An Efficient Retrieval System for Biomedical Images Based on Radial Associated Laguerre Moments

The ability of any retrieval system to extract features by using its feature descriptor is the primary criterion to measure its efficiency. In this paper a novel technique for feature extraction of biomedical images is presented. The mooted system uses the Radial Associated Laguerre Moments (RALMs) as a feature descriptor to obtain features from two types of medical images: computer tomography (CT) and magnetic resonance images (MRI). RALMs represent one sort of discrete orthogonal moments. RALMs extract the features from images using orthogonal moments to retrieve images from a database. Our approach is extensively assessed with noise-free and noisy images from three different benchmark databases: Emphysema-CT, NEMA CT, and NEMA MRI. The first two databases are used for CT image retrieval, while the third is for MR image retrieval. The proposed approach was tested against the state-of-the art local feature descriptors: Local Binary Pattern (LBP), and local diagonal extrema pattern (LDEP). It was also evaluated against orthogonal Fourier-Mellin moments (OFMMs) as a global descriptor. The comparison shows a significant improvement in favor of the proposed approach in terms of three different performance metrics: ARP, ARR, and F_score. The proposed approach was also compared against the convolutional neural network (CNN) as a deep learning based method over the NEMA-MRI dataset. The RALMs based approach showed a significant improvement when compared against two state-of-the-art medical image retrieval approaches: Histogram of Compressed Scattering Coefficients (HCSCs) and a local bit-plane decoding-based AlexNet descriptor (LBpDAD), the study has done over the TCIA-CT dataset. The proposed approach was also tested with big well-known dataset from the international skin imaging collaboration (ISIC) 2018.


