Spurious Structures Research Articles

AntiHalluciNet: A Potential Auditing Tool of the Behavior of Deep Learning Denoising Models in Low-Dose Computed Tomography.

Gaining the ability to audit the behavior of deep learning (DL) denoising models is of crucial importance to prevent potential hallucinations and adversarial clinical consequences. We present a preliminary version of AntiHalluciNet, which is designed to predict spurious structural components embedded in the residual noise from DL denoising models in low-dose CT and assess its feasibility for auditing the behavior of DL denoising models. We created a paired set of structure-embedded and pure noise images and trained AntiHalluciNet to predict spurious structures in the structure-embedded noise images. The performance of AntiHalluciNet was evaluated by using a newly devised residual structure index (RSI), which represents the prediction confidence based on the presence of structural components in the residual noise image. We also evaluated whether AntiHalluciNet could assess the image fidelity of a denoised image by using only a noise component instead of measuring the SSIM, which requires both reference and test images. Then, we explored the potential of AntiHalluciNet for auditing the behavior of DL denoising models. AntiHalluciNet was applied to three DL denoising models (two pre-trained models, RED-CNN and CTformer, and a commercial software, ClariCT.AI [version 1.2.3]), and whether AntiHalluciNet could discriminate between the noise purity performances of DL denoising models was assessed. AntiHalluciNet demonstrated an excellent performance in predicting the presence of structural components. The RSI values for the structural-embedded and pure noise images measured using the 50% low-dose dataset were 0.57 ± 31 and 0.02 ± 0.02, respectively, showing a substantial difference with a p-value < 0.0001. The AntiHalluciNet-derived RSI could differentiate between the quality of the degraded denoised images, with measurement values of 0.27, 0.41, 0.48, and 0.52 for the 25%, 50%, 75%, and 100% mixing rates of the degradation component, which showed a higher differentiation potential compared with the SSIM values of 0.9603, 0.9579, 0.9490, and 0.9333. The RSI measurements from the residual images of the three DL denoising models showed a distinct distribution, being 0.28 ± 0.06, 0.21 ± 0.06, and 0.15 ± 0.03 for RED-CNN, CTformer, and ClariCT.AI, respectively. AntiHalluciNet has the potential to predict the structural components embedded in the residual noise from DL denoising models in low-dose CT. With AntiHalluciNet, it is feasible to audit the performance and behavior of DL denoising models in clinical environments where only residual noise images are available.

Unsupervised metal artifacts reduction network for CT images based on efficient transformer

In computed tomography (CT) imaging, artifacts caused by metals can seriously interfere with the accurate judgment, evaluation, and analysis of object structures. Deep learning presented new opportunities for minimizing metal artifacts. The currently proposed supervised methods mainly resort to simulated data for network training, which is difficult to be applied in real scenarios. Unsupervised methods do not completely suppress artifacts and are prone to instability in the corrected results. Therefore, this paper proposes an unsupervised CycleGAN model based on the efficient Transformer for metal artifact reduction in CT images. The encoder and decoder based on the efficient Transformer achieve the extraction and processing of global image content features and artifact features. By correlating global features through attention mechanisms, vital features are generated to enhance the consistency of recovery information. The efficient Transformer framework reduces the computational complexity of the attention mechanism, allowing efficient processing of standard medical CT images with 512 × 512 pixels. Projection preserving loss uses the metal trace outer projection as a fidelity constraint to overcome the problem that unsupervised networks are difficult to train and prone to spurious information. Experimental results indicate that the proposed method outperforms the original CycleGAN and ADN networks in suppressing metal artifacts while avoiding introducing spurious structures. Specifically, the proposed method improved the PSNR of the correction results by 9.23% and reduced the NMAD by 13.21% compared to the original CycleGAN, and improved the PSNR by 5.17% and reduced the NMAD by 5.57% compared to the ADN.

