Enhancement of retinal images through modified anisotropic diffusion

Introduction

The global disease outbreak level of diabetes mellitus has been achieved. Diabetes has appeared in about 463 million adults (20–79 years) in 2019, which will gradually rise to 700 million by 2045 (1). Diabetic retinopathy (DR) is one of the most severe diabetes complications that can have adverse eye effects. The primary cause of vision problems and blindness among working adults is DR. The prevalence of DR is around one-third among persons with diabetes.

DR is a significant contributor to blindness among individuals aged 20 to 64 years, particularly in those who had diabetes for an extended duration. The primary cause of DR lies in the damage to blood vessels within the retina, often presenting early symptoms like microaneurysms (MAs) in the eye. Projections indicate a notable increase in DR cases in the future due to the rising prevalence of diabetes. Detecting the disease in its early stages and administering appropriate treatment is crucial to prevent blindness. This necessitates the utilization of robust computer-assisted diagnostic software founded on image processing techniques to distinguish between affected and healthy retinal tissue.

Medical professionals, including ophthalmologists, employ computerized systems in conjunction with non-mydriatic cameras to identify various disease states in patients. DR is classified based on its severity, categorized as proliferative DR, non-proliferative DR, and diabetic macular edema (DME). Non-proliferative DR is further subcategorized into mild, moderate, and severe retinal damage. Clinical experts have outlined five stages for assessing fundus images: normal retina, minimally affected, non-proliferative DR, severely affected non-proliferative DR retina, and proliferative DR retina. Normal retinas exhibit no DR symptoms, while mild non-proliferative DR reveals MAs. Moderate non-proliferative DR encompasses MAs, hard exudates (HE), hemorrhages (HRs), and distended blood vessels. Severe non-proliferative DR manifests with symptoms like blocked retinal blood vessels and the formation of new blood vessels (neovascularization). Neovascularization in PDR-affected retinas occurs in the inner eye, potentially leading to vision blurring. Retinal lesions resulting from DR, including MAs, HRs, HE, and cotton-wool spots (CWS), can be identified in retinal images (2).

This paper conducts a comprehensive review of recent advancements in DR diagnosis, incorporating the latest knowledge. Existing methods and research insights are critically evaluated. The challenge lies in achieving early detection while minimizing costs, which is tackled through automated detection approaches utilizing retinal images. However, transitioning DR diagnosis to automated systems raises both scientific and non-scientific issues. These concerns can be assessed by comparing the detection performance of automated systems with that of human experts. Additionally, the time required for diagnosis is quantifiable, but ethical and political aspects remain unresolved. Striking a balance between false positive and false negative rates is essential, and this necessitates a thorough analysis of potential limitations and benefits (3).

Clinical imaging has undergone a significant transformation in recent years, owing to the introduction of cutting-edge imaging technologies and modalities. With the enormous potential in the early detection of medical problems, clinical imaging has attracted many research interests. The early detection of DR can be crucial in preventing complete vision loss. Multiple symptoms and disorders can be determined from the same imaging method, an important aspect of clinical imaging. For example, retinal imaging may aid in the identification of DR, hypertensive retinopathy, cataracts, blurry vision, and other eye conditions. Various factors, such as uneven illumination, blurring and low-contrast images, render accurate detection of the disease. Computer-aided diagnosis (CAD) of DR can adequately minimize the possibility of having vision loss, as per clinical evidence, by applying various imaging techniques.

Image preprocessing is an essential step towards a better identification of retinal signs in degraded retinal images. The contrast of the image decreases while acquiring the retinal images, hindering the process for adequate diagnosis of the disease. A high-performance camera enhances the quality of the image directly. However, it is costly and difficult to spread across less developed areas.

Enhancement improves the pathological and retinal changes and improves the image’s illumination, resulting in a better diagnosis of the disease. Enhancement of retinal images is essential for detecting and analyzing anomalies such as MAs, CWS, HRs, and various kinds for diagnosing the retinal disease early. There are diverse enhancement techniques implemented so far (4).

The global histogram equalization (GHE) technique enhances global image contrast, resulting in poor contrast stretching. In the contrast-limited adaptive histogram equalization (CLAHE), the whole image is divided into several tiles with the same transformation feature used in GHE but with CLAHE. A clip limit is set for the redistribution of the resulting histogram. However, the enhancement of the image occurs in CLAHE, particularly in regions with gray-level variations (5).

