Operations In Frequency Domain Research Articles

Robust back-scattered light estimation for underwater image enhancement with polarization

The scattering of particles in the turbid underwater environment reduces the contrast of the image, which can be alleviated by underwater image enhancement. However, the noise in the imaging process often interferes with the enhancement. In this paper, we propose a novel polarization-based approach that robustly estimates the background light to reduce the impact of noise. Specifically, we present a polarization parameter estimation method that adopts both spatial and frequency-domain operations. With these polarization parameters, the background light is estimated by combining the image information before and after filtering in the frequency-domain. For accurately estimating the back-scattered light at the infinity point, we exploit the characteristics of the polarization difference image and use a quad-tree method to determine it. The proposed approach can reduce the influence of the biased estimated parameters, boosting the image quality effectively. Experiments demonstrate that the our method produces better visual effect and robustness than the classic polarization-based and traditional underwater enhancement algorithms for different concentrations.

Application of High-Tc Josephson Detectors for Spectral Characterization of THz Quantum Cascade Lasers

We have demonstrated the potential of high- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_c</i> Josephson junctions (JJ) for broadband spectral characterization of electromagnetic radiation from terahertz (THz) quantum cascade lasers (QCLs). We have used frequency-selective Josephson detection with Hilbert-transform spectral analysis (HTSA) and classical detection in YBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7-x</sub> bicrystal junctions to measure and interpret the spectra of QCL radiation from a few tens of GHz to 2.5 THz. The dominant part in the measured spectra concentrates near the designed frequency of 2.2 THz and includes several lines with the frequencies of the spatial modes in the QCL. We have found that, in addition to expected 2.2 THz radiation, QCL spectra demonstrate a low-frequency part with the frequencies <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> < 400 GHz and an intermediate region with increasing intensity for the frequencies from 500 GHz to 2 THz. We have found that intensities and spectral contents of three parts non-monotonically depend on the injection current of QCLs. We interpret the recovered spectra as an interplay of designed QCL operation with nonlinear effects of 2nd and 3rd orders in the active volume of QCLs. Compared to conventional techniques, the advantages of high- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_c</i> JJs with HTSA are in frequency-domain operation and extended ranges, including THz, sub-THz, and GHz frequencies of QCL nonlinear dynamics.

Hybrid Energy Efficiency Friendly Frequency Domain TR Algorithm Based on PSO Algorithm Evaluated by Novel Maximizing HPA Efficiency Evaluation Criteria

Smart Grids (SGs) expedite secure, large-scale and efficient two-way communication between the power supply and management, but under a sophisticated 5G communication infrastructure, the multi carrier system is the principle system. The high peak-to-average power ratio (PAPR) is one of the significant limitations of the 5G multi carrier (MC) system, as it impedes the efficient design of the 5G analogue front end. Tone reservation (TR) is a highly efficient scheme without signal distortion, which is designed by increasing the freedom in the frequency domain for PAPR reduction. In this paper, a particle swarm optimization (PSO) based TR (PSO-TR) scheme proceeding with an optimal input power back off-modulation error ratio (IBO-MER) convergence criterion is proposed to improve high power amplifier (HPA) efficiency for OFDM systems. A probabilistic analysis of TR predistribution and freedom in the frequency domain, in relationship with the amplitude of its constituent samples, is carried out. This yields the theoretical framework employed in design of the proposed high computing-enhanced solutions. The proposed PSO-TR essentially make the frequency domain distribution and operation itself adaptive, that is, it adjusts to comply with the changing HPA efficiency and redundant cost during application runtime.