Probing Accretion Turbulence in the Galactic Center with EHT Polarimetry

Magnetic fields grown by instabilities driven by differential rotation are believed to be essential to accretion onto black holes. These instabilities saturate in a turbulent state; therefore, the spatial and temporal variability in the horizon-resolving images of Sagittarius A* (Sgr A*) will be able to empirically assess this critical aspect of accretion theory. However, interstellar scattering blurs high-frequency radio images from the Galactic center and introduces spurious small-scale structures, complicating the interpretation of spatial fluctuations in the image. We explore the impact of interstellar scattering on the polarized images of Sgr A* and demonstrate that for credible physical parameters, the intervening scattering is non-birefringent. Therefore, we construct a scattering mitigation scheme that exploits horizon-resolving polarized millimeter/submillimeter VLBI observations to generate statistical measures of the intrinsic spatial fluctuations and therefore the underlying accretion flow turbulence. An optimal polarization basis is identified, corresponding to measurements of the fluctuations in magnetic field orientation in three dimensions. We validate our mitigation scheme using simulated data sets and find that current and future ground-based experiments will readily be able to accurately measure the image-fluctuation power spectrum.

Skeleton-stabilized divergence-conforming B-spline discretizations for incompressible flow problems of high Reynolds number

We consider a stabilization method for divergence-conforming B-spline discretizations of the incompressible Navier–Stokes problem wherein jumps in high-order normal derivatives of the velocity field are penalized across interior mesh facets. We prove that this method is pressure robust, consistent, and energy stable, and we show how to select the stabilization parameter appearing in the method so that excessive numerical dissipation is avoided in both the cross-wind direction and in the diffusion-dominated regime. We examine the efficacy of the method using a suite of numerical experiments, and we find the method yields optimal L2 and H1 convergence rates for the velocity field, eliminates spurious small-scale structures that pollute Galerkin approximations, and is effective as an Implicit Large Eddy Simulation (ILES) methodology.

Decoding ‘Maximum Entropy’ Deconvolution

For over five decades, the mathematical procedure termed “maximum entropy” (M-E) has been used to deconvolve structure in spectra, optical and otherwise, although quantitative measures of performance remain unknown. Here, we examine this procedure analytically for the lowest two orders for a Lorentzian feature, obtaining expressions for the amount of sharpening and identifying how spurious structures appear. Illustrative examples are provided. These results enhance the utility of this widely used deconvolution approach to spectral analysis.

A Variational Method for Analyzing Vortex Flows in Radar-Scanned Tornadic Mesocyclones. Part IV: Applications to the 20 May 2013 Oklahoma Tornadic Mesocyclone

Abstract The variational method for vortex flow (VF) analyses, called VF-Var (formulated in Part I), is applied to the 20 May 2013 Newcastle–Moore tornadic mesocyclone observed from the operational KTLX radar and an experimental phased-array radar. The dual-Doppler-analyzed VF field reveals the following features: The axisymmetric part of the VF is a well-defined slantwise two-cell vortex in which the maximum tangential velocity is nearly 40 m s−1 at the edge of the vortex core (0.6 km from the vortex center), the central downdraft velocity reaches −35 m s−1 at 3-km height, and the surrounding-updraft velocity reaches 26 m s−1 at 5-km height. The total VF field is a loosely defined slantwise two-cell vortex consisting of a nearly axisymmetric vortex core (in which the ground-relative surface wind speed reaches 50 m s−1 on the southeast edge), a strong nonaxisymmetric slantwise downdraft in the vortex core, and a main updraft in a banana-shaped area southeast of the vortex core, which extends slantwise upward and spirals cyclonically around the vortex core. The single-Doppler analysis with observations from the KTLX radar only exhibits roughly the same features as the dual-Doppler analysis but contains spurious vertical-motion structures in and around the vortex core. Analysis errors are assessed by leveraging the findings from Parts II and III, which indicate that the dual-Doppler-analyzed VF is accurate enough to represent the true VF but the single-Doppler-analyzed VF is not (especially for nonaxisymmetric vertical motions in and around the vortex core), so the dual-Doppler-analyzed VF should be useful for initializing/verifying high-resolution tornado simulations. Significance Statement After the variational method for vortex flow (VF) analyses, called VF-Var (formulated in Part I of this paper series), was tested successfully with simulated radar observations in Part II and its sensitivity to vortex center location error was examined in Part III, the method is now applied to the 20 May 2013 Newcastle–Moore tornadic mesocyclone observed from the operational KTLX radar and an experimental phased-array radar. Analysis errors are assessed by leveraging the findings from Parts II and III. The results indicate that the dual-Doppler-analyzed VF is accurate enough to represent the true VF (although the single-Doppler-analyzed VF is not especially for nonaxisymmetric vertical motions in and around the vortex core) and thus should be useful for initializing/verifying high-resolution tornado simulations.

