel thresholding is the easiest method in image segmentation. In color images, multilevel thresholding partitions, images into different classes based on threshold levels of each R, G, B histogram components. The thresholding based segmentation method is divided into parametric and nonparametric. Note that the parametric method calculates the probability density function of each class, whereas the nonparametric measure class variance, entropy to get the optimal threshold values [3]. Due to the computational complexity of the parametric approach, nonparametric methods are used. Various optimization techniques are used in multilevel thresholding using nonparametric approaches to get the best threshold values. Segmentation of medical images is popular in recent years as it is helpful for analysis of a particular part of the body.
In this work, a new optimization technique called Harris HawksCuckoo Search (HHOCS) is investigated. The Harris Hawks optimizer is found more popular for function optimization. However, its exploitation capability is limited, thereby not yielding to optimal or near optimal solutions. This has motivated us to incorporate the exploitation capability of the cuckoo search strategy. This is the real motivation behind the investigation of the proposed HHOCS algorithm. Two different objective functions are used for a comparison. The suggested algorithm is used to obtain the optimal threshold values to segment colour thermogram images. The effectiveness of HHOCS algorithm is validated with a set of 23 Benchmark functions and compared with Harris Hawks optimization [4] and Cuckoo Search algorithm [5]. For multilevel thresholding of thermogram images, experiments are performed based on Otsu’s betweenclass variance and Kapur's entropy as the fitness functions. Our proposed HHOCS technique is evaluated based on the performance metrics – peak signal to noise ratio (PSNR), Feature similarity index (FSIM), Structure Similarity Index (SSIM). Results of objective function values, threshold levels of RGB component are also evaluated.
Converting colour thermal images into grayscale images makes it a difficult task to extract features due to poor contrast, low visual perception. Therefore, it is necessary to perform full colour image processing of the clinical images for research support. For the past few years, many optimization techniques are used to perform segmentation to get better quality segmented images. This has motivated us to investigate a method to segment colour thermogram images. Results are presented using 1D Otsu’s objective function and Kapur’s entropy.
Organization of the paper is as follows: Section 2 discusses the related work. The proposed HHOCS algorithm is presented in Section 3. The methodology is discussed in Section 4. Results are presented in Section 5. Conclusions are given in Section 6.
DíazCortés et al. [6] in 2018 presented multilevel thresholding of Breast Thermal images using Dragonfly algorithm. The Segmentation of grayscale breast thermal images is performed by using the energy curve of images as an input. The colour Segmentation of satellite images using natureinspired optimization algorithms are proposed by Bhandari et al. [7]. The performance of the algorithms was performed based on Otsu’s betweenclass variance and Kapur’s entropy as the objective functions. The Kapur’s entropy based objective function has better performance and the Cuckoo search algorithm was found to be more efficient for Colour segmentation of satellite images.
He and Huang [8] presented an efficient krill herd (EKH) optimization technique for multilevel thresholding of colour images using Otsu’s method, Kapur and Tsallis entropy as the objective functions. The efficient krill herd (EKH) algorithm shows better performance as compared to the krill herd algorithm (KH). Electromagnetism optimization (EMO) algorithm based multilevel thresholding is presented by Oliva et al. [9]. The Otsu’s and Kapur's entropy criterion used as objective functions and the histogram of images are taken as the input. Oliva et al. [3] presented a hybrid Artificial Bee colonySalp Swarm algorithm (ABCSSA), for image segmentation. The hybrid approach performs better than ABC, SCA, SSO, SSA algorithms in a multilevel thresholding problem using Kapur’s entropy as the objective function. Multilevel thresholding of Satellite images proposed by Pare et al. [10] using optimization techniques WDO, BFO, FA, ABC, DE and PSO by taking energy curves of image as an input. The objective functions based on Kapur’s entropy, Tsallis entropy and Otsu’s method are used. The Kapur’s entropy based DE techniques produces better segmented images.