A non-local method in peridynamic theory for simulating elastic wave propagation in solids

In order to simulate the elastic wave propagation in unbounded solids, this paper introduces a non-local method to construct absorbing boundary conditions in the bond-based peridynamic theory. To construct non-local absorbing boundary conditions in the form of absorbing layers with increasing damping, we first re-derived the particle motion equilibrium equation of the bond-based peridynamic theory, based on the principle of virtual work and Lagrange's equation on the premise of considering material damping. We also give the expression for the inter-particle damping force density which satisfies the balance laws of linear momentum and angular momentum. This paper also provides a process and algorithm for realizing the non-local absorbing boundary conditions in the bond-based peridynamic theory, and adopts the Fortran language for computer program compilation. Finally, we simulate the elastic wave propagation in semi-unbounded and unbounded solids as numerical examples. The results show that such non-local absorbing boundary conditions can stably absorb and attenuate incident elastic waves. Since it is derived in the time domain, this method does not require frequency-domain operations, such as Fourier and Laplace transformations, nor does it require wave field splitting.

Frequency based signal processing technique for pulse modulation ground penetrating radar system

This paper discusses the method of processing the pulse modulation (PM) ground penetrating radar (GPR) system to detect an embedded object underground. The proposed technique is using frequency domain operation which can be classified based on two parameters which are magnitude and phase. The process of detecting the position and depth of iron objects in dry sandy soil is easier to identify using the techniques and parameters that have been introduced. The selection of the Dipole antenna as a sensor device to detect iron objects has been designed in a frequency range of 70 MHz to 80 MHz. Based on the simulation, the proposed technique seems to be able to detect underground iron objects. By using the magnitude value, the underground iron object that can be detected as displayed in GPR radargram is in the depth range from 0 mm until 1000 mm. Meanwhile, by using the phase value, the embedded underground iron object detected is in the range of depth between 900 mm and 1000 mm. Therefore, based on this promising result, the proposed technique and parameters are considered to be used in

Terahertz dual-comb spectroscopy: A comparison between time- and frequency-domain operation modes

In terahertz dual-comb spectroscopies (THz-DCSs), electrical time delay lines are utilized to replace the mechanical ones widely used in traditional terahertz time-domain spectroscopic systems (THz-TDSs). Due to the usage of electrical delay line, the sampling time is effectively prolonged and the consecutive terahertz pulses can be sampled continuously, which leads to the improvement of frequency resolution and makes it possible for THz-DCSs work in dual (frequency- and time-domain, FD and TD) operation modes. Here, a THz-DCS is established by using two repetition-frequency-locked femtosecond (fs) lasers with a slight repetition frequency difference. A spectrum analyzer is used to directly record the terahertz spectral data. Alternatively, the terahertz transient pulses are sampled and recorded, and the terahertz spectra are obtained by Fourier transforming the TD data. The experimental results show that the terahertz spectra acquired in FD and TD are in good agreement with each other. For the dual-mode THz-DCS, the wideband terahertz spectral information and the specified narrowband spectral information with high frequency resolution can be simultaneously acquired, which is helpful for searching sharp-peaked fingerprint spectral features in a broad terahertz frequency range.

Spectrum analysis of moving average operator and construction of time-frequency hybrid sequence operator

PurposeThe purpose of this paper is to analyze the spectral characteristics of moving average operator and to propose a novel time-frequency hybrid sequence operator.Design/methodology/approachFirstly, the complex data is converted into frequency domain data by Fourier transform. An appropriate frequency domain operator is constructed to eliminate the impact of disturbance. Then, the inverse Fourier transform transforms the frequency domain data in which the disturbance is removed, into time domain data. Finally, an appropriate moving average operator of N items is selected based on spectral characteristics to eliminate the influence of periodic factors and noise.FindingsThrough the spectrum analysis of the real-time data sensed and recorded by microwave sensors, the spectral characteristics and the ranges of information, noise and shock disturbance factors in the data can be clarified.Practical implicationsThe real-time data analysis results for a drug component monitoring show that the hybrid sequence operator has a good effect on suppressing disturbances, periodic factors and noise implied in the data.Originality/valueFirstly, the spectral analysis of moving average operator and the novel time-frequency hybrid sequence operator were presented in this paper. For complex data, the ideal effect is difficult to achieve by applying the frequency domain operator or time domain operator alone. The more satisfactory results can be obtained by time-frequency hybrid sequence operator.

