Choice Of Threshold Research Articles

Nonlinear wavelet shrinkage estimator of nonparametric regularity regression function via cross-validation with simulation study

Nonparametric regression techniques provide a very effective and simple way of finding structure in data sets without the imposition of a parametric regression model. Wavelet theory has the potential to provide statisticians with powerful new techniques for nonparametric inference. In this paper, we consider the wavelet shrinkage kernel estimator of regression function with a common one-dimensional probability density function. We investigate a new nonparametric curve estimator and convergence ratio of given estimator by using cross-validation method to choice of wavelet threshold when the observations are taken on the regular grid. At the end we used simulation study to examine our proposed estimator. We survey the theoretical outcomes with numerical computation by using [Formula: see text] software to compare purpose estimator with another estimators.

Structural health monitoring of bridges: a model-free ANN-based approach to damage detection

As civil engineering structures are growing in dimension and longevity, there is an associated increase in concern regarding the maintenance of such structures. Bridges, in particular, are critical links in today’s transportation networks and hence fundamental for the development of society. In this context, the demand for novel damage detection techniques and reliable structural health monitoring systems is currently high. This paper presents a model-free damage detection approach based on machine learning techniques. The method is applied to data on the structural condition of a fictitious railway bridge gathered in a numerical experiment using a three-dimensional finite element model. Data are collected from the dynamic response of the structure, which is simulated in the course of the passage of a train, considering the bridge in healthy and two different damaged scenarios. In the first stage of the proposed method, artificial neural networks are trained with an unsupervised learning approach with input data composed of accelerations gathered on the healthy bridge. Based on the acceleration values at previous instants in time, the networks are able to predict future accelerations. In the second stage, the prediction errors of each network are statistically characterized by a Gaussian process that supports the choice of a damage detection threshold. Subsequent to this, by comparing damage indices with said threshold, it is possible to discriminate between different structural conditions, namely between healthy and damaged. From here and for each damage case scenario, receiver operating characteristic curves that illustrate the trade-off between true and false positives can be obtained. Lastly, based on the Bayes’ Theorem, a simplified method for the calculation of the expected total cost of the proposed strategy, as a function of the chosen threshold, is suggested.

Seasonal Variations in Severe Weather Forecast Skill in an Experimental Convection-Allowing Model

Abstract Eight years of daily, experimental, deterministic, convection-allowing model (CAM) forecasts, produced by the National Severe Storms Laboratory, were evaluated to assess their ability at predicting severe weather hazards over a diverse collection of seasons, regions, and environments. To do so, forecasts of severe weather hazards were produced and verified as in previous studies using CAM output, namely by thresholding the updraft helicity (UH) field, smoothing the resulting binary field to create surrogate severe probability forecasts (SSPFs), and verifying the SSPFs against observed storm reports. SSPFs were most skillful during the spring and fall, with a relative minimum in skill observed during the summer. SSPF skill during the winter months was more variable than during other seasons, partly due to the limited sample size of events, but was often less than that during the warm season. The seasonal behavior of SSPF skill was partly driven by the relationship between the UH threshold and the likelihood of obtaining severe storm reports. Varying UH thresholds by season and region produced SSPFs that were more skillful than using a fixed UH threshold to identify severe convection. Accounting for this variability was most important during the cool season, when a lower UH threshold produced larger SSPF skill compared to warm-season events, and during the summer, when large differences in skill occurred within different parts of the continental United States (CONUS), depending on the choice of UH threshold. This relationship between UH threshold and SSPF skill is discussed within the larger scope of generating skillful CAM-based guidance for hazardous convective weather and verifying CAM predictions.

Forensic application of decision theory for the choice of DNA identity threshold: Verifying the model parameters by empirical data

Apart from assessing the objective statistical value for DNA identification reliability, choosing the criterion to establish the genetic identity inevitably invokes the subjective factor. The crucial point of decision-making regarding the identity threshold is unavoidable given any degree the DNA identification reliability. In 2001 Goubko and Perepechina have developed the mathematical model based on DNA information describing forensic aspects of applying decision theory to court sentences. The model is rooted in the hypothesis of rational behavior to reveal the factors influencing decision-making and aims to study the border probability values sufficient for the judgment. The key element of the model was to determine empirically the balance of type I vs. type II judgment errors perceived by the society, that could be elicited from a special poll. Recently (2015) the model was refined and the preliminary survey on the limited sample was carried out. The present paper reports the results of the further research and discusses the empirical data concerning type I vs. type II judgment errors. The results obtained seem to be noteworthy when dealing with the problem of evaluating the identity threshold.