Multilevel thresholding using WDO and CS was proposed by Bhandari et al. [11] using Kapur’s entropy as the objective function. Multilevel thresholding using various Optimization techniques are reported in the studies [1215]. Horng et al. [16] presented multilevel thresholding based on honey bee mating optimization using the cross entropy as the objective function. Bhandari et al. [17] proposed a modified artificial Bee colony (MABC) optimizer for multilevel thresholding of satellite images through maximization of Otsu’s betweenclass variance, Kapur’s and Tsallis entropy. The MABC algorithm produces better segmented images as compared to ABC method.
2.1 Harris Hawks Optimization
A natureinspired Optimization algorithm called “HarrisHawks optimization”algorithm was proposed by Heidari et al. in 2019. The Harrishawks optimization technique is inspired by the hunting strategy of Harrishawks and escaping of prey. The Harrishawks catch prey by a “Surprise Pounce” or also known as“Seven kills”strategy. The Harrishawks optimization technique also features exploration and exploitation phase [4].
2.1.1 Exploration phase
The exploration phase of HHO algorithm consists of two strategies to detect the prey (Rabbit) by perching randomly on some locations, taking an equal chance q (in each perching plan), the perch based on the position of other hawks. The location of the rabbit is known as $\begin{equation}X_{\text {rabbit }}\end{equation}$. The rabbit location for the condition q< 0.5 described in Eq. (1). When q $\begin{equation}\geq\end{equation}$ 0.5, hawks roost on random high trees inside their range of location.
$\begin{equation}
X(t+1)=\left\{\begin{array}{l}
X_{\text {rand}}r_{1}\leftX_{\text {rend}}(t)2 r_{2} X(t)\right, q \geq 0.5 \\
\left(X_{\text {rabbit}}(t)X_{m}(t)\right)r_{3}\left(L B+r_{4}(U BL B)\right), q<0.5
\end{array}\right.
\end{equation}$ (1)
where, The term X(t+1) represents updated position of Hawks in each iteration, $\begin{equation}X_{\text {rabbit}}(t)\end{equation}$ is the postion of rabbit, $\begin{equation}X_{\text {rand}}(t)\end{equation}$ is the position of Hawks chosen randomly, LB is the lower bound, UB is the upper bound, and $\begin{equation}X_{m}(t)\end{equation}$ is the average position of hawks. Random numbers $\begin{equation}\mathrm{r}_{1}, \mathrm{r}_{2}, \mathrm{r}_{3}, \mathrm{r}_{4}\end{equation}$ are used to explore different regions of Search space for the Hawks. The equation for the average position of hawks is given by:
$\begin{equation}
X_{m}(t)=\frac{1}{N} \sum_{i=1}^{N} X_{i}(t)
\end{equation}$ (2)
where, $\begin{equation}\mathrm{X}_{\mathrm{i}}(\mathrm{t})\end{equation}$ and N represents the location of each Hawk in iteration t and number of Hawks, respectively. The transition from the Exploration Phase to Exploitation Phase occurs depending on the Perching strategy of Hawks on escaping prey (Rabbit). The initial energy $\begin{equation}\mathrm{E}_{0}\end{equation}$ The value ranges from 1 to 1 for every iteration t. When the value of $\begin{equation}\mathrm{E}_{0}\end{equation}$ decreases from 0 to 1, it signifies a weakening of the prey. In case the value of $\begin{equation}\mathrm{E}_{0}\end{equation}$ increases from 0 to 1, it signifies strengthening of the prey. The escaping energy of the Prey also a key factor in the transition, which is modelled as:
$\begin{equation}
E=2 E_{0}\left(1\frac{t}{T}\right)
\end{equation}$ (3)
2.1.2 Exploitation phase
The Hawks perform the “Surprise Pounce” strategy to catch the prey. There is also an escaping factor ‘r’ of the prey, where the value of r is greater than 0.5 signify higher chance of escape and less than or equal to 0 signify lower chance of escape of the rabbit. There are different phases of exploitation of prey based on the escaping factor and energy of the prey. The exploitation phases are shown in Figure 1.
Figure 1. Exploitation phases of HHO
a. Soft Besiege
The Hawks perform Soft Besiege based on Rabbit’s energy. The position of hawks for soft Besiege models as below.
$\begin{equation}
X(t+1)=\Delta X(t)E / J X_{\text {rabbit}}(t)X(t) /
\end{equation}$ (4)
$\begin{equation}
\Delta X(t)=X_{\text {rabbit}}(t)X(t)
\end{equation}$ (5)
where, “J” is known as“Jump strength”of the Rabbit.
b. Hard Besiege