I. INTRODUCTION
Everywhere in the world hospitals and medical institutes create and store a large variety of datasets of biomedical images (BMI) during the routine clinical practices. These datasets contain the images produced by the diverse biomedical modalities, which include X-Ray, ultrasound (US), computed tomography (CT), and magnetic resonance imaging (MRI). Such imaging modalities allow physicians to make their diagnosis effectively. The mastery to retrieve the BMI correctly is crucial for the researchers in medical sciences The associate editor coordinating the review of this manuscript and approving it for publication was Zhenhua Guo .
where: it helps the physicians to make precise diagnosis [1], it provides real-time decision support [2] and it has its benefits when used as a part of a radiology teaching system [3]. Also it used as a tool for teaching and research in the medical institutes. For these reasons, studies have recently carried out to specify the importance of biomedical image retrieval (BMIR) as a core area of research.
Images can be recognized and retrieved via content-based image retrieval (CBIR) systems. Rao et al. [4], introduced CBIR system using Exact Legendre Moments (ELM) [5] for gray scale images. Rao and Rao [6], introduced a CBIR system to retrieve natural and texture images. Mudhafar et al. [7], proposed an effective image retrieval method based on a new support vector machine NSVM and convolution neural network CNN. BMIR systems represent one type of image retrieval systems based totally on the extraction of appropriate features (i.e. shape, color, texture, etc). There are two main types of features: local and global. Global features describe the entire image, while local features describe the part or some parts of the image. Global features usually used in object detection, classification, and image retrieval, whereas the local descriptors used for object identification or recognition. It observed that the texture feature is the most common amongst many BMIR systems [8]- [12]. However, because of the importance of medical images, only texture feature is not sufficient to describe the image, hence the aggregate of many descriptors such as texture, shape, edges, etc., is required for constructing an efficient BMIR system.
The medical images are available in a different format. But we restricted our study with only two types of biomedical images: CT and MRI. The earliest studies on CT and MRI introduced by Manjunath et al. [13]. Felipe et al. [14], suggested the co-occurrence matrix (CM) technique for CT and MRI images. Unary et al. [15], introduced a robust and fast retrieval system for MRI of brain images. Ojala et al. [16], suggested an efficient texture feature descriptor called local binary pattern (LBP). Based on LBP, the feature vector formed through the intensity of each pixel. LBP, joint LBP, and image intensity histograms are used by Sørensen et al. [17], to make quantitative analysis to CT images of pulmonary emphysema. Peng et al. [18], introduced a feature extractor technique primarily based on the structure and the local brightness to analyze the CT images of the chest. Hosny et al. [19], presented an accurate method based on orthogonal moments for the reconstruction of noisy medical images. Quddus and Basir [20], introduced an approach based on noisy and multimodal observations to retrieve the 2-D MRI images. Murala and Wu presented essential contributions concerning the retrieval of CT and MRI images [21]- [23]. Moreover, Murala et al. [21] introduced a local ternary cooccurrence pattern (LTCoP). Later on Murala and Wu [22] suggested a strategy to retrieve BMI known as local mesh pattern (LMeP). The method presented in [22] developed to construct an algorithm called LMePVEP [23].
Local diagonal extrema pattern (LDEP) is a novel strategy introduced by Dubey et al. [24] to retrieve CT images. The main idea of LDEP is that the local extremes for local diagonals computed through first-order derivatives for local diagonals. The relationship between the central pixel and its neighbors computed via the comparison amongst the central pixel's intensity value and the local extrema of its neighbors. Later on Dubey et al. [25] suggested another method called LWP. According to LWP, the local wavelet decomposition for the local neighborhood of any pixel computed. Then the values obtained are compared with the transformed values of the central pixel. LWP calculated for all pixels of the image. Finally, the histogram computed as a feature vector. Depending on a novel method called local bit plane dissimilarity pattern (LBDISP) Dubey et al. [26] introduced the BMIR system for CT images. LBDISP proposed to handle the problem of both less discriminative and high discriminative. Based on LBDISP, Dubey et al. [27] suggested a new technique named as, local bit-plane decoded pattern (LBDP). The main reason that makes LDEP and its variants superior over other methods such as LBP, LTCoP, and LMeP is the high performance with shallow dimension in the feature vector.
Deep et al. [28] suggested a new technique named directional local ternary quantized extrema pattern (DLTerQEP) for BMIR. The proposed strategy exceeds the LBP, where it considers the pixels around the central pixel through four directions: 0 • , 45 • , 90 • , and 135 • . In contrast, the LBP considers only the local region around the central pixel. Deep et al. [29] introduced a novel local feature vector for MRI, and CT BMI named local mesh ternary pattern (LMeTP), which also based on ternary patterns. Recently, Deep et al. [30] introduced a new descriptor called local quantized extrema quinary pattern (LQEQryP) for BMI indexing and retrieval pattern. Verma and Raman [31] introduced a novel texture descriptor for image retrieval, and it named as, local tridirectional pattern (LTDP). Most of the previous local patterns consider only the center pixel for information extraction; according to LTDP, all pixels in the neighborhood found where they compared with the nearest pixels and center pixel for pattern information. Another feature descriptor called local neighborhood difference pattern (LNDP) is introduced by Verma and Raman [32], based on the differences in the intensity of the pixel. Pang et al. [33] introduced BMIR and indexing system based on deep preference learning.
Rehman S. U et al. introduced several studies for seizure effective image features using Convolutional neural network (CNN), hence using it in machine learning applications [34]- [38]. Lan et al. [39] introduced medical image retrieval system for CT images. They used scattering transform and particular variation of deep convolutional networks to derive texture characteristics of medical CT images then a novel feature, named histogram of compressed scattering coefficients (HCSCs), using the scattering representations of CT images is introduced. Dubey et al. [40] suggested biomedical image retrieval system called a local bit-plane decodingbased AlexNet descriptor (LBpDAD). It combines the advantages of local bit-plane decoded features and the convolutional neural network-based features such as AlexNet.
Several pre-mentioned methods have an essential role in BMI retrieval and many other pattern matching applications, but still, the main problem is that all of them are local descriptors. Medical datasets classified into different classes based on two different criteria. These criteria include both the images that represent the whole body parts and the images that describe the type of tissues of the same part or organ. Subsequently, the descriptors used with BMI must have the ability to differentiate between the entire BM images of various body parts and also between the local changes in the shape or the texture of the same organ. Thus both local and global descriptors are required for efficient retrieval of BM images. Global descriptors are also required to differentiate between the images of various body parts. In contrast, local descriptors can distinguish between the different kinds tissues of the same organ (like, tumorous or non-tumorous) or the same structure (like the shape of ventricular in brain MRI). The reason behind the failure of the pre-mentioned techniques to be highly efficient in retrieving BM images not only their local nature but also their low performance against noisy datasets; since BM images sometimes may be noisy in life.
Kumar et al. [41] proposed an efficient approach based on Zernike moments as a global descriptor to retrieve CT and MRI images. Ashutosh et al. [42] introduced a new global descriptor based on orthogonal Fourier-Mellin moments (OFMMs) for efficient indexing and retrieval of BM images: CT and MRI.
Laguerre moments represent one type of discrete orthogonal moments [43], [44]. The experimental results obtained by Qjidaa et al. [43] specified the effectiveness of Laguerre moments as feature descriptors. Bojun et al. [44] suggested a kind of discrete orthogonal moments called RALMs for invariant pattern recognition and image reconstruction. The numerical results obtained in [44] proved that RALMs perform better than orthogonal Fourier-Mellin Moments (OFFMs) in image reconstruction and rotation invariant for both noisy and free noisy images. So, RALMs will be more appropriate for BMIR applications. So, in this study, we present a retrieval system based on RALMs for biomedical uses.
The current study encompasses some contributions that can be summarized as follows: • A novel method was introduced for BMIR based on RALMs. It is useful and efficient, as it can capture multipronged edge information, texture, shapes and structural from BMI.
• Elaborated experiments were performed to specify the performance and ability of the RALMs to retrieve the BM images against other state-of-the-art approaches.
The results show the superiority of the proposed method over the compared methods on three medical datasets: Emphysema-CT, NEMA CT, and NEMA MRI.
• Other experiments were performed to specify the outperform of the proposed approach with noisy images.
The remainder of this study comes in four sections as follows: Section 2 discusses, in brief, the compared techniques. The proposed RALMs-based retrieval approach presented in Section 3. Our results figured and discussed in Section 4. Finally, section 5 offers a conclusion.

