1. Introduction
Image Segmentation is a key component of various computer vision applications. It aims to divide a given image into perceptual regions, in which pixels in each region belong to a same visual object with small feature variations. Image segmentation approaches have been widely implemented in various applications, such as object detection [
1,
2], remote sensing images [
3,
4], medical images [
5], agriculture image [
6] and many other applications.
One of the most effective segmentation methods is called superpixel segmentation, which implements an over-segmentation on input images. The process of superpixel segmentation is to divide a given image into small, compact and regular regions, that contain pixels with similar texture, spatial positions brightness, color, and so on [
7]. In contrast to other segmentation approaches, in general superpixel has strong boundary coherence and it is easy to control the produced segments [
7]. Therefore, superpixel segmentation approach has received wide attentions and have been adopted in different applications, such as object tracking [
8,
9], boundary detection [
10], object detection [
11], and others [
12,
13,
14,
15,
16].
Earlier, various methods have been adopted for image segmentation with superpixels. Levinshtein et al. [
17] proposed a geometric flow algorithm depending on the local gradient of the image to initiate superpixels with uniform sizes and compactness. In [
18], a method called USEQ was proposed for superpixel extraction. The spatial and color information were utilized to represent pixels and superpixels, and to reduce computational cost. After that they adopted a maximum posteriori estimation to generate superpixels. Di et al. [
19] proposed a superpixel image segmentation method using a hierarchical multi-level segmentation scheme. They applied simple liner iterative clustering approach to segment the input image, and then they applied simple liner iterative clustering to further segment the generated superpixels. Finally, adjacent superpixels are merged depending on probability distribution similarity. More so, different images were considered to evaluate the proposed method, including Berkeley and 3Dircadb datasets. In literature, different machine learning and deep learning approaches have been adopted with superpixels for image segmentations. For example, in [
20], superpixels method based on the unsupervised learning technique was employed for oropharyngeal cancer image segmentation. Mi and Chen [
21] presented a superpixel-enhanced Deep Neural Forest (DNF) for semantic segmentation of remote sensing images. The DNF was developed to enhance classification accuracy, and a Superpixel-enhanced Region Module was developed to reduce noise. Huang and Ding [
22] developed a generic image segmentation algorithm using the properties of a fully convolutional network and superpixels. Most recently, metaheuristic optimization algorithms also have been adopted in a few studies for superpixel segmentation, and they showed prominent performance. For example, Mittal and Saraswat [
23] applied a modified gravitational search algorithm with superpixel clustering for nuclei segmentation. Moreover, Chakraborty and Mali [
24] proposed superpixel based image segmentation for COVID-19 CT scan images using a modified flower pollination algorithm (FPA) with type 2 fuzzy clustering.
In general, the superpixel image segmentation based on clustering techniques have been established their performance in comparison with the other image segmentation methods. However, the main drawbacks of these clustering image segmentation method is the process of determine the number of clusters and their cluster centers. To tackling this limitation, several automatic clustering image segmentation have been developed. For example, the automatic fuzzy clustering method is presented in [
25]. It is depends on using Density peaks clustering (DPC) to determine the number of clusters. In, authors presented a robust self-sparse fuzzy clustering and applied it to segmented the image using clustering techniques. These methods provided results better than those methods that required to determine the number of clusters.
However, these methods have some limitations that influence on its quality and still require more enhancements. For example, they are use the traditional DPC that depends on the linear generalized extreme value (GEV) distribution [
26] to determine the cluster center. This traditional GEV is not more accurate since the estimation of the distribution based on extracted blocks maxima, considered by this approach, involves a loss of information.
Therefore, this motivated us to propose an alternative clustering method based on modified DPC using q-Generalized Pareto distribution under linear normalization (q-GPDL). In addition, using the Hunger Games Search (HGS) [
27] to determine the cluster centers. HGS was inspired by the social animals’ characteristics in searching for food. For each iteration, the HGS searches for an optimal location, similar to animals forage, and hunger values or weights simulate the impact of animals’ hunger. It was evaluated with different optimization problems, and it achieved prominent performance compared to other swarm intelligence and MH algorithms.
