**4. Experimental Results and Discussion**

The proposed method was implemented in the language of MATLAB 2014b on a personal computer with a 2.30 GHz CPU and 8.00 GB RAM on a Windows 8 operating system. To assess the quality of the proposed technique, public databases were utilized to extract features based on Gabor filter with several orientations and frequencies, as described in this section.

#### *4.1. Databases Description*

To evaluate the performance of the proposed texture classification method optimized by HALO, three public texture databases were used in the experiment. The first database CGT [37] offers digital pictures of all sorts of materials with the pictures of fabric, wood, metal, bricks, plastic, and these texture images can be used for graphic design and visual effects. In the experiments, 18 homogeneous texture images from the database were as shown in Figure 2, all chosen texture images without any rotation and 10 images for each class were utilized as training samples, while the other 50 images were used as testing samples.

**Figure 2.** Samples of the 18 categories randomly selected from the CGT database.

The second database Kylberg [38] was imaged under only one light setting from one direction on the same distance. Textured surfaces are arranged, such as oatmeals, linseeds, lentils, the texture samples with the same category have 12 different angles of rotation with 30 degrees increment. In the experiments, 20 homogeneous texture images from the database were as shown in Figure 3, and images without any rotation were utilized as training samples with the number per category set as 15, and 60 images with other angles of rotation per category were used as testing samples.

**Figure 3.** Samples of the 20 categories randomly selected from the Kylberg database.

The third database is Brodatz [39] with different background intensities, and the figure below gives an example of 40 different texture features organized into 5 columns. For example, D6 has a black background, whereas D10 has gray and white backgrounds, and D101 is a regular texture, whereas the texture type of D111 is irregular. In the experiments, 30 homogeneous texture images from the database were as shown in Figure 4, all of the images were rotated with a 20◦ step, images with 20◦ rotation were utilized as training samples with the number set as 6 for each class. The rest of the 48 images were utilized as testing samples.

**Figure 4.** Samples of the 30 categories randomly selected from the Brodatz database.

### *4.2. Parameters Setting for Different Algorithms*

As detailed in Section 2, the optimization ability does not rely on any parameter settings in HALO, thus it is prevented from becoming trapped in the local optimal solution to a great extent. In addition, some commonly used swarm intelligence algorithms, such as PSO algorithm [40], DE algorithm [41], CS algorithm [42] and gray wolf optimizer (GWO) [43], were used for an intuition comparison between the optimization abilities. All of these algorithms are based on hybrid decimal and binary coding. Moreover, other types of Gabor filter were used for further comparison. For a relatively fair comparison, the number of function evaluations was used as the terminal criterion; that is, all algorithms stopped when the iteration number reached 20 combined with part of experimental results as the fitness value

did not improve, and all algorithms performed 30 independent operations. Our primary interest was the integrated optimization of parameters and features of Gabor filter, and this was shown by the fitness value of the objective function and the classification accuracy for the testing samples in each database. Table 1 shows the parameter settings of the above algorithms.


**Table 1.** Parameter settings for different algorithms.

#### *4.3. Experiments for Different Swarm Intelligence Algorithms*

A preliminary test of the proposed texture classification approach on three public texture databases, namely CGT, Kylberg, and Brodatz, was conducted, as described here. The size of the training samples was extracted as 128 × 128 with different angles of rotation. In Table 2, *Fiv* is the average fitness value calculated by Equation (11) using the integrated optimization for each filter bank handled by different swarm intelligence algorithms, and *Fn* and Time, respectively, indicate the selected number of features and CPU time, on average, for each training process.


**Table 2.** Result of different algorithms for public texture databases.

As shown in Table 2, the average fitness value using the proposed method was the highest for all databases, proving that the optimization ability of HALO was superior to that of PSO, DE, CS, and GWO. The discrimination ability of each category was enhanced since the fitness value exceeded 16. More importantly, the process of ALO is based on the hunting behavior of antlions and has no parameters to be set. Hybrid decimal and binary encoding qA utilized to conduct integrated optimization of the parameters and features of Gabor filter; this strategy improved the exploitation ability compared with the use of only one ant encoding. Moreover, the selected number of features was the lowest among all of the algorithms involved: the number was higher than 20 for the CGT and Kylberg databases using PSO and DE algorithms, and HALO abandoned more than 50% of the redundant features from Gabor filter. From the aspect of operating efficiency, HALO had a faster convergence rate because it had fewer multiplications compared with the other algorithms. The difference in CPU time reached 0.7 s for the Kylberg and Brodatz databases, and HALO only needed

10.6732 s to select the best feature subset by obvious distinction for the CGT database. Overall, it can be deduced that the optimization ability and operating efficiency are improved by using HALO, which has the desired adaptability to obtain suitable parameters and features of Gabor filter.