Matched Filter and morphological operators were proposed for automatic detection of the lesion. Enhancement of image has been done by removing the noise using matched filters. Retinal vessels were extracted through CLAHE. Identification of lesions was made by the morphology method. Experimental evaluation has been done on DIARET DB1 datasets and achieves the accuracy of 98.43%/98.06%/98.68% for diagnosing micro-aneurysms/exudate/HRs. The computational time of the proposed algorithm is 19.82 s, which is less than the various evolution algorithm (6).

The image enhancement scheme has been introduced by authors using particle swarm optimization (PSO) for diagnosing retinal diseases. Low contrast images were identified by fitness function using PSO. The information quantity of the image was optimized using fuzzification and intensification parameters. The performance has been evaluated on DRIVE and DIARET DB1 dataset and achieves the improved linear index of fuzziness (LIF), universal quality index (UQI), structural similarity index measure (SSIM), fuzzy quality index (Q/FS), intuitionistic fuzzy quality index (Q/IFS) values as 0.221, 0.9853, 0.9781, 0.8511, 0.8873 for DRIVE and 0.229, 0.9852, 0.9975, 0.8642, 0.8828 for DIARET DB1. It has been concluded that the proposed scheme performs better than the existing state-of-the-art technique. However, removal of noise and deblurring can be implemented in the future to improve the scheme’s stability (7).

The basic image enhancement methods have been performed by Binti Mohd Sharif et al. (8). The performance has been evaluated on a private dataset and achieves mean squared error (MSE), entropy and peak signal-to-noise ratio (PSNR). It is concluded from the study that the contrast stretching method outperforms for enhancing the image. The proposed methods achieve the MSE, entropy and PSNR values as 9,229.13/5.04/8.48, respectively.

An adaptive fuzzy gray level histogram equalization algorithm has been proposed for providing an accurate interpretation of the disease. Binary similar patterns are used to compute the gray level difference. The possibility of uncertainty in the image has been deals with by fuzzification of differences of gray level. The significant amount of contrast enhancement has been computed by fuzzy gray level difference. Then equalization of the fuzzy clipped algorithm was performed for contrast enhancement images. Evaluation of algorithm has been done on 320 MR medical images and achieves the measures of entropy, PSNR, contrast improvement index (CII), Weber contrast (WC), Michelson contrast (MC), measurement of enhancement (EME) and EME by entropy (EMEE) as 7.01, 38.15, 7.4, 0.97, 0.95, 7.11, 0.03 values (9).

Image enhancement has been done by splitting the image to base, detail and noise layers. The noise suppression and detail enhancement have been implemented through the weighted fusion technique. However, for correction of uneven illumination visual adaptation model has been employed. The proposed method’s performance has been on the DIARET DB0 and DIARET DB1 datasets and achieves the average entropy values of 16.29 and 16.23 for DIARET DB0 and DIARET DB1 dataset. The average time is 14.32 s. The future work involves the reduction of computational cost and time complexity (10).

The method is proposed for eliminating noisy and irrelevant information to enhance the image. The mean shift algorithm is exploited for replacing irrelevant pixels with the significant pixel density denoted as local maxima. Redistribution of the reduced histogram has been done by moth swarm algorithm to maximize the KL entropy. Experimental results have been evaluated on CSIQ and TID2013 datasets. A comparison with the existing state-of-the-art algorithms has been made to test the proposed approach performance. The results suggested improved performance for evaluating the quality of enhanced images (11).

For detection of image quality, Blind/Reference less Image spatial Quality Evaluator has been used. In low-contrast retinal images and non-uniform illumination, contrast and brightness problems foster precise detection of lesions. Kandpal and Jain (12) have implemented edge-based texture equalization (ETHE) for enhancing the image quality. It has been implemented on STARE and DIARET DB0, DIARET DB1, CHASE datasets and achieves the average percentage change by 15.12543%. However, ETHE requires less time to simulate than dominant orientation-based histogram equalization (DOTHE).

