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Classification of galaxy color images using quaternion polar complex exponential transform and binary Stochastic Fractal Search

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Abstract

Galaxies’ studies play an important role in the astronomic. Accurate classification of these galaxies enables scientists to understand the formation and evolution of the Universe. During the last decades, there have been several methods applied to classify the galaxy images. However, these methods encounter three big challenges. First, most existing methods converted the color images of galaxies into gray images which result in losing the essential color information. Second, the utilized feature selection methods, that used to remove the irrelevant features, may be stuck at the attractive local point. Third, using an irrelevant classifier could lead to decrease the classification accuracy. In this paper, a new algorithm is proposed to classify color images of galaxies. In this algorithm, highly accurate non-redundant color features are extracted from the color images of galaxies by using the quaternion polar complex exponential transform moments (QPCET). The quaternion representation deals with a color image in a holistic way which keeps the correlation between components and then successfully represents the color images. The QPCET moments are highly accurate, noise resistant, and numerically stable. Moreover, these moments are invariants with respect to rotation, scaling and translation (RST). These characteristics assure the excellency of the extracted color features. The Stochastic Fractal Search (SFS) has a very high ability to avoid the stuck at local point. Its binary version is utilized to select the most appropriate features which improve the classification process. The Extreme Machine learning (EML) is used to classify the color images of galaxies using the selected color features. Experiments are performed with the well-known datasets of galaxies (EFIGI catalog), where the proposed algorithm achieved high classification rate. The obtained results clearly show that the proposed method outperformed all existing galaxies classification methods.

Introduction

Galaxies are fundamental units of matter in space, the main objects in our Universe, and they have been seen through a telescope in different shapes (Selim and Abd El Aziz, 2017). The variety in their appearance leads to the variety in their types (Wollack, 2010). Studying the different types of galaxies is an important issue for understanding how they formed and evolved. The galaxies can be naturally divided into more than five categories. Galaxy morphological classification is a system used to divide galaxies into groups based on their visual appearance. Therefore, morphological classification of galaxies is an interesting topic for researchers. In astrophysics, galaxy classification into different morphological classes is a challenging problem where the galaxy classification enables astrophysicists to know about the shape of galaxies. This process was done using huge information to help astrophysicists in testing theories and find new conclusions to explain the physics-based processes which governthe elevation of galaxies, star-formation, and the evolution of Universe (Wollack, 2010). ​ Historically, the first classifications of galaxies were made using the astronomical observation in optical wavelengths which are restricted to relatively nearby galaxies. After establishing the extragalactic nature of the ‘white nebulae’, Hubble (1922) developed a galaxy classification system which is still in use up to now. In this classification system, the image of a galaxy can be characterized in an entirely objective and non-controversial way by its total integrated magnitude, its integrated colors, U–B, B–V, V–R etc., and the more complex structure could be seen in a few of the brighter cases. Moreover, parametric methods were used to quantify the structural of galaxies and measure the shape and size by finding a best-fit parametric model of its two-dimensional surface brightness profile. It generates a range of profile models image and determines the best-fit model by comparing models with the galaxy light profile (Mosleh et al., 2013).

Previous work of galaxies classification helps in understanding the processes of creating galaxies which share similar structures. During the past decades, advancements in computational tools and algorithms establish the automatic analysis of galaxy morphology. Several machine learning algorithms have been used to automate the classification process. Goderya et al. (2004) used supervised ANN to classify galaxies where Difference Boosting Neural Network was able to learn 98.3% of the galaxies correctly and identify 89.9% of galaxy images. Calleja and Fuentes (2004) presented an experimental study using machine learning and image analysis to perform automated morphological galaxy classification. They used a neural network and a locally weighted regression method and implemented homogeneous ensembles of classifiers.