In this study, we propose superpixel-Based automatic clustering method for color image segmentation. The developed method, named ASCQPHGS, starts by applying superpixel algorithm to presegmented the image. Followed by using the modified DPC based on GEVL to automatic determine the number of clusters. Then, the HGS generates a set of solutions and each of them represents the clustering centers. To evaluate the quality of each solution, the fitness function that uses CS-index is computed and the best of them is determined. The next process is to update the solutions using the operators of HGS and check the stop conditions and in case they are met then the best solution is used to segmented the image and compute the performance measures.
Therefore, the summary of the main contributions and novelty of this study are:
Proposed an superpixel-based automatic clustering method and applied it for color image segmentation.
Present an extension for Generalized Pareto distribution under linear normalization (GPDL), named q-GPDL. In addition, deduce its quantile function and estimate its parameters using Maximum Likelihood Estimation.
Improve the behavior of DPC by using q-GPDL.
Apply Hunger Games Search (HGS) as clustering method to determine the center of each cluster then segmented the image.
Evaluate the performance of the developed method using real-world datasets and compared it with other MH techniques and state-of-the-art methods.
The rest of this study is introduced as: In
Section 2, preliminaries of Clustering problem formulation for image segmentation, q-Generalized Pareto distribution under linear normalization, and Hunger Games Search are introduced.
Section 3 presents the proposed automatic superpixel clustering method for color image segmentation, and
Section 4 introduces the comparison results and discussion of the developed method with other methods.
Section 5 presents the conclusion and future work of this study.
4. Experimental and Results
To evaluate the performance of the developed method, a set of different MH techniques are used in the comparison. For example, Slime mould algorithm (SMA) [
33], Barnacles mating optimizer (BMO) [
34], atom search optimization (ASO) [
35], ASO based on particle swarm optimization (ASOPSO) [
36], Hunger games search (HGS) [
37]. In addition, the automatic fuzzy clustering framework (FCM) [
25], and Density Peaks clustering (DPC) [
29]. In addition, we compare the results of developed method with the modified version of FCM and DPC using the QGEV and this modifications given as FCMQGPDL and DPCQGPDL, respectively. The parameter setting of these algorithms depends on the original implementation of each of them. In addition, there are three parameters for FCM namely maximal number of iterations (is 50), minimal error threshold (
) and the weighting exponent (is 2).
4.1. Datasets Description
Within this section, we used two real-world dataset images to assess the performance of the developed method. The images in the first dataset are collected from Berkeley segmentation dataset and benchmark (BSDS500) [
38]. These images are divided into testing and training sets which consists of 200 and 300 images, respectively each of them has size 481 × 321. An example of BSDS500 is given in
Figure 2 shows an example of four images from this type of images. Moreover, there is a set of ground truth for each image variant from four to nine and each of these ground truth is obtained by one human subject. The Stanford background dataset (SBD) [
39] is the second dataset and it contains 715 images which represents an outdoor images.
Figure 3 shows an example of four images from this type of images. In these images, there are objects with vague foreground boundaries, multiple foreground objects and the accommodation of detailed background regions in ground truth segmentations. This makes these images are more challenging when applied to evaluate the superpixels segmentation methods.
4.2. Performance Metrics
A set of performance metrics are used to measure the quality of the competitive segmentation approaches. These metrics are probabilistic rand index (PRI), the variation of information (VI), the global consistency error (GCE), and the boundary displacement error (BDE) [
40]. The definition of these metrics are given in the following:
probabilistic rand index (
): It computes the the similarity of labels and it is applied to compute the classification of pixel-wise.
where
and
denote the event that pixels
i and
j have the same label and its probability.
variation of information (
): is applied for clustering comparison and it depends on the distance of the conditional entropy between results of two clusters.
where
and
are the conditional entropies.
global consistency error (GCE): It measures the global error between two segmented images that are mutually consistent.
boundary displacement error (BDE): It computes the average of the displacement error of pixels between two segmented images.
In general, the algorithm that provides higher PRI with low value of VOI, BDE, and GCE is considered the best one.
4.3. Results and Discussion
The comparison results between the developed method and other methods using BSDS500 are given in
Table 1. It can be observed that the developed HGS provides better results than other methods in terms of performance measures. In terms of RI, VOI, and BDE, the ASOPSO allocates the second rank, followed HGS, which provides results better than other MH techniques. However, the BMO provides better results than other MH methods in terms of GCE.