Contrast Enhancement of the images can be done by histogram equalization. Chang et al. (13) have proposed a quad histogram equalization technique to enhance X-ray radiographs. The authors have employed the mean-variance analysis method on the greyscale image by splitting the images into four sub-images. Based on the PSNR value, the performance of the proposed algorithm was evaluated to be superior to that of current contrast enhancement methodologies.

Visual perception of the diseases can be improved by enhancing the contrast of the medical images. For better visibility of the features, the fundus images should be enhanced in terms of contrast and preserving the brightness. Suma and Saravana Kumar (14) have reviewed and implemented various image enhancement methods based on histogram equalization. The experimental analysis has been done DRIVE dataset and achieves the entropy values for image quality measurement. It has been evaluated from the results that adaptive histogram equalization (AHE) performs the best enhancement technique for the detection of DR in fundus images.

Luminosity and local contrast are important factors for evaluating the fundus images quality. A hybrid approach has been proposed in (5), for enhanced fundus images. While singular value equalization is used to improve the image’s luminosity, the discrete wavelet transform is used to obtain the image’s low-frequency components. CLAHE performs the local contrast enhancement in L*a*b color space. The framework has been tested on MESSIDOR and local datasets both qualitatively and quantitatively on absolute mean brightness error (AMBE), discrete entropy (DE), the measure of enhancement parameters (MEP), and PSNR.

Palanisamy et al. (15) have proposed the hybrid technique that focuses on the image’s low frequency and high-frequency components for better contrast, luminosity, and accurate edge details. Shearlet transform and singular value decomposition have been applied for low-frequency components, soft thresholding, inverse shearlet and CLAHE have been used to enhance luminosity and contrast in retinal images. The approach has been implemented on Messidor. The local dataset and objective analysis have been carried out on PSNR, noise suppression measures, edge-based contrast measure quality index, and feature similarity index.

The comparison of the existing literature is shown in Table 1.

The research contributions for the manuscript are:

• A novel framework has been developed for attaining quality images that help in segmentation for CAD in DR.
• This manuscript compares state-of-the-art methods with the proposed image enhancement method.
• The performance measures such as PSNR, MSE, SSIM, and entropy is used to validate the framework.

The rest of the manuscript is as follows: the following section presents the methodology opted in the proposed method. Performance evaluation has been discussed in the Experimental setup section, followed by plotting the values of evaluation in the Discussion section. Finally, the conclusion is discussed in the following section.

Methods

The workflow of the proposed method is represented as a flow diagram in Figure 1. This method includes four stages: image acquisition (image preprocessing in which color transformation from RGB to HSV conversion), Wiener filter, anisotropic diffusion and unsharp masking. Then, the performance of the proposed method has been evaluated using PSNR, MSE, SSIM and entropy of the enhanced image. Based on the values of performance measures, the proposed method has been compared with the existing state-of-the-art method, which outperforms the existing method.

Figure 1 Proposed workflow.

Image acquisition

Retinal Images can be captured in two ways, either through a mydriatic or non-mydriatic camera. In the mydriatic, pupil dilation occurs before capturing the retinal images, which is a cumbersome task. However, in non-mydriatic camera, fundus images are captured directly through an indirect ophthalmoscope. While capturing images in non-mydriatic manners, the retinal images were distorted due to uneven illumination, poor contrast, etc. Thus, an enhancement method needs to smoothen the next step of segmentation for easily diagnosing DR through CAD. In this proposed method, gold standard benchmark datasets have been used to enhance the images. In the field of medical image analysis, particularly for research on retinal images, the DRIVE and STARE databases are essential. 40 high-resolution retinal fundus images are included in DRIVE, which also includes manual annotations for blood vessel segmentation. This data will be used to help create algorithms for diagnosing problems like DR, hypertensive retinopathy. The STARE dataset, on the other hand, is larger and contains 400 retinal images with a variety of resolutions and pathologies, making it useful for a variety of retinal image processing tasks, such as vessel segmentation and lesion detection. Together, these datasets enable researchers to improve computer-aided diagnostic tools, ultimately improving early identification and management of retinal diseases, including DR, a key contributor to vision impairment in diabetic patients. As the above mentioned datasets are publicly available, so there is noise present in the images. In order to remove the noise the authors have implemented image preprocessing technique.

