Problem Of Quantification Research Articles

Secondary ion mass spectrometry quantification: Do you remember when a factor of 2 was good enough?

Well, do you remember when a factor of 2 was good enough? Probably, not unless you have been around secondary ion mass spectrometry (SIMS) since the early 1960s, like one of us has been. This paper will give many references back to the early days of quantification when a local thermal equilibrium model was used to obtain the first results that were accurate to within a factor of 2, but only 60% of the time. It only worked for bulk silicate matrixes. People were not even using SIMS on semiconductors in those days. Several early references showing profiles of ion implants in Si will be referenced, but it was not until 1980 that the first paper was published that explicitly showed how to use ion implants as SIMS standards. People were using ion implants as standards before 1980, but only in limited cases, and with no formal published equations specifying how to use them. But, the samples for which ion implants were used as standards were for dilute concentrations in a single matrix, which had a uniform matrix composition with depth. The rest of the paper will show how we at Eurofins EAG Laboratories tackled the problem of quantification of both major and minor elements in nonuniform, multi-element matrices with continuously graded composition changes using point-by-point CORrected-SIMS. These include SiGe heterostructure bipolar transistors, AlGaAs vertical cavity surface emitting lasers, and B plasma-implanted poly-silicon gates.

Comparison of intra- and inter-patient intensity standardization methods for multi-parametric whole-body MRI

Objective. To test and compare different intensity standardization approaches for whole-body multi-parametric MR images, aiming to compensate voxel intensity differences between scans. These differences, common for magnetic resonance imaging, pose problems in image quantification, assessment of changes between a baseline and follow-up scan, and hinder performance of image processing and machine learning algorithms. Approach. In this work, we present a comparison on the accuracy of intensity standardization approaches with increasing complexity, for intra- and inter-patient multi-parametric whole-body MRI. Several approaches were used: z-scoring of the intensities, piecewise linear mapping and deformable mapping of intensity distributions into established reference intensity space. For each method, the impact on standardization algorithm on the use of single image or average population distribution reference; as well as, whole image and region of interest were additionally investigated. All methods were validated on a data set of 18 whole-body anatomical and diffusion-weighted MR scans consisting of baseline and follow-up examinations acquired from advanced prostate cancer patients and healthy volunteers. Main results. The piecewise linear intensity standardisation approach provided the best compromise between standardization accuracy and method stability, with average deviations in intensity profile of 0.011-0.027 and mean absolute difference of 0.29-0.37 standard score (intra-patient) and 0.014-0.056 (inter-patient), depending on the type of used MR modality. Significance. Linear piecewise approaches showed the overall best performance across multiple validation metrics, mostly because of its robustness. The inter-patient standardization proved to perform better when using population average reference image; in contrary to intra-patient approach, where the best results were achieved by standardizing towards a reference image taken as the baseline scan.

Physics-informed information field theory for modeling physical systems with uncertainty quantification

Data-driven approaches coupled with physical knowledge are powerful techniques to model engineering systems. The goal of such models is to efficiently solve for the underlying physical field through combining measurements with known physical laws. As many physical systems contain unknown elements, such as missing parameters, noisy measurements, or incomplete physical laws, this is widely approached as an uncertainty quantification problem. The common techniques to handle all of these variables typically depend on the specific numerical scheme used to approximate the posterior, and it is desirable to have a method which is independent of any such discretization. Information field theory (IFT) provides the tools necessary to perform statistics over fields that are not necessarily Gaussian. The objective of this paper is to extend IFT to physics-informed information field theory (PIFT) by encoding the functional priors with information about the physical laws which describe the field. The posteriors derived from this PIFT remain independent of any numerical scheme, and can capture multiple modes which allows for the solution of problems which are not well-posed. We demonstrate our approach through an analytical example involving the Klein-Gordon equation. We then develop a variant of stochastic gradient Langevin dynamics to draw samples from the field posterior and from the posterior of any model parameters. We apply our method to several numerical examples with various degrees of model-form error and to inverse problems involving non-linear differential equations. As an addendum, the method is equipped with a metric which allows the posterior to automatically quantify model-form uncertainty. Because of this, our numerical experiments show that the method remains robust to even an incorrect representation of the physics given sufficient data. We numerically demonstrate that the method correctly identifies when the physics cannot be trusted, in which case it automatically treats learning the field as a regression problem.