When the Rabbit is fagging, the hawks perform “Surprise Pounce” tactics, when the escaping factor value “r” is greater than or equal to 0.5 and the escaping energy is less than 0.5. For each iteration, the positions of hawks are updated using the equation.
$\begin{equation}
X(t+1)=X_{\text {rabbit}}(t)E\Delta X(t)
\end{equation}$ (6)
where, E is the energy.
c. Soft Besiege with progressive rapid dives
In Case of Escaping energy greater than or equal to 0.5 and the escaping factor less than 0.5 of the rabbit, the hawks perform soft besiege with progressive rapid dives. In this condition, the rabbit has sufficient energy to outflow). The Levy flight movement of Hawks depends on the zigzag motion of the rabbit [6]. The Hawks update their position concerning the movements of the rabbit. The equations for this strategy can be described as below:
$\begin{equation}
Y=X_{\text {rabbir}}(t)E\leftJ X_{\text {rabbit}}(t)X(t)\right
\end{equation}$ (7)
$\begin{equation}
Z=Y+S \times L F(D)
\end{equation}$ (8)
$\begin{equation}
L F(x)=0.01 \times \frac{u \times \sigma}{v^{\frac{1}{\beta}}}
\end{equation}$ (9)
where,
$\begin{equation}
\begin{array}{l}
\sigma=\left(\frac{\Gamma(1+\beta) \times \sin \left(\frac{\pi \beta}{2}\right)}{\Gamma\left(\frac{1+\beta}{2}\right) \times \beta \times 2^{\left(\frac{\beta1}{2}\right)}}\right)^{\frac{1}{\beta}} \\
X(t+1)=\left\{\begin{array}{l}
Y, F(Y)<F(X(t)) \\
Z, F(Y)<F(X(t))
\end{array}\right.
\end{array}
\end{equation}$ (10)
Note that LF is the Levy flight.
d. Hard Besiege with progressive rapid dives
When Escaping energy is less than 0.5 and escaping factor is less than 0.5, the rabbit is completely exhausted and has lowlevel energy, the Hawks perform hard besiege with rapid dives to catch the rabbit. In this stage, the hawks successfully catch the rabbit. The Levy flight method is also used in this phase. The equation for the position of hawks, for each iteration, is given below:
$\begin{equation}
X(t+1)==\left\{\begin{array}{ll}
Y, & \text { if } F(Y)<F(X(t)) \\
Z, & \text { if } F(Z)<F(X(t))
\end{array}\right.
\end{equation}$ (11)
$\begin{equation}
Y=X_{\text {rabbit}}(t)E \mid J X_{\text {rabbit}}(t)X_{m}(t)
\end{equation}$ (12)
$\begin{equation}
Z=Y+S \times L F(D)
\end{equation}$ (13)
2.2 Cuckoo search optimization
Natureinspired Cuckoo Search optimization was proposed by Yang and Deb in 2009 [5]. The Cuckoo Search algorithm is based on the brooding parasitism of Cuckoo birds as they use another host bird’s nest for breeding. The phases of the cuckoo search algorithm are described below
1) A cuckoo bird lays one egg at a time and pass down to another bird’s nest;
2) The best nests with good quality eggs are carried over to the next generations;
3) The number of host nests is ﬁxed, and the host bird can discover an egg with a probability of $\begin{equation}p_{a}\end{equation}$ ∈ [0,1]. Interestingly, the host bird can either throw the egg or abandon the nest immediately. The number of nests “n” and“ $\begin{equation}p_{a}\end{equation}$ ”are replaced with new solutions.
The mathematical equation, for each iteration, is modelled as below.
$\begin{equation}
x_{i}^{(t+1)}=x_{i}^{(t)}+\alpha \oplus \text {Lévy}(\lambda)
\end{equation}$ (14)
The equation for the levy flight mechanism is given below.
$\begin{equation}
\text { Lévy } \sim u=t^{\lambda},(1<\lambda \leq 3)
\end{equation}$ (15)
where, ‘u’ is the variable and ‘$\begin{equation}\lambda\end{equation}$’ is a constant.
Harris Hawks Optimization technique performs good exploration tactics to catch the prey to reach a global best solution, whereas the weak exploitation capability of hawks signifies a higher chance of getting into local optima. To enhance the performance of HHO, the exploitation capability of Cuckoo search mechanism is inherited here. The location of hawks is updated by:
$\begin{equation}
\begin{array}{l}
X(t+1)= \\
\left\{\begin{array}{c}
X_{\text {rand}}(t)r_{1}\leftX_{\text {rand}}(t)2 r_{2} X(t)\right+\alpha \oplus \text {Lévy}(\lambda), q \geq 0.5 \\
\left.X_{\text {rabbit}}(t)X_{m}(t)\right)r_{3}\left(L B+r_{4}(L B+(U BL B))+\alpha \oplus\right. \text {Lévy}(\lambda) \\
q<0.5,E \geq 1
\end{array}\right.
\end{array}
\end{equation}$ (16)
Figure 2. Flow diagram of HHOCS
The flow diagram of HHOCS method is displayed in Figure 2.
Table 1. Parameter settings
Algorithm 
Parameter 
Value 
HHOCS 
N $\begin{equation} $\begin{equation} 
30 0.25 1.5 
HHO 
N 
30 
Table 2. Results of benchmark functions ( $\begin{equation}f_{1}\end{equation}$  $\begin{equation}f_{13}\end{equation}$ ), with 30 dimensions
Function 