Image preprocessing

Image preprocessing is the essential step for enhancing images. For the removal of unwanted noise and illumination correction, diverse image enhancement methods were proposed. The preprocessing method employed in these tasks typically comprises several key steps: RGB to HSV conversion, anisotropic diffusion, Weiner filtering, and unsharp masking. Each of these steps serves a unique purpose, such as converting color spaces for improved feature extraction, reducing noise, enhancing image details, and sharpening edges. The rationale behind utilizing this approach, as well as a detailed explanation of each step, will be further elucidated in subsequent discussions.

RGB to HSV conversion

The images acquired from the dataset are in RGB format. However, the disease can be diagnosed better in a saturated channel that can accurately capture brightness variation. The saturation channel of the HSV model is calculated as the ratio of dominant RGB channel and least prevailing color. It can be formulated as:

SHSV=max(R,G,B)−min(R,G,B)max(R,G,B)[1]

The classification of images based on brightness information has been implemented through the V channel in the HSV model (14). So, for the proposed method, conversion of RGB images to HSV images is the preliminary step to enhance images. Though the value channel is considered for enhancement, Hue and saturation channels are kept unchanged as they are color components of the image (15).

Anisotropic diffusion for denoising the images

Perona-Malik model

The Perona-Malik model suggested by Perona and Malik is based on a heat conduction equation which can be expressed as

{∂Ii(m,n)∂x=div[di(m,n)⋅∇Ii(m,n)]Ii=0=It[2]

Where I_t is the assessment image at i=0, divergence operator is represented as div, image gradient is represented as ∇Ii(m,n) and ci(m,n) represents the diffusion coefficient.

The Laplacian operator and the four nearest-neighbor pixels N₄(m,n) can be used to estimate anisotropic diffusion individually, as shown in Eq. [3]:

Ii+1(m,n)=Ii(m,n)+14∑t4[di(t)(m,n)⋅∇Ii(t)(m,n)][3]

Where ∇Ii(t)(m,n), t=1 to 4, is the four neighbors gradient. Therefore

∇Ii(1)(m,n)=Ii(m,n−1)−Ii(m,n);∇Ii(2)(m,n)=Ii(m,n+1)−Ii(m,n);∇Ii(3)(m,n)=Ii(m+1,n)−Ii(m,n);∇Ii(4)(m,n)=Ii(m−1,n)−Ii(m,n)[4]

where diffusion coefficient is represented as di(t)(m,n), which is usually represented as the gradient function ∇Ii(t)(m,n) in the mentioned model as follows:

di(t)(m,n)=g[∇Ii(t)(m,n)][5]

The diffusion coefficient function is expressed as

g(∇I)=exp[−(|∇I|2h)]g(∇I)=11+(|∇I|2h)'[6]

Where the fixed threshold value has been represented by h.

The Perona-Malik model’s diffusion coefficient g(∇I) is adaptively fixed during all iterations. It tends to discern the image’s edges by lowering edge directions diffusion. Diffusion is not stable in the Perona-Malik model. As a result, artifacts might be seen in the image.

Adaptive Perona-Malik model

An adaptive Perona-Malik model based on a variable exponent has been proposed (16). An appropriate diffusion mode regulates the boundary region and the interior noise in the model via the edge indicator. It may keep the image’s fine details as well as the image’s edges. The model is shown in the following equation.

∂u∂i=div[∇I1+(|∇I|/kα(x))]−λ(1−f),(x,i)∈'Ω∗(0,T)[7]

The following equations represent the edge indicator α(x)

α(|∇Gσ∗n|)=2−21+k|∇Gσ∗n|2[8]

or,

α(|∇Gσ∗I|)=2−21+k|∇Gσ∗I|2[9]

Where noise is represented as n and image smoothening is represented as I, and weight parameter is denoted as λ.

