Underwater images are important carriers and forms of underwater information, playing a vital role in exploring and utilizing marine resources. However, underwater images have characteristics of low contrast and blurred details because of the absorption and scattering of light. In recent years, deep learning has been widely used in underwater image enhancement and restoration because of its powerful feature learning capabilities, but there are still shortcomings in detailed enhancement. To address the problem, this paper proposes a deep supervised residual dense network (DS_RD_Net), which is used to better learn the mapping relationship between clear in-air images and synthetic underwater degraded images. DS_RD_Net first uses residual dense blocks to extract features to enhance feature utilization; then, it adds residual path blocks between the encoder and decoder to reduce the semantic differences between the low-level features and high-level features; finally, it employs a deep supervision mechanism to guide network training to improve gradient propagation. Experiments results  demonstrated that the proposed method can fully retain the local details of the image while performing color restoration and defogging compared with other image enhancement methods, achieving good qualitative and quantitative effects. In recent years, marine information processing technology has developed vigorously, and the application of underwater object detection technology has become increasingly widespread. It involves the laying of submarine optical cables, the construction and maintenance of underwater oil platforms, the salvage of sunken submarine ships, the fishing of marine organisms, marine ecosystem research, and other fields. Underwater optical image has high resolution and abundant information with obvious advantages in short-distance underwater target detection. However, because of the influence of scattering and absorption of light, underwater images often have many quality problems such as noise interference, fuzzy texture features, low contrast, and color distortion. These lead to the lack of useful details in the target recognition of underwater images, bringing significant challenges to the marine fishery and other fields. Underwater image enhancement technology can effectively improve the quality of underwater images and provide powerful help for the realization of advanced tasks such as positioning and tracking of marine organisms. Therefore, in order for underwater images with high resolution and high color saturation to be obtained, it is of great significance to enhance the details of underwater images.Compared with atmospheric optical imaging technology, underwater optical imaging technology is deeply affected by the absorption and scattering of light by water bodies. On the one hand, absorption is the energy loss caused by light reflected from an object entering the camera because water absorbs light of different wavelengths differently. Absorption can cause color attenuation. The energy absorption of red light is the largest, and that of blue-green light is the least, and thus underwater images show a blue-green tone. On the other hand, scattering is the energy loss caused by the change of direction of light in the transmission process caused by suspended particles or ambient light. In underwater imaging, the backscattering will cause background noise in the image and reduce the image contrast. The forward scattering causes the point light source to diffuse into a dispersion circle, resulting in fuzzy features such as textures, edges, colors, etc. Many underwater image processing technologies have emerged in order to solve the above problems, and they are mainly divided into image enhancement methods based on the non-physical model, image restoration methods based on the physical model, and image enhancement methods based on deep learning.The non-physical model method mainly improves the visual effect by directly adjusting the pixel value of the image. For example, Iqbal et al.  proposedThe physical model method is to build a mathematical model for the degradation process of underwater images. First, one estimates the parameters according to the model, and after that reverses the clear underwater image. For example, Drews et al.  (UDCP) pAs is broadly known, deep learning has developed rapidly and is widely used in various computer vision and image processing tasks. Some studies have tried to use data-driven technologies  to cope with the problem of image improvement. WaterGAN  took in-On the basis of the above research, this paper proposes a deep supervised residual dense network (DS_RD_Net) for underwater image enhancement, which trains an encoding-decoding network to learn the mapping relationship between clear in-air images and synthetic underwater degraded images. It fully preserves the detailed information, such as the content structure of the original image while restoring the color and removing the fog of the original image. (1)Because it is difficult to obtain real clear underwater images, taking real underwater images, in-air images, and depth maps as input, we used UWGAN to generate a large training dataset of paired images by training generator and discriminator.(2)DS_RD_Net is proposed for underwater image detailed enhancement. Residual dense blocks are adopted to fully extract features of different levels and different scales in order to reduce the loss of details during feature propagation. Residual path blocks are added to the skip connection between the encoder and decoder, which balances the semantic differences between the low-level features and high-level features and reduces the loss of details in the down-sampling process.(3)A deep supervised mechanism is introduced to guide the DS_RD_Net training and improve the gradient propagation, thereby enhancing the robustness of the network and enabling the model to achieve a good enhancement effect on images with different degrees of degradation.(4)We executed extensive performance comparisons between DS_RD_Net and other underwater image enhancement methods and demonstrated the effectiveness of the proposed method quantitatively and qualitatively.The remainder of this paper is structured as follows. In When propagating in water, light is strongly attenuated by the scattering of particles and impurities and the absorption of the water medium. Scattering is a small-angle deflection phenomenon when light travels along a straight line. Absorption is the energy loss caused by light in the propagation process. According to Jaffe , as showIn general, the typical characteristics of images taken in an underwater environment are as follows. One is the contrast reduction caused by backscattering and the details blurring caused by the forward scattering. The other is color attenuation caused by the different absorption of light by different wavelengths of water. The energy absorption of red light is the largest, and that of blue-green light is the least; thus, underwater images show a blue-green tone. Therefore, it is of great significance to study the imaging principle of underwater images, which can help us to better refine underwater images.Deep learning has demonstrated brilliant success in modeling complex nonlinear systems. Still, it requires much training data that are difficult to obtain in deep-sea environments, and it is also difficult for underwater images to have corresponding label values. The generative adversarial network can generate a large training dataset of paired imagery, including synthetic underwater images and real in-air images. These data serve as input to a novel end-to-end network for color correction.UWGAN , a generIn this paper, a deep supervised residual dense network for image enhancement is proposed to better learn the mapping relationship between the in-air images and the synthetic underwater degraded images. We designed the modules of feature extraction, feature fusion, and supervision mechanism to preserve the structure and content details of the original image as much as possible while restoring color and defogging so that the image will not be affected when used for advanced computer vision tasks . The overall network architecture is shown in The absorption degree of water medium to the light of different wavelengths is different, leading to the color polarization of underwater images. Scattering caused by water impurities will reduce the image contrast. Distortion caused by scattering will blur image details. Therefore, this increases the difficulty of information extraction, making underwater images difficult to recognize. It is especially important to retain the detailed features of the original image when enhancing the image. The residual dense blocks can make full use of the features of different levels and scales to extract detailed features such as edges, textures, and colors as much as possible to reduce the loss of details during feature propagation.In the paper, residual dense blocks  were useThe encoder: Firstly, similar to ResNet , the ResThe decoder: The ResDense Decoder block b also coUnderwater images are blurry and distorted in color. Aquaculture creatures such as holothurians, echinus, and scallops tend to be small and occupy a small pixel area in the images with blurred boundaries. Down-sampling can shrink the size of the feature map and reduce the number of parameters and the amount of calculation, but it will lose the spatial location and details of the target. In order to reduce the loss of details in the down-sampling, one needs to introduce the residual path blocks into the feature fusion module.In the paper, residual path block  Figure c was addIn most networks, only the results of the output layer are supervised, while the supervision of hidden layer features is ignored. Deep supervised mechanism  introducThe paper uses L1_L2 joint loss function as the loss function of the backbone network and the branch network. L1 loss is defined as Equation (2), L2 loss is defined as Equation (3), and L1_L2 joint loss is defined as Equation (4) .