Moreover, the comparative results of the developed HGS with other models using SBD dataset are given in
Table 2. One can be seen from these results that HGS provides better results in terms of RI, VOI, and BDE. However, the FCM based on QGEV provides results better than other methods in terms of GCE.
Figure 4 depicts the average of the developed method and other methods among the tested two real-world images datasets. From these results it can be seen that the developed ASCQPHGS image segmentation method provides better average among the two datasets in terms of all performance measures.
For further analysis the performance of the developed method, the non-parametric Friedman test is applied to the obtained results. This test is used to determine if there is a significant difference between ASCQPHGS and other algorithms or not. This decision is taken based on the p-value obtained by Friedman test and in case of the p-value is less than 0.05, then there is a significant difference. Otherwise (i.e., p-value > 0.05), this indicates there is no a significant difference between ASCQPHGS and competitive algorithms.
Table 3 depicts the mean rank obtained by Friedman test for each algorithm over the two tested datasets (i.e., SBD and BSD500). It can be observed from these results that the developed ASCQPHGS has the largest mean rank in terms of RI, and smallest mean rank in terms of VOI, GCE, and BDE. In addition, ASOPSO allocates the second rank in terms of RI, followed by modified version of FCM (i.e., FCMQGPDL). Meanwhile, in terms of VOI, each of SMA and ASO allocates the second rank, followed by DPCQGPDL and ASOPSO. In terms of GCE, FCM, BMO, and SMA allocate the second, third, and fourth rank, respectively. Finally, the FCMQGPDL, ASOPSO, and DPCQGPDL acheive the second, third, and fourth rank, respectively.
Figure 5 and
Figure 6 depict the segmentation of
and
from BSDS500 and BSD datasets. It can be seen from this segmentation, the high ability of the developed method to split the objects inside the image. In addition, the influence of q-GPDL is better than other traditional GEV.
4.4. Comparison with Literature Works
The results of the ASCQPHGS method is compared with a set of well-known superpixel cluster methods that have been applied to segmented the BSDS500 dataset. The methods including FCM [
41], Superpixel-based fast FCM (SFFCM) [
31], Significantly fast and robust FCM (FRFCM) [
42], Neighbourhood weighted FCM (NWFCM) [
43], Adaptive FCM based on local noise detecting (NDFCM) [
44], A fuzzy clustering approach toward hidden Markov random field models for enhanced spatially constrained (HMRF-FCM) [
45], fast and robust FCM algorithms incorporating local information (FGFCM) [
46], A robust fuzzy local information C-means clustering (FLICM) [
47], A possibilistic FCM (PFCM) [
48], General type-2 FCM for uncertain fuzzy clustering (MSFCM) [
49], FCM with local information and kernel metric (KWFLICM) [
50], A novel type-2 FCM (AWSFCM) [
51].
Table 4 shows the comparison between the results of developed method and the collected results of other literature works. From these results, we observed that the developed ASCQPHGS has better results than other methods in terms of performance measures. The main reason of this high quality of the developed ASCQPHGS is combining the behaviour of superpixel algorithm that leads to decrease the computational time and memory requirements. As well as, using the modified version of DPC based on Generalized Extreme Types Under Linear Normalization (GEVL).
5. Conclusions
In this paper, an alternative color image segmentation method has been developed. This method depends on using the superixel algorithm to reduce the memory requirements. In addition, to determine the number of clusters, a modified version of density peak clustering algorithm has been introduced based on a definition of Generalized Pareto distribution under linear normalization (GPDL), named q-GPDL. This distribution avoid the limitations of traditional generalized extreme value that used in DPC. Finally, to determine the cluster centers, the Hunger Games Search has been used since it has high ability to explore the search space which leads to enhance the convergence towards the optimal solution. The comparison results between the developed method and other methods based on metaheuristic techniques have been conducted using two real image datasets named BSDS500 and Stanford background dataset (SBD). These results provide evident about the superiority of the developed method over either the MH techniques or the state-of-the-art methods.
Besides, the developed method can be applied in future to different clustering-based image segmentation problems. In addition, it can be extent as multi-objective clustering optimization problems. Also, it can applied to different applications such as remote sensing, medical image classification and others.