Modified Perona-Malik model

In retinal images, edges and local details are the key findings for diagnosing ocular disease. Therefore, preserving and enhancing the edges and removing noise is necessary for the accurate diagnosis of the disease. For the removal of noise, various approaches have been proposed such as linear and nonlinear filtering. Anisotropic diffusion filtering is the most commonly used technique which Perona and Malik developed. This technique is based on heat diffusion equation and involves a multi-scale smoothing and edge detection scheme. The high gradients of the image were reduced due to diffusion function, which depends on the gradient of the image. The diffusion functions smoothen the inhomogeneities of the image resulting in identical information in all directions and is given by:

∂I∂t=div(D⋅∇I)[10]

Where (∂I∂t) represents the intensity change w.r.t time, and D is the diffusion tensor. If D is homogeneous in the image, then the diffusion is known as isotropic. The problem with the traditional model is that although noise removal occurs in the image, the blurring of edges occurs in the image, resulting in a poor diagnosis of the disease (17). The new model replaced the traditional one in which intensity remains constant while smoothening of the image occurs D=d(|∇I|). The anisotropic diffusion equation is given by:

{d→0for|∇I|→∞d→1for|∇I|→0[11]

However, Perona and Malik described the equation for d(|∇I|) as:

d(|∇I|)=11+(|∇I|K)2[12]

d(|∇I|)=e−(|∇I|k)2[13]

Eq. [3] identifies the high-contrast edges from low-contrast edges; however, Eq. [4] deals with the wide area over the smaller region representing the diffusion magnitude. The lower value of k signifies the lower intensity of gradients. The range value of k lies between 20 and 100 (18).

Wiener filter

After smoothening the images and preserving the edges through anisotropic diffusion, some noise in the image can be smoothened. To avoid this situation, the irregularity feature of noise can be used. In the retinal image, blood vessels and noise are hard to differentiate (19). So Wiener filter is used for adaptive noise removal without damaging blood vessels. This low pass filtering technique is based on statistical feature estimation of neighborhood pixels of size I-by-J. The calculation of the local mean and variance of the neighborhood is done in a Wiener filter. High variation indicates weaker smoothing, whereas low variation indicates stronger smoothing (20).

Unsharp masking

Unsharp masking is performed after a Wiener filter for sharpening the image without increasing the noise. In this step, sharp edges have been extracted by subtracting the smoothened image from the input image (21). Nonlinear median filter M is used for smoothening the image and is given by:

r1(s,t)=median{f(i+s,j+t),(i,j)∈R}[14]

Where r1(s,t) represents the smoothened image, f(i,j) represents the input image and Median filter M covers r region.

The unsharp masking operation is given by:

r2(i,j)=f(i,j)−r1(i,j)[15]

Where r2(i,j) represents the unsharp masked image, f(i,j) represents the input image and r1(i,j) represents the smoothed image.

Results

The evaluation of the performance of the proposed method was applied to two standard benchmark datasets, namely STARE and DRIVE. The comparison of the methods with the existing state of the methods has been made, and it has been concluded from the results that the proposed method outperforms the existing state-of-the-art methods. The study provides enhanced retinal images that help the ophthalmologist in clinical use.

Experimental setup

This study has been implemented in MATLAB 2021a and conducted on a 64-bit personal computer with Intel i5-6200 CPU at 2.30 GHz, 8 GB RAM, Windows 10 operating system. The proposed method has been implemented on the publicly available dataset: DRIVE and STARE.

Subjective evaluation

The subjective evaluation of the proposed technique was conducted on the DRIVE and STARE datasets using consistent parameters. The parameters used, such as k=0.5, B0=5×5, and n=7, were determined based on experimental results. Figure 2 showcases the enhanced examples of a randomly selected image from the DRIVE dataset. The sequence of image processing steps applied includes RGB to HSV conversion, followed by anisotropic diffusion filtering using a 5×5 window. A Wiener filter was then employed for smoothing, and unsharp masking was used for image sharpening. Similarly, Figure 3 presents the enhanced examples of a randomly selected image from the STARE dataset.

Figure 2 Sample example results for comparison of enhanced retinal images based on preprocessing filters on DRIVE dataset. (A) Input image; (B) V channel; (C) anisotropic diffusion filter; (D) Wiener filter; (E) unsharp masking.

Figure 3 Sample example results for comparison of enhanced retinal images based on preprocessing filters on STARE dataset. (A) Input image; (B) V channel; (C) anisotropic diffusion filter; (D) Wiener filter; (E) unsharp masking.