II. FEATURE EXTRACTION TECHNIQUES
In the following subsections, the study briefly explains the local and global descriptors included in the comparison: LBP, LDEP, and OFMMs.

A. LBP TECHNIQUE
Ojala et al. [16] proposed an LBP operator. This operator was used by Sørensen et al. [17] to make quantitative analysis for the CT of pulmonary emphysema. LBP distinguishes each pixel in the image with a decimal value called LBPs code. This decimal value has been resulted from the subtraction of the central pixel's value from its surrounding pixel values.
If the resulting value is negative, it is encoded to 0; otherwise, it is encoded to 1. As shown in Fig.1, the binary code 10111010 occurred as a result of concatenating all the binary values in a clockwise direction starting from the value at the northwest corner. The decimal value equivalent to the binary code 10111010 would be 186, this value is called the LBPs code for the given 3 × 3 window. Consider a pixel at (x c , y c ), then LBP at (x c , y c ) is obtained in decimal form as: where, g c and g s represent gray values of that pixel at the center and the other pixels around it, R is the radius of the circle neighborhood pixels, and N is the number of pixels in the neighborhood of the central pixel.
The threshold function Th (x) is defined as: The most popular form of LBP is LBP 8,1 . It used in a variety of applications in imaging sciences and also used for retrieval of MRI and CT images. The main advantage of LBP is the simplest form of its formula and also the simplicity of its implementation.
Ojala et al. [16] proposed the LBP for the texture analysis in the first place. Then, its uses has expanded to comprise image analysis [45], [46], retrieval of images and videos [47], [48], environment modeling [49], [50], visual inspection [51], [52], motion analysis [53], [54], biomedical and atmospheric image analysis [55], [56], remote sensing [57], and so on. The main problem of LBP is that its feature vector has a high dimension; this creates a problem in its computational complexity. For example, in the case of LBP 8,1 , The feature vector contains 256 features from a single image. These features represent the binary codes acquired from the eight surrounding neighbors. To overcome that drawback, LBP extended to ULBP. U is known as the measure of uniformity, and it refers to the number of the bits transitioned between 0 and 1. LBP is called ULBP if U ≤ 2. For example, patterns like 11111111 (0 transitions), 10001111 (2 transitions), and 00110000 (2 transitions) are ULBP, while 00110110 (4 transitions), and 10101000 (5 transitions) are LBP.