HHOCS 
HHO 
f _{1} 
Avg Std Min Max 
8.8674E95 4.8557E94 4.5074E115 2.6596E93 
1.6694E94 6.9584E94 1.9980E121 3.6163E93 
f _{2} 
Avg Std Min Max 
5.9147E49 2.3401E48 3.3248E59 1.2151E47 
1.3618E49 7.2705E49 3.4078E59 3.9850E48 
f _{3} 
Avg Std Min Max 
2.6211E72 1.4357E71 1.2370E98 7.8634E71 
8.4362E76 3.3003E75 4.5853E99 1.5885E74 
f _{4} 
Avg Std Min Max 
2.5076E49 9.4690E49 6.2383E58 5.0141E48 
8.8527E49 3.6383E48 4.5837E58 1.9624E47 
f _{5} 
Avg Std Min Max 
0.0290 0.0524 3.9738E5 0.2504 
0.0172 0.0339 1.7375E5 0.1741 
f _{6} 
Avg Std Min Max 
1.0566E04 1.2169E04 9.8245E08 4.9675E04 
1.2869E04 1.5884E04 4.6149E07 6.6066E04 
f _{7} 
Avg Std Min Max 
1.4913E04 2.0653E04 1.0482E05 8.6431E04 
1.7717E04 1.4357E04 3.0423E06 6.6621E04 
f _{8} 
Avg Std Min Max 
1.2486E+04 45.2858 1.2569E+04 1.2350E+04 
1.2562E+04 40.0058 1.2569E+04 1.2350E+04 
f _{9} 
Avg Std Min Max 
0 0 0 0 
0 0 0 0 
f _{10} 
Avg Std Min Max 
8.8818E16 1.47E+02 8.8818E16 8.8818E16 
8.8818E16 1.47E+02 8.8818E16 8.8818E16 
f 11 
Avg Std Min Max 
0 0 0 0 
0 0 0 0 
f 12 
Avg Std Min Max 
5.9841E06 9.2809E06 1.4347E08 3.4656E05 
1.1300E05 2.2354E05 7.8338E09 1.1656E04 
f 13 
Avg Std Min Max 
7.0957E05 1.2754E04 2.4497E08 6.3517E04 
8.1648E05 9.4889E05 5.8620E09 3.5137E04 
Figure 3. Convergence curves of HHOCS and HH
Table 3. Results of benchmark functions ($\begin{equation}f_{14}f_{23}\end{equation}$)
Function 