(2)Ll1XThe in-air datasets we used were images of indoor scenes that had been labeled in the NYU Depth dataset V1  and the The training settings of our proposed method are presented in detail in this section. Our models were trained in the computer with the following configurations: Intel i9-10920X processor, 64 GB RAM, GeForce RTX 2080Ti graphics card.Firstly, UWGAN was trained to synthesize underwater degraded images using the labeled NYU Depth V1 and NYU Depth Dataset V2, and the 2020 Underwater Object Detection Algorithm Contest datasets. The model was trained for 30 epochs, using Adam optimizer with a learning rate of 0.0001, and the momentum term was set to 0.5. The batch size was set to 8 with output images set to 608 × 608. Secondly, DS_RD_Net was trained as an image enhancement network using synthetic pairs (including 3733 clear in-air images and 3733 synthetic underwater degraded images). The batch size was set to 2 and the output image size was 608 × 608. The learning rate was set to 0.0001 according to Adam optimizer, and the momentum term was set to 0.5. Our model was trained for 200 epochs.To verify the effectiveness of our proposed method, we conducted five ablation experiments to evaluate the residual dense blocks, the residual path blocks, and the deep supervised mechanism. First, the Unet   for image enhancement can be used as an indicator of image enhancement performance . We ran In underwater image enhancement based on deep learning, it is challenging to collect large sets of underwater data in deep-sea environments. Obtaining the ground truth of the true colors of natural seabed scenes is also an open problem. In addition, most deep learning models fail to retain and transmit details of underwater images fully, and do not fully extract depth features of underwater images, resulting in color imbalance and detail blurriness of recovered images, which limit their applications in practical scenarios. This paper proposes a deep supervised residual dense network for underwater image enhancement that better learns the mapping relationship between clear in-air images and synthetic underwater degraded images. Compared with the other underwater image enhancement method, the proposed method fully retains the details of the content and structure of the original image while defogging and recovering color, obtaining good quantitative and qualitative results.Considering that it is difficult to obtain many paired underwater datasets, UWGAN is used for modelling underwater images from in-air images and depths. The generative adversarial network incorporates the process of underwater image formation to generate underwater degraded output images. The synthetic underwater images will be used in the image enhancement network.In view of the loss of details in the process of underwater image enhancement, we proposed a deep supervised residual dense network. The network uses residual dense blocks to extract features of different levels and different scales, which can realize feature reuse and reduce loss during feature propagation; moreover, residual path blocks are added to the skip connection between encoder and decoder, which balances the semantic differences between low-level features and high-level features and reduces the loss of spatial information in the down-sampling process.A deep supervision mechanism is introduced to construct the accompanying objective function for the hidden layer output of the network, and it guides the network training process and improves the phenomenon that the gradient disappears during the backpropagation of the deep convolutional neural network. This improves the robustness of the network and enables the model to achieve a good enhancement effect on images with different degrees of degradation.The proposed method is helpful for future research on underwater image enhancement based on deep learning algorithms. Future work will focus on improving the image generation method to produce more realistic underwater degraded images to improve the effectiveness of our DS_RD_Net further.


In contrast, EFA, highlighted a five-factor model which reflects the segregation of the D-KEFS battery into its main tasks while still clustering higher-level tasks together. However, this model was poorly supported in the subsamples. Thus, the parsimonious two-factors model revealed by OPNMF encompasses the more complex factorization yielded by EFA while enjoying higher generalizability. Hence, OPNMF provides a conceptually meaningful, technically robust, and generalizable factorization for psychometric tools.While a replicability crisis has shaken psychological sciences, the replicability of multivariate approaches for psychometric data factorization has received little attention. In particular, Exploratory Factor Analysis (EFA) is frequently promoted as the gold standard in psychological sciences. However, the application of EFA to executive functioning, a core concept in psychology and cognitive neuroscience, has led to divergent conceptual models. This heterogeneity severely limits the generalizability and replicability of findings. To tackle this issue, in this study, we propose to capitalize on a machine learning approach, OPNMF , and leverage internal cross-validation to promote generalizability to an independent dataset. We examined its application on the scores of 334 adults at the Delis–Kaplan Executive Function System (D-KEFS), while comparing to standard EFA and Principal Component Analysis (PCA). We further evaluated the replicability of the derived factorization across specific gender and age subsamples. Overall, OPNMF and PCA both converge towards a two-factor model as the best data-fit model. The derived factorization suggests a division between  This crisis stems from the finding that a vast number of research results are difficult or impossible to replicate8. Several contributing factors have been pointed out and possible solutions have been proposed. Among the contributing factors, the limited sample size and the flexibility in the choice of analysis appear to play an important role12. Specific choices in the sample selection, measure of interest, and the criteria for significance, together with specific criteria for evaluating the relevance or validity of the analysis’ outcomes are examples of factors that directly influence the final findings and conclusions of any study. This problem has been fully acknowledged and extensively discussed in the context of hypothesis-driven studies , and potential solutions for the problem have been suggested. Pre-registration of confirmatory hypotheses has been recommended to limit a-posteriori choices driven by questionable practices such as p-hacking and data-fishing13. However, these practices are more difficult to implement in the case of exploratory studies of human behavior, where the analysis is data-driven rather than hypothesis-driven. This applies to the search for latent structure in psychological data capitalizing on multivariate approaches. Actually, the replicability issue has been rarely raised in this domain, despite the influence of the choice of analysis on the findings has been often discussed15.As of late, research in psychological and medical sciences has been subject to a replication crisis16. It aims to reduce a number of observed variables to fewer unobserved factors in order to identify a hidden structure in the data and to facilitate interpretability14. In a conceptual or theoretical perspective, these structures are used as constructs in sophisticated models describing different aspects of human behavior. The established models and structures are then considered as a ground theory on which following studies can build to further characterize human behavior. For example, studies have built on derived factorial models of executive functioning to establish relationships with other aspects of human behavior17, to examine genetic influences18, or to propose neural substrates19 of this cognitive function. In that context, an exploratory factor analysis is generally used to identify latent structure in a set of behavioral variables, such as a test battery, and the derived structure then serves as a model which is usually a-priori imposed on a new dataset using a confirmatory factorial analysis12. Nevertheless, as noted by Treiblmaier and Filzmoser14, many factor solutions can be derived from one correlation matrix and the final solution represents just one of many possible choices. Analyses methods, such as the EFA, involve a number of choices that require the researcher to make crucial decisions that have a substantial impact on the results and subsequent interpretation23. Such decisions include the number of factors to retain and the criteria used to select this, the type of rotation applied, and the interpretation of the resulting factor solution24. These are choices, that, in addition to the data collection aspects such as sample size and test battery, can have an influence on any type of study. Consequently, the lack of replicability of factorizations in the literature has been reported in a number of fields. For instance, one can point out the diverse and inconsistent factor solutions proposed for psychiatric scales25; personality scores26, and executive functioning31. In this context, and considering the broader framework of the replication crisis in psychological research, it appears necessary to question the utility and generalizability  of exploratory approaches to identify latent structure in psychological tools. Traditionally, Principal Component Analysis (PCA) has also been used for the investigation of the latent structure of behavioral data. To date, the literature is not in agreement as to which method is most appropriate in the context of behavioral data. Many authors argue against the use of PCA mainly because this is considered to be solely a data reduction method and not a true method of factor analysis in a psychological sciences perspective35. However, other authors disagree37. Generally, the main point of debate concerns the perspective in which the factorization is applied. As aforementioned, EFA specifically aims to identify hypothetical constructs . In the behavioral sciences, these latent dimensions are assumed to be unobservable characteristics of people. Accordingly, the factors derived from an EFA are expected to have a theoretical validity. In contrast, PCA aims to provide a summary representation of the original variables into components, without having the specific aim to reflect theoretical constructs. Given their different aims, EFA and PCA have different ways of conceptualizing sources of variance in measured variables. EFA assumes that factors are not perfectly reflected by the measured variables, and thus distinguishes between