Probabilistic mass-mapping with neural score estimation

Context.Weak lensing mass-mapping is a useful tool for accessing the full distribution of dark matter on the sky, but because of intrinsic galaxy ellipticies, finite fields, and missing data, the recovery of dark matter maps constitutes a challenging, ill-posed inverse problemAims.We introduce a novel methodology that enables the efficient sampling of the high-dimensional Bayesian posterior of the weak lensing mass-mapping problem, relying on simulations to define a fully non-Gaussian prior. We aim to demonstrate the accuracy of the method to simulated fields, and then proceed to apply it to the mass reconstruction of the HST/ACS COSMOS field.Methods.The proposed methodology combines elements of Bayesian statistics, analytic theory, and a recent class of deep generative models based on neural score matching. This approach allows us to make full use of analytic cosmological theory to constrain the 2pt statistics of the solution, to understand any differences between this analytic prior and full simulations from cosmological simulations, and to obtain samples from the full Bayesian posterior of the problem for robust uncertainty quantification.Results.We demonstrate the method in theκTNG simulations and find that the posterior mean significantly outperfoms previous methods (Kaiser–Squires, Wiener filter, Sparsity priors) both for the root-mean-square error and in terms of the Pearson correlation. We further illustrate the interpretability of the recovered posterior by establishing a close correlation between posterior convergence values and the S/N of the clusters artificially introduced into a field. Finally, we apply the method to the reconstruction of the HST/ACS COSMOS field, which yields the highest-quality convergence map of this field to date.Conclusions.We find the proposed approach to be superior to previous algorithms, scalable, providing uncertainties, and using a fully non-Gaussian prior.

Adaptive Suppression Method of LiDAR Background Noise Based on Threshold Detection

Background radiation in the LiDAR detection field of view is complex and variable, and the background noise generated can easily cause false alarms in the receiver, which affects the effective detection of the system. Through the analysis of the influence of background radiation noise of LiDAR on the detection performance, an adaptive suppression method of LiDAR background noise is proposed. This method realizes the rapid suppression of background noise in the instantaneous field of view through an adaptive threshold adjustment of current steering architecture with a back-end digital-to-analog converter (DAC) correction based on the principle of constant false alarm rate (CFAR) control. Aiming at the problem of accurate noise detection and quantification in a very short time, a dynamic comparator is used to replace the traditional continuous comparator. While detecting the number of noise pulses, the measurement of the pulse duration of noise is realized, which improves the accuracy of short-time noise detection. In order to verify the actual effect of the adaptive method, experiments were carried out based on the team’s self-developed LiDAR. The experimental results show that the measured noise ratio of the adaptive mode by using this method is the lowest. Even at 12 a.m., the noise ratio of the point cloud obtained by the adaptive mode is 0.012%, compared with 0.08% obtained by the traditional mode, which proves that this method has a good ability to suppress background noise. The proportion of noise reduction of the adaptive mode is more than 80% compared with the traditional mode. It achieves noise suppression through hardware at each detection, and each adjustment can be completed within a single period of pulse detection. Therefore, it has great advantages in real-time detection compared with the back-end software noise reduction processing method, and it is suitable for the application of LiDAR in the complex background environment.

Uncertainty Quantification of Imperfect Diagnostics

The operable state of a system is maintained during operation, which requires knowledge of the system’s state. Technical diagnostics, as a process of accurately obtaining information about the system state, becomes a crucial stage in the life cycle of any system. The study deals with the relevant problem of uncertainty quantification of imperfect diagnostics. We considered the most general case when the object of diagnostics, the diagnostic tool, and the human operator can each be in one of the many states. The concept of a diagnostic error is introduced, in which the object of diagnostics is in one of many states but is erroneously identified as being in any other state. We derived the generalized formulas for the probability of a diagnostic error, the probability of correct diagnosis, and the total probability of a diagnostic error. The proposed generalized formulas make it possible to determine the probabilistic indicators of diagnosis uncertainty for any structures of diagnostics systems and any types of failures of the diagnostic tool and human operator. We demonstrated the theoretical material by computing the probabilistic indicators of diagnosis uncertainty for an aircraft VHF communication system and fatigue cracks in the aircraft wings.

