A novel hybrid approach of ABC with SCA for the parameter optimization of SVR in blind image quality assessment

Abstract

Images may be distorted to different degrees in the process of acquisition, transmission, and reconstruction, which is not conducive to the perception and recognition of the human eye. Therefore, it is necessary to reasonably quantify the image quality through image quality assessment. This enables people to correctly understand the image content. In practical applications, blind image quality assessment (BIQA) has attracted widespread attention in the field of image processing because it can evaluate the image itself without any prior knowledge. Support vector regression (SVR) is widely adopted in the field of BIQA, which is one important step in many BIQA methods based on a two-step framework that contains feature extraction and SVR. However, the parameters of SVR greatly affect its predictive performance and generalization ability. Therefore, grid search (GS) is usually utilized to select the appropriate parameters of SVR in the field of BIQA. However, GS may cause the omission of potential solutions when searching the best parameters of SVR, degenerating the performance of SVR. To search the promising parameters of SVR, a novel meta-heuristic algorithm named hybrid artificial bee colony and sine cosine algorithm (ABC-SCA) is proposed. Besides, a feasible scheme for SVR parameter selection is given to further improve the prediction accuracy of the BIQA algorithm. The proposed SVR parameter selection algorithm is compared with GS and several other meta-heuristic algorithms on the three image databases (LIVE, TID2013, and CSIQ) with three BIQA schemes. The experimental results show that the proposed ABC-SCA can effectively obtain the optimal parameters of SVR in the field of BIQA.

Appendix of “A novel hybrid approach of ABC with SCA to optimize parameters of blind image quality assessment based on SVR”

1.1 Part I. Details of benchmark functions and performance evaluation index

1.1.1 Details of CEC2013 benchmark functions

The CEC2013 is executed to systematically appraise the performance of ABC-SCA. The CEC2013 contains 28 benchmark functions [46] including the complex shifted or shifted rotated benchmark functions listed in Table 11. Functions $F_{1} {-}F_{5}$, functions $F_{6} {-}F_{20}$, and functions $F_{21} {-}F_{28}$ belong to unimodal, multimodal, and composition functions, respectively. They are executed to evaluate the diverse algorithms in extremely complex cases.

Table 11 The complicated function test suite includes 28 extremely complex CEC2013 benchmark functions; for each function, both its initialization and search range are located in [− 100, 100]^D; D and $F_{\min }$ [x*] are the dimension number and the minimum value for each function, detailed in [46]

1.1.2 Performance evaluation index

The error mean value (Mean) and the standard deviation value (Std) are two commonly adopted indicators for evaluating the performance of the meta-heuristic algorithm. For each benchmark function, the smaller the Mean, the better the performance of the algorithm; if the Mean value is the same, the smaller the Std, the better the performance of the algorithm. The two indicators are calculated as follows:

$${\text{Mean}} = \mathop \sum \limits_{i = 1}^{{{\text{runs}}}} \frac{{\left[ {F_{i} \left( x \right) - F_{\min } \left( {x^{*} } \right)} \right]}}{{{\text{runs}}}}$$

(20)

$${\text{Std}} = \sqrt {\frac{{\mathop \sum \nolimits_{i = 1}^{{{\text{runs}}}} \left[ {F_{i} \left( x \right) - {\text{Mean}}} \right]^{2} }}{{{\text{runs}} - 1}}}$$

(21)

where $i = 1,2, \ldots ,{\text{runs}}$ represents the number of operations on the benchmark function; $F_{i} \left( x \right)$ represents the best fitness value obtained by the algorithm; $F_{\min } \left( {x^{*} } \right)$ represents the global optimum fitness value.

1.2 Part II. Parameters setting of ABC-SCA algorithm

The proposed ABC-SCA mainly contains three uncertain parameters: ${\upomega }$, ${\text{limit}}$, and $a$. The parameter ${\upomega }$ is employed to balance the exploration and exploitation in the iterative search process; the parameter ${\text{limit}}$ is utilized to preset the maximum number of stagnation times that allow the global optimal value to stagnate; the parameter $a$ is employed to control the range of the parameter $r_{1}$. The ABC-SCA will show different performance with different parameter pairs. To ascertain the appropriate values of three parameters, ABC-SCA is executed on CEC2013. The algorithm runs 30 times on 28 benchmark functions of CEC2013, the algorithm’s population size is set to 50, and the maximum number of iterations is set to 6000. Tables 12, 13 and 14 give the experimental results involving mean error and standard deviation values for three different parameters in different scenarios. In  Tables 12, 13 and 14, the optimal result are highlighted in bold.