variance in measures due to the common factors and variance due to unique factors. On the other hand, PCA does not make such a distinction and the resulting components contain a combination of common and unique variance38. Considering this distinction further implies that EFA factors are assumed to reflect latent constructs, and thus should not be expected to vary across subsamples. In contrast, from a data-science perspective, PCA and data reduction approaches in general, could be expected to provide different representations depending on the datasets by extracting a simplified representation of the data. Given these differences between the two approaches, the choice of one approach over the other can influence the result, perpetuating the problem of replicability in the identification of latent structures.A popular exploratory method widely used in psychological research is exploratory factor analysis (EFA), which has been introduced in the field by Spearman39. However, despite its significance, the true nature of executive abilities remains rather elusive. One of the main reasons for this is that executive functioning is not a single process but rather a “macro-construct” encompassing various aspects of mental functioning40. Moreover, the lack of a clear formal definition of executive functioning is also due to the nature of the aspects that constitute it, the relationship among these and their contribution to the overall concept41. As a result, there is a constant interest in the study of the structure of executive functioning and its relationship with other traits and behaviors17. Throughout the years, several neuropsychological tests have been designed to capture and measure different executive abilities. However, the measurement of executive functioning poses several challenges44 including the fact that executive functioning tests tend to be inherently impure29. Executive functioning operates on other cognitive processes, and thus any score derived from an executive functioning task will unavoidably include systematic variance that can be attributed to non-executive functioning processes associated with that specific task context44. This latter issue is referred to as the task impurity problem and is addressed by using factor analytical techniques. These map the shared variance between tests of executive functioning to a set of latent variables, providing a cleaner estimate of these higher-order cognitive abilities than the individual tests45. Consequently, numerous studies have investigated the latent structure of executive functioning using different factorization methods and executive functioning batteries. However, the different studies have resulted in diverse findings and conceptual models31. The long-term study of factors, or components, of executive functioning is thus particularly illustrative of the plurality of latent structures that can be derived from factorization methods in psychological research for a particular concept.Executive functioning is one of the most studied psychological concepts in psychology and is continuously examined in cognitive neuroscience. Executive functioning refers to processes central to coordinated, goal-directed behavior and is thought to play a major role in a wide range of different psychiatric and neurological diseases44. One such test battery that has become increasingly common in clinical practice, as well as in research, is the Delis–Kaplan Executive Function System46. The D-KEFS is one of the first normed set of tests developed specifically to assess executive functioning. It consists of nine tests comprising traditional and newly developed tests covering a wide spectrum of verbal and non-verbal executive functions, which are all designed to be stand-alone instruments that can be administered individually or together with other D-KEFS tests. Past studies have used different methods to attempt to evaluate the latent structure of this particular battery, identifying some evidence of diverse latent factors explaining performance on individual tests48. In summary, the D-KEFS represents a widely used psychological tool with applications in clinical settings, but for which different factorizations could be proposed in the healthy population.In the clinic, the most popular way of assessing executive functioning is by using test batteries that evaluate the diverse higher-order abilities through multiple testsConsidering the heterogeneous factorization results in the literature of executive functioning and psychology in general, generalizability should be a crucial criterion of validity in order to reach a conceptual consensus in psychological sciences. However, as can be seen in the study of executive functioning, a plethora of models exists. In the context of a replicability crisis in psychological sciences, the heterogeneity of models is particularly problematic. The use of different models that examine different aspects of interindividual variability prevents comparison and integration across studies. However, practically evaluating generalizability is hard due to lack of data . This is particularly the case for factorization analyses, which require large sample sizes for each evaluation. Nevertheless, internal cross-validation can be used to give insight on how the model will generalize to unseen data that are not used for model derivation. As a common approach in the machine learning field, cross-validation consists of the partitioning of a dataset into subsets. The analysis is then performed on one subset (the training set) and validated on the other subset (the test set) across multiple runs with different training and test sets.25. The new factor-structure was moreover shown to more reliably relate to specific brain functions than the original PANSS subscales, demonstrating the usefulness of this OPNMF approach49. This technique could hence significantly contribute to the definition of robust factorization of psychological variables, in particular for widely used psychological tools, such as standard neuropsychological batteries, socio-affective questionnaires and clinical scales.In recent years, the increased use of machine learning approaches has emphasized the use of internal cross-validation to increase robustness and to estimate generalizability to an independent dataset. This has led to the popularization of novel methods, which can also be used as factorization techniques, thus offering a novel perspective for behavioral sciences. While these novel approaches are commonly perceived as lacking interpretability and validity when compared to classical statistical approaches, some methods have been developed with the purpose of increasing these aspects by adding additional constraints. One such method, the OPNMF , provides a relatively higher interpretability as compared to more traditional methods, such as the classic NMF. OPNMF was recently used to identify a robust and generalizable factor structure of Positive and Negative Syndrome Scale (PANSS) data from participants with schizophrenia50. Furthermore, the choice of the optimal number of factors or components for these traditional approaches was based on recent guidelines in the field, while the choice of the optimal number of components for OPNMF was based on standard criteria assessing not only the quality of the data representation, but also its generalizability. Finally, to further evaluate the quality of the different factorizations, we examine the stability or generalizability across age and gender subsamples.The motivation of this study was two-fold. Firstly, given the importance of generalizability in the identification of latent structures, one main goal of the present study was to compare the factorization obtained when using a machine learning approach (OPNMF) with a cross-validation scheme, with the factorization derived from more traditional approaches that tend to lack the generalizability aspect, in particular EFA, but also PCA. Furthermore, a second motivation of this study was to better understand the nature of EF and the tasks commonly used to investigate it. To this end, we capitalized on a large open access dataset of healthy adult scores of the D-KEFS provided by the Enhanced Nathan Kline Institute – Rockland Sample. This dataset is heterogenous in covering the whole adult life span, providing a good gender balance and including participants from the whole population (including different ethnicities), thus making it optimal for this study in which generalizability is central. EFA and PCA were here performed by using standard statistical techniques as implemented in open access statistical tools such as JASP51. Written informed consent was obtained from all participants. The local ethics committee of the Heinrich-Heine University in Düsseldorf, Germany approved analysis of the data and all methods were carried out in accordance with relevant guidelines and regulations. The main variables of the analyses included 17 D-KEFS Total Achievement Scores  groups: (1) the full dataset including 334 adults; (2) a subset of the data including only males (n = 101); (3) a subset of the data including only females (n = 233); (4) a subset of the data only including subjects aged over 50 (n = 144); and (5) a subset of the data only including subjects aged 50 or under (n = 220).The current study used age-corrected scaled D-KEFS scores of 334 adults  obtained from the Enhanced Nathan Kline Institute—Rockland Sample (eNKI)Trail Making Test, which aims at assessing attention, resistance to distraction and cognitive flexibility; (b) Verbal Fluency Test, which assesses the ability of generating words fluently from overlearned concepts and thus reflects efficient organization of such concepts; (c) Design Fluency Test, which is a non-verbal version of the Verbal Fluency Test and assesses the ability of quickly generating designs; (d) Color-Word Interference Test, which taps into inhibition and cognitive flexibility by assessing the ability to inhibit an overlearned verbal response in order to generate a conflicting response; (e) Sorting Test, aims at measuring multiple components of concept-formation and problem-solving abilities; (f) Twenty Questions Test, which assesses the ability to formulate abstract questions and to come up with problem-solving strategies; (g) Word Context Test, assesses skills such as deductive reasoning, information integration, hypothesis testing, and flexibility of