HHOCS 
HHO 
f 14 
Avg Std Min Max 
1.5585 1.2876 0.9980 5.9288 
1.3280 0.9466 0.9980 5.9288 
f 15 
Avg Std Min Max 
3.4236E04 2.9925E05 3.0756E04 4.4702E04 
3.8963E04 2.6287E04 3.0771E04 1.8000E03 
f 16 
Avg Std Min Max 
1.0316 6.78E16 1.0316 1.0316 
1.0316 6.78E16 1.0316 1.0316 
f 17 
Avg Std Min Max 
0.3979 2.54E06 0.3979 0.3979 
0.3979 2.54E06 0.3979 0.3979 
f 18 
Avg Std Min Max 
3 0 3 3 
3 0 3 3 
f 19 
Avg Std Min Max 
3.6028 1.4095 3.8628 3.8599 
3.8590 0.0061 3.8628 3.8333 
f 20 
Avg Std Min Max 
3.1250 0.0726 3.2605 2.9690 
3.0913 0.0988 3.2836 2.8111 
f 21 
Avg Std Min Max 
5.5267 1.4608 10.0063 5.0028 
5.1375 1.0277 10.0464 2.6226 
f 22 
Avg Std Min Max 
5.2484 0.9042 10.0360 5.0679 
5.2495 0.9097 10.0658 5.0685 
f 23 
Avg Std Min Max 
5.4583 1.2722 10.4055 5.1106 
5.3041 0.9876 10.5332 5.1076 
Benchmark Function Optimization
To test the effectiveness of HHOCS, HHO, and CS algorithms, a set of 23 standard benchmark functions including unimodal, multimodal, multimodal with fixed dimension functions ( $\begin{equation}f_{1}f_{23}\end{equation}$ ) are taken for a minimization problem. The unimodal functions are used to test the exploitation capability of optimizers and the multimodal functions are used to test the exploration ability. The unimodal functions also signify the ability to reach the global best while the performance of the multimodal functions shows the local optima avoidance. The dimension size is set to 30. The population size N is 30 and the maximum iteration is 500. All the algorithms are run in MATLAB R2018 having an Intel Core i58265U CPU clocked at 1.60GHz with 4GB RAM, with windows 10 operating system. The parameter settings are shown in Table 1. The results of an Average (Avg), Standard deviation (Std), Minima (Min) and Maxima (Max) of 30 runs of each benchmark functions are shown in Table 2&3. The boldface letters indicate the best results. The convergence curves are shown in Figure 3.
In summary, the proposed HHOCS algorithm performs better than the HHO for the multimodal test functions. However, the performance of our method is similar to that of the HHO for some of the functions. Nevertheless, the suggested algorithm ensures a better convergence, because of its enhanced exploitation capability.
Multilevel thresholding of color thermogram images is solved using the RGB histogram as the input, considering that the color images contain more information, better visual perception of the human eye with contrary to grayscale images, where we cannot see the temperature variations. The multilevel thresholding technique is used to get better results.
4.1 Otsu’s between class variance
The bilevel and multilevel thresholding of images based on the between class variance was first proposed by Otsu [18]. Bilevel thresholding and multilevel thresholding separate images into classes when the maximum variance is calculated. This method considers histogram of an image as an input. The probability distribution of intensity levels of R, G, B channel is obtained. The optimal threshold values are obtained for each channel of the colour image. The mathematical representation is given below
$\begin{equation}
\sigma^{2}=\sum_{k=1}^{n t} \sigma_{k}=\sum_{k=1}^{n t} \omega_{k}\left(\mu_{k}\mu_{\tau}\right)^{2}
\end{equation}$ (17)
$\begin{equation}
\mu_{\star}=\sum_{i=t h k}^{t h_{k+1}1} \frac{k P E_{i}}{\omega_{i}\left(t h_{i}\right)}
\end{equation}$ (18)
where,
$\begin{equation}
\omega_{k}=\sum_{i=t h k}^{t h k+11} P E_{i}
\end{equation}$ (19)
$\begin{equation}
f_{\text {otsu}}(t h)=\max \left(\sigma^{2}(t h)\right), 0 \leq \text { th } \leq \mathrm{L}1
\end{equation}$ (20)
where, $\begin{equation}\sigma^{2}\end{equation}$ is the variance, µ is the mean.
4.2 Kapur’s entropy
Kapur’s entropy method measures the entropy of different classes of an image. To segment colour images, the Kapur’s entropy maximizes the entropy and obtain optimal threshold values of each R, G, B channel. The probability distribution of intensity levels of each R, G, B channel is used to measure the entropy criterion. Segmentation of Colour images performed by maximizing Kapur’s entropy, which is taken as the objective function [19]. The mathematical formulations for Kapur’s entropy are
$\begin{equation}
f_{\text {Kapur}}(t h)=\max \left(\sum_{k=1}^{n t} H_{k}\right)
\end{equation}$ (21)
where, entropy of each class is calculated by
$\begin{equation}
H_{k}=\sum_{i=t h k}^{t h k+11} \frac{P E_{i}}{\omega_{k}} \ln \left(\frac{P E_{i}}{\omega_{k}}\right)
\end{equation}$ (22)
In summary, the proposed Harris HawksCuckoo Search Optimizer (Eq. (16)) is used to optimize the fitness functions shown in Eq. (20) (Otsu’s method) and Eq. (21) (Kapur’s method). It is reiterated that the optimum threshold values are obtained through the maximization.
The multilevel colour thermogram image thresholding method is implemented using both Otsu’s betweenclass variance and Kapur’s entropy as the fitness functions. The proposed HHOCS, CS and HHO algorithms are implemented to get optimal results. The multilevel colour thermogram image thresholding method is shown in Figure 4.
Figure 4. Multilevel thresholding of thermal images
The benchmark images are displayed in Figure 5. The experiments are based on a set of 8 different images acquired from the Database for Research Mastology with Infrared images [20]. The images are captured using a FLIR SC620 Thermal Camera. The selected images and their respective histogram plots are described in Figure 5. For experimental purposes, images with size 341 x 256 are taken.
The population size and the maximum number of iterations of each algorithm are set to 30 and 500, respectively. The Lower bound (LB) and upper bound (UB) of the algorithm is set to 0 to 255. The performance of the algorithms is evaluated, which is composed of 20 runs of the same algorithm using a specific image and calculating the average of objective function values, PSNR, SSIM and FSIM [2124].
Figure 5. Benchmark images and their respective histograms
5.1 Benchmark images
The Peak Signal to noise ratio (PSNR) is a widely used performance metric for measuring the quality of the original image with the reconstructed images. Structure Similarity Index (SSIM) and Feature Similarity index (FSIM) quality metric measure the similarity between the original image and the output segmented image. SSIM specify quality degradation due to data processing. All experiments are performed on MATLAB R2018a with 4GB RAM on an Intel core i5 CPU clocked at 1.6 GHz frequency.
5.2 Experiment 1: Based on Otsu’s between class variance
Optimal threshold values are obtained using HHOCS algorithm and presented in Table 4. Objective function values and PSNR values obtained from HHOCS and HHO algorithms using Otsu’s between class variance are displayed in Table 5. Remarkable differences are found. It is observed that the suggested HHOCS method outperforms as compared to HHO. Similarly, a significant improvement over the HHO algorithm is seen with respect to the PSNR values. The reason could be the enhanced exploitation capability of HHOCS method to get the best solutions. For instance, an improvement of 3% in PSNR value is seen in the test image sample TH1 with threshold level K=4 (see Table 5). The SSIM and FSIM values obtained from HHOCS and HHO algorithms using Otsu’s betweenclass variance are shown in Table 6. Interestingly, the suggested technique has shown better values (for SSIM and FSIM) than HHO.
Table 4. Threshold values obtained using HHOCS algorithm
Image 
K 
HHOCS 