Anthropogenic land‒use impacts on the size structure of macroinvertebrate assemblages are jointly modulated by local conditions and spatial processes.

Body size descriptors and associated resemblance measurements may provide useful tools for forecasting ecological responses to increasing anthropogenic land‒use disturbances. Yet, the influences of agriculture and urbanisation on the size structure of biotic assemblages have seldom been investigated in running waters. Using a comprehensive dataset on stream macroinvertebrates from 21 river basins across Western Finland, we assessed whether the structure of assemblages via changes in taxonomic composition and body size distributions responded predictably to anthropogenic land‒use impacts. Specifically, we applied a combination of resemblance measurements based on cumulative abundance profiles and spatially constrained null models to understand faunal impairment by agricultural and urban development, and the most likely mechanisms underlying the observed shifts in assemblage size structure. Anthropogenically impacted stream sites showed less variation in assemblage composition and size distributions compared with least‒disturbed sites, with strong declines in internal variation also occurring for the transition from near‒pristine to moderately impacted landscapes. These results were consistent whether based on species‒level or genus‒level data. Variation in assemblage size structure seemed to be more predictable than taxonomic composition, supporting the notion that resemblance measurements based on body size distributions can represent an improvement to more traditional approaches based on taxonomic identities alone. In addition, we showed that macroinvertebrate assemblages resulted from effects of land‒use degradation mediated through local conditions and spurious spatial structures in the distribution of anthropogenic activities across the landscape. Overall, our findings suggest that existing water policies and agri‒environment schemes should be guided not only by understanding the individual effects of agricultural and urban development on taxonomic composition at a given stream site. Rather, we should also acknowledge the size structure of stream assemblages and whether concomitant changes in local conditions and the non‒random distribution of human infrastructures are likely to mitigate or accelerate these effects.

Transdimensional Bayesian inversion of magnetotelluric data in anisotropic layered media with galvanic distortion correction

SUMMARYPresence of electrical anisotropy in the lithosphere can provide useful constraints on regional structure patterns and dynamics of tectonic processes, and they can be imaged by magnetotelluric (MT) data. However, Inversion of MT data for anisotropic structures using standard gradient-based approaches requires subjective choices of model regularization for constraining structure and anisotropy complexity. Furthermore, the ubiquitous presence of galvanic distortion due to small-scale near-surface conductivity inhomogeneities prevents accurate imaging of subsurface structures if ignored or not properly removed. Here, we present a transdimensional Bayesian approach for inverting MT data in layered anisotropic media. The algorithm allows flexible model parametrization, in which both the number of layers and model parameters of each layer are treated as unknowns. In this manner, the presence or absence of anisotropy within the layers, as well as the level of model complexity, is determined adaptively by the data. In addition, to account for the effects of galvanic distortion, three frequency-independent distortion parameters resulting from the distortion decomposition are treated as additional variables during the inversion. We demonstrate the efficiency of the algorithm to resolve both isotropic and anisotropic structures with synthetic and field MT data sets affected by galvanic distortion effects. The transdimensional inversion results for the field data are compatible with results from previous studies, and our results improve the constraints on the magnitude and the azimuth (i.e. most conductive direction) of electrically anisotropic structures. For practical applications, the validity of 1-D anisotropic approximation should be first tested prior to the use of our approach. Otherwise it may produce spurious anisotropic structures due to the inapplicability of the anisotropic 1-D inversion for MT data affected by 2-D or 3-D electrical resistivity structures.

Temporally aware volumetric generative adversarial network-based MR image reconstruction with simultaneous respiratory motion compensation: Initial feasibility in 3D dynamic cine cardiac MRI.