#### *4.4. Application for Texture Classification*

Next, each texture sample was classified by using the optimal parameters and features of Gabor filter. Figures 5–7 indicate the difference in the average eigenvalues between the training and testing samples for the categories with the highest classification accuracy using the selected parameters and features of Gabor filter. Tables 3–5 show the classification accuracy using the newly proposed Log-Gabor filter [44], DS-Gabor filter [18], the only parameter optimization-based Gabor (OP-Gabor) filter, and the proposed method. In the tables, OA and Kappa are the overall classification accuracy and Kappa coefficient, respectively, obtained by using different texture classification methods. The Kappa coefficient is defined below:

$$k = \frac{P\_o - P\_c}{1 - P\_c} \tag{12}$$

where *Po* is the relative observed agreement, and *Pe* is the hypothetical probability of chance agreement.


**Table 3.** Overall classification accuracy and Kappa coefficient for CGT database.

**Table 4.** Overall classification accuracy and Kappa coefficient for Kylberg database.



**Table 5.** Overall classification accuracy and Kappa coefficient for Brodatz database.

**Figure 5.** Difference of average eigenvalues between training and testing samples for CGT database.

**Figure 6.** Difference of average eigenvalues between training and testing samples for Kylberg database.

Tables 3–5 reveal that the classification accuracy was increased, with a difference of more than 2%, by removing some redundant features of Gabor filter. In addition, more than 40 samples were misclassified for the Kylberg database. Although the classification accuracy for the Leather, Road, and Wood classes in the CGT database was relatively high, misclassification still had a certain influence on the overall process. Moreover, the Kappa coefficient was more than 0.93 for all databases, illustrating that the precision could adapt to a number of application demands. The difference in the average eigenvalues between the training and testing samples was lower than 0.03, and the change trend was similar to that shown in Figures 5–7, thus proving the discriminability and identity of each Gabor filter. The overall classification accuracy of the Log-Gabor filter and DS-Gabor filter was unsatisfactory: it was lower than 85% for the CGT database and only 86.56% and 82.58%, respectively, for the Kylberg

database. With these two methods, very few samples were correctly classified for the Wheel, Brick, Sand, and Stone slab categories, thus it was difficult for them to extract texture features from the whole database. In brief, the proposed approach is a reliable, efficient, and reasonable method for texture classification.

**Figure 7.** Difference of average eigenvalues between training and testing samples for Brodatz database.

#### **5. Conclusions**

This paper details a texture classification method based on the integrated optimization of the parameters and features of Gabor filter using HALO. Three public texture databases with different types of texture features were utilized for its evaluation. The experimental results were firstly compared with those of some commonly used swarm intelligence algorithms, such as PSO, DE, CS, and GWO. In general, it was demonstrated that swarm intelligence algorithms are well coded to solve parameter optimization and feature selection problems at the same time. Among them, HALO with hybrid binary-decimal coding has great optimization ability, and its fitness value is distinctly higher than that of the other algorithms. Thus, the proposed method is more appropriate for texture classification, and it is fast enough to meet real-time application needs. Moreover, for a more comprehensive comparison, Log-Gabor, DS-Gabor filter, and the only parameter optimization-based Gabor filter were also utilized. It was observed that the proposed texture classification method is robust, and the classification accuracy is satisfactory for multi-classification problems, especially those based on texture features. In sum, the multi-orientation and multiscale nature of Gabor filter can enhance the discrimination of texture features. Further, the disadvantage of high time complexity can be overcome to a great extent with HALO. The proposed texture classification method has an excellent balance between efficiency and accuracy, making it a good candidate to deal with practical applications. In the future, we will collect some geological texture samples and use them for the classification of more texture features.

**Author Contributions:** M.W. methodology; L.G. validation; X.H. formal analysis; Y.J. investigation; X.G. writing.

**Funding:** This work was funded by the National Key Research & Development Program of China under Grant No. 2017YFC1502406-03; the National Natural Science Foundation of China under Grant No. U1711266; and the Open Fund of State Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University under Grant No. 18R04.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

### **References**


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