Table 12 Comparisons among different settings of $\omega_{0}$ with ${\text{limit}} =$ 700 and $a =$ 1 being unchanged

Table 13 Comparisons among different settings of limit with ${\varvec{\omega}}_{0} =$ 0.6 and $a =1$ being unchanged

Table 14 Comparisons among different settings of $a$ with $\omega_{0} =$ 0.6 and $a =$ 1 being unchanged

1.2.1 Comparisons among different settings of ${\varvec{\omega}}_{0}$

In this experiment, we set the parameter ${\text{limit}} = 700$, the parameter $a = 1$, and experimented on the parameters $\omega_{0} = 0.5,0.6,0.7$ and $0.8$, respectively. Table 12 gives the corresponding experimental results, and the best results are bold italics. Table 12 shows that ${\upomega } =$ 0.6 gives better overall performance for ABC-SCA on CEC2013 compared with $\omega_{0}$ = 0.5, 0.7 and 0.8.

1.2.2 Comparisons among different settings of limit

In this experiment, we set the parameter $\omega_{0} = 0.6$ the parameter $a = 1$, and experimented on the parameters ${\text{limit}} = 500,600,700$, and $800$, respectively. Table 13 gives the corresponding experimental results, and the best results are bold italics. Table 13 shows that ${\text{limit}} =$ 700 gives better overall performance for ABC-SCA on CEC2013 compared with ${\text{limit}}$ = 500, 600 and 800.

1.2.3 Comparisons among different settings of ${\varvec{a}}$

In this experiment, we set the parameter $\omega_{0} = 0.6$ the parameter ${\text{limit}} = 700$, and experimented on the parameters $a = 1,2,3$ and $4$, respectively. Table 14 gives the corresponding experimental results, and the best results are bold italics. Table 14 shows that ${\text{a}} =$ 1 gives better overall performance for ABC-SCA on CEC2013 compared with $a$ = 2, 3 and 4.

It can be seen from the experimental results that the ABC-SCA has the best performance when ${ }\omega_{0} = 0.6$, ${\text{limit}} = 700$, and $a = 1$. Therefore, the set of parameters ($\omega_{0} = 0.6$, ${\text{limit}} = 700$, and $a = 1$) are recommended on CEC2013. In particular,, due to $a =$ 1, $r_{1}$ is linearly decreasing between 1 and 0.

1.3 Part III: experimental comparisons with four meta-heuristic algorithms

To verify the performance of the proposed ABC-SCA algorithm, the ABC-SCA is compared with four meta-heuristic algorithms: ABC [47], SCA [44], PSO [48], and ABCGLN [49] on CEC2013. We run each algorithm on each benchmark function 30 times, each algorithm’s population size is set to 50 (The population size of ABCGLN is consistent with the original text.), and the maximum number of iterations is set to 6000.

On CEC2013, the error mean value and the standard deviation value of the 28 functions of the five algorithms are listed in Table 15. For 28 functions, the optimal results of the five algorithms are bold .

Table 15 Comparison of ABC-SCA and four meta-heuristic algorithms on CEC2013

We compared the performance of ABC-SCA with the four meta-heuristic algorithms ABC, SCA, PSO, and ABCGLN on CEC2013. The performance of the five algorithms in the unimodal functions, the multimodal functions and the composition functions are analyzed.

In the performance of the unimodal functions, ABC-SCA ranks first on $F_{1} ,F_{2} ,{ }F_{5}$ and ranks second on $F_{3} ,F_{4}$. ABC ranks third on $F_{1} ,F_{3} ,F_{5}$, and fourth on $F_{2} { },F_{4}$. SCA ranks fifth on $F_{1} ,F_{2} { },F_{3} ,F_{5}$, and third on $F_{4}$. PSO ranks first on $F_{3} ,F_{4}$, second on $F_{1} ,{ }F_{5}$, and third on $F_{2}$. ABCGLN ranks second on $F_{2}$, fourth on $F_{1} ,F_{3} ,F_{5}$, and fifth on $F_{4}$. Therefore, for unimodal functions, ABC-SCA is superior to the other four algorithms. For the final ranking of all unimodal functions performance, ABC-SCA, PSO, ABC, ABCGLN and SCA are first, second, third, fourth and fifth, respectively.