Empirical Consequences of Current Recommendations for the Design and Interpretation of Noninferiority Trials

BackgroundNoninferiority trials are increasingly common, though they have less standardized designs and their interpretation is less familiar to clinicians than superiority trials.ObjectiveTo empirically evaluate a cohort of noninferiority trials to determine 1) their interpretation as recommended by CONSORT, 2) choice of alpha threshold and its sidedness, and 3) differences between methods of analysis such as intention-to-treat and per-protocol.DesignWe searched MEDLINE for parallel-group randomized controlled noninferiority trials published in the five highest-impact general medical journals between 2011 and 2016.Main MeasuresData abstracted included trial design parameters, results, and interpretation of results based on CONSORT recommendations.Key ResultsOne hundred sixty-three trials and 182 noninferiority comparisons were included in our analysis. Based on CONSORT-recommended interpretation, 79% of experimental therapies met criteria for noninferiority, 13% met criteria for superiority, 20% were declared inconclusive, and 2% met criteria for inferiority. However, for 12% of trials, the experimental therapy was statistically significantly worse than the active control, but CONSORT recommended an interpretation of inconclusive or noninferior. A two-sided alpha equivalent of greater than 0.05 was used in 34% of the trials, and in five of these trials, the use of a standard two-sided alpha of 0.05 led to changes in the interpretation of results that disfavored the experimental therapy. In four of the five comparisons where different methods of analysis (e.g., intention-to-treat and per-protocol) yielded different results, the intention-to-treat analysis was the more conservative. In 11% of trials, a secondary advantage of the new therapy was neither reported nor could it be inferred by reviewers.ConclusionsIn this cohort, the design and interpretation of noninferiority trials led to significant and systematic bias in favor of the experimental therapy. Clinicians should exercise caution when interpreting these trials. Future trials may be more reliable if design parameters are standardized.

Score normalization applied to adaptive biometric systems

Biometric authentication systems have certain limitations. Recent studies have shown that biometric features may change over time, which can entail a decrease in recognition performance of the biometric system. An adaptive biometric system addresses this problem by adapting the biometric reference/template over time, thereby tracking the changes automatically. However, the use of these systems usually requires the adoption of a high threshold value to avoid the inclusion of impostor patterns into the genuine biometric reference. In this study, we hypothesize that score normalization procedures, which have been used to improve the recognition performance of biometric systems through a better refinement of their decision, can also improve the overall performance of adaptive systems. With such a normalization, a better threshold choice could also be made, which would then increase the number of genuine samples used for adaptation. To the best of our knowledge, this is the first investigation towards the use of score normalization to enhance adaptive biometric systems dealing with the change of user features over time. Through a systematic experimental design tested on two behavioral biometric traits, the obtained results indeed support our conjecture. Moreover, the experimental results show that the performance gain brought by adaptation can have a higher overall impact than score normalization alone.

THE RATIO OF THE HARMONICS LEVELS OF THE SCATTERED FIELD IN NONLINEAR LOCATIONS

The article discusses about the advantages of using the methods of nonlinear location in the field of technical protection of information. It is shown that searching for radio electronic equipment as a nonlinear scattered (NS) efficiently implement the Non Linear Junction Detector (NLJD). The efficiency of NLJD associated with the choice of thresholds of the ratio of the received multiple harmonics levels. It becomes relevant analytical estimation of the optimal values of the thresholds of identification, with considering the power level of the probing signal of NLJD and the non-linear effective square of scatterer of mortgaged devices. It is advisable to use the simulator of mortgaged device on the basis of two-way flat spiral antenna with semiconductor diode in the load. Working on the simulator in the microwave field from NLJD leads to deformation of the current-voltage characteristics of the diode. During the investigations, it was found that the overestimation of threshold is only suitable to mask for high-power NLJD radiation in probing the LDCs with a small non-linear effective square of scatterer. The threshold is a criterion of reliable identification of inefficient for low-power NLJD radiation in probing the NS with the big non-linear effective square of scatterer.