R 
G 
B 
TH1 
2 
137,239 
110,210 
82,163 
3 
141,176,230 
60,153,182 
62,130,149 

4 
44,58,113,145 
44,102,160,230 
46,86,135,250 

5 
145,191,196,197,254 
61,87,168,173,255 
83,98,152,196,236 

TH2 
2 
138,236 
82,88 
81,190 
3 
108,212,228 
62,60,140 
51,86,118 

4 
101,155,176,255 
93,130,167,228 
46,94,185,198 

5 
112,180,183,224,255 
83,96,126,200,247 
82,128,137,239,254 

TH3 
2 
125,229 
102,238 
83,86 
3 
136,147,180 
81,151,215 
63,110,196 

4 
140,188,212,249 
59,91,140,243 
63,104,195,248 

5 
32,153,155,190,249 
83,96,97,103,231 
60,76,86,164,196 

TH4 
2 
148,203 
95,174 
77,90 
3 
100,189,222 
56,130,217 
52,107,108 

4 
104,164,194,250 
110,148,175,251 
80,114,190,215 

5 
106,111,184,249,254 
64,69,88,123,217 
58,88,64,65,104 

TH5 
2 
137,138 
101,209 
75,88 
3 
113,141,201 
60,134,141 
47,63,126 

4 
155,162,172,254 
112,146,147,219 
84,94,202,215 

5 
130,165,192,217,253 
86,166,174,187,218 
76,96,176,209,220 

TH6 
2 
128,137 
47,100 
85,147 
3 
117,134,206 
56,131,209 
71,138,166 

4 
130,143,170,254 
118,120,126,216 
60,117,202,244 

5 
66,185,195,199,245 
94,107,119,148,208 
55,84,93,162,247 

TH7 
2 
139,184 
93,97 
56,85 
3 
115,124,214 
63,136,158 
59,61,129 

4 
219,237,241,251 
110,167,184,232 
91,120,243,246 

5 
114,118,142,250,255 
78,138,186,191,240 
29,68,92,133,207 

TH8 
2 
125,139 
100,126 
92,130 
3 
97,190,243 
43,64,131 
54,83,169 

4 
125,156,162,253 
126,134,218,233 
94,95,131,213 

5 
141,156,159,213,247 
93,115,182,238,253 
21,63,98,241,247 
Table 5. Comparison of objective function and PSNR values obtained from HHOCS and HHO algorithms using Otsu’s betweenclass variance


OBJECTIVE FUNCTION 
PSNR 

Images 
K 
HHOCS 
HHO 
HHOCS 
HHO 
TH1 
2 3 4 5 
1.3864 E+04 1.4623 E+04 1.7680 E+04 1.9050 E+04 
1.3829E+04 1.4581E+04 1.7483E+04 1.8744E+04 
55.0114 62.7343 69.6979 74.3875 
53.4132 62.5010 67.6563 73.3842 
TH2 
2 3 4 5 
1.5874 E+04 1.6509 E+04 1.9470 E+04 2.0844 E+04 
1.5860E+04 1.6499E+04 1.8832E+04 1.9810E+04 
55.3194 62.4648 66.3321 72.0098 
54.1919 61.3768 65.7321 71.8845 
TH3 
2 3 4 5 
1.2160 E+04 1.3104 E+04 1.8422 E+04 2.0441 E+04 
1.2133E+04 1.3012E+04 1.7919E+04 1.8662E+04 
55.3793 62.1599 65.2385 68.4839 
53.9000 60.9659 64.2440 66.8464 
TH4 
2 3 4 5 
1.6818 E+04 1.7437 E+04 2.1086 E+04 2.2654 E+04 
1.6807E+04 1.7369E+04 1.9552E+04 2.1593E+04 
56.1415 58.5895 64.3450 66.0842 
54.938 55.1351 60.9177 64.0399 
TH5 
2 3 4 5 
1.2864 E+04 1.3962 E+04 1.8368 E+04 2.0739 E+04 
1.2858E+04 1.3833E+04 1.7688E+04 1.9943E+04 
56.2041 57.7679 59.3859 62.8876 
55.5316 56.0270 58.7054 61.4830 
TH6 
2 3 4 5 
1.4484 E+04 1.5325 E+04 2.0903 E+04 2.2077 E+04 
1.4467E+04 1.5185E+04 2.0314E+04 2.1627E+04 
56.5041 58.1370 64.2811 66.2539 
55.0818 57.5004 63.2488 65.4236 
TH7 
2 3 4 5 
1.8836 E+04 1.9405 E+04 2.2614 E+04 2.5290 E+04 
1.8825E+04 1.9340E+04 2.1881E+04 2.3362E+04 
57.6207 63.8870 65.7686 66.2036 
55.0971 62.9271 63.9271 65.7404 
TH8 
2 3 4 5 
1.4799 E+04 1.5705 E+04 2.1482 E+04 2.2905 E+04 
1.4757E+04 1.5658E+04 2.1221E+04 2.2280E+04 
57.6318 64.2626 67.8773 69.2639 
56.5587 64.2060 67.5404 68.6456 
Table 6. Comparison of SSIM and FSIM values obtained from HHOCS and HHO algorithms using Otsu’s between class variance