In the implementation of the multimodal functions, ABC-SCA ranks first on the six functions $F_{8} ,F_{11} { },F_{14} ,F_{15} ,F_{16}$. It only performed poorly on $F_{12}$, ranking fourth. According to the results in Table 15, the final rank of ABC-SCA, ABC, PSO, ABCGLN and SCA on all multimodal functions is first, second, third, fourth and fifth, respectively. Therefore, the overall performance of ABC-SCA in solving the problem of the multimodal functions is relatively good.

In the performance of the composition functions, ABC-SCA ranks first on $F_{21} ,F_{23} { },F_{26}$, and third on $F_{22}$. The other four functions rank second. According to the results in Table 15, the final rank of ABC-SCA, ABCGLN, ABC, PSO and SCA on all composition functions isfirst, second, third, fourth and fifth, respectively.

1.4 Part IV: the details of image databases

To measure the performance of image quality assessment (IQA) algorithms, many organizations and researchers have created multiple IQA databases that contain a series of images and their corresponding human subjective scores. Human subjective scores are expressed with mean opinion score (MOS) or differential mean opinion score (DMOS). A larger MOS indicates better image quality; otherwise, the image quality is worse. DMOS is the opposite of MOS. When constructing the database, each high-quality original image is employed as a reference image, simulated distortion is introduced into the reference image. Then, all images are subjectively scored, and a database containing various distorted images and their subjective scores is obtained. The commonly added simulated distortions are the common Gaussian blur (GB), additive white Gaussian noise (WN), JPEG2000 compression (JP2K), and JPEG compression (JPEG). The most commonly utilized databases for measuring the performance of IQA algorithms are LIVE [51], CSIQ [52], and TID2013 [53], which are three traditionally synthetically distorted image databases. The reference images in the three image databases are corrupted by a single type of distortion, and each simulated distortion is introduced into the reference image in different magnitudes. The three databases are described in detail as follows:

1.4.1 LIVE

The LIVE database contains 29 reference images with an image resolution ratio ranging from 634 pixels $\times$ 438 pixels to 768 pixels $\times$ 512 pixels. These reference images are degraded with five types of distortions: GB, WN, JP2K, JPEG, and FF, resulting in a total of 779 distortion images. The human subjective score of the image is given in the range [0, 100] with the form of DMOS. More details can be found in [51].

1.4.2 CSIQ

The CSIQ database contains 30 reference images with an image resolution ratio is 512 pixels $\times$ 512 pixels. These reference images are degraded with GB, WN, JP2K, JPEG, pink Gaussian noise (PGN), and global contrast decrements (GCD). Each distortion type has 4 or 5 different levels, resulting in a total of 866 distortion images. The human subjective score of the image is given in the range [0, 1] with the form of DMOS. More details can be found in [52].

1.4.3 TID2013

The TID2013 database is an upgraded version of the TID2008 database that adds seven new distortion types to the TID2008 database. The TID2013 database contains 25 reference images with an image resolution ratio is 512 pixels $\times$ 384 pixels. These reference images are degraded with 24 types of distortion. Each distortion type has 5 different levels, resulting in a total of 3000 distortion images. The human subjective score of the image is given in the range [0, 9] with the form of MOS. The 24 distortion types are: T01 WN; T02 WN in color components is more intensive than WN in the luminance component; T03 spatially correlated noise; T04 masked noise; T05 high-frequency noise; T06 impulse noise; T07 quantization noise; T08 GB; T09 image denoising; T10 JPEG; T11 JPEG2000 transmission errors; T14 non-eccentricity pattern noise; T15 local block-wise distortions of different intensities; T16 mean shift (intensity shift); T17 contrast change; T18 change of color saturation; T19 multiplicative Gaussian noise; T20 comfort noise; T21 lossy compression of noisy images; T22 image color quantization with dither; T23 chromatic aberrations; T24 sparse sampling and reconstruction. More details can be found in [53].

The range or change trend of human subjective scores in different image databases is not exactly the same. For example, in the image database, some human subjective scores range are [0, 1], some are [0, 9], and others are [0, 100]. To maintain the consistency of the calculated indicators and avoid the occurrence of numerical problems, the human subjective scores in all image databases are normalized to [0,100].