B. LDEP TECHNIQUE
Dubey et al. [24], presented a new technique called LDEP. They used it as a retrieval system for CT images. As in [24], LDEP demonstrated high performance over many other approaches such as LTP, LTCoP, LMeP, etc. Therefore, LDEP is used to compare RALMs-based approaches. LDEP approach uses the first derivative of the local diagonal to find the values and indexes of the local diagonal extrema to take advantage of the linkage among any pixel at the center and its neighbors at the local diagonal. What makes LDEP more efficient is that it considers only the diagonal neighbors. So, the dimension of the feature vector shrinks, and the retrieval task consequently increases in speed.
LDEP for any central pixel (x, y) calculated as follows: At first, the difference between the value of the pixel at the center (x, y) and its local diagonal extrema computed as illustrated below x,y both I x,y ϕ min and I x,y ϕ max refer to the intensity values of the local diagonal extremes of the pixel (x, y).
The relationship among the central pixel and its local diagonal extrema is defined as such that, Finally, the components of the LDEP vector of a pixel (x, y) computed as where, LDEP x,y J is the component number J . Hence, the LDEP feature vector for any pixel (x, y) is given by: where dim is the length of the vector.

C. OFMMS TECHNIQUE
OFMMs were firstly introduced by Sheng and Shen [58] for invariant pattern recognition. For the function f (r, ϕ), OFMMs of order n and repetition l is defined as where Q n (r) is the radial function that is defined as The radial function Q n (r) is orthogonal over the range δ mn is the Kronecker delta, and r = 1 is the maximum size of any encountered object in a particular application. Hence the basis functions Q n (r)e −ilϕ are orthogonal over the interior of the unit circle. For digital images, it required to use the modified form of (9) which introduced by Sheng et al. [58], where the coordinates (x i , y k ) are given by

III. PROPOSED RADIAL ASSOCIATED LAGUERRE MOMENTS (RALMS)-BASED IMAGE RETRIEVAL SYSTEM
In this section, we propose the RALMs as a global descriptor to retrieve the biomedical images. The ALMs [43] is one kind of discrete orthogonal moments. ALMs defined in the existence of the associated Laguerre polynomials (ALPs) [60]- [62] (basis functions), which are orthogonal over the whole right-half plane. ALMs of the image I (x, y) with an order of m + n and a size of NxN are defined as follows: where, L α m , for α > −1 are the ALPs that are orthogonal to the weight function w (  where, δ nm is a Kronecker delta, δ nm = 1 if m = n and δ nm = 0 otherwise. The ALPs defined as: but due to the high increase of the polynomial values with increasing of the order, we restrict our study with the normalized orthogonal ALPsL α n (x), that is defined as: As shown in Fig. (3) and Fig. (4) it is noted that the values of the normalized polynomialsL α n (x) are bounded on a finite interval, a thing that doesn't occur with non-normalized polynomials L α n (x). As shown in (13) ALMs are defined over the Cartesian coordinates so that it is not suitable for identifying the rotational invariance, so that we have the motive to define the RALMs of order p and repetition l as  where, I (r, θ) , refers to the image intensity function in polar coordinates. The image has a size of N × N pixels, and m denotes N/2. Since θ is a real quantity measured in radians, one can rewrite (17) as follow: where n is at 360. Radial representation aims to deduce the rotation invariants easily as follow: consider the image I (r, θ), which become I (r, θ + ∅) after rotation by angle ∅. In this case, RALMs represent as from (17), one can deduce the following From (25) It evident that RALMs are with rotational invariance.
The value of the parameter α has an essential role in pattern recognition. It controls the shifting to the image region of interest. The authors in [40] proved that the most accurate recognition occurs at the values of α from 6 to 10 in case of noisy and noisy free images, so that, in our study, we use the same values.
The superiority of the RALMs in many image recognition applications in noise-free and noisy cases is due to the following worthwhile properties: This change in the values of the features is due to the representation of those values, where it represents the differences between the center pixel and its neighbors in the spatial domain. These inter-pixel differences tend to change with any changes in the image, such as rotation, scaling, and noisy cases. However, in the case of RALMs, it's values are still the same before and after any change in the image because of its orthogonality property. Therefore, RALMs are more suitable for real-life applications such as BMIR

IV. EXPERIMENTAL RESULTS AND DISCUSSIONS
In the following subsections, the study exposes the datasets that used to test our strategy. It also discusses the experimental results in detail through some evaluation measures.