Meanwhile, there are other methods that used central concentration (Mosleh et al., 2013) and asymmetry of galaxies light (Doi et al., 1993, Shimasaku et al., 2001, Abraham et al., 1996) to find the galaxy’s types in the Hubble sequence. In addition, there is another kind of methods called parametric methods that have been applied to improve the classification of galaxy images such as GALFIT (Peng et al., 2002) and GIM2D (Simard, 1998). In contrast, there are non-parametric catalogs (Lotz et al., 2004, Somerville et al., 2004, Barkana and Loeb, 1999), and (Abraham et al., 1999).

Currently, the huge number of images required automated methods for fast image processing, image recognition, and image classification. Accurate automated method to distinguish between similar astronomical object types is one of the most challenging problems.

Machine learning approaches were applied to improve the performance of galaxy classification (Selim and Abd El Aziz, 2017). Shamir (2009); Huertas-Company et al. (2010) proposed a galaxy classification method to classify three types of galaxy images (i.e., spiral, elliptical, and edge-on). Huertas-Company et al. (2010) used the Support Vector Machine (SVM) to classify SDSS DR7 images. Banerji et al. (2010) used the neural network for classification the three classes of the Galaxy Zoo project (Lintott et al., 2008), namely: Early types, Spirals, and Point Sources/Artifacts. However, this model depends on features that annotated by humans. De La Calleja and Fuentes (2004) proposed a classification galaxy model which consists of three phases. The first phase is the image analysis which aims to extract the features from the image using principal component analysis (PCA). The extracted features include galaxies position, scale, and rotation invariant. Ata et al. (2009), used 10 artificial NN classifiers with the extracted features from galaxy image and compared their results with the PCA (De La Calleja and Fuentes, 2004).

Dieleman et al. (2015) applied a CNN architecture which consists of 7 layers for classification the galaxy. Aniyan and Thorat (2017) proposed CNN-based method to classify the radio galaxies into Fanaro–Riley Class II, Fanaro–Riley Class I and bent-tailed radio galaxies. Zhu et al. (2019) introduced a variant of the residual networks, ResNets, to improve the morphology classification of galaxies. This variant was combined with other convolutional neural networks (CNNs) and applied to Galaxy Zoo 2 dataset. The results of this model are better than the results of the other networks such as Dieleman, AlexNet, and VGG. Khalifa et al. (2018) used deep learning in galaxies classification. They collected 1356 images from the EFIGI catalog and achieved an accuracy rate, 97%, which outperformed the existing galaxies classification methods.

Recently, the theory of orthogonal moments was applied by Elaziz et al. (2019) where the orthogonal Gegenbauer moments were utilized to extract the features from gray-level images of galaxies and the artificial bee colony (ABC) was used to select the most proper features. The best accuracy achieved by this method was 94.63. Ibrahim et al. (2018a) proposed hybrid optimization method in which the brainstorm optimization and the moth flame optimization methods were applied to improve the classification of the galaxy.

In all aforementioned methods, the color images of galaxies were converted into gray images which results in lossing of the important color information of these color images.

This challenging problem motivates the authors to propose a new algorithm to classify the color images of galaxies. In this algorithm, the features are extracted from the color images of galaxies and then, the extreme machine learning model is used as a classifier to avoid the limitations of other classifiers.

The quaternion polar complex exponential transform moments (QPCETs) (Wang et al., 2015) are used to extract the features from the color images. QPCETs are used to represent color images with a minimum information redundancy and show robustness against different kind of noise. The extracted features using QPCETs are able to discriminate between similar images. Based on these characteristics, the QPCET moments are successfully utilized in several applications such as watermarking of the digital images (Xiang-yang et al., 2014, Hosny and Mohamed, 2017), copy-move forgery detection (Hosny et al., 2018a, Hosny et al., 2019), robust image hashing (Hosny et al., 2018b) and image retrieval (Liu et al., 2019) and Iris recognition (Kaur et al., 2018).