Fast Steady-State Computation of Electrical Networks Involving Nonlinear and Photovoltaic Components

Electromagnetic transients (EMT) analysis heavily relies on computational simulation of power networks. Initialization of simulation at a given operating point, i.e., stationary state, requires either long simulation time-windows, especially for poorly damped networks or networks with very distinct time delays, or the use of alternative software tools. EMT-type programs are computationally very intensive as nonlinear components have to be brought to steady state and, in case of power electronic devices (PEDs)-based networks, a very small time-step has to be utilized. This article proposes a fast methodology to calculate steady state of networks involving both nonlinear loads and PEDs. The proposed approach relies on: (a) frequency-domain representation of PEDs via the chain-matrix and (b) using Fast Fourier Transform/Inverse Fast Fourier Transform (FFT/IFFT) operations for the nonlinear elements, thus avoiding problems with transients. The fact that the methodology uses frequency-domain operations permits to naturally obtain harmonics and/or interharmonics. A test system including a nonlinear reactor and a photovoltaic (PV) generator is used to illustrate the performance of the proposed methodology.

Fabric Defect Detection Using Computer Vision Techniques: A Comprehensive Review

There are different applications of computer vision and digital image processing in various applied domains and automated production process. In textile industry, fabric defect detection is considered as a challenging task as the quality and the price of any textile product are dependent on the efficiency and effectiveness of the automatic defect detection. Previously, manual human efforts are applied in textile industry to detect the defects in the fabric production process. Lack of concentration, human fatigue, and time consumption are the main drawbacks associated with the manual fabric defect detection process. Applications based on computer vision and digital image processing can address the abovementioned limitations and drawbacks. Since the last two decades, various computer vision-based applications are proposed in various research articles to address these limitations. In this review article, we aim to present a detailed study about various computer vision-based approaches with application in textile industry to detect fabric defects. The proposed study presents a detailed overview of histogram-based approaches, color-based approaches, image segmentation-based approaches, frequency domain operations, texture-based defect detection, sparse feature-based operation, image morphology operations, and recent trends of deep learning. The performance evaluation criteria for automatic fabric defect detection is also presented and discussed. The drawbacks and limitations associated with the existing published research are discussed in detail, and possible future research directions are also mentioned. This research study provides comprehensive details about computer vision and digital image processing applications to detect different types of fabric defects.

Fractal loaded circular patch antenna for super wide band operation in THz frequency region

In this article a microstrip line fed circular fractal curve loaded circular shaped patch antenna is presented for Super Wide Band (SWB) operation in THz frequency domain. Impedance matching over the entire operating frequency band is obtained by etching a circular shaped slot from the radiating patch and using a circular shaped partial ground plane. The fractal structure is suitably embedded with the radiating patch so that the lower edge frequency of operation of the proposed design is sufficiently reduced and the antenna can operate over the entire spectrum of 0.1 THz to 10 THz (with ratio impedance bandwidth of 100:1) for S11≤-10 dB. A relatively stable radiation pattern with acceptable value of gain are obtained over the entire operation band. The designed antenna has advantage of highest ratio impedance bandwidth with smallest physical dimension over previously reported SWB antenna structures for THz applications.

Time-Domain Investigation of Switchable Filter Wide-Band Antenna for Microwave Breast Imaging

This paper investigates the time-domain performance of a switchable filter impulse radio ultra-wideband (IR-UWB) antenna for microwave breast imaging applications. A miniaturized CPW-fed integrated filter antenna with switchable performance in the range of the Worldwide Interoperability for Microwave Access (WiMAX) and Wireless Local Area Network (WLAN) bands could operate well within a 3.0 to 11 GHz frequency range. The time-domain performance of the filter antenna was investigated in comparison to that of the designed reference wideband antenna. By comparing both antennas’ time-domain characteristics, it was seen that the switchable filter antenna had good time-domain resolution along with the frequency-domain operation. Additionally, the time-domain investigation revealed that the switchable filter wide-band antenna performed similarly to the reference wide band antenna. This antenna was also utilized for a tumor detection application, and it was seen that the switchable filter wide-band antenna could detect a miniaturized irregularly shaped tumor easily, which is quite promising. Such an antenna with a good time-domain resolution and tumor detection capability will be a good candidate and will find potential applications in microwave breast imaging.