A. DATASETS
The evaluation of our system done through three benchmark datasets.
Emphysema-CT dataset: The first dataset [63] comprises 168 tissue images of the same body part for 39 various cases. Images in Emphysema-CT come in three classes based on the texture of lung tissues: Centrilobular Emphysema (CLE) that contain 50 images, Normal tissue (NT) that VOLUME 8, 2020 includes 59 images and Paraceptal Emphysema (PSE) that contain 59 images.
The NEMA-CT dataset: The second dataset [64] consists of different categories of CT images for different body parts that created to assist in the research and diagnosis purpose. In our study, we considered the following cases of NEMA-CT database: CT0001, CT003, CT0021, CT0030, CT0031, Ct0053, CT0054, CT0057, CT0060, and CT0083. We collected 608 CT images have the dimension 512 × 512. These images represent different body parts. Images are grouped into 10  As we mentioned that the BMI in the first database (Emphysema-CT) are of the same organ, while the second and the third (NEMA-CT and NEMA-MRI) comprise BMI for various organs. For better results, any retrieval system to give better results with such datasets, must have the ability to distinguish among the BM images that seem to be the same but are different locally as in the Emphysema-CT database. Also the retrieval system must have the ability to differentiate between the BM images which are globally different as in NEMA-CT and NEMA-MRI databases.

B. EVALUATION MEASURES
To specify the performance of our system, three experiments were carried out and showed in-detail through the following subsections. A comparison between the performance of the RALMs approach and other recently released approaches: LBP, LDEP, OFMMs, HCSCs and LBpDAD is performed. Further experiments were carried out under noisy conditions to specify the high efficiency of our approach as a retrieval system when compared with the other methods. In our study, we have used the same evaluation criteria used in [24]. To estimate the likeness between the feature vectors of two images, we use the following distance similarity measure where dim represents the length of the feature vectors; f DB ji denotes ith feature for jth image and f Q i is the ith feature of the query image. Fig. 2 represents the framework of the proposed system. The current study compared the performance of the present approach with the existing methods through two evaluation measures. These measures used by Murla and Jonathan [21], [24] are called average retrieval precision (ARP), and average  retrieval rate (ARR). ARP was also used by Girgis and Reda [66]. We used another performance measure called F_score.
As shown in Fig. 5. q is a query image, R(q) represents the set of all images that are retrieved by our system, and L(q) represents the set of all images that are relevant to the query image. Precision and recall defined as follow: - where the |•| operator represents the cardinality of a set (i.e., the number of objects in the collection). Hence, ARP and ARR can be defined as follow: ARR (%) = 100 where |DB| represent the count of all images in the dataset. In our experiment, we consider every image in the dataset as a query image, while the rest images in the DB represent target images for the query.

C. EMPIRICAL FINDINGS OVER EMPHYSEMA-CT DATASET
Emphysema-CT database [63] exists mainly to help physicians diagnosing chronic obstructive pulmonary disease (COPD). The main characteristic of Emphysema is its ability to damage the lung tissues. Appropriate classification of healthy lung tissues and emphysematous is essential for accurate diagnosis of the disease. Fig. 6 depicts one image from each class of the Emphysema-CT Database. Fig. 7 shows the retrieval performance in terms of ARP, ARR, and F_score for the proposed RALMs technique against the compared methods at different values for the number of returned images. Table1 summarizes the results of the performance measures. From table 1, one can observe that the RALMs approach is superior over LBP, LDEP, and OFMMs techniques in terms of the performance metrics: ARP, ARR, and F_score. The improvement in the retrieval rate for the proposed approach when compared with that of the existing methods is showed through table 1. The average gain of the RALMs approach increased in comparison with OFMMs, LBP, and LDEP approaches by the percentages 7.44%, 18.06%, and 18.65%, respectively, in terms of all the performance metrics. Fig. 8 presents the query results of the RALMs approach over the Emphysema-CT dataset.