Hermann von Helmholtz and the Quantification Problem of Psychophysics

Hermann von Helmholtz has been widely acknowledged as one of the forerunners of contemporary theories of measurement. However, his conception of measurement differs from later, representational conceptions in two main respects. Firstly, Helmholtz advocated an empiricist philosophy of arithmetic as grounded in some psychological facts concerning quantification. Secondly, his theory implies that mathematical structures are common to both subjective experiences and objective ones. My suggestion is that both of these differences depend on a classical approach to measurement, according to which the arithmetic laws of addition define what is measurable as a particular domain for their application, and, at the same time, the extensibility of these laws to all known physical processes works as a heuristic principle for empirical research. Such an approach is worth reconsidering, not only because it lends plausibility to some of the controversial aspects of Helmholtz’s theory, but also because it offers a philosophical perspective on quantification problems that originated in the nineteenth-century.This paper draws insights on Helmholtz’s philosophical views from his engagement with the measurability of sensations via Fechner’s psychophysical law. This seems to be in contrast with the fact that the reception of Helmholtz’s theory culminated with the formulation of the theory of extensive measurement. I will contend that Helmholtz reached a no less important standpoint in the nineteenth-century debate on whether sensations are different (i.e., intensive) kinds of magnitudes and on how, if at all, they can be measured.

Uncertainty quantification of multimodal surface wave inversion using artificial neural networks

An inversion of surface wave dispersion curves (DCs) is a nonunique and ill-conditioned problem. The inversion result has a probabilistic nature, which becomes apparent when simultaneously restoring the S-wave velocity and layer thickness. Therefore, the problem of uncertainty quantification is relevant. Existing methods through deterministic or global optimization approaches of uncertainty quantification via posterior probability density (PPD) of the model parameters are not computationally efficient because they demand multiple solutions to the inverse problem. We have developed an alternative method based on a multilayer fully connected artificial neural network (ANN). We improve the current unimodal approach, which is known from publications, to multimodal inversion. We use Cox’s and Teague’s algorithm to determine optimal parameterization (number of layers) and the ranges of possible model parameters. We uniformly draw training data sets within estimated ranges and train the ANN. Saved ANN weights map the phase velocity DCs to values of the S-wave velocity and layers thickness. To estimate the uncertainties, we adapt the Monte Carlo simulation strategy, according to which the frequency dependent data noise and the inverse operator errors are projected onto the resulting velocity model. The inverse operator errors are evaluated by the prediction of the training data set. The proposed combination of surface wave data processing methods, configured with each other, provides a novel surface wave multimodal dispersion data inversion and uncertainty quantification approach. We first test our approach on synthetic experiments for various velocity models: a positive gradient velocity, a low-velocity layer, and a high-velocity layer. This is done considering unimodal inversion at first and then compared with the multimodal inversion. Afterward, we apply our approach to field data and compare the resulting models with the body S-wave processing by the generalized reciprocal method. The experiments indicate high-potential results — using ANN yields the possibility to accurately estimate the PPD of restored model parameters without a significant computational effort. The PPD-based comparison demonstrates the advantages of a multimodal inversion over a unimodal inversion. The trained ANN provides reasonable model parameters predictions and related uncertainties in real time.

Flight Training Risk Identification and Assessment Based on the HHM-RFRM Model

Due to the unavoidable operational risks and insufficient risk management capabilities of beginner pilots in flight training, the challenge of risk control in aviation schools has become increasingly prominent. To ensure the safety of flight training in aviation schools and to reduce costs and increase revenue, the essential prerequisite for improving efficiency is risk management. Therefore, it is necessary to explore risk identification and assessment methods. This paper adopts the holographic modeling (HHM) method and risk filtering, rating and management (RFRM) theory. First, the HHM idea is used to construct a risk identification framework (HHM-PAVE) for flight training. Second, based on the dual criteria, multiple criteria and cloud model (CM) in the RFRM approach, an improved risk assessment matrix-cloud model (IPC-CM) is proposed and combined with the N-K model and Bayes’ theorem to propose a coupled risk scenario hazard measurement model (CR-HM) based on the HHM-RFRM approach in risk assessment. In the assessment process, the impact of risk factors on system stability as well as the uncertainty problem and coupling–risk quantification problem in expert assessment are considered to obtain scientific and objective quantitative assessment results. Finally, the risk identification and assessment experiments were conducted using HHM-RFRM on the flight training. The results show that the method can more accurately identify critical risk factors in a flight training system and provide a new perspective for risk prevention and control.