Develop a novel three-dimensional (3D) generative adversarial network (GAN)-based technique for simultaneous image reconstruction and respiratory motion compensation of 4D MRI. Our goal was to enable high-acceleration factors 10.7X-15.8X, while maintaining robust and diagnostic image quality superior to state-of-the-art self-gating (SG) compressed sensing wavelet (CS-WV) reconstruction at lower acceleration factors 3.5X-7.9X. Our GAN was trained based on pixel-wise content loss functions, adversarial loss function, and a novel data-driven temporal aware loss function to maintain anatomical accuracy and temporal coherence. Besides image reconstruction, our network also performs respiratory motion compensation for free-breathing scans. A novel progressive growing-based strategy was adapted to make the training process possible for the proposed GAN-based structure. The proposed method was developed and thoroughly evaluated qualitatively and quantitatively based on 3D cardiac cine data from 42 patients. Our proposed method achieved significantly better scores in general image quality and image artifacts at 10.7X-15.8X acceleration than the SG CS-WV approach at 3.5X-7.9X acceleration (4.53 ± 0.540 vs. 3.13 ± 0.681 for general image quality, 4.12 ± 0.429 vs. 2.97 ± 0.434 for image artifacts, P < .05 for both). No spurious anatomical structures were observed in our images. The proposed method enabled similar cardiac-function quantification as conventional SG CS-WV. The proposed method achieved faster central processing unit-based image reconstruction (6 s/cardiac phase) than the SG CS-WV (312 s/cardiac phase). The proposed method showed promising potential for high-resolution (1 mm3 ) free-breathing 4D MR data acquisition with simultaneous respiratory motion compensation and fast reconstruction time.

Measurement on Spurious Phase Stability in Optoelectronic Oscillators

Long loop delay in optoelectronic oscillator (OEO) helps to achieve high Q factor, but it also produces narrowly spaced spurious modes, which is hard to be filtered out. To suppress spurious modes, dual-loop and inject-locking structures have been studied. Besides, feedforward technique may also be used for spurious suppression. The more stable the spurious phase relative to the principal mode in OEO, the better the suppression can be obtained. To assess the phase stability of spurious mode, we built up a phase measurement system using digital IF structure. OEOs oscillated at 10GHz with different fiber lengths were set up. The results showed that the stability of the spurious phase improved with the increase of fiber length. This article provided experimental evidence of a possible method of spurious suppression for future work.

SLITRONOMY: Towards a fully wavelet-based strong lensing inversion technique

Strong gravitational lensing provides a wealth of astrophysical information on the baryonic and dark matter content of galaxies. It also serves as a valuable cosmological probe by allowing us to measure the Hubble constant independently of other methods. These applications all require the difficult task of inverting the lens equation and simultaneously reconstructing the mass profile of the lens along with the original light profile of the unlensed source. As there is no reason for either the lens or the source to be simple, we need methods that both invert the lens equation with a large number of degrees of freedom and also enforce a well-controlled regularisation that avoids the appearance of spurious structures. This can be beautifully accomplished by representing signals in wavelet space. Building on the Sparse Lens Inversion Technique (SLIT), we present an improved sparsity-based method that describes lensed sources using wavelets and optimises over the parameters given an analytical lens mass profile. We applied our technique on simulated HST and E-ELT data, as well as on real HST images of lenses from the Sloan Lens ACS sample, assuming a lens model. We show that wavelets allowed us to reconstruct lensed sources containing detailed substructures when using both present-day data and very high-resolution images expected from future thirty-metre-class telescopes. In the latter case, wavelets moreover provide a much more tractable solution in terms of quality and computation time compared to using a source model that combines smooth analytical profiles and shapelets. Requiring very little human interaction, our flexible pixel-based technique fits into the ongoing effort to devise automated modelling schemes. It can be incorporated in the standard workflow of sampling analytical lens model parameters while modelling the source on a pixelated grid. The method, which we call SLITRONOMY, is freely available as a new plug-in to the modelling software LENSTRONOMY.

Identifying and tracking bubbles and drops in simulations: A toolbox for obtaining sizes, lineages, and breakup and coalescence statistics