SSIM 
FSIM 

Images 
K 
HHOCS 
HHO 
HHOCS 
HHO 
TH1 
2 3 4 5 
0.7342 0.7829 0.8280 0.8604 
0.6967 0.7355 0.8181 0.8523 
0.7515 0.8029 0.8140 0.8396 
0.7486 0.7992 0.8110 0.8347 
TH2 
2 3 4 5 
0.7114 0.8079 0.8501 0.9109 
0.6912 0.7904 0.8483 0.8976 
0.7586 0.7946 0.8267 0.8438 
0.7170 0.7781 0.8231 0.8362 
TH3 
2 3 4 5 
0.7281 0.7964 0.8248 0.8787 
0.7060 0.7784 0.8174 0.8653 
0.7676 0.8025 0.8238 0.8449 
0.7468 0.7970 0.8258 0.8418 
TH4 
2 3 4 5 
0.6699 0.8010 0.8324 0.8963 
0.6662 0.7934 0.8292 0.8714 
0.7840 0.8170 0.8344 0.8570 
0.7698 0.8106 0.8210 0.8359 
TH5 
2 3 4 5 
0.7401 0.8007 0.8591 0.8729 
0.7238 0.7952 0.8470 0.8667 
0.7419 0.7739 0.8255 0.8996 
0.7361 0.7680 0.8137 0.8811 
TH6 
2 3 4 5 
0.7287 0.7728 0.8421 0.8899 
0.7207 0.7702 0.8388 0.8890 
0.7676 0.8272 0.8310 0.8485 
0.7533 0.8158 0.8237 0.8442 
TH7 
2 3 4 5 
0.7009 0.7765 0.8461 0.8914 
0.6941 0.7507 0.8422 0.8884 
0.7920 0.8189 0.8335 0.8628 
0.7823 0.8153 0.8266 0.8445 
TH8 
2 3 4 5 
0.7194 0.8192 0.8476 0.8777 
0.6839 0.8119 0.8426 0.8701 
0.7921 0.8213 0.8418 0.8550 
0.7907 0.8177 0.8356 0.8521 
5.3 Results of HHOCS algorithm using Otsu’ betweenclass variance
Segmented results of HHOCS algorithm using Otsu’s method is shown in Figure 6. Both the low contrast and high contrast visual features are retained. The quality of the output is implicit. The proposed method may attract radio physicists to use it as an additional tool for diagnosis.
Figure 6. Results of HHOCS algorithm using Otsu’s method
5.4 Experiment 2: Based on Kapur’s entropy
Optimal threshold values, obtained using HHOCS algorithm, are displayed in Table 7. Objective function values and PSNR values obtained from HHOCS and HHO methods using Kapur’s entropy are presented in Table 8. Profound differences are seen. It is observed that the suggested HHOCS method performs better than the HHO. Similarly, a significant improvement over the HHO algorithm is seen with respect to the PSNR values. The reason could be the enhanced exploitation capability of HHOCS algorithm to achieve the best solutions. Our method has shown consistently better PSNR values than HHO (see Table 8). The SSIM and FSIM values obtained from HHOCS and HHO algorithms using Kapur’s entropy are shown in Table 9. Interestingly, our method has shown better values (for the SSIM and FSIM) than the HHO.
Table 7. Threshold values of HHOCS
Images 
K 
HHOCS 



R 
G 
B 
TH1 
2 
227,234 
42,179 
233,252 
3 
190,229,255 
125,145,200 
51,71,189 

4 
132,137,187,247 
15,104,136,210 
32,42,141,233 

5 
98,115,202,203,212 
3,75,102,115,186 
25,112,158,188,232 

TH2 
2 
239,255 
106,206 
25,191 
3 
208,235,255 
16,132,247 
35,88,238 

4 
166,200,218,250 
141,216,245,251 
38,68,199,228 

5 
116,153,168,190,250 
98,103,177,200,215 
42,60,80,176,198 

TH3 
2 
221,227 
230,239 
186,255 
3 
126,230,244 
87,137,154 
21,33,131 

4 
129,156,204,223 
80,84,187,227 
126,190,222,227 

5 
104,138,143,228,255 
54,82,130,169,223 
16,36,58,205,238 

TH4 
2 
227,255 
47,120 
169,255 
3 
137,158,236 
82,121,254 
62,120,190 

4 
136,194,209,224 
51,57,80,249 
41,46,144,182 

5 
164,166,239,245,254 
5,51,59,114,118 
85,164,176,187,207 

TH5 
2 
236,249 
87,254 
44,148 
3 
189,203,255 
31,229,244 
191,219,233 

4 
188,202,219,253 
115,147,239,250 
3,40,132,252 

5 
99,160,176,197,250 
49,82,124,231,250 
70,85,109,133,226 

TH6 
2 
212,229 
45,117 
119,245 
3 
137,168,203 
115,129,218 
3,73,153 

4 
105,123,200,250 
77,92,138,250 
74,133,136,252 

5 
147,196,209,230,252 
19,35,66,133,164 
36,69,188,222,243 

TH7 
2 
250,252 
179,242 
178,243 
3 
215,220,254 
3,102,158 
126,150,157 

4 
104,184,237,246 
33,49,156,208 
5,68,117,245 

5 
150,151,200,209,251 
25,159,180,196,229 
9,31,34,106,191 

TH8 
2 
233,249 
251,252 
30,163 
3 
219,225,233 
14,142,219 
69,100,124 

4 
179,198,211,242 
35,63,83,129 
3,131,181,246 

5 
89,139,166,202,234 
26,79,102,114,251 
27,34,74,149,159 
Table 8. Comparison of objective function values and PSNR obtained from HHOCS and HHO algorithms using Kapur’s entropy