Three-dimensional shape measurement based on binary fringe conventional projection

A three-dimensional (3D) shape measurement method based on binary fringe conventional projection is proposed. In traditional 3D shape measurement methods based on binary fringe projection, the binary fringe is used as an approximate sinusoidal fringe by defocusing projection or even directly used as an approximate sinusoidal fringe by nonlinear error suppression feature of large-step phase measuring profilometry (PMP). In the proposed method (Prop), neither defocusing projection is needed nor large-step PMP must be used. When the binary fringe is conventionally projected on the measured object, just by filtering operation in spatial frequency domain from the captured deformed pattern, the nearly unbroken sinusoidal deformed pattern can be extracted efficiently. While N ( N≥3) frames binary fringes with 1/ N period misalignment between each adjacent fringe are conventionally projected onto the measured object sequentially, the corresponding nearly unbroken N-step sinusoidal deformed patterns extracted from the N frames captured deformed patterns can be used to reconstruct the 3D shape of the measured object with N-step PMP algorithm. The experimental results show the feasibility and validity of the Prop. It is more flexible for its optional fringe period and optional phase-shifting steps. It has potential application in the real-time 3D shape measurement.

A GPU-based Soft Real-Time System for Simultaneous EEG Processing and Visualization

EEG processing is generally acknowledged as a computationally very intensive task. The execution of pre-processing steps, frequency domain operations and source localisation algorithms result in long execution times, which prohibit the use of high-resolution EEG brain imaging techniques outside research laboratory settings. We present a novel GPU-based streaming architecture, which has the potential to drastically reduce execution times and, at the same time, provide simultaneous 2D and 3D visualization facilities. The system uses a highly-optimised and re-configurable pipeline of CPU and GPU cores that attempts to exploit the tremendous computing power whenever possible. The system can process live data arriving from an EEG device or data stored in EEG data files. The computer drives a large display wall system consisting of four 46-inch monitors, which provides a 4K-resolution drawing surface for visualising raw EEG data, potential maps and various 3D views of the patient head. Two example brain imaging algorithms, the surface Laplacian and the spherical forward solution are used as an illustration for the effective use of the massively parallel GPU hardware in speeding up computations. The paper describes the architecture of the system, the key design decisions, and the performance optimization steps that were required to achieve sub-millisecond per-sample execution times. The control ow of the system is expressed in a very modular fashion in Java but the performance-critical algorithms are programmed in CUDA and run on the GPU. Relying on the CUDA-OpenGL interoperability bridge, the computing subsystem feeds visualisation results directly into the OpenGL pipeline, eliminating unnecessary GPU-Host data transfers. The system demonstrates that up to three orders of magnitude speedups are achievable compared to MATLAB implementations, and this processing speed can be maintained during simultaneous interactive 3D visualisation of the results.

A Low-Complexity Architecture for PAPR Reduction in OFDM Systems With Near-Optimal Performance

Selected mapping (SLM) schemes are widely used to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency-division multiplexing (OFDM) systems. Various time-domain approaches have been proposed for reducing the number of inverse fast Fourier transform (IFFT) operations required to generate the candidate signals in traditional SLM schemes. However, the resulting time-domain-generated signals are somewhat correlated, and thus, the PAPR reduction performance is seriously degraded. Accordingly, this paper proposes a novel PAPR reduction method in which frequency-domain phase rotation, cyclic shifting, complex conjugate, and subcarrier reversal operations are all employed to increase the diversity of the candidate signals. Furthermore, to circumvent the multiple-IFFT problem, all of the frequency-domain operations are converted into time-domain equivalents. It is shown that the subcarrier partitioning and reassembling processes are key to realizing low-complexity time-domain equivalent operations. Moreover, it is shown theoretically and numerically that the computational complexity of the proposed scheme is significantly lower than that of the traditional SLM method and that the PAPR reduction performance is within 0.001 dB of that of SLM. Overall, the results indicate that among all of the low-complexity architectures proposed in the literature, the method proposed in this paper most closely approximates the PAPR reduction performance of the traditional SLM scheme.