thinking; (h) Tower Test, which assesses spatial planning and rule learning; and (i) the Proverb Test, which tests abstraction abilities. All variables included in the present study are presented in Table The D-KEFS battery offers a wide range of tests that tap into many of the established constructs of executive functioning. The D-KEFS battery includes the following tests: (a) 52, classification of cancer subtypes54, identification of structural brain networks55, and identification of dimensions of schizophrenia symptoms25. Such applications of NMF and its variants have shown that such methods do not require the input data to be normally distributed. One such variant, the OPNMF, has in fact been shown to derive stable and generalizable factor solutions for data with skewed distributions49. The present study aims at discovering the latent structure of executive functioning by applying this promising method to D-KEFS performance scores. In order to achieve this in an interpretable fashion, the present study adopted a specific variant of NMF, the OPNMF, which adds additional constraints to the algorithm in an effort to promote sparsity and hence improved interpretability to the results56.NMF is a factorization method that enables the decomposition of a given matrix into two non-negative matrices: (1) a basis matrix with columns representing the resulting latent factors and (2) a factor-loading matrix representing the loading coefficients. The two resulting matrices together should approximate the original data matrix. NMF and its variants have been widely used in various recent biomedical studies including metagene discovery25. Considering the different sizes of the sub-samples, the cross-validation scheme that was used , ensured the robustness of all analyses, including the ones using smaller subsets of the dataset, in a more direct way than classical power and its use in classical statistics. Specifically, the eNKI sample was split into two halves, and OPNMF was performed on each split sample to derive the basis matrix. Subsequently, each item was assigned to a specific factor based on its largest coefficient within the basis matrix. The adjusted Rand index57, and variation of information58 were then employed to assess the stability of item-to-factor assignments between the basis matrices derived from the two split samples. Although OPNMF generates almost clustering-like structure, it allows small contributions from multiple items to specific factors. Hence we further evaluated the stability of the whole entries by comparing the two basis matrices as assessed by the concordance index59. For the adjusted Rand-index and concordance index, a higher value indicates better stability across splits, while for the variation of information metric, better stability corresponds to lower values. Generalizability was assessed by quantifying out-of-sample reconstruction error by projecting the data of one split sample onto the basis matrix from the other split sample. A lower increase in out-of-sample error compared with within-sample reconstruction error indicates better generalizability25. All analyses were run using Matlab R2018a with customized codes, which are available upon request.The OPNMF algorithm was first applied to D-KEFS total achievement scores coming from the whole sample, with the number of factors ranging from 2 to 9. Additionally, the algorithm was applied to the subsets of the dataset that were split by gender and age. The optimal number of factors, and hence the most robust, stable, and generalizable factor model, was identified by using cross-validation in 10,000 split-half analyses15. An oblique rotation  was chosen because of an a priori expectation that higher order factors would reflect a coherent domain of executive functioning, as suggested by the goals of the D-KEFS46. Furthermore, previous studies showed that executive functioning tasks tend to be correlated62, hence justifying the use of oblique rotation. In both EFA and PCA, the optimal number of factors/components was determined by using two different methods: the Scree test63 and eigenvalue Monte Carlo simulation approach64,  The Scree Test has been traditionally used for the selection of number of factors and involves plotting the eigenvalues in descending order of their magnitude and determining where they level off to ultimately select the number of meaningful factors that capture a substantial amount of variance in the data65. On the other hand, parallel analysis simulates a set of random data with the same number of variables and participants as the real data from which eigenvalues are computed. The eigenvalues extracted from real data that exceed those extracted from random data then indicate the number of factors to retain15. This method formally tests the probability that a factor is due to chance and hence minimizes the over-identification of factors based on sampling error66. It is thus superior to the reliance upon eigenvalue scores generated by factor analytic processes alone. Parallel Analysis has also been shown to perform well when determining the threshold for significant components, variable loadings, and analytical statistics when decomposing a correlation matrix67. Finally, for the reader’s information, we also reported here a typical goodness-of-fit measure in EFA, the Tucker-Lewis Index (TLI). TLI reflects the ratio of the model chi-square and a null-model chi-square. In the null-model, the measured variables are uncorrelated (thus there are no latent variables), consequently the null-model has usually a large chi-square . TLI values express the goodness-of-fit of the found model relative to the null-model and usually range between 0 and 1. As a rule of thumb, a value > 0.95 indicates a good fit , a value > 0.90 indicates an acceptable fit for and a value < 0.90 indicates a poor fit68.Data from each of the five different matrices was additionally subjected to exploratory factor analysis (EFA) and principal component analysis (PCA). In both analyses, loading matrices were rotated using promax oblique rotation as currently suggested in the fieldBased on results of the stability measures Fig. , the OPNIn the case of the OPNMF carried out on the full dataset, the resulting two factor solution consisted of one factor strongly loading on Color-Word Interference (CWI), Verbal Fluency and Design Fluency scores and moderately loading on switching components of the Design Fluency Test and the Trail Making Test. The second factor featured strong loadings on the Sorting Test, Proverbs Test, Word Context Test and the 20 Questions Test and a weaker loading on the Tower test , and resulted in virtually identical results.The EFA analyses resulted in a more heterogenous picture. The EFA analysis of the full dataset resulted in a five-factor solution consisting of one factor including scores from the Sorting Test; one factor that included scores from the CWI Test and the TMT test; one factor including scores from the Design Fluency Test; one factor including scores from the Proverbs Test, Word Context Test, 20 Questions Test and Tower Test; and another factor including scores from the Verbal Fluency Test. The EFA results for the males only dataset showed a three-factor solution with one factor including scores from the Sorting Test; one factor including scores from the Tower Test, Word Context Test and 20 Questions Test and the switching component of the Verbal Fluency Test; and one factor including the rest of the scores from the Verbal Fluency Test; the Trail Making Test, the Color-Word Interference Test, and the Design Fluency Test. In the females only dataset, the resulting factor structure consisted of a five-factor solution with one factor including scores from the Sorting Test; one factor including scores from the Verbal Fluency Test; one factor including two scores from the Design Fluency Test; one factor including the Trail Making Test, scores from the Color-Word Interference Test, the switching component of the Design Fluency Test, the Tower Test and the Word Context Test; and a final factor including scores from the Proverb Test and 20 Questions Test. When the full dataset was split by age, the EFA resulted in a four-factor solution in both subsets. In the case of the older adults dataset, the resulting factor structure consisted of one factor including scores from the Sorting Test; one factor including scores from the Verbal Fluency Test, the Color-Word Interference Test, the Trail Making Test and the Word Context Test; one factor including scores from the Design Fluency Test and the Tower Test; and a final factor including scores from the Proverb Test and 20 Questions Test. In the case of the younger adults dataset, results showed one factor including scores from the Verbal Fluency Test; one factor including scores from the Design Fluency Test; one factor including scores from the Color-Word Interference Test, and the Trail Making Test; and a factor grouping scores from the Sorting Test, Tower Test, Proverb Test, Word Context and 20 Questions Test. Result figures for each of the subsets can be found in the supplementary material. Importantly, all EFA and PCA analyses were replicated using another open access statistical software, JamoviAlthough the field of psychology has acknowledged and discussed the existence of a replicability crisis extensively, this issue has received less attention in the context of multivariate approaches for psychometric data factorization. This has resulted in heterogenous factorization results for several constructs in psychology, including executive functioning. Given the importance of replicability and generalizability in the identification of latent structures, the main goal of the present study was to compare the factorization obtained when using a machine learning approach (OPNMF) with a cross-validation scheme with the factorization derived from more traditional approaches, in particular EFA, but also PCA, in the D-KEFS. These latter approaches were performed as typically implemented in standard statistical software and following current guidelines, which usually do not include generalizability evaluation. In addition to the evaluation of factorization approaches, this study provides further insight into the specific nature of the D-KEFS and hence also contributes more generally to the understanding of executive functioning. The following paragraphs start with a discussion of the results