Seismic fragility analysis using stochastic polynomial chaos expansions

Within the performance-based earthquake engineering (PBEE) framework, the fragility model plays a pivotal role. Such a model represents the probability that the engineering demand parameter (EDP) exceeds a certain safety threshold given a set of selected intensity measures (IMs) that characterize the earthquake load. The-state-of-the art methods for fragility computation rely on full non-linear time–history analyses. Within this perimeter, there are two main approaches: the first relies on the selection and scaling of recorded ground motions; the second, based on random vibration theory, characterizes the seismic input with a parametric stochastic ground motion model (SGMM). The latter case has the great advantage that the problem of seismic risk analysis is framed as a forward uncertainty quantification problem. However, running classical full-scale Monte Carlo simulations is intractable because of the prohibitive computational cost of typical finite element models. Therefore, it is of great interest to define fragility models that link an EDP of interest with the SGMM parameters — which are regarded as IMs in this context. The computation of such fragility models is a challenge on its own and, despite a few recent studies, there is still an important research gap in this domain. This comes with no surprise as classical surrogate modeling techniques cannot be applied due to the stochastic nature of SGMM. This study tackles this computational challenge by using stochastic polynomial chaos expansions to represent the statistical dependence of EDP on IMs. More precisely, this surrogate model estimates the full conditional probability distribution of EDP conditioned on IMs. We compare the proposed approach with some state-of-the-art methods in two case studies. The numerical results show that the new method prevails over its competitors in estimating both the conditional distribution and the fragility functions.

EFFICIENT APPROXIMATION OF HIGH-DIMENSIONAL EXPONENTIALS BY TENSOR NETWORKS

In this work a general approach to compute a compressed representation of the exponential $\exp(h)$ of a high-dimensional function $h$ is presented. Such exponential functions play an important role in several problems in Uncertainty Quantification, e.g. the approximation of log-normal random fields or the evaluation of Bayesian posterior measures. Usually, these high-dimensional objects are intractable numerically and can only be accessed pointwise in sampling methods. In contrast, the proposed method constructs a functional representation of the exponential by exploiting its nature as a solution of an ordinary differential equation. The application of a Petrov--Galerkin scheme to this equation provides a tensor train representation of the solution for which we derive an efficient and reliable a posteriori error estimator. Numerical experiments with a log-normal random field and a Bayesian likelihood illustrate the performance of the approach in comparison to other recent low-rank representations for the respective applications. Although the present work considers only a specific differential equation, the presented method can be applied in a more general setting. We show that the composition of a generic holonomic function and a high-dimensional function corresponds to a differential equation that can be used in our method. Moreover, the differential equation can be modified to adapt the norm in the a posteriori error estimates to the problem at hand.

Design of intelligent robots for tourism management service based on green computing.

The modular intelligent robot platform has important application prospects in the field of tourism management services. Based on the intelligent robot in the scenic area, this paper constructs a partial differential analysis system for tourism management services, and adopts the modular design method to complete the hardware design of the intelligent robot system. Through system analysis, the whole system is divided into 5 major modules, including core control module, power supply module, motor control module, sensor measurement module, wireless sensor network module, to solve the problem of quantification of tourism management services. In the simulation process, the hardware development of wireless sensor network node is carried out based on MSP430F169 microcontroller and CC2420 radio frequency wireless communication chip, and the corresponding physical layer and MAC (Media Access Control) layer data definition and data definition of IEEE802.15.4 protocol are completed for software implementation, and data transmission and networking verification. The experimental results show that the encoder resolution is 1024P/R, the power supply voltage is DC5V5%, and the maximum response frequency is 100 kHz. The algorithm designed by MATLAB software can avoid the existing shortcomings and meet the real-time requirements of the system, which significantly improves the sensitivity and robustness of the intelligent robot.

Using GQIM Model and Gompertz Model to Measure, Analyze, and Optimize the Whole Process of Software Project

This paper proposes a novel concept of using defect management technology to measure, predict, and optimize the management of the entire software project cycle. It first utilizes the software defect measurement GQIM model and prediction Gompertz model to track and quantify the defects of the entire project cycle. Then, the specific optimization strategy is proposed to manage the core processes of the project management, including project scope management, project time management, project quality management, project human resource management, project communication management, and project risk management. This study solves the quantification problems that are common in the current software project management process, such as complex testing procedures, high defect repair costs, and high communication costs. Furthermore, it contributes to promote the overall level of project management in the software industry. Taking the SDLM’s electronic banking software project management as an example, the various management quality indicators before and after the optimization of the project management process strongly indicate that using software defect management technology to optimize the software project management process is feasible and effective.