2-D Fourier transform analysis of the gravitational field of Northern Sinai Peninsula

The Sinai Peninsula has fascinated the consideration of many geophysical studies as it is influenced by major tectonic events. Those are (1) the Mesozoic to Early Cenozoic tectonically active opening of Tethys, (2) the Late Cretaceous to Early Tertiary (Laramide) Syrian arc system, due to closing of the Tethys (3) the Oligo-Miocene Gulf of Suez rifted basin, and (4) the Late Miocene to Recent transform Dead Sea-Gulf of Aqaba rift. Moreover, the shear zones inside Sinai have affected intensely the structure development of the northern Sinai area. 2-D fast Fourier transform (FFT) analysis has been applied to transfer the data from space domain to frequency domain, in which basic gradients and derived gradients have been estimated. The frequency domain operations resulted in frequency filtering, first and second degree xyz gradients, horizontal, total (analytical signal) and tilt gradients, maximum horizontal gradient amplitude (total horizontal derivative), and theta map. As a result, the basic and derived gradient maps have succeeded to outline the major structure elements of Northern Sinai Peninsula. Comparisons with some well known surface structures showed a large degree of matching.

Identification of Application-Suitability of Point Operations on Digital Images using MATLAB

Spatial Domain and Frequency Domain operations play an important role in Digital Image Processing. Spatial Domain operations directly manipulate the pixels of a given image and contain a different category of operations, which include point, local and global operations. This paper mainly deals with point operations in order to identify their applicationsuitability on digital images using MATLAB and proposes a new function on contrast-stretching.

Image segmentation based on Frequency domain operation (FFT) and plugin implementation for ImageJ

Event Abstract Back to Event Image segmentation based on Frequency domain operation (FFT) and plugin implementation for ImageJ Víctor J. García Fernández1* and Dimiter Prodanov2 1 IMEC, Belgium 2 IMEC, EHS, Belgium In order to better measure cell’s response to different chemical or mechanical stimuli robust quantification of the cell spatio-temporal organization is required. Accurate identification of individual cellular phenotypes can be obtained by combining automated microscopic acquisition with extensive morphological feature extraction and data mining strategies. The aim of the present work is to implement filter banks allowing for measurement of scale-invariant features which will be used for downstream image classification operations. A generic way of segmenting images is by using multi-scale approaches, such as wavelet filter banks or scale spaces. Fourier domain filtering encodes image information in a distributed manner that allows manipulation of the global information content of the image scaling the performance of such filtering operations. The poster and the software demo will present a generic framework for Fourier domain filtering made available as a plugin to the popular public domain image processing software ImageJ. Filter implementations include Gaussian, Laplacian of Gaussian and Fractional Laplacian operators. We could successfully apply this plugin for example in segmentation of histological images. Acknowledgements The work has been supported in part by a grant from Research Fund - Flanders (FWO), contract number 0880.212.840. References Prodanov D (2013). Open source image analysis software toolboxes for microscopic applications. Front. Neuroinform. Conference Abstract: Imaging the brain at different scales: How to integrate multi-scale structural information?. doi: 10.3389/conf.fninf.2013.10.00005 Lindeberg, T. (1994). Scale-space theory: A basic tool for analysing structures at different scales. J App Stat. 21 (2): 224–270. Mols K, Prodanov D and Bonin V (2013). Scale-space based segmentation of cells in functional two-photon in vivo images. Front. Neuroinform. Conference Abstract: Imaging the brain at different scales: How to integrate multi-scale structural information?. doi: 10.3389/conf.fninf.2013.10.00033 Keywords: Image Processing, Computer-Assisted, FFT, filtering, Cell segmentation, ImageJ Conference: Second Belgian Neuroinformatics Congress, Leuven, Belgium, 4 Dec - 4 Dec, 2015. Presentation Type: Poster Presentation Topic: Brain Imaging Citation: García Fernández VJ and Prodanov D (2015). Image segmentation based on Frequency domain operation (FFT) and plugin implementation for ImageJ. Front. Neuroinform. Conference Abstract: Second Belgian Neuroinformatics Congress. doi: 10.3389/conf.fninf.2015.19.00010 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 31 Oct 2015; Published Online: 17 Nov 2015. * Correspondence: Mr. Víctor J García Fernández, IMEC, Leuven, Belgium, victorjgf@gmail.com Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Víctor J García Fernández Dimiter Prodanov Google Víctor J García Fernández Dimiter Prodanov Google Scholar Víctor J García Fernández Dimiter Prodanov PubMed Víctor J García Fernández Dimiter Prodanov Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Application Study of Edge Detection for Droplet in Laser Enhanced GMAW Welding