D. EMPIRICAL FINDINGS OVER NEMA-CT DATASET
The NEMA-CT (National Electrical Manufactures Association-Computed Tomography) [64] is an open-access information resource for medical researches. All image datasets are in DICOM format. Fig. 9 depicts sample images from each category of the dataset. Graphs in fig. 11 shows the excellence of the RALMs technique when it is compared with the other methods in terms of the performance measures ARP, ARR, and F_score at different values for the top matches. Table 2 summarizes the results obtained when comparing VOLUME 8, 2020 the RALMs with the OFMMs, LBP, and LDEP approaches. From table 2, it is obvious that the average gain in retrieval rates of the three performance measures of RALMs comes in following percentages 5.48%, 10.006%, and 6.15% when compared with the approaches OFMMs, LBP and LDEP respectively. Fig. 10 depicts the query results of the RALMsbased approach over the NEMA-CT database. Results in table  1 and table 2 show the superiority of the retrieval process in case of NEMA-CT over that of Emphysema-CT. This  superiority is due to that the three classes of Emphysema-CT contain images of different tissues of the same body part (i.e. lung) while each category in NEMA-CT includes images of various body parts. Hence, it is easy to distinguish between BM images of different organs if it is compared to images of the same lung tissue part.

E. EMPIRICAL FINDINGS OVER NEMA-MRI DATABASE
Magnetic resonance images (MRI) are helpful in diagnosis. They facilitate the distinction between the diseased and healthy tissues of the body. Fig. 12 depicts an example from different classes of the NEMA-MRI dataset [65]. Graphs in fig. 14 shows the superiority of the RALMs proposed approach over the compared methods in case of the performance metrics: ARP, ARR, and F score at different values for the top matches images. Table 3 summarizes the results obtained when comparing the RALMs with the OFMMs, LBP, and LDEP approaches. From table 3, it is obvious that the average gain in retrieval rates of the three performance measures of RALMs comes in following percentages 1.48%, 3.24% and 6.09% when compared with the approaches OFMMs, LBP and LDEP respectively. The query results of the RALMs-based methods over the NEMA-MRI database are depicted in Fig. 13. Table 3 shows that the retrieval rate is higher in case of the NEMA-MRI dataset when compared to NEMA-CT. This occurs because NEMA-MRI, contains only five categories that are very different from each other as observed in Fig. 12. Hence the misclassification among these different categories would be very rare.
Furthermore, we investigated the efficiency of the proposed method (i.e. RALMs) against the convolutional neural network CNN as a deep learning based method over NEMA_MRI dataset. We used two sequence CNN layers with CNN architecture. The first uses 128 filters with kernel size of 3 × 3, while the second uses 64 filters with kernel size of 3 × 3. We used Max-Pooling technique in both two layers. Next a flatten layer followed by a fully-connected layer of 32 nodes. A dropout technique is applied with 0.4 value to decrease the overfitting, also all layers used RELU activation function. The comparison occurred with maximum number of returned images equal 60. Table 4, shows the obtained results over the three performance measures: ARP, ARR and F_score. The results specified the superiority of CNN in case of ARR and F_score but not in case of ARP. Despite of the superiority of CNN but still there are some challenges which push us to invest in such moments based approach (i.e. RALMs). The most important of these challenges are: lack of data, overfitting and imbalance datasets. All these challenges occur due to CNN requires huge number of data to train, the quality of data (i.e. noisy images or low quality images) and when number of images in some classes dominate over other classes respectively. All the pre mentioned problems push us to research in different approaches like the proposed approach (RALMs), which do not require any data to train and not affected by noise conditions as proved through subsection F.

F. EMPIRICAL FINDINGS OVER TCIA-CT DATABASE
The efficiency of the proposed approach was also compared against other two medical image retrieval approaches named HCSCs [39] and LBpDAD [40]. These two approaches were tested over a benchmark dataset called VOLUME 8, 2020 The Cancer Image Archive (TCIA-CT) [67] as discussed in [39], [40]. TCIA contains a large number of cancer images. In our study we used the TCIA-CT dataset; it contains 604 Colo_prone 1.  Fig. 15 depicts a sample image from each class. As reported in [39], [40], in the current study we used 10 images as a maximum number of returned images. The retrieval performance in terms of ARP, ARR and Fscore is shown in table 5 and the obtained results show a significant improvement in favor of the proposed approach. The average gain in retrieval rates of the three performance measures of RALMs comes in following percentages 0.9840% and 1.5207% when compared with the approaches LBpDAD and HCSCs respectively. Fig. 16 depicts the query results of the RALMs-based approach over the TCIA-CT dataset.