Efficient estimation of return value distributions from non-stationary marginal extreme value models using Bayesian inference

Extreme values of an environmental response can be estimated by fitting the generalised Pareto distribution to a sample of exceedances of a high threshold. In oceanographic applications to responses such as ocean storm severity, threshold and model parameters are typically functions of physical covariates. A fundamental difficulty is selection or estimation of an appropriate threshold or interval of thresholds, of particular concern since inferences for return values vary with threshold choice. Historical studies suggest that evidence for threshold selection is weak in typical samples.Hence, following Randell et al. (2016), a piecewise gamma-generalised Pareto model for a sample of storm peak significant wave height, non-stationary with respect to storm directional and seasonal covariates, is estimated here using Bayesian inference. Quantile regression (for a fixed quantile threshold probability) is used to partition the sample prior to independent gamma (body) and generalised Pareto (tail) estimation. An ensemble of independent models, each member of which corresponds to a choice of quantile probability from a wide interval of quantile threshold probabilities, is estimated. Diagnostic tools are then used to select an interval of quantile threshold probabilities corresponding to reasonable model performance, for subsequent inference of extreme quantiles incorporating threshold uncertainty.The estimated posterior predictive return value distribution (for a long return period of the order of 10,000 years) is a particularly useful diagnostic tool for threshold selection, since this return value is a key deliverable in metocean design. Estimating the distribution using Monte Carlo simulation becomes computationally demanding as return period increases. We present an alternative numerical integration scheme, the computation time for which is effectively independent of return period, dramatically improving computational efficiency for longer return periods.The methodology is illustrated in application to storm peak and sea state significant wave height at a South China Sea location, subject to monsoon conditions, showing directional and seasonal variability.

Projected effect of fecal immunochemical test threshold for colorectal cancer screening on outcomes and costs for Canada using the OncoSim microsimulation model

BackgroundImmunochemical faecal testing (FIT) is used in Canada for colorectal cancer (CRC) screening. The threshold for FIT abnormality is under operator control and this study uses a simulation model to predict the effect of threshold selection on outcomes including years-of-life gained, CRC incidence and mortality, and direct health system costs. MethodThe OncoSim Model was used to predict outcomes of biennial screening between ages 50–74 years in a cohort aged 45 years followed until death for eight FIT threshold values between 50 and 225ng/ml. The literature on FIT performance was reviewed and seven parameter sets of sensitivity and specificity values by FIT threshold were created to span published variation in test performance in subjects with CRC, adenomas or no colorectal neoplasia. ResultsReducing the FIT threshold reduced both projected CRC incidence and mortality for all parameter sets, although cost impacts and cost-effectiveness varied compared to no screening. Biennial FIT was projected to be cost-effective at all thresholds considered with a maximum of CAD$ 5400 per QALY over the seven parameter sets and a maximum of CAD$ 6800 per QALY for a one level change in the eight threshold levels considered. Demand for colonoscopy varied strongly with FIT threshold and was greatest for the lowest threshold (50ng/ml) but the magnitude varied across the 7 parameter sets. ConclusionsCompared to no screening, all thresholds of FIT examined were predicted to be cost-effective in the prevention and management of CRC. Threshold choice strongly influences predicted demand placed upon colonoscopy resources.

Effect of image segmentation & voxel size on micro-CT computed effective transport & elastic properties

Digital rock technology is rapidly evolving interdisciplinary field with many promises, including fast turnaround times for core analysis, repeatable analysis, and multiphysics simulation. We study the impact of the image segmentation threshold and image voxel size on image-computed permeability, elastic moduli, and electrical conductivity. Improved quantitative understanding of such effects is critically important when comparing laboratory-measured rock properties with those computed on digital images of rocks. We analyze properties of over 500 binary microstructures (each of size 10243 voxels) segmented using different segmentation algorithms. We find that uncertainty in computed rock properties, induced due to the choice of segmentation threshold, increases with coarsening of image voxels. Segmentation of the same rock, acquired with different voxels sizes, lead to small variations in porosity but induces relatively large variation in flow and electrical rock properties. This uncertainty is larger for rocks of lower porosity. We find that coarsening of image voxels also leads to rounding and smoothing of pore throats and a sharp decline in specific surface area which results in an increase in computed permeability. We propose simple models to remove the bias in rock properties when image-derived porosity is either overestimated or underestimated due to the choice of the segmentation threshold. This approach is particularly useful when comparing laboratory-measured rock properties to those derived from digital rocks since often the image calculated porosity and the laboratory-measured porosity are not the same. Even after such corrections, the impact of finite image voxel size would still need to be compensated.