Retrieval of initial condition for Burgers' equation using reduced-order EnKF via POD-based sparse observations

<p style='text-indent:20px;'>The data assimilation (DA) is a popular method to solve uncertainty quantification problem which has attracted more and more attention in disaster assessment and climate change research. However, the DA usually faces the computational problem associated with "the curse of dimensionality'' when the high-dimensional inverse problem is involved. For this, the usual strategy is to combine the dimensionality reduction method with the DA to mitigate the computational demand in practical application. In this paper, we develop a reduced-order model (ROM)-based EnKF used for retrieving the initial condition, where the prediction model and the observation model are all POD-dependent. In addition to the reduced-order model (ROM) being prediction model, the idea of compressed sensing motivates the acquisition of the observation model that allows an efficient combination of the EnKF with QD algorithm to obtain the optimal sparse observation locations. In this way, computational acceleration is gained in retrieving the initial condition. The effectiveness of this algorithm is demonstrated through retrieving the initial condition of an one-dimensional (1-D) Burgers' equation. Experimental results show that a satisfactory retrieval result is obtained using the current ROM-based EnKF with the computational (CPU) time, <inline-formula><tex-math id="M1">\begin{document}$ 42.64\rm{s} $\end{document}</tex-math></inline-formula>, nearly 25 times faster, and the error result <inline-formula><tex-math id="M2">\begin{document}$ 7.47\times 10^{-3} $\end{document}</tex-math></inline-formula>, two order of magnitude <inline-formula><tex-math id="M3">\begin{document}$ O(10^2) $\end{document}</tex-math></inline-formula> more accurate, than the implementation of the traditional full-order model (FOM)-based EnKF where the computational instability is observed at each iteration though in the same condition as set in the ROM-based EnKF, leading to a poor result (the CPU time <inline-formula><tex-math id="M4">\begin{document}$ 1057.97\rm{s} $\end{document}</tex-math></inline-formula>, and the error accuracy <inline-formula><tex-math id="M5">\begin{document}$ 4.06\times 10^{-1}) $\end{document}</tex-math></inline-formula>. The present study extends the application of ROM to efficiently dealing with ill-posed problem as a regularization strategy through replacing the FOM with the ROM such that the low-order truncation of the POD basis leads to the ROM with as few degrees of freedom as possible, which can efficiently inhibit the higher frequency errors, and hence achieve stability of the proposed approach.</p>

Protein Pull-down Assay Using HiBiT-tag-dependent Luciferase Activity Measurement.

Co-immunoprecipitation or pull-down assays are frequently used to analyze protein-protein interactions. In these experiments, western blotting is commonly used to detect prey proteins. However, sensitivity and quantification problems remain in this detection system. Recently, the HiBiT-tag-dependent NanoLuc luciferase system was developed as a highly sensitive detection system for small amounts of proteins. In this report, we introduce the method of using HiBiT technology for the detection of prey protein in a pull-down assay. Using this protocol, we demonstrate the formation of a ternary complex consisting of Japanese encephalitis virus NS4B and two host factors, namely valosin-containing protein, and nuclear protein localization protein 4, which is a critical biological event during flavivirus replication in cells.

Methods for characterizing the interfacial adhesion in thermal barrier coating systems

Thermal barrier coatings (TBC) are widely used to protect the hot section structural components, such as aircraft gas turbine, against hot corrosion and large thermal gradients during the service life. The resistance to interfacial debonding (adhesion) is one of the key factors for predicting the TBC durability during operation. The goal of the study is analysis of the existing approaches to quantification of the interfacial adhesion for multi-layered thermal barrier coating systems and thermally-grown oxide on Ni-based superalloys and discussion of the problem regarding the reasons for a large spread of the adhesion characteristics. Theoretical prerequisites for determining the adhesion characteristics are considered to provide a theoretical background for quantification of the interfacial adhesion. The absence of national standard tests applicable to TBC is marked along with a significant scatter of the values obtained using international test-regulating documents and proprietary technologies. The values of the intensity of the strain energy release are found to vary from 0.3 to 230 J/m2 depending on the method for measuring adhesion, experimental details and type of the system considered. The factors that determine a large spread of the interfacial adhesion values were divided into two groups: 1 — intrinsic, attributed to the features of TBC layer formation and temperature affecting the value and distribution of residual strains and stresses and direction of the failure initiation; 2 — extrinsic, which are related to test conditions and technique of experimental data processing. A complex approach involving both intrinsic and extrinsic parameters is required to address the problem of interfacial adhesion quantification.