Objective evaluation

While visual methods give the effectiveness of the results, quantitative validation is necessary to prove the effectiveness. For evaluating the proposed method, the authors used PSNR, MSE, SSIM, and entropy, as shown in Table 2. The proposed method has also been compared with the methods’ existing state, as shown in Table 3. The performance measures are explained as follows:

PSNR

The reconstruction quality of the image is measured using PSNR. It is represented in decibel scale, and it is described as the ratio of the maximum possible power of the signal to the power of corrupting noise. MSE value is primarily evaluated for getting the PSNR value and is described in equation 10. After calculation of MSE Value, root MSE is employed for PSNR as follows:

PSNR(db)=10log2552MSE[16]

PSNR is directly proportional to image quality. Higher the value of PSNR indicated the high quality of the enhanced image (22).

SSIM

Structural similarity between the input and enhanced image is calculated using SSIM. Higher value of SSIM indicates a better contrast identical image. SSIM is calculated as:

SSIM(X,Y)=[l(X,Y)]α⋅[c(X,Y)]β⋅[s(X,Y)]γ[17]

Where x,y represents the dimension of original and enhanced image; α, β, γ represent constant whose values are always greater than 0 and l, c, s denote luminance, contrast components and structure (23).

MSE

MSE (22) is the distortion measure for finding the difference between the input image and enhanced image and is expressed as:

MSE=1mn∑i=1m∑i=1n(Aij−Bij)2[18]

Entropy

Entropy describes the average content information of the image. Entropy is directly proportional to image quality. Higher the entropy, the better the image quality. Entropy is formulated as:

ENT=−∑l=0G−1I(l)logI(l)[19]

Where ENT (entropy) represents the gray level, l means intensity levels and I(l) represents probability density function (23-26).

Table 4 represents the comparison with the state of the art results.

Discussion

In summary, the research successfully addressed the preprocessing challenges associated with retinal images by implementing a comprehensive methodology. The achieved results showcase the potential of the proposed method to significantly enhance retinal images, enabling better segmentation outcomes. This work contributes to the field of retinal image analysis and offers valuable insights for future advancements in this area.

To evaluate the performance of the proposed method, the DRIVE and STARE datasets were utilized. The results obtained were highly promising, with an average PSNR of 45.31±40.78, an average SSIM of 0.97, and an average entropy value of 7.18±6.17. These quantitative evaluation metrics clearly indicate the effectiveness of the proposed approach.

This research focused on preprocessing retinal images, specifically targeting noise removal and image enhancement. The proposed method employed various filtering techniques to achieve these objectives. The process began by converting the RGB image to a saturated channel through HSV conversion, followed by the application of anisotropic filtering to effectively eliminate noise using a smoothing filter. Subsequently, a Wiener filter was applied, and unsharp masking was performed to further enhance the images.

Furthermore, when compared to existing state-of-the-art methods, the proposed method demonstrated superior performance, surpassing them in terms of image quality and segmentation accuracy. The achieved results highlight the practicality and usefulness of the proposed method for retinal image segmentation purposes.

Despite the promising results, it is essential to acknowledge the limitations of this work such as potential challenges in scalability to larger datasets or variations in image quality across different sources.

The developed technique can be seamlessly integrated into existing workflows for computer-aided decision-making in retinal image analysis. Its ability to enhance image quality and improve segmentation outcomes can significantly impact diagnostic accuracy and treatment planning.

Conclusions

The research successfully tackled the challenges involved in preprocessing retinal images by implementing a comprehensive methodology. The results demonstrate the potential of the proposed method to significantly improve retinal images, leading to better segmentation outcomes. This work contributes to the field of retinal image analysis and provides valuable insights for future advancements. To evaluate the performance of the proposed method, the DRIVE and STARE datasets were used. The results were highly promising, with an average PSNR of 45.31±40.78, an average SSIM of 0.97, and an average entropy value of 7.18±6.17. These quantitative evaluation metrics clearly indicate the effectiveness of the proposed approach. The research focused on preprocessing retinal images, specifically targeting noise removal and image enhancement. The proposed method employed various filtering techniques to achieve these goals.

Acknowledgments

Funding: None.

Footnote

Peer Review File: Available at https://jmai.amegroups.com/article/view/10.21037/jmai-23-80/prf

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://jmai.amegroups.com/article/view/10.21037/jmai-23-80/coif). The authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. This article does not contain any studies with human participants performed by any of the authors. IRB approval and Informed consent were waived as no patients were involved.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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