Identifying optimal threshold statistics for elimination of hookworm using a stochastic simulation model

BackgroundThere is an increased focus on whether mass drug administration (MDA) programmes alone can interrupt the transmission of soil-transmitted helminths (STH). Mathematical models can be used to model these interventions and are increasingly being implemented to inform investigators about expected trial outcome and the choice of optimum study design. One key factor is the choice of threshold for detecting elimination. However, there are currently no thresholds defined for STH regarding breaking transmission.MethodsWe develop a simulation of an elimination study, based on the DeWorm3 project, using an individual-based stochastic disease transmission model in conjunction with models of MDA, sampling, diagnostics and the construction of study clusters. The simulation is then used to analyse the relationship between the study end-point elimination threshold and whether elimination is achieved in the long term within the model. We analyse the quality of a range of statistics in terms of the positive predictive values (PPV) and how they depend on a range of covariates, including threshold values, baseline prevalence, measurement time point and how clusters are constructed.ResultsEnd-point infection prevalence performs well in discriminating between villages that achieve interruption of transmission and those that do not, although the quality of the threshold is sensitive to baseline prevalence and threshold value. Optimal post-treatment prevalence threshold value for determining elimination is in the range 2% or less when the baseline prevalence range is broad. For multiple clusters of communities, both the probability of elimination and the ability of thresholds to detect it are strongly dependent on the size of the cluster and the size distribution of the constituent communities. Number of communities in a cluster is a key indicator of probability of elimination and PPV. Extending the time, post-study endpoint, at which the threshold statistic is measured improves PPV value in discriminating between eliminating clusters and those that bounce back.ConclusionsThe probability of elimination and PPV are very sensitive to baseline prevalence for individual communities. However, most studies and programmes are constructed on the basis of clusters. Since elimination occurs within smaller population sub-units, the construction of clusters introduces new sensitivities for elimination threshold values to cluster size and the underlying population structure. Study simulation offers an opportunity to investigate key sources of sensitivity for elimination studies and programme designs in advance and to tailor interventions to prevailing local or national conditions.

Hora est 10. Implantaat ondersteunde frame­prothesen in een Kennedy klasse I-situatie in de onderkaak

Implant-supported removable partial dentures in the mandible often cause problems, which means that patients wear their dentures seldom if at all. A solution is to place implants that the dentures can be snapped onto. There is, however, no consensus about the best position of the implants in the mandible yet. In addition, it is worthwhile to balance the cost of treatment with its effectiveness. In a randomised cross-over clinical trial involving 30 patients with a shortened dental arch, the implant-supported removable partial denture in the mandible was evaluated based on the experience of the patient, mean time of wearing, chewing ability and the clinical and radiographic parameters in relation to 2 different implant positions: 2 in the pre-molar region or 2 in the molar region. The cost-effectiveness of both treatments was also evaluated. From the patient's point of view, the implant-supported removable partial dentures are best supported by implants placed in the molar region. The research also revealed, however, that significantly more bleeding occurred around implants placed in the molar region and from a clinical perspective placement in the pre-molar region would have preference. The cost-effectiveness of the treatment with an implant-supported removable partial denture depends on the choice of outcome measurement and monetary threshold.

A Probabilistic Approach to Robust Fault Detection for a Class of Nonlinear Systems

This paper presents a probabilistic approach to fault detection (FD) for nonlinear systems subject to $l_{2}[0,N]$ -norm bounded unknown input. The major contribution is to design an evaluation function for robust FD in a unified framework of $l_{2}$ -norm estimation of unknown input and determine a threshold based on probabilistic analysis of FD performance. The problem of robust FD is first formulated as to find a minimal estimation of the $l_{2}[0,N]$ -norm of unknown input including unknown initial state. It is shown that such an estimation leads to a unified design of evaluation function for FD using extended Kalman filter or $H_{i}/H_{\infty }$ optimization-based FD filter. Based on this, a probabilistic approach to threshold determination and FD performance verification is proposed. In particular, if the $l_{2}[0,N]$ -norm boundedness of unknown input is not available, a choice of threshold can be made in the framework of probabilistic analysis for achieving a tradeoff between false alarm rate and FD rate. Finally, a nonlinear UAV control system model is given to demonstrate the effectiveness of the proposed method and show the feasibility of practical application.