of the EFA analysis with regards to previous literature together with EFA theoretical background. We then discuss the convergent results obtained when using OPNMF and PCA from a methodological point of view and also with regards to previous literature on executive functioning and the related evaluation tools. Finally, we discuss the resulting two-factor solution in the context of a parsimonious and robust representation of executive functioning for various applications.70 to six factors71.Using traditional EFA analysis, our investigations of the factorization across subsamples first indicate that the optimal solution can vary across subsamples, hence suggesting that the generalizability of the factor solution derived by an EFA analysis can be relatively limited. Overall, in the whole dataset, a five-factor solution appeared to be the best model fit. This result suggests a segregation that reflects the structure of the D-KEFS battery with the Sorting, Design Fluency and Verbal Fluency Tests each being assigned to their own factors, while tasks that require a certain level of abstraction and problem-solving abilities were grouped together in one factor. Thus, overall, the factorial analysis was here strongly influenced by the specific structure of the test battery that was used. It is noteworthy that this finding is somewhat contradictory with the core assumption behind EFA that states that EFA reveals unobservable latent variables reflecting meaningful psychological constructs. A similar, albeit not identical structure is seen when performing an EFA on females only. In the case of males, results suggested a three-factor solution, while in both younger and older adults the EFA indicated a four-factor solution. The evaluation of the theoretical validity of the factorization derived here by the EFA in a psychological science perspective is complicated by the fact that the literature reports a multitude of different factor models, including various factor solutions, all using different methods of factorization, datasets and test batteries. In particular, similar exploratory studies that used EFA have also resulted in heterogenous factor solutions ranging from one42. This influential study uses a confirmatory analysis approach as opposed to the exploratory approach established in the present study, and factorizes executive functioning into shifting, inhibition and updating. Shifting refers to the ability to switch between operations and perform new operations while being faced with interference42. Inhibition requires the ability to purposefully control automatic or dominant responses42. Finally, the updating factor represents tasks that require the monitoring and evaluating of new information and, if necessary, the updating of information in working memory for the successful completion of the task at hand42. Interestingly, the EFA findings of the present study do not overlap with the shifting, inhibition and updating factors suggested by Miyake et al.42. However, it is noteworthy that the three-factor model presented by Miyake and colleagues42 was based on a limited set of tasks and did not include an exhaustive list of executive functions. Specifically, Miyake’s study42 and others72, have focused mostly on tasks that require simpler cognitive abilities, and thus tend to not include tasks that tap into more complex abilities, such as problem-solving, abstraction and strategic thinking. On the other hand, the D-KEFS battery, which was used in the present study, offers a wide range of tests that tap into many of the established constructs of executive functioning, including more complex abilities, such as abstraction, reasoning, and problem solving73. Unsurprisingly, the specific set of tasks used will heavily impact the resulting factor model. The literature does include studies that have attempted to factorize D-KEFS measures using both confirmatory and exploratory approaches. Hence, Karr and colleagues45 used confirmatory factor analysis, which led them to the conclusion that the D-KEFS taps into three EF factors, namely, inhibition, shifting and fluency. However, this study chose not to include tasks that tap into more complex abilities  in the input variables. On the other hand, Latzman and colleagues17 used EFA to factorize D-KEFS measures and reported a three-factor model comprising Conceptual Flexibility, Monitoring and Inhibition, which was likened to the Miyake model by the authors.One model of executive functioning that has acquired a significant amount of empirical support is the three-factor model by Miyake et al.42 by reporting similar three factor solutions from a series of confirmatory factor analyses of diverse cognitive tasks74. Other similar confirmatory approaches have resulted in different factor solutions depending on the age group that was investigated79. To further understand the heterogeneity of findings reported in the literature and the divergence between the results of the EFA in the current study and previous conceptualization, it is important to note here that there is a fundamental difference between confirmatory and exploratory approaches in terms of their use to identify latent factors. Confirmatory approaches, such as Confirmatory Factor Analyses, use knowledge of the theory of the construct and previous empirical findings to test a hypothesis that has been postulated a priori. Therefore, the aim of this approach is to verify a specific factor structure of a set of observed variables. This approach will hence provide an evaluation that is in alignment with current research45, however will be undeniably impacted by the initial research hypothesis used. On the other hand, exploratory approaches identify the underlying factor structure of a set of variables without the need of establishing an a priori hypothesis. The latter, thus, allows for the deeper understanding of a construct in an exploratory fashion. In other words, confirmatory approaches can be considered as “hypothesis-driven” approaches to some extent, while exploratory approaches can be considered as “data-driven” approaches. Differences in results when comparing confirmatory and exploratory factor analyses are therefore not surprising.A number of subsequent studies have supported the three factors of shifting, inhibition and updating presented by Miyake et al.Simple and Complex (or low- vs high-level) executive functioning tasks. While previous factorization findings of executive functioning do not seem to support our findings indicating a split between Simple and Complex tasks, it has been previously shown that people suffering from executive functioning impairment, such as in the case of patients with mild cognitive impairment, tend to exhibit selective rather than global impairment with some studies showing a separation between impairment on simple versus more complex tasks82. The idea of simple versus complex is also reflected in neurobiological literature in which a separation of tasks between the dorsolateral prefrontal cortex and the ventrolateral prefrontal cortex83 has been suggested. The former has been implicated in the context of more complex aspects of executive functioning although not all evidence supports this83. The notion of separation of tasks based on complexity is also in line with the proposed hierarchical organization of the frontal cortex84. When taking a deeper look at the individual measures that were included in the present study, it becomes apparent that there is a noteworthy difference between the different measurement approaches used and the subsequent processes that they could be eliciting. Specifically, while some of the variables are measures of accuracy , others rely more heavily on time pressure and processing speed . This difference in measurement approaches seems to be reflected in the resulting dichotomy between Simple and Complex tasks. In fact, whereas the Complex tasks quite clearly emphasize accuracy, the Simple tasks appear to be more overtly driven by the element of time. The number-letter switching task, CWI and CWI switching are all direct measures of time while the other variables that have been grouped together with the Simple factor are measures of fluency which arguably also involves an aspect of time pressure since its measurement is related to time efficiency when recalling items. Additionally, although the factor labelled as Complex in the present study includes measures that tap into abilities such as reasoning, abstraction, problem-solving, and strategic thinking, this factor also includes measures coming from the Sorting Test. The D-KEFS Sorting Test and tests with a similar procedure, such as the Wisconsin Card Sorting Test85, have been traditionally associated with the Shifting or Conceptual Flexibility factor74. This association appears to be appropriate since the Sorting Test and its variants require participants to shift from previous sorting rules to new rules to achieve a greater number of accurate sorts. However, the Sorting Test also taps into more abstract problem-solving strategies that go beyond simple shifting. This complexity of the Sorting Test is reflected by the results of the present study. Thus, the factorization derived from PCA and OPNMF appears parsimonious and meaningful from a psychological construct standpoint. This study hence demonstrated that the application of machine learning approaches to psychometric data can provide interpretable outcomes in a psychological science perspective. It should be noted here as well that OPNMF further promotes out-of-sample generalizability by evaluating reconstruction error in a left out set across multiple runs, which is a crucial aspect considering the replication issues in psychological sciences.While suggesting a different factorization than EFA, PCA and OPNMF together converge toward a similar 2-component model. It is noteworthy that this convergence was observed despite the fact that the choice of optimal factor solution was based on different criteria within and between approaches including the part of variance explained, data representation quality and stability evaluations. PCA and OPNMF factorization methods here resulted in one factor that designated loadings to Color-Word Interference scores, Verbal Fluency, Design Fluency Test and the Trail Making Test. The second factor featured strong loadings from the Sorting Test, Proverbs Test, Word Context Test and the 20 Questions Test and a weaker