G. EMPIRICAL FINDINGS OVER ISIC 2018 DATABASE
The proposed approach was also tested over a big well-known database from the International Skin Imaging Collaboration (ISIC) 2018 [68]. This database contains 10,015 skin images, grouped into seven classes: MEL contains 1113, NV contains 6705 images, BCC contains 514 images, AKIEC contains 327 images, BKL contains 1099 images, DF contains 115 images, and VASC contains 142 images. Fig. 17 depicts one sample image from each class.
The retrieval performance in terms of ARP, ARR and Fscore with maximum number of 100 returned images is  shown in table 6. According to the results obtained in table 6, the retrieval rate is low when compared to the results obtained by NEMA-CT and NEMA-MRI. Furthermore, this low rate is attributed to that the seven classes of ISIC 2018 contain different images for the same body part (i.e., skin), while each class in both NEMA-CT and NEMA-MRI contains images of various body parts. Hence, it is easy to distinguish between images of different organs if this is compared to images of the same part. Fig. 18 depicts the query results of the RALMs- based approach over the ISIC 2018 dataset. It is worthy noted that the query image and the retrieved images are of the same class (i.e., NV).

H. EMPIRICAL FINDINGS OVER NOISY DATABASES
The present study employs Gaussian white noise with zero means to test the efficiency of RALMs against the other     7, 9, and 12 we observed that the average efficiency gain in retrieval rates is in favor of RALMs at the expense of the compared methods for the three databases (Emphysema-CT, NEMA-CT, and NEMA-MRI) with the following percentages (7.24%, 21.74%, 21.28%), (13.17%, 61.14%, 66.14%) and (3.95%, 42.99%, 40.82%) respectively, overall the three performance measures. Figs. 23, 24, and 25 show a comparison between the proposed approach and the compared approaches in terms of ARP and ARR retrieval performance metrics, on noisy and noisy free cases of Emphysema-CT, NEMA-CT, and NEMA-MRI databases respectively.  We observed that the maximum drop for Emphysema-CT, NEMA-CT, and NEMA-MRI was in favor of LBP, followed by LDEP, then OFMMs in case of noisy datasets. For the noisy free datasets, the maximum drop was in favor of LDEP followed by LBP, then OFMMs in both of Emphysema-CT   and NEMA-MRI, but in case of NEMA-CT the maximum reduction was in favor of LBP followed by LDEP then OFMMs. Figs. 20, 26, and 28 represent the query results of RALMs approach over noisy Emphysema-CT, noisy NEMA-  CT, and noisy NEMA-MRI, respectively. From figs. 23, 24, and 25, we observed that there exists a drop in case of noisy images when compared to noisy free images on all three noisy test datasets in case of ARP and ARR performance measures. This drop is high in case of the compared methods but still relatively low with the proposed approach. All these indicators establish the truth of the robustness of the RALMs values against noisy conditions. Furthermore, the study investigated the effectiveness of the proposed approach (RALMs) against another type of noise (i.e., Pepper & salt). Tables 8, 10 and 11 show the comparison between the retrieval performance of RALMs with Gaussian noise and Pepper & salt noise over noisy Emphysema-CT, noisy NEMA-CT, and noisy NEMA-MRI, respectively. The results obtained ensure the robustness of RALMs against the different types of noise. To avoid any redundancy, we plotted only the results concerning the Gaussian white noise.

V. CONCLUSION
In conclusion, this study presented a new retrieval system for biomedical images proposed using Radial Associated Laguerre Moments (RALMs) as a global descriptor. Thanks to the orthogonality of its basis functions (ALPs), which allow a multidimensional view of an image and invariant of the coefficients of RALMs. The performance of the proposed system assessed through several experiments that applied on three BM datasets: Emphysema-CT, NEMA-CT for computer tomography images, and NEMA-MRI for magnetic resonance images. The experiments performed with noise-free and noisy datasets. The numerical results after being investigated show a significant improvement in favor of the proposed approach against the compared techniques: OFMMs as a global descriptor, LBP, and LDEP as local descriptors in terms of the three performance measures ARP, ARR, and F_score. The RALMs based approach was also specified a significant improvement when compared with the HCSCs and the LBpDAD approaches over the TCIA-CT dataset. Good results obtained when tested the proposed approach over a big well-known dataset (i.e., ISIC 2018). Due to the leverage of the proposed approach in the case of gray medical images, it could upgrade through the quaternion concept that is applicable to color images.