A Method for Optimizing Height Threshold When Computing Airborne Laser Scanning Metrics

In airborne laser scanning (<small>ALS</small>), a reference height threshold is employed for computation of height and density metrics, which are used as auxiliary variables for predicting forest attributes. Lacking consensus, practitioners employ different criteria to define a height threshold, which is applied to all the metrics collectively. In this paper, we propose a change of paradigm in ALS metric computation: height thresholds must be optimized for each metric individually, instead of applying a single one for all them. We present an optimization method based on the maximal information coefficient (MIC), which is applied for each metric, one-by-one. Results showed how a bad choice of height thresholds damages the predictive potential of most metrics. While increasing thresholds strengthened height metrics' relationship to volume, it weakened for density metrics, and therefore choosing different thresholds makes sense.

Clustering multiply imputed multivariate high-dimensional longitudinal profiles.

In this paper, we propose a method to cluster multivariate functional data with missing observations. Analysis of functional data often encompasses dimension reduction techniques such as principal component analysis (PCA). These techniques require complete data matrices. In this paper, the data are completed by means of multiple imputation, and subsequently each imputed data set is submitted to a cluster procedure. The final partition of the data, summarizing the partitions obtained for the imputed data sets, is obtained by means of ensemble clustering. The uncertainty in cluster membership, due to missing data, is characterized by means of the agreement between the members of the ensemble and fuzziness of the consensus clustering. The potential of the method was brought out on the heart failure (HF) data. Daily measurement for four biomarkers (heart rate, diastolic, and systolic blood pressure, weight) were used to cluster the patients. To normalize the distributions of the longitudinal outcomes, the data were transformed with a natural logarithm function. A cubic spline base with 69 basis functions was employed to smooth the profiles. The proposed algorithm indicates the existence of a latent structure and divides the HF patients into two clusters, showing a different evolution in blood pressure values and weight. In general, cluster results are sensitive to choices made. Likewise for the proposed approach, alternative choices for the distance measure, procedure to optimize the objective function, choice of the scree-test threshold, or the number of principal components, to be used in the approximation of the surrogate density, could all influence the final partition. For the HF data set, the final partition depends on the number of principal components used in the procedure.

Serum ferritin thresholds for the diagnosis of iron deficiency in pregnancy: a systematic review.

SUMMARYThe aim of this review was to understand the landscape of serum ferritin in diagnosing iron deficiency in the aetiology of anaemia in pregnancy. Iron deficiency in pregnancy is a major public health problem leading to the development of anaemia. Reducing the global prevalence of anaemia in women of reproductive age is a 2025 global nutrition target. Bone marrow aspiration is the gold standard test for iron deficiency but requires an invasive procedure; therefore, serum ferritin is the most clinically useful test. We undertook a systematic search of electronic databases and trial registers from inception to January 2016. Studies of iron or micronutrient supplementation in pregnancy with pre‐defined serum ferritin thresholds were included. Two independent reviewers selected studies, extracted data and assessed quality. There were 76 relevant studies mainly of observational study design (57%). The most commonly used thresholds of serum ferritin for the diagnosis of iron deficiency were <12 and <15 ng mL−1 (68%). Most primary studies provided no justification for the choice of serum ferritin threshold used, but 25 studies (33%) used thresholds defined by expert consensus in a guideline development process. There were five studies (7%) using a serum ferritin threshold defining iron deficiency derived from primary studies of bone marrow aspiration. Unified international thresholds of iron deficiency for women throughout pregnancy are required for accurate assessments of the global disease burden and for evaluating effectiveness of interventions addressing this problem.

Analysis of design choices for a slope stability scenario in the humid tropics

Prediction of the conditions under which landslides may occur is essential for designing sustainable risk-mitigation measures and cost-effective geotechnical structures. Slope stability analyses typically account for slope geometry, soil mechanical properties and groundwater conditions to determine the performance of a slope with respect to a specified factor of safety. These properties vary both spatially and over time; geotechnical design codes require the use of factored design parameter values to account for possible worst-case conditions. Furthermore, standard geotechnical analyses typically exclude the dynamic hydrological processes of rainfall infiltration and loss of matric suction that often trigger landslides. Slope stability assessment is particularly challenging in developing countries with limited resources for acquiring slope data, meeting conservative design standards and mitigating landslide risk. This study applied a combined slope hydrology and stability model to address these issues for a residual soil slope in the tropics. This paper presents a method for maximising stability information from limited data, disaggregating the effects of three different design parameter sets and factor of safety threshold choices, as well as diagnosing the dominant geotechnical and dynamic landslide-triggering factors. This modelling approach provides a more transparent basis for sustainable slope-management decisions.

Optimization of intra-voxel incoherent motion measurement in diffusion-weighted imaging of breast cancer.