loading for the Tower test. These results seem to indicate a division between tasks that require monitoring and task-switching, and more complex tasks that require concept formation, abstraction, and problem-solving. Specifically, tasks that require a certain level of abstraction, strategic thinking and problem-solving abilities, such as the Sorting Test, Twenty Questions Test, Word Context Test, Tower Test, and the Proverb Test, were all grouped into one factor. On the other hand, tasks that require less complex abilities were grouped in another factor. The latter factor includes tests that tap into abilities such as monitoring, fluency, cognitive flexibility, and inhibition. Hence, in contrast to previous results, our results obtained from the OPNMF and PCA analyses suggest a stable and robust two factor model indicating a division between Simple and Complex is better at reflecting consensual real-world concepts than models with a higher number of factors. Considering these scientific qualities, the robust and parsimonious two-factor model that emerged from this study should be of higher practical utility for characterizing inter-individual variability in executive functioning performance at both the biological level (such as genetic and brain subtrates) and the environnmental level .Despite the apparent divergence of factorization results between EFA on the one hand and OPNMF and PCA on the other hand, it should be noted that the results of our EFA analyses provide a higher factor model that reflects the segregation of tasks that was used in the D-KEFS battery while still assigning a single factor to tasks that require abstraction and problem-solving skills. Hence, the parsimonious two factor model can also be seen as encompassing the more complex factorization yielded by EFA. The results of the present study thus suggest that the OPNMF and PCA results provide a robust and stable two factor solution that separates tasks that require monitoring and task-switching from more complex tasks that require concept formation, abstraction, and problem-solving. Considering all the points discussed above, together with the fact that both methods converged towards one robust model, we suggest that our results may reflect a robust factor model that applies across a wide age range and across different factorization methods. Given the uncertainty and diverse findings of the factorial structure of executive functioning in the literature, this model offers a more scientifically parsimonious model from both technical and conceptual standpoints. From a technical standpoint, the approach established in the present study  is the most reasonable to our knowledge since it is commonly known that different approaches can result in different factor solutions. From a conceptual standpoint, the 2 factor solution presented in this study results in a scientifically parsimonious model since the differentiation between low-level and high-level executive functioning measures, a model further supported in subsamples. In contrast, EFA, highlighted a five-factor model as the better fit to the overall cohort, but which was poorly supported in the subsamples. This five-factor factorization reflects the segregation of the D-KEFS battery into its main tasks while still clustering higher-level tasks together. Thus, the parsimonious two-factors model revealed by OPNMF underlies the more complex factorization yielded by EFA while enjoying higher generalizability. Hence the application of OPNMF to psychometric data in the present study provides conceptually meaningful, technically robust and generalizable factorization for psychometric tools.In addition to demonstrating the advantages of a machine learning approach for the factorization of psychometric data in a replicability perspective, this study also provides a robust model of factorization of the D-KEFS. The derived factorization suggests a division between Supplementary Figure 1.Supplementary Figure 2.Supplementary Figure 3.Supplementary Figure 4.Supplementary Figure 5.Supplementary Figure 6.Supplementary Figure 7.Supplementary Figure 8.Supplementary Figure 9.Supplementary Figure 10.Supplementary Figure 11.Supplementary Figure Legends.


The reinforced concrete (RC) member’s shear strength estimation has been experimentally studied in most cases due to its nonlinear behavior. Many empirical equations have been derived from the experimental data; however, even those adopted in the construction codes do not thoroughly and accurately describe their shear behavior. Theoretically explained equations, on the other hand, are aligned with the experiment; however, they are complicated to use in practice. As shear behavior research is data-driven, the machine learning technique is applicable. Herein, an artificial neural network (ANN) algorithm is trained with 776 experiment results collected from available publications. The raw data is preprocessed by principal component analysis (PCA) before the application of the ANN technique. The predictions of the trained algorithm using ANN with PCA are compared to those of formulae adopted in a few existing building codes. Finally, a parametric study is conducted, and the significance of each variable to the strength of RC members is analyzed. Unlike the bending and compressive behaviors of reinforced concrete (RC), their shear behavior has yet to be theoretically well described. Typical equations that explain an RC member’s bending and compression behaviors begin from decent assumptions and arrive at their final expressions through mathematical derivation. Meanwhile, the equations that describe the shear behavior still predominantly depend on statistical analysis and regression based on laboratory experiments.For such empirical equations to better predict the behavior of the RC elements, collecting more data and considering a more comprehensive range of input parameters is preferable and can provide more generality. Such prerequisites make research on the shear behaviors of RC members an excellent subject in which to apply machine learning (ML) techniques, as a more extensive data set is typically more beneficial for training a learning algorithm.The empirical approach has a potential drawback. In contrast to the analytically derived equations, where the dependency on specific variables is apparent, researchers do not know whether a particular variable is a control parameter or not. For this reason, it is considered safer to keep more variables as potential control parameters when experimenting; however, such practice inevitably increases the size of the dataset. The bigger size of the dataset, as a consequence, slows the training speed of a learning algorithm and sometimes even harms the prediction accuracy. This compensation is known as the curse of dimensionality. To overcome such a curse, raw data is preprocessed before being fed into the learning algorithm. Among many candidates of preprocessing techniques, this article specifically focuses on the method called principal component analysis (PCA). It seeks the applicability of PCA to the raw dataset as a means of preprocessing.PCA can reduce the size of the dataset. PCA can reduce the number of input variables  through statistical analysis of the relationships between the features in the dataset. Although there are many available features in the dataset, not all of them equally affect the behavior of the RC member . When PCA preprocesses a dataset, it returns a set of mutually independent linear combinations of the existing features in the dataset. These processed features are called the principal components.There can be a couple of strategies once we obtain the principal components. One can select a few components that describe the correlation in the dataset better than other components. On the other hand, one can choose all principal components without benefiting from dimension reduction but only taking advantage of orthogonalization. If a few principal components are selected, the training speed is expected to be faster since the dimension is reduced. Suppose all of the principal components are selected. Although we may not notice any speedup in training, the quality of the result is expected to be better due to the orthogonalization of the input dataset.Since the early 2000s, researchers in the structural engineering field have begun to adopt ML techniques into their research, particularly to predict the shear behaviors of RC members better. The main learning algorithm considered has been a feed-forward backpropagation artificial neural network (FFBP ANN), where the input variables are selected according to the characteristics of the experiments. Sanad and Saka  trained Although there have been many previous studies, the number of experimental data used for training and validation has rarely exceeded 500, and none of them has preprocessed the raw data using PCA to boost the training efficiency and prediction accuracy. The research introduced in this article uses a data set consisting of 776 shear experimental results and secured data from the precedent publications ,28,29,30The study on the shear behavior of RC members is data-dependent, and the effectiveness and correlations between the control parameters of the experiment are not foreseeable. Based on such character, this article proposes an ANN approach with 776 PCA preprocessed experiment data ,28,29,30The design equation for the shear strength of reinforced concrete beams specified in ACI 318-19 [uV is the factored shear force at a section, ϕ is the strength reduction factor. In this equation, For non-prestressed members the concrete shear contribution, If The size effect factor, vA represents the area of shear reinforcement, The shear reinforcement contribution is based on the 45° truss model, using the following equation,sV in Equation (6) is derived from equilibrium in the 45 degrees truss model. The 45 degrees truss model assumes:(a)A diagonal crack occurs in the concrete principal compressive stress direction.(b)A diagonal crack occurs at 45 degrees and is uniformly distributed in the web of concrete.(c)The tensile strength of concrete on the cracked surface can be neglected. The dowel and interlock actions are also not directly considered.