Knowledge of bubble and drop size distributions in two-phase flows is important for characterizing a wide range of phenomena, including combustor ignition, sonar communication, and cloud formation. The physical mechanisms driving the background flow also drive the time evolution of these distributions. Accurate and robust identification and tracking algorithms for the dispersed phase are necessary to reliably measure this evolution and thereby quantify the underlying mechanisms in interface-resolving flow simulations. The identification of individual bubbles and drops traditionally relies on an algorithm used to identify connected regions. This traditional algorithm can be sensitive to the presence of spurious structures. A cost-effective refinement is proposed to maximize volume accuracy while minimizing the identification of spurious bubbles and drops. An accurate identification scheme is crucial for distinguishing bubble and drop pairs with large size ratios. The identified bubbles and drops need to be tracked in time to obtain breakup and coalescence statistics that characterize the evolution of the size distribution, including breakup and coalescence frequencies, and the probability distributions of parent and child bubble and drop sizes. An algorithm based on mass conservation is proposed to construct bubble and drop lineages using simulation snapshots that are not necessarily from consecutive time steps. These lineages are then used to detect breakup and coalescence events, and obtain the desired statistics. Accurate identification of large-size-ratio bubble and drop pairs enables accurate detection of breakup and coalescence events over a large size range. Accurate detection of successive breakup and coalescence events requires that the snapshot interval be an order of magnitude smaller than the characteristic breakup and coalescence times to capture these successive events while minimizing the identification of repeated confounding events. Together, these algorithms serve as a toolbox for detailed analysis of two-phase simulations, and enable insights into the mechanisms behind bubble and drop formation and evolution in flows of practical importance.

Efficacy of the Cell Perturbation Method in Large-Eddy Simulations of Boundary Layer Flow over Complex Terrain

A challenge to simulating turbulent flow in multiscale atmospheric applications is the efficient generation of resolved turbulence motions over an area of interest. One approach is to apply small perturbations to flow variables near the inflow planes of turbulence-resolving simulation domains nested within larger mesoscale domains. While this approach has been examined in numerous idealized and simple terrain cases, its efficacy in complex terrain environments has not yet been fully explored. Here, we examine the benefits of the stochastic cell perturbation method (CPM) over real complex terrain using data from the 2017 Perdigão field campaign, conducted in an approximately 2-km wide valley situated between two nearly parallel ridges. Following a typical configuration for multiscale simulation using nested domains within the Weather Research and Forecasting (WRF) model to downscale from the mesoscale to a large-eddy simulation (LES), we apply the CPM on a domain with horizontal grid spacing of 150 m. At this resolution, spurious coherent structures are often observed under unstable atmospheric conditions with moderate mean wind speeds. Results from such an intermediate resolution grid are often nested down for finer, more detailed LES, where these spurious structures adversely affect the development of turbulence on the subsequent finer grid nest. We therefore examine the impacts of the CPM on the representation of turbulence within the nested LES domain under moderate mean flow conditions in three different stability regimes: weakly convective, strongly convective, and weakly stable. In addition, two different resolutions of the underlying terrain are used to explore the role of the complex topography itself in generating turbulent structures. We demonstrate that the CPM improves the representation of turbulence within the LES domain, relative to the use of high-resolution complex terrain alone. During the convective conditions, the CPM improves the rate at which smaller-scales of turbulence form, while also accelerating the attenuation of the spurious numerically generated roll structures near the inflow boundary. During stable conditions, the coarse mesh spacing of the intermediate LES domain used herein was insufficient to maintain resolved turbulence using CPM as the flow develops downstream, highlighting the need for yet higher resolution under even weakly stable conditions, and the importance of accurate representation of flow on intermediate LES grids.

Mapping flows on sparse networks with missing links

Unreliable network data can cause community-detection methods to overfit and highlight spurious structures with misleading information about the organization and function of complex systems. Here we show how to detect significant flow-based communities in sparse networks with missing links using the map equation. Since the map equation builds on Shannon entropy estimation, it assumes complete data such that analyzing undersampled networks can lead to overfitting. To overcome this problem, we incorporate a Bayesian approach with assumptions about network uncertainties into the map equation framework. Results in both synthetic and real-world networks show that the Bayesian estimate of the map equation provides a principled approach to revealing significant structures in undersampled networks.

Low shear diffusion central schemes for particle methods

We present the first application of a central scheme in an unstructured meshless code and extend it to limit diffusion in shearing flows.Some numerical diffusion is required in simulations of compressible fluids to maintain stability and prevent formation of spurious structures. The Kurganov-Tadmor (KT) central scheme uses a signal velocity and a linear reconstruction of fields to limit numerical diffusion away from discontinuities.We implement the KT scheme as a drop-in replacement for the Riemann solver in the GIZMO hydrodynamics code. Both the original finite-volume version of the KT scheme, which is quasi-Lagrangian in meshless geometry, as well as a new fully-Lagrangian finite-mass variant are presented. In addition, to mitigate excessive diffusion, a new shear-based switch is proposed. The new methods, as well as the default Riemann solver, were applied to a set of test problems. The results show that, although the KT scheme is more diffusive than the Riemann solver, it produces correct results with better convergence. The switch is shown to reduce diffusion in shearing cases, while not compromising stability in the supersonic regime. The fully-Lagrangian variant is shown to behave similarly to its Riemann solver counterpart. We conclude that the new variants of the KT scheme are good alternatives to Riemann solvers in meshless geometry, especially where its simplicity is desirable, such as for a complex equation of state.