PurposeThe purpose of this study was to optimize intra‐voxel incoherent motion (IVIM) measurement in diffusion‐weighted imaging (DWI) of breast cancer by separating perfusion and diffusion effects through the determination of an optimal threshold b‐value, thus benign and cancerous breast tissues can be accurately differentiated using IVIM‐derived diffusion and perfusion parameters.Materials and MethodsTwenty‐eight patients, with biopsy‐confirmed breast cancers, were studied with a 3T MRI scanner, using T1‐weighted dynamic contrast‐enhanced MRI images, and diffusion‐weighted images with nine b‐values, ranging from 0 to 1000 s/mm². IVIM‐derived parameter maps for tissue diffusion coefficients D, perfusion fraction f, and pseudo‐diffusion coefficients D* were computed using the segmented fitting method with optimized threshold b‐value, and the sum of squared residuals (SSR) were calculated for IVIM‐derived parameters in different breast lesions.ResultsThe IVIM analysis method developed in this work can separate perfusion and diffusion effects with the optimal threshold b‐value of 300 s/mm², and the results of diffusion and perfusion parameters from IVIM analysis can be used to differentiate pathological changes in breast tissues. It was found that the averages and standard deviations of the diffusion and perfusion parameters, D, f, D*, are the following, for malignant, benign and normal breast tissues respectively: D (0.813 ± 0.225 × 10−3 mm2/s, 1.437 ± 0.538 × 10−3 mm2/s, 1.838 ± 0.213 × 10−3 mm2/s), f (10.73 ± 3.44%, 7.86 ± 3.70%, 8.92 ± 3.72%), D* (15.23 ± 12.17×10−3 mm²/s, 12.02 ± 3.19 × 10−3 mm2/s, 12.03 ± 7.21 × 10−3 mm2/s).Conclusion IVIM‐derived diffusion and perfusion parameter maps depend highly on the choice of threshold b‐value. Using the methodology developed in this work, and with the optimized threshold b‐value, the diffusion and perfusion parameters of breast tissues can be accurately assessed, making IVIM MRI a technique of choice for differential diagnosis of breast cancer.

Hypothesis testing in functional linear models.

Functional data arise frequently in biomedical studies, where it is often of interest to investigate the association between functional predictors and a scalar response variable. While functional linear models (FLM) are widely used to address these questions, hypothesis testing for the functional association in the FLM framework remains challenging. A popular approach to testing the functional effects is through dimension reduction by functional principal component (PC) analysis. However, its power performance depends on the choice of the number of PCs, and is not systematically studied. In this article, we first investigate the power performance of the Wald-type test with varying thresholds in selecting the number of PCs for the functional covariates, and show that the power is sensitive to the choice of thresholds. To circumvent the issue, we propose a new method of ordering and selecting principal components to construct test statistics. The proposed method takes into account both the association with the response and the variation along each eigenfunction. We establish its theoretical properties and assess the finite sample properties through simulations. Our simulation results show that the proposed test is more robust against the choice of threshold while being as powerful as, and often more powerful than, the existing method. We then apply the proposed method to the cerebral white matter tracts data obtained from a diffusion tensor imaging tractography study.

A spectral method for sizing cracks using ultrasonic arrays

Ultrasonic phased array systems are becoming increasingly popular as tools for the inspection of safety-critical structures within the non-destructive evaluation industry. The data-sets captured by these arrays can be used to image the internal structure of individual components, allowing the location and nature of any defects to be deduced. Although there exist strict procedures for measuring defects via these imaging algorithms, sizing flaws which are smaller than two wavelengths in diameter can prove problematic and the choice of threshold at which the defect measurements are made can introduce an aspect of subjectivity. This paper puts forward a completely objective approach specific to cracks based on the Kirchhoff scattering model and the approximation of the resulting scattering matrices by Toeplitz matrices. A mathematical expression relating the crack size to the maximum eigenvalue of the associated scattering matrix is derived. Analysis of this approximation shows that the method will provide a unique crack size for a given maximum eigenvalue whilst providing a quick calculation method which avoids the need to numerically generate model scattering matrices (the computation time is up to times faster). A sensitivity analysis demonstrates that the method is most effective for sizing defects that are commensurate with or smaller than the wavelength of the ultrasonic wave. The method is applied to simulated FMC data arising from finite element calculations where the crack length to wavelength ratios range between 0.6 and 1.9. The recovered objective crack size exhibits an error of 12%.