(d)The stress developed in the transverse reinforcement is equal to its yield stress, and the longitudinal reinforcement does not yield and remains in the elastic range.The 45 degrees truss model provides a simplified model that helps to easily calculate the shear strength of the beam; however, the model tends to underestimate the shear strength since it fixes the crack angle at 45 degrees.EC2-04  providesk is the size effect coefficient, When Equation (8) must not exceed . EC2-04  neglectsThe classical shear design equations have been improved by compatibility-aided truss models, such as the modified compression field theory (MCFT), rotating angle softened truss model (RA-STM), and fixed angle softened truss model (FA-STM). These sophisticated theories can predict the shear strengths of the beams more accurately; however, the calculations become more complex as they come to involve additional variables and conditional equations. Nevertheless, calculating the yield shear strength, which is slightly smaller than the ultimate shear strength, is relatively simple. Based on this fact, Lee and Kim  suggestef1 is the principal tensile stress of concrete, k is the modification factor reflecting the effective principal compressive strain of concrete The equation considers the ratio of longitudinal reinforcement, shear span, and the moment at the critical section, and is expressed as follows:Instead of directly using the experimental data to train the machine learning algorithm, it is preprocessed beforehand so as to yield faster training and better accuracy. The method used is called principal component analysis (PCA).Let a set of experimental data new data ,35. In anew data , since tPCA is an orthogonal projection of aximized . In ordeThe typical PCA procedure on a data set Here, Next, the correlation As Here, The size of One may use all the principal components for the training. Such an approach would not reduce the dimension of the data set; however, each column in the preprocessed data set The data set eriments ,28,29,30The first three variables, Performing PCA on this data set yielded the following Scree plot for each principal component, shown in The architecture of FFBP ANN used in this research in shown in In order to assess the prediction by ANN, three additional measures were calculated: relative absolute error (RAE), root relative square error (RRSE), and the correlation coefficient of the prediction to the experimental measurements.To construct and compare the errors, the model was validated using a 10-fold cross-validation technique. The training data was arbitrarily divided into ten groups . The final ANN model utilized all the training data. Eight RC test points were excluded from the training set to spare for performance evaluation of the finalized ANN model.The accuracy of the predictions of the trained algorithm along with those of the shear strength equations suggested in the three different design codes introduced in ACI 318-19  Figure b also unIt must be noted here that there is a philosophical difference between the equations in the design codes and the equations for the analysis purpose. ACI 318-19  are desiThe test data of the total eight reinforced concrete beams under monotonic loading was additionally collected aside from the training set to use for the validation set. In The ultimate shear strengths of the specimens were calculated using two design codes of ACI 318-19 , the proIf the equations or the ANN model predict the shear strength of the RC beam correctly, the markers will be near the dashed line and form a horizontal line. In the cases of ACI 318-19 , and LeeACI318-19  overestiBased on the validation data set, a parametric study was conducted on the various input variables that could affect the RC beam’s shear strength. The concrete beams used in the parametric study had the same cross-section and material details as those of specimen 1 listed in The x-axes in I 318-19 , and LeeI 318-19 , respectThis subsection discusses The discrepancy between ANN and the other three equations is apparent in In The strength of longitudinal reinforcement, The longitudinal reinforcement f is closIn I 318-19  predicteI 318-19  and ANN As it is commonly applied to experiment-based studies, the prediction by ANN is neither safe nor accurate where the test data exist sparsely. For example, if the effective depth is less than 200mm, both test points and estimation by other equations tell that the shear capacity is less than 7, while the ANN model predicts its exponential growth b. Such aThe prediction by ANN appears in the middle somewhere between EC2-04  and ACI This article trained an artificial neural network (ANN) with a dataset consisting of 776 experimental data. The data were preprocessed by principal component analysis (PCA) for variable orthogonalization (de-correlation). The trained ANN predicts the shear strength of reinforced concrete (RC) beams with transverse reinforcement. When preprocessing with PCA, dimension reduction was not used in this research because only eight variables were in the dataset. The preprocessed data was used to train the neural network. The configuration of the neural network was determined through trial and error while numerous combinations of hidden layers and neurons in the layer were sought; the single hidden layer with 43 neurons returned the lowest root mean square error (RMSE).The preprocessed data was used to train the neural network. The configuration of the neural network was determined through trial and error, while numerous combinations of hidden layers and neurons in the layer were sought; the single hidden layer with 43 neurons returned the lowest root mean square error (RMSE).Eight additional experiments were conducted in order to obtain the validation set, and the prediction of the trained ANN model was compared to three different shear design equations: ACI 318-19 , and theA parametric study was also conducted in order to determine the effects of the input variables considered in this research. In this way, variables that were generally not considered in the shear design equations could be investigated, and their effectiveness to the shear strength could be studied. In addition, ANN reflected the effect of shear span ratio well while the other models did not. The shear strength tended to decrease when the shear span ratio increased from 2 to 3.5. The effect of concrete compressive strength was also observed. ACI 318-19  could no


Ultra-widefield fluorescein angiography (UWFA) is an emerging imaging modality used to characterise pathologies in the retinal vasculature, such as microaneurysms (MAs) and vascular leakages. Despite its potential value for diagnosis and disease screening, objective quantitative assessment of retinal pathologies by UWFA is currently limited because laborious manual processing is required. In this report, we describe a geometrical method for uneven brightness compensation inherent to UWFA imaging technique. The correction function is based on the geometrical eyeball shape, therefore it is fully automated and depends only on pixel distance from the center of the imaged retina. The method’s performance was assessed on a database containing 256 UWFA images with the use of several image quality measures that show the correction method improves image quality. The method is also compared to the commonly used CLAHE approach and was also employed in a pilot study for vascular segmentation, giving a noticeable improvement in segmentation results. Therefore, the method can be used as an image preprocessing step in retinal UWFA image analysis. Fluorescein angiography was introduced as a diagnostic tool over 50 years ago. Because of its constant development, it still remains a reliable diagnostic tool for many retinal diseases, i.e., diabetic retinopathy, retinal vein occlusion, age-related macular degeneration retinopathy, uveitis, or retinal/choroidal dystrophy ,2. The lneration . In receneration ,4. Ultration [∘) . CompariThe optical system, as well as the software processing UWFA images after the acquisition, are still sources of some issues that need to be improved. The associated deformations of the peripheral area may disrupt the effects of the quantitative analysis of those areas by artificially increasing the obtained values. Mapping and optimization of the three-dimensional spherical surface onto a flat image are one of the key transformations performed during the acquisition ,6,7. AnoThe vital issue, which needs to be addressed during UWFA images processing, is the uneven brightness of the image. The further away from the central area, the darker the image and the lower the contrast are. This resembles the problem of bias correction known in other imaging modalities . Uneven The inhomogeneous brightness of retinal angiographic images stems from the geometry of the imaged structure, therefore the transformations most often applied at the preprocessing stage should be local in nature, depending on regional image properties. One such transformation, very often applied to retinal angiographic images, is the technique of Contrast Limited Adaptive Histogram Equalization (CLAHE) , which dThe main goal of this work is to develop a brightness correction method, especially for UWFA images, that enhances the peripheral retinal areas without causing disruptions in the central regions. To achieve this goal, we propose an automated gamma correction procedure. The gamma value for this procedure is computed locally based on the geometrical conditions resulting from the image acquisition technique. Our method is validated on 256 images, taking into consideration the image acquisition phases  and exhibiting physiological and pathologic features  in patients diagnosed with diabetic retinopathy. Several image quality measures are calculated for the central and peripheral image regions, showing that the method introduces negligible image distortion in central areas while enhancing the peripheral image regions. The presented procedure may provide new opportunities for detecting, analyzing, and evaluating underlying image features that have important clinical and research applications.Ultra-widefield fluorescein angiography images require brightness compensation, especially in the peripheral areas. It is inducted by the spherical shape of the retina and properties of the image acquisition technique. We propose a method inspired by the retina shape to overcome these inconveniences. Our proposition is presented in two following steps. The first one is a simplified 2D case, which results in a 1D correction function, and the second one is