However, similar to other methods, the extracted features using QPCETs are not all relevant. Therefore, a feature selection technique could be used to reduce the number of features and selected the most proper ones. In addition, the extreme machine learning (EML) method is used in several applications as a classifier (Huang et al., 2004). It is considered as a single hidden layer feedforward neural networks (SLFNs) where only the output weights need to be determined. The SLFN has been applied in several applications including the image classification (Jun et al., 2011), big data (Kasun et al., 2013), Selection of relevant features (Blum and Langley, 1997), and others (Huang et al., 2011).

This paper proposed a new galaxy classification method which depends on three steps. First, extract the features from the input color images using the QPCETs. Second, the binary version of the SFS algorithm (BSFS) is used to find the optimal subset of features to reduce the negative effect of irrelevant or redundant feature on the performance of the classification method. Third, utilizing the selected highly accurate features to classify the galaxy color images with very high classification rates.

Since, the study of galaxies is an observational one and observations are tied to one single viewing angle. The main problem with classifying galaxies is that no galaxy can be brought into our laboratory so that it can be viewed from any particular direction or distance. The rotation and scaling invariance of the QPCETs are very useful where the magnitude values of the QPCETs for a galaxy image are unchanged with changing the viewing angle and the distance of the between the observer and the galaxy.

In BSFS, a set of solution is generated randomly then each solution is converted to a binary solution and the quality of the selected feature is computed and the best solution is then determined. After that, the operators of the SFS used in updating the current set of solutions and repeated until they reached the stop conditions. The output from the BSFS is the best solution that represents the subset of features that maximize the accuracy of the EML classifier. Meanwhile, the last phase is the testing phase which aims to evaluate the quality of the selected features by selecting the same features from the testing set and passed to the EML method to predict the output label of each galaxy image. The main contributions of this paper can be summarized as follows:

  • 1-

    Proposing a new method for galaxy image classification in which the images of galaxies could be accurately classified without the need to any color conversion.

  • 2-

    Utilizing the QPCETs to extract RST invariant features from the input images of galaxies.

  • 3-

    Modify the SFS algorithm to select the most relevant independent features and ignore the irrelevant redundant features.

  • 4-

    Utilize a highly accurate and numerically stable method to extract the RST invariant features.

  • 5-

    Implement the EML to significantly improve the classification performance.

To the best of our knowledge, this the first time to use the QPCETs, binary SFS, and EML in galaxy image classification problem.

The rest of this paper is organized as the follows: Section 2 presents the background of the QPCET for Color Images, Stochastic Fractal Search (SFS) algorithm, Extreme Learning Machine. The proposed galaxy classification method is introduced in Section 3. The results and discussion of the proposed method are given in Section 4. The conclusion and future work are discussed in Section 5.

Section snippets

Proposed method for feature extraction and selection

In this section, the proposed method for feature extraction using the QPCET, and feature selection using the Stochastic Fractal Search, and Extreme Learning Machine are presented.

The proposed galaxy classification method

The proposed method to predict the label of the galaxy images is presented as in Fig. 4. The proposed method aims to extract the suitable set of features from the color images without converting it into the gray-level. Then those features are reduced by removing the irrelevant features from them and this is performed by using a new feature selection method. In order to evaluate the performance of the selected features the EML is used which produces the accuracy that is considered as an

Experimental results and discussions

In this section, different experiments are performed to evaluate the performance of the proposed method with dataset of galaxy images. In addition, the performance of the proposed approach is compared with a set of well-known methods either as feature selection or as classifiers.

Conclusions

In this paper, a new method for color images galaxy classification is proposed. The proposed classification technique is an interesting avenue to feed into a machine learning where there is clear need for improved galaxies classification schemes especially the cases for using the color images. In the proposed technique, highly accurate, RST-invariant features are extracted from the input images of the galaxy without converting them to gray-image which keep the essential color information and

CRediT authorship contribution statement

K.M. Hosny: Conceptualization, Methodology, Writing - review & editing, Supervision. M.A. Elaziz: Conceptualization, Methodology, Writing - review & editing. I.M. Selim: Conceptualization, Resources, Validation, Writing - original draft. M.M. Darwish: Conceptualization, Methodology, Software, Validation, Writing - original draft.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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