SINGV‐DA: A data assimilation system for convective‐scale numerical weather prediction over Singapore

AbstractSINGV‐DA is a convective‐scale numerical weather prediction system with regional data assimilation for Singapore and the surrounding region. This article documents SINGV‐DA's current operational configuration and the sensitivity studies that influenced its development. We show that background error covariances derived by bootstrapping (via the lagged National Meteorological Centre method) contain spurious vertical structures at higher model levels that may degrade forecast performance. We found that SINGV‐DA precipitation forecasts are sensitive to horizontal resolution and lateral boundary conditions. Our observing system experiments reveal that satellite radiance assimilation, while clearly beneficial for precipitation forecasts in this region, adversely affected model background temperatures and winds at higher altitudes. Benchmarked against the forecast model in isolation, the regional DA system adds significant value to precipitation forecasts in the nowcasting range, but not at longer lead times. Our findings point to the need for further research and development to improve the system.

Vertical Resolution Requirements in Atmospheric Simulation

Abstract The role of vertical mesh spacing in the convergence of full-physics global atmospheric model solutions is examined for synoptic, mesoscale, and convective-scale horizontal resolutions. Using the MPAS-Atmosphere model, convergence is evaluated for three solution metrics: the horizontal kinetic energy spectrum, the Richardson number probability density function, and resolved flow features. All three metrics exhibit convergence in the free atmosphere for a 15-km horizontal mesh when the vertical grid spacing is less than or equal to 200 m. Nonconvergence is accompanied by noise, spurious structures, reduced levels of mesoscale kinetic energy, and reduced Richardson number peak frequencies. Coarser horizontal mesh solutions converge in a similar manner but contain much less noise than the 15-km solutions for coarse vertical resolution. For convective-scale resolution simulations with 3-km cell spacing on a variable-resolution mesh, solution convergence is almost attained with a vertical mesh spacing of 200 m. The boundary layer scheme is the dominant source of vertical filtering in the free atmosphere. Although the increased vertical mixing at coarser vertical mesh spacing depresses the kinetic energy spectra and Richardson number convergence, it does not produce sufficient dissipation to effectively halt scale collapse. These results confirm and extend the results from a number of previous studies, and further emphasize the sensitivity of the energetics to the vertical mixing formulations in the model.

3D inversion of airborne gravity gradiometry data for the Budgell Harbour Stock, Newfoundland: A case history using a probabilistic approach

We have studied the Mesozoic Budgell Harbour Stock, a gabbroic intrusion in north-central Newfoundland, Canada, using 3D inversion of airborne gravity gradiometry data based on a probabilistic inversion method. Significantly, differences were observed between the results when inverting the single [Formula: see text] component and when inverting the 5C combination. We also found that the [Formula: see text] model failed to reproduce the long-wavelength signals from other components, whereas the model recovered from five components accommodated all of the signals from all of the components. To estimate the influence of long-wavelength signals from targets other than the intrusion, such as deeper bodies or large-scale terrain variations, inversion tests are performed on a synthetic model. The inversion results for the synthetic example indicate that the joint inversion of five components is more sensitive to long-wavelength signals, which can generate spurious structures to fit all of the signals from the five components. In contrast, the [Formula: see text] model is less affected by the long-wavelength signals and thus tends to produce a stable solution, despite failing to incorporate all of the long-wavelength signals from the tensor data. We found that gravity gradiometry data could be used to delineate the intrusion within this study area, which is also consistent with the susceptibility model recovered from inversion of aeromagnetic data and with results from a previous geophysical study. Moreover, the differences between the [Formula: see text] model and the 5C model may reflect the long-wavelength signals in the gravity gradiometry data.