generalized to the spatial 3D case, which results in a 2D correction function. Both are based on the assumption that the eyeball can be approximated as a sphere, which is often encountered in the retinal image analysis ,6,24.p . This image profile, to simplify further mathematical considerations, is duplicated and is placed inside the eyeball . Other pixels that express retina points situated farther away from the center require revision that depends on pixel location (represented by the distance from the center). The farther away the pixel from the center is, the more substantial pixel value correction is required. A direction of increasing demand for correction is presented in r denotes the radius of the eyeball and x is an integer number of pixels between A onto image profile, and the central axis  of the eyeball or point O. This value is within the range r and The proposed principle of correcting factor determination indirectly stems from the geometric distance from the center, measured by the curve length:r can be expressed using the number of pixels as Moreover, the retina radius Finally, using the inverse trigonometric function r represents a constant scaling factor in this equation. Because we focus solely on the proportions within the eyeball, we assume the eyeball to be a unit sphere, therefore This distance function is proportional to the angle In order to adjust these mathematical conditions to the properties of the retinal acquisition technique, we propose the correction function for the 2D case projected onto 1D space to be defined asx are then used as an argument for the gamma image correction stage [p located at x. For This on stage  accordinC and any other retina element e.g., point A. This distance is an arc The method presented above needs a generalization for spatial conditions projected onto the 2D case, as shown in C and A on the surface of a sphere, measured along the surface of the sphere. To compute the distance in spaces with curvature, straight lines are replaced with geodesics. Geodesics on the sphere are circles on the sphere whose centers coincide with the center of the sphere and are called great circles or orthodromes. The determination of the great circle distance (or orthodromic distance) is part of a more general problem of great circle navigation, which also computes the azimuths at the end-points and intermediate way-points.This curve part is the shortest distance between two points denoted as C and A in Through any two points on a sphere  of the image size, i.e., Gamma correction is a nonlinear operation that allows the visibility of dark . The written informed consent from the participants had been obtained. Among patient inclusion criteria were: age 18 or greater, diabetes mellitus type 1 or 2, nonproliferative diabetic retinopathy. Among the exclusion criteria were: retinal photocoagulation, history of pars plana vitrectomy or cataract surgery with posterior capsule rupture, media opacity disabling to assess the fundus of the eye, proliferative diabetic retinopathy, vitreoretinal traction in the macula, nonperfusion of the foveal area, any concurrent nondiabetic retinal disease. Patient preparation to image acquisition involved pupils dilation by administration of 1% tropicamide  and phenylephrine 2.5% to the conjunctival sac followed by intravenous sodium fluorescein  administration. A more detailed description of the patient cohort and the medical aspects are presented in .Fluorescein angiography retinal images were taken using Optos California P200DTx  device during three phases : early  ,30, indition (β) ,32, meastion (β) , Qualityn (β) [Q , and then (β) [Q . DefinitVerification of the method was performed using the aforementioned image database  considerThe qualitative performance of the proposed methodology is presented on exemplary images taken from the database. The images before and after the correction procedure are shown in Because the CLAHE  is oThe obtained for CLAHE quality measure values are presented graphically in Average values of the quality measures for the central and peripheral regions for both proposed and CLAHE methods are presented in Visual inspection and comparison of the resulting images obtained using both approaches are shown in For the proposed method, as can be seen from the From pression , it indiThe pixel-to-pixel measures values are higher than the corresponding values in the central image regions yet are still close to 0, which shows that the method does not introduce significant errors (noise) to the images in the peripheral regions. The distribution of one of the pixel-to-pixel measures—Absolute Error —is presented in The CLAHE method does not consider spatial relations in the image, therefore the processing is performed in the same manner in all image regions, which contrasts with the presented approach. CLAHE influences central image regions more, which is indicated by worse values of all the quality measures compared to the proposed method , Table 3In the peripheral image regions characterized by much lower contrast and overall brightness, the influence of the CLAHE approach is lower than the proposed method. It is shown by the measures from the pixel-to-pixel group  that for the CLAHE are lower than for the presented approach , Table 3For underexposed images like d the CLASummarised interpretation of the obtained quality measures’ values is presented in To conclude, the advantage over the CLAHE approach of the proposed method is in brightness enhancement resulting in more even intensity distribution over the whole retina image without the extra sharpening. The technique might be beneficial for underexposed images. Last but not least, the proposed approach does not require the setting of any controlling parameters. Therefore it is easy to be applied, especially by inexperienced technicians. At the same time, it does not exclude the application of more advanced processing methods if required in clinical practice for specific cases.The paper presents a straightforward, geometry-based and parameterless method for UWFA image preprocessing. The method assumes that the eyeball is spherical, and the correction depends on the distance from the centre. The contrast enhancement is done locally in non-overlapping blocks with the gamma correction method, in which the gamma value is calculated automatically. The method was assessed and compared to the commonly used CLAHE algorithm using several image quality measures that show its performance and usefulness in UWFA image processing.The proposed UWFA image preprocessing was also applied during a pilot study dedicated to retinal blood vessels segmentation. The experiment consisted of vascular segmentation from original and brightness-enhanced images obtained by the presented approach. To detect the blood vessels, an algorithm optimized for UWFA images was adopted . The dat


Fucus spiralis that was collected in the four seasons was submitted to an extraction with ethanol:water (crude extracts Et80), followed by a liquid–liquid fractionation with organic solvents , with the aim of obtaining phlorotannin-enriched extracts. All the extracts  that were obtained for the F. spiralis of the four seasons were evaluated for their antioxidant capacity and total phenolic compounds. The summer extracts presented the highest contents in polyphenols (TPC), as well as the highest ferric reducing antioxidant power (FRAP), when compared to the samples from the other seasons. The reductive percentage of the DPPH  compound was similar between the seasons. For all the seasons, the EA extract showed the highest polyphenol content (TPC), and the highest antioxidant capacity (highest ferric reducing power (FRAP) and lowest concentration needed to reduce 50% of the DPPH compound), which is in agreement with a phlorotannin-enriched fraction. This study revealed that the polyphenol content and antioxidant power of the F. spiralis extracts are influenced by the time of harvest, as well as by the solvents used for their extraction. Fucus is an abundant and widely distributed genus of brown, perennial and edible macroalgae that inhabits the cold-temperate water regions along the littoral and sublittoral rocky shorelines of the Northern Hemisphere. However, the population is dependent on the season, solar exposure, salinity, and geographical origin. Since they inhabit intertidal zones, which is an environment of rapidly changing physical conditions due to the turning tides, they need to develop a series of metabolites that will help them endure this highly competitive and aggressive environment. This leads to the production of quite specific and potent bioactive molecules, which may be a valuable resource as nutritional or pharmaceutical supplements , and IC50 is the concentration of extract needed to reduce half the DPPH radical.The half maximal inhibitory concentration (ICtion (2) , as follp-value ≤ 0.05) [The statistical analysis of the data was carried out using the software Rstudio AGLP v3. All the results were considered statistically significant at the 5% significance level ( ≤ 0.05) . ResultsF. spiralis.The present study revealed a variability in the phenolic content, as well as the antioxidant properties, relative to the different extracts obtained from the extraction and subsequent fractionation of The EA extracts from this alga showed a higher total polyphenolic content, and, as expected, the iron chelating activity (FRAP) and DPPH radical scavenging activity were significantly higher in these extracts when compared to the others, showing that the extraction of enriched algal extracts using adequate solvents can increase the antioxidant activity of the samples.F. spiralis extracts. The extracts that were obtained from F. spiralis collected during the summer season showed a higher total phenolic content out of every season, and demonstrated the best iron chelating and DPPH scavenging activities as well.Since biotic and abiotic factors may affect the production and concentration of antioxidant compounds in brown algae, seasonal variations can also be observed in the content of phenolic compounds, as well as the antioxidant activities of The biochemical composition observed, as well as the high functional bioactivity values shown by the summer EA extract, provided information on the best extract and period of the year to collect this seaweed for its potential use as a natural antioxidant for food products.