Multivariate expectile-based distribution: Properties, Bayesian inference, and applications

Expectiles form a family of risk measures that have recently gained interest over the more common value-at-risk or return levels, primarily due to their capability to be determined by the probabilities of tail values and magnitudes of realizations at once. However, a prevalent and ongoing challenge of expectile inference is the problem of uncertainty quantification, which is especially critical in sensitive applications, such as in medical, environmental, or engineering tasks. We address this issue by developing a novel distribution, termed the multivariate expectile-based distribution (MED), that possesses an expectile as a closed-form parameter. Desirable properties of the distribution, such as log-concavity, make it an excellent fitting distribution in multivariate applications. Maximum likelihood estimation and Bayesian inference algorithms are described. Simulated examples and applications to expectile and mode estimation illustrate the usefulness of the MED for uncertainty quantification.

VB-DeepONet: A Bayesian operator learning framework for uncertainty quantification

Neural network based data-driven operator learning schemes have shown tremendous potential in computational mechanics. DeepONet is one such neural network architecture which has gained widespread appreciation owing to its excellent prediction capabilities. Having said that, being set in a deterministic framework exposes DeepONet architecture to the risk of overfitting, poor generalization and in its unaltered form, it is incapable of quantifying the uncertainties associated with its predictions. To address these challenges, we propose a novel Bayesian operator learning framework referred to as the Variational Bayes DeepONet (VB-DeepONet). VB-DeepONet is rooted in Bayesian statistics and hence, (a) is less prone to overfitting as compared to its deterministic counterpart, (b) has better generalization, and (c) yields predictive uncertainty which is instrumental when decision making is concerned. VB-DeepONet exploits variational inference and hence has the capacity to take into account high dimensional posterior distributions while keeping the associated computational cost reasonable. Different examples covering mechanics problems like diffusion reaction, gravity pendulum, advection diffusion have been considered to illustrate the performance of the proposed VB-DeepONet and comparisons have been drawn against DeepONet set in deterministic framework, Proper Orthogonal Decomposition based Gaussian Process and DenseED. The results obtained illustrate the efficacy of the proposed approach in solving uncertainty quantification problems.

Hybrid Polynomial Chaos Expansion and proper generalized decomposition approach for uncertainty quantification problems in the frame of elasticity

Polynomial Chaos Expansion (PCE) is a powerful and flexible metamodeling technique, but suffers from the fact that the number of required training samples grows exponentially with the dimensionality of the problem. Recently, proper generalized decomposition (PGD) has become a popular way to address this challenge since its complexity grows linearly with the dimension of the problem. In this work, we present a new technique called PGD–PCE, which combines the advantages of both methods. The algorithm is based on separate representations and constructed by orthonormal polynomial functions. We test the proposed approach on simple toy problems and engineering finite element problems. The results show that PGD–PCE performs well in terms of accuracy and computational efficiency when dealing with large problems. • We propagate uncertainties in mechanical problems. • We develop a simple to implement and non-intrusive method. • We show that accuracy is preserved while cost drastically decrease. • We illustrate the capabilities of the approach on various numerical tests.

Automated method for routine microplastic detection and quantification

Microplastics (MPs) are a heterogeneous group of solid polymers with dimensions <5 mm, which are a widespread contaminant of the environment. Their ubiquitous presence grabbed researchers' attention in the last decade, and the problem of MPs detection and quantification is currently a topic of utmost importance. Most identification and quantification protocols are still based on the visual count, which is an extremely time-consuming and error-prone task due to operator subjectivity. To address such an issue, different software analysis procedures are available, but they mainly rely either on the use of optical microscopy, covering a minimal area for each sample (mm2 size), or they allow only the identification of the largest particles (>1 mm). Here, a semi-automatic innovative image processing method for quantifying and measuring microplastics on filter membrane substrates is presented and validated, comparing results with data obtained using visual counting performed by an experienced operator. The algorithm was tested with artificially generated microplastic images and samples taken from natural environments. Samples of Borgio Verezzi show cave sediment and Po River water were filtered on a glass filter membrane, and photographs were taken under 365 nm illumination, both without and with Nile Red staining. The proposed image analysis method, implemented in an easy-to-use Python script, was quite accurate and fast (about 10 s/image average processing time), showing an average deviation below 10 %, which is further reduced to about 8 % if the samples are stained with Nile Red.