Ambient pressure has a certain inhibiting effect on underwater welding droplet transfer and the stability of welding process. Good droplet transfer of underwater welding plays an important role in improving repairing quality of underwater structures. As an additional droplet separating force, laser provides effective means in improving the welding quality. For quantitative analysis and comparison of laser enhanced effect on droplet transfer, a high-speed camera system to shoot the process of welding droplet transfer was designed and by adopting the frequency domain operation, a filter aiming at image processing of welding droplet was also designed to filter the ambient noise and diffraction fringe. Through edge detection algorithm, edges of droplet images were detected, and the size of droplet was computed accurately with welding wire as the reference. At last, droplets’ statues under different welding parameters were compared. The results show that the clear images of GMAW droplet separated from the noise background can be acquired, which makes the high-precision quantitative analysis of laser enhanced effect possible. All of the results lay a foundation for further test of laser enhanced hyperbaric underwater welding.

Study of inspection on metal sheet with subsurface defects using linear frequency modulated ultrasound excitation thermal-wave imaging (LFM-UTWI)

The linear frequency modulated ultrasound excitation thermal wave imaging (LFM-UTWI) was investigated on detection of subsurface defects of metal sheet. A numerical finite element analysis is carried out to calculate thermal wave signal dependence of time by linear frequency modulated ultrasonic wave excitation. Cross-correlation operation in time domain and frequency domain are used to extract the main peak value and the corresponding delay time, respectively. Fourier transform (FT) is applied to calculate the amplitude and phase angle of harmonic component of thermal wave. Experimental results show that various deep subsurface defects are readily detected using LFM-UTWI with once excitation, and LFM-UTWI has an advantage of better defect detectability compared to ultrasound lock-in thermography (ULIT).

Retina Verification System Based on Biometric Graph Matching

This paper presents an automatic retina verification framework based on the biometric graph matching (BGM) algorithm. The retinal vasculature is extracted using a family of matched filters in the frequency domain and morphological operators. Then, retinal templates are defined as formal spatial graphs derived from the retinal vasculature. The BGM algorithm, a noisy graph matching algorithm, robust to translation, non-linear distortion, and small rotations, is used to compare retinal templates. The BGM algorithm uses graph topology to define three distance measures between a pair of graphs, two of which are new. A support vector machine (SVM) classifier is used to distinguish between genuine and imposter comparisons. Using single as well as multiple graph measures, the classifier achieves complete separation on a training set of images from the VARIA database (60% of the data), equaling the state-of-the-art for retina verification. Because the available data set is small, kernel density estimation (KDE) of the genuine and imposter score distributions of the training set are used to measure performance of the BGM algorithm. In the one dimensional case, the KDE model is validated with the testing set. A 0 EER on testing shows that the KDE model is a good fit for the empirical distribution. For the multiple graph measures, a novel combination of the SVM boundary and the KDE model is used to obtain a fair comparison with the KDE model for the single measure. A clear benefit in using multiple graph measures over a single measure to distinguish genuine and imposter comparisons is demonstrated by a drop in theoretical error of between 60% and more than two orders of magnitude.