OBJECTIVE FUNCTION 
PSNR 

Image 
K 
HHOCS 
HHO 
HHOCS 
HHO 
TH1 
2 3 4 5 
25.3967 36.4699 42.8620 50.2350 
23.8390 34.0063 39.4868 48.4930 
48.8151 53.1784 55.0468 59.3109 
48.3047 52.8795 54.5950 58.2001 
TH2 
2 3 4 5 
25.8282 32.0311 40.5143 50.2481 
25.6571 31.2724 40.2226 48.3490 
53.1854 58.6532 62.7254 65.2311 
52.9000 58.1990 62.0969 65.6008 
TH3 
2 3 4 5 
26.7611 33.3907 41.5988 51.4126 
26.6938 32.1520 40.8171 50.8451 
50.1649 52.0191 56.6610 60.1033 
48.5777 51.0425 56.1281 59.7543 
TH4 
2 3 4 5 
26.8261 32.5919 37.2682 46.2737 
23.7504 31.6829 37.0698 46.1896 
53.8566 56.3193 61.9640 65.6875 
52.0168 55.2586 61.7853 65.5550 
TH5 
2 3 4 5 
27.6672 34.4082 40.0538 48.3672 
27.1914 34.3798 39.3762 47.7147 
50.1393 54.0606 58.6640 60.4075 
48.6514 53.9827 57.6439 59.3283 
TH6 
2 3 4 5 
26.9100 35.6760 44.2570 50.4478 
23.9546 33.8006 40.7154 50.3543 
50.3106 53.5330 62.0879 63.5159 
46.0928 51.0713 55.1715 63.5070 
TH7 
2 3 4 5 
25.7328 32.2351 41.8437 45.9847 
25.5387 32.1220 41.7025 45.5572 
50.1983 53.8161 58.3176 60.1012 
50.1500 53.1795 57.5759 59.5965 
TH8 
2 3 4 5 
25.8521 33.2082 40.5836 49.3672 
25.4122 32.3197 39.5286 49.3606 
48.1895 53.7797 58.8640 63.8921 
47.3364 53.6042 57.9005 63.8803 
Table 9. Comparison of SSIM and FSIM values from HHOCS and HHO algorithms using Kapur’s entropy


SSIM 
FSIM 

Image 
K 
HHOCS 
HHO 
HHOCS 
HHO 
TH1 
2 3 4 5 
0.6241 0.6707 0.8155 0.8571 
0.5798 0.6643 0.8028 0.8317 
0.6870 0.7283 0.7510 0.7849 
0.6632 0.7103 0.7496 0.7835 
TH2 
2 3 4 5 
0.5481 0.7343 0.7836 0.8283 
0.4899 0.6783 0.7482 0.8315 
0.7122 0.7438 0.7630 0.7782 
0.7084 0.7417 0.7583 0.7992 
TH3 
2 3 4 5 
0.5980 0.7112 0.7358 0.8388 
0.5208 0.6878 0.7033 0.8058 
0.6772 0.7294 0.7668 0.7705 
0.6623 0.7228 0.7655 0.7765 
TH4 
2 3 4 5 
0.5191 0.7289 0.7478 0.8016 
0.5160 0.6951 0.7266 0.7959 
0.7124 0.7456 0.7621 0.7926 
0.7100 0.7425 0.7617 0.7878 
TH5 
2 3 4 5 
0.6818 0.7089 0.7416 0.8283 
0.5718 0.6686 0.7132 0.8208 
0.6790 0.7141 0.7284 0.7311 
0.6773 0.6978 0.7165 0.7298 
TH6 
2 3 4 5 
0.4988 0.6538 0.7238 0.7364 
0.4164 0.5617 0.6815 0.7157 
0.7221 0.7579 0.7994 0.8185 
0.6941 0.7565 0.7879 0.8237 
TH7 
2 3 4 5 
0.4523 0.6513 0.7897 0.7911 
0.4510 0.5336 0.6850 0.7208 
0.7920 0.8193 0.8335 0.8628 
0.7823 0.8189 0.8266 0.8445 
TH8 
2 3 4 5 
0.4331 0.6004 0.7162 0.7819 
0.3654 0.4711 0.5864 0.6146 
0.7909 0.8213 0.8418 0.8550 
0.7921 0.8177 0.8356 0.8521 
Figure 7. Results of HHOCS algorithm using Kapur’s entropy
Segmented results of HHOCS algorithm using Kapur’s entropy is shown in Figure 7. Both the low contrast and high contrast visual features are retained.
From this study, it is believed that the 1D Otsu’s between class variance method outperforms 1D Kapur’s entropy based technique. Because, infrared images, mostly have low contrast features. Therefore, between class variance helps us to compute optimal threshold values for separating different classes. It seems that the between class variance information is more than the entropy information in thermograms. In summary, the suggested multilevel colour image thresholding technique is useful for thermogram image analysis.
Unlike early multilevel thresholding method reported in the breast thermogram analysis, based on the graylevel images, the suggested method uses R, G, B colour components. The suggested technique is useful for the breast thermogram analysis. Results using the colour images may assist the clinicians, as an extra support, in the breast thermogram analysis. Nevertheless, the proposed HHOCS optimizer helps us to compute optimal values for colour image thresholding. The exploitation capability of the HHO is enhanced, because the exploitation feature of CS is integrated in the system. Profound differences are observed while studying the convergence curves presented in this paper. The suggested HHOCS performs better than both the HHO and CS optimizers. The speed of convergence is implicit (see Figure 3). The method has shown its ability to extract both the low and high resolution visual features, because all three colour components are used. The quality of the visual results is explicit (from Figure 6, 7). From Tables 46, it is observed that the RGB components based thresholding method using Otsu’s objective function is better than the Kapur’s entropy based approach; the reason is that the former fitness function could preserve more details. Therefore, the suggested RGB component based method using Otsu’s between class variance may be suitable for pathological investigations. To figure out other merits, our method is faster and more accurate. It is reiterated that the proposed technique may attract the use of low cost and portable infrared cameras for analysis of breast thermograms. The proposal would be useful for analysis of other infrared images together with a clinical study. It is also believed that the suggested HHOCS optimizer would be useful for function optimization to solve real world engineering problems.
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