Combining multi-scale composite windows with hierarchical smoothing strategy for fingerprint orientation field computation

BackgroundOrientation field (OF) plays a very significant role in automatic fingerprint recognition systems. Many algorithms have been proposed for the estimation of fingerprints’ OF but it is hard to solve the dilemma of correcting spurious ridge structure and avoiding singularity location deviation, especially for poor images. So far, the following drawbacks still need to be solved for OF construction methods for practical application: (1) How to adaptively choose block scales to resolve the contradiction between accuracy and anti-noise, since small scale is beneficial to accuracy but is sensitive to noise, while large scale is more resistant to noise, but the accuracy is deteriorated. (2) How to construct the genuine OF in the areas close-by singular points and to evade singularity location deviation? Current block based methods give spurious OF estimates in the area near singular points because these areas have large curvature thus the detected singular points deviate from the genuine localizations. When these singular points are used as the anchor for referencing minutiae, it makes the average error of matching or recognition even larger. Therefore, it is essentials to construct the genuine OF in the areas close-by singular points and to evade singularity deviation.MethodsTo overcome the above-mentioned limitations, a novel method, combining a weighted multi-scale composite window (WMCM) with a hierarchical smoothing strategy has been proposed for the computation of fingerprint OF. This method mainly contains two procedures: the approximate OF estimation and the hierarchical OF smoothing. In the first procedure, a series of OFs are established under multiple scales of composite windows by using a gradient based method then a coarse OF is estimated using the weight of each scale determined by a squared gradient consistency. In the second procedure, the OF is first quantized into a two-digitized orientation zone and a two-orientation-zone filtering strategy is adapted to the OF blocks based on a filtering mask obtained after eliminating the isolated blocks. In the end a similar three-digitized orientation zone is performed to obtain an accurate and smooth OF. To validate the performance, the proposed method has been applied to OF computation using the FVC2004 databases and three experiments are designed. Experiment 1 aims to validate whether the weighted multi-scale composite window can balance the dilemma of accuracy and robustness more effectively than the previous works do. Experiment 2 is designed to examine whether the hierarchical smoothing method can correct the spurious ridge flow and preserve the genuine localization of singular points. The purpose of experiment 3 is to test the performance of the proposed method on OF reconstruction in low quality fingerprint images. The fingerprint databases FVC 2004 DB1–DB4 are employed in this study.ResultsThe results of experiment I shows that the proposed method is capable to extract the information of OF reliably and it is more robust against singularity localization deviation in comparison with the other three gradient based methods. The results of experiment II indicates that the proposed smoothing method can balance the contradiction in correcting spurious ridge structures and preserving genuine singularity localization. The results of experiment III illustrates that our approach combing WMCW with the hierarchical smoothing method is capable to extract the information of OF ridge reliably and it is more robust against singularity deviation in comparison with the other three gradient based methods. In a word, the experiment results demonstrate that the proposed method can correct spurious ridge structure and meanwhile avoid singularity deviation compared with the previous works.ConclusionsA novel gradient based algorithm has been proposed which is more reliable for the estimation of the ridge information for fingerprint OF and is more accurate in preserving the singularity localization. Compared with the previously proposed gradient based methods, the advantages of the proposed RBSF lie in three aspects. Firstly a weighted multi-scale composite window is put forward to replace the single window used by conventional gradient based methods and to adaptively choose the scales of the blocks. Secondly, a hierarchical smoothing strategy is proposed to enhance the OF by using the two-orientation-zone filtering and the three-orientation-zone filtering, aiming to correct the spurious ridges and preserving the genuine location of singular points. Finally, three experiments are designed to test the proposed algorithm together with other popular gradient based methods on real fingerprint images, which are selected from different categories and all are suffering from obvious noise effects. All the experiment results show that the proposed method is superior with respect to reliable OF construction and avoiding singularity localization deviation.

Second-Order Chaos Indicators MEGNO2 and OMEGNO2: Theory

Modifications of the Mean Exponential Growth factor of Nearby Orbits (MEGNO) linear variational method called MEGNO2 and OMEGNO2 indicators are introduced. The modifications are based on taking into account not only the linear, but also the nonlinear part of the increment of the phase flow in the divergence among nearby trajectories according to the second-order formulas. The new indicators allow one to determine more quickly the nature of the orbits under study in dynamical systems with zero or small Lyapunov exponents in comparison with the first-order variational indicators. They improve the analysis of regular regions and, in particular, periodic orbits as well as prevent the